TSTP Solution File: ALG414-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : ALG414-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n024.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 : Thu Jul 14 12:10:49 EDT 2022
% Result : Unsatisfiable 1.97s 2.39s
% Output : Refutation 1.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ALG414-1 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Wed Jun 8 17:46:34 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.88/1.27 *** allocated 10000 integers for termspace/termends
% 0.88/1.27 *** allocated 10000 integers for clauses
% 0.88/1.27 *** allocated 10000 integers for justifications
% 0.88/1.27 *** allocated 15000 integers for termspace/termends
% 0.88/1.27 *** allocated 22500 integers for termspace/termends
% 0.88/1.27 Bliksem 1.12
% 0.88/1.27
% 0.88/1.27
% 0.88/1.27 Automatic Strategy Selection
% 0.88/1.27
% 0.88/1.27 Clauses:
% 0.88/1.27 [
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.88/1.27 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X
% 0.88/1.27 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 0.88/1.27 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, T,
% 0.88/1.27 X ), Z, X ) ) ],
% 0.88/1.27 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 0.88/1.27 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 0.88/1.27 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.27 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 0.88/1.27 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.27 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.88/1.27 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.27 Z, T, X ), X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ), =( T, U ), =( Z,
% 0.88/1.27 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.88/1.27 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.27 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.88/1.27 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.88/1.27 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 0.88/1.27 , X ), Z, X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.88/1.27 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.88/1.27 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 0.88/1.27 , X ), Z, X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.88/1.27 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 0.88/1.27 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ]
% 0.88/1.27 ,
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.88/1.27 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 0.88/1.27 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 0.88/1.27 ,
% 0.88/1.27 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.88/1.27 'c_Polynomial_Odegree'( 'c_HOL_Ouminus__class_Ouminus'( Y,
% 0.88/1.27 'tc_Polynomial_Opoly'( X ) ), X ), 'c_Polynomial_Odegree'( Y, X ) ) ]
% 0.88/1.27 ,
% 0.88/1.27 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.88/1.27 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.27 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), X ), Z ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.88/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.27 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.88/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.27 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.27 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.27 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.27 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 0.88/1.27 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 0.88/1.27 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.27 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Y, X
% 0.88/1.27 ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 0.88/1.27 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.88/1.27 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 0.88/1.27 X ) ],
% 0.88/1.27 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.88/1.27 , X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Y,
% 0.88/1.27 'c_HOL_Oone__class_Oone'( X ), X ), X ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.88/1.27 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.27 X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 0.88/1.27 X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.88/1.27 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.27 X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 0.88/1.27 , Z, X ) ) ],
% 0.88/1.27 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 0.88/1.27 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ),
% 0.88/1.27 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Osgn__class_Osgn'( Y, X ), X ) ) ]
% 0.88/1.27 ,
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.88/1.27 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 0.88/1.27 , 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 0.88/1.27 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, T, X )
% 0.88/1.27 , 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.88/1.27 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.88/1.27 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.88/1.27 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y,
% 0.88/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Otimes__class_Otimes'( Z,
% 0.88/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.88/1.27 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.27 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.27 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), X ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.88/1.27 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.88/1.27 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 0.88/1.27 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.88/1.27 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Y, X ) ],
% 0.88/1.27 [ ~( 'class_RealVector_Oreal__vector'( X ) ), =(
% 0.88/1.27 'c_RealVector_OscaleR__class_OscaleR'( Y, 'c_HOL_Ominus__class_Ominus'( Z
% 0.88/1.27 , T, X ), X ), 'c_HOL_Ominus__class_Ominus'(
% 0.88/1.27 'c_RealVector_OscaleR__class_OscaleR'( Y, Z, X ),
% 0.88/1.27 'c_RealVector_OscaleR__class_OscaleR'( Y, T, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 0.88/1.27 'c_RealVector_OscaleR__class_OscaleR'( Y, 'c_HOL_Ominus__class_Ominus'( Z
% 0.88/1.27 , T, X ), X ), 'c_HOL_Ominus__class_Ominus'(
% 0.88/1.27 'c_RealVector_OscaleR__class_OscaleR'( Y, Z, X ),
% 0.88/1.27 'c_RealVector_OscaleR__class_OscaleR'( Y, T, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.88/1.27 'c_Polynomial_Ocoeff'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.88/1.27 'tc_Polynomial_Opoly'( X ) ), T, X ), 'c_HOL_Ominus__class_Ominus'(
% 0.88/1.27 'c_Polynomial_Ocoeff'( Y, T, X ), 'c_Polynomial_Ocoeff'( Z, T, X ), X ) )
% 0.88/1.27 ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.88/1.27 ), =( Z, Y ) ],
% 0.88/1.27 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.88/1.27 ) ],
% 0.88/1.27 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.88/1.27 ) ],
% 0.88/1.27 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.88/1.27 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y, Z ), ~(
% 0.88/1.27 'c_Polynomial_Opdivmod__rel'( T, U, W, Z, X ) ), ~(
% 0.88/1.27 'c_Polynomial_Opdivmod__rel'( T, U, V0, Y, X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y, Z ), ~(
% 0.88/1.27 'c_Polynomial_Opdivmod__rel'( T, U, Z, W, X ) ), ~(
% 0.88/1.27 'c_Polynomial_Opdivmod__rel'( T, U, Y, V0, X ) ) ],
% 0.88/1.27 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.88/1.27 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 0.88/1.27 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =(
% 0.88/1.27 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 0.88/1.27 , X ) ) ), =( Y, Z ) ],
% 0.88/1.27 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.88/1.27 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 0.88/1.27 , X ) ) ), =( Y, Z ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 0.88/1.27 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Oinverse__class_Odivide'(
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), Y, X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 0.88/1.27 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), Y, X ), Z ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.88/1.27 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 0.88/1.27 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.88/1.27 , Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.88/1.27 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.88/1.27 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.88/1.27 , Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.88/1.27 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.27 Z, Y, X ) ) ],
% 0.88/1.27 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.27 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 0.88/1.27 , X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( 'c_Polynomial_Opdivmod'(
% 0.88/1.27 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), Y, X ),
% 0.88/1.27 'c_Pair'( 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ),
% 0.88/1.27 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ),
% 0.88/1.27 'tc_Polynomial_Opoly'( X ), 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.88/1.27 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.88/1.27 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 0.88/1.27 , 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 0.88/1.27 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X
% 0.88/1.27 ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.88/1.27 , Z, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Osgn__if'( X ) ), =(
% 0.88/1.27 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ), ~(
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =(
% 0.88/1.27 Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 0.88/1.27 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 0.88/1.27 ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( 'c_Polynomial_Odegree'(
% 0.88/1.27 'c_Polynomial_Osmult'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), X ),
% 0.88/1.27 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.88/1.27 ,
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.88/1.27 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 0.88/1.27 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 0.88/1.27 X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 0.88/1.27 Z, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.88/1.27 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.88/1.27 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 0.88/1.27 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 0.88/1.27 Z, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.88/1.27 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 0.88/1.27 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 0.88/1.27 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.88/1.27 X ), Z, X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 0.88/1.27 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 0.88/1.27 Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.27 X ), Z, X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 0.88/1.27 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.88/1.27 X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.27 X ), T, X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.27 'c_Polynomial_Opos__poly'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.88/1.27 'tc_Polynomial_Opoly'( X ) ), X ), ~( 'c_Polynomial_Opos__poly'( Z, X ) )
% 0.88/1.27 , ~( 'c_Polynomial_Opos__poly'( Y, X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.88/1.27 'c_Polynomial_Osmult'( Y, 'c_Polynomial_OpCons'( Z, T, X ), X ),
% 0.88/1.27 'c_Polynomial_OpCons'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.27 'c_Polynomial_Osmult'( Y, T, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.88/1.27 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.27 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.88/1.27 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.27 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.88/1.27 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.27 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.88/1.27 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.27 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ],
% 0.88/1.27 [ ~( =( 'c_Pair'( X, Y, Z, T ), 'c_Pair'( U, W, Z, T ) ) ), =( Y, W ) ]
% 0.88/1.27 ,
% 0.88/1.27 [ ~( =( 'c_Pair'( X, Y, Z, T ), 'c_Pair'( U, W, Z, T ) ) ), =( X, U ) ]
% 0.88/1.27 ,
% 0.88/1.27 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.88/1.27 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.88/1.27 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~(
% 0.88/1.27 'c_HOL_Oord__class_Oless'( T, U, X ) ) ],
% 0.88/1.27 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 0.88/1.27 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.88/1.27 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( T, U, X ), ~(
% 0.88/1.27 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( 'c_Polynomial_Odegree'(
% 0.88/1.27 'c_Polynomial_Osmult'( Y, Z, X ), X ), 'c_Polynomial_Odegree'( Z, X ) ),
% 0.88/1.27 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.27 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.27 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.88/1.27 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ),
% 0.88/1.27 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.88/1.27 ) ) ],
% 0.88/1.27 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.27 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.27 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 0.88/1.27 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 0.88/1.27 ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 0.88/1.27 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 0.88/1.27 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.27 'c_HOL_Ominus__class_Ominus'( Z, 'c_HOL_Otimes__class_Otimes'( T, U, X )
% 0.88/1.27 , X ), W, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 0.88/1.27 'c_HOL_Oplus__class_Oplus'( Z, W, X ), X ) ), ~(
% 0.88/1.27 'c_Ring__and__Field_Odvd__class_Odvd'( Y, U, X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 0.88/1.27 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 0.88/1.27 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 0.88/1.27 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 0.88/1.27 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Z,
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( U, W, X ), X ), T, X ), X ) ), ~(
% 0.88/1.27 'c_Ring__and__Field_Odvd__class_Odvd'( Y, W, X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.88/1.27 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_Osmult'( Y, Z, X ),
% 0.88/1.27 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ),
% 0.88/1.27 'tc_Polynomial_Opoly'( X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z
% 0.88/1.27 , 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ),
% 0.88/1.27 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 0.88/1.27 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X )
% 0.88/1.27 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ],
% 0.88/1.27 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ouminus__class_Ouminus'(
% 0.88/1.27 Y, X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'(
% 0.88/1.27 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ],
% 0.88/1.27 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.88/1.27 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.88/1.27 T, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.88/1.27 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.88/1.27 X ), Z, X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.88/1.27 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 0.88/1.27 T, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.88/1.27 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.88/1.27 X ), T, X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.88/1.27 , X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 0.88/1.27 T, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.88/1.27 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.88/1.27 X ), T, X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.88/1.27 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.88/1.27 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.88/1.27 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.88/1.27 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.88/1.27 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.88/1.27 'tc_Polynomial_Opoly'( X ) ), T, 'tc_Polynomial_Opoly'( X ) ),
% 0.88/1.27 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.88/1.27 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Otimes__class_Otimes'( Z, T,
% 0.88/1.27 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.88/1.27 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.88/1.27 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.88/1.27 'c_Polynomial_Ocoeff'( 'c_HOL_Ouminus__class_Ouminus'( Y,
% 0.88/1.27 'tc_Polynomial_Opoly'( X ) ), Z, X ), 'c_HOL_Ouminus__class_Ouminus'(
% 0.88/1.27 'c_Polynomial_Ocoeff'( Y, Z, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.27 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.27 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.27 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.88/1.27 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_Osmult'( Y, Z, X ),
% 0.88/1.27 T, 'tc_Polynomial_Opoly'( X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'(
% 0.88/1.27 Z, T, 'tc_Polynomial_Opoly'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.88/1.27 ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.88/1.27 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_Polynomial_Opoly'( X ) )
% 0.88/1.27 , =( T, 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 0.88/1.27 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_Osmult'( T, Y, X ),
% 0.88/1.27 Z, 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.88/1.27 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Polynomial_Osmult'( Z, T, X
% 0.88/1.27 ), 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.88/1.27 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, 'tc_Polynomial_Opoly'( X ) )
% 0.88/1.27 ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.88/1.27 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_Polynomial_Opoly'( X ) )
% 0.88/1.27 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Polynomial_Osmult'( T,
% 0.88/1.27 Z, X ), 'tc_Polynomial_Opoly'( X ) ) ), =( T, 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.27 X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.88/1.27 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_Osmult'( Y, Z, X ),
% 0.88/1.27 T, 'tc_Polynomial_Opoly'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.88/1.27 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, 'tc_Polynomial_Opoly'(
% 0.88/1.27 X ) ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.88/1.27 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_Polynomial_Opoly'( X ) )
% 0.88/1.27 , =( T, 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 0.88/1.27 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Polynomial_Osmult'( T, Z, X
% 0.88/1.27 ), 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.88/1.27 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.88/1.27 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ),
% 0.88/1.27 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Z, Y, X ), X ) )
% 0.88/1.27 ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.88/1.27 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.88/1.27 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 0.88/1.27 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 0.88/1.27 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.88/1.27 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 0.88/1.27 ), X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'(
% 0.88/1.27 Y, X ), Z, X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.27 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.27 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.88/1.27 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 0.88/1.27 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.88/1.27 [ ~( 'class_HOL_Ozero'( X ) ), ~( 'class_HOL_Oeq'( X ) ),
% 0.88/1.27 'c_HOL_Oeq__class_Oeq'( Y, Y, 'tc_Polynomial_Opoly'( X ) ) ],
% 0.88/1.27 [ ~( 'class_HOL_Oeq'( X ) ), 'c_HOL_Oeq__class_Oeq'( Y, Y, X ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.27 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 0.88/1.27 ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.88/1.27 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 0.88/1.27 , 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 0.88/1.27 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'(
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.88/1.27 , Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ), =( U,
% 0.88/1.27 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 0.88/1.27 ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.27 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 0.88/1.27 'c_HOL_Oone__class_Oone'( X ), X ), X ) ],
% 0.88/1.27 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 0.88/1.27 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.88/1.27 X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 0.88/1.27 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.88/1.27 X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 0.88/1.27 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.88/1.27 X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 0.88/1.27 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.88/1.27 X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =(
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.88/1.27 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.27 Y, Y, X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.88/1.27 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.27 Y, Z, X ) ) ],
% 0.88/1.27 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.88/1.27 'c_HOL_Ominus__class_Ominus'( 'c_Polynomial_OpCons'( Y, Z, X ),
% 0.88/1.27 'c_Polynomial_OpCons'( T, U, X ), 'tc_Polynomial_Opoly'( X ) ),
% 0.88/1.27 'c_Polynomial_OpCons'( 'c_HOL_Ominus__class_Ominus'( Y, T, X ),
% 0.88/1.27 'c_HOL_Ominus__class_Ominus'( Z, U, 'tc_Polynomial_Opoly'( X ) ), X ) ) ]
% 0.88/1.27 ,
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.88/1.27 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Osgn__class_Osgn'( Y, X ), X ),
% 0.88/1.27 'c_HOL_Osgn__class_Osgn'( Y, X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.88/1.27 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y
% 0.88/1.27 , X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.88/1.27 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 0.88/1.27 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 0.88/1.27 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.88/1.27 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ]
% 0.88/1.27 ,
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.88/1.27 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 0.88/1.27 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.27 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 0.88/1.27 X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.88/1.27 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 0.88/1.27 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 0.88/1.27 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 0.88/1.27 X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.88/1.27 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 0.88/1.27 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 0.88/1.27 , X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.88/1.27 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 0.88/1.27 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.27 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.88/1.27 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ]
% 0.88/1.27 ,
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.88/1.27 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 0.88/1.27 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.27 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 0.88/1.27 T, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.27 Y, T, X ), Z, X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.88/1.27 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 0.88/1.27 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.27 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 0.88/1.27 T, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.27 Y, T, X ), Z, X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.88/1.27 'c_Polynomial_Osmult'( Y, 'c_Polynomial_Omonom'( Z, T, X ), X ),
% 0.88/1.27 'c_Polynomial_Omonom'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ) )
% 0.88/1.27 ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.88/1.27 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z, X )
% 0.88/1.27 , 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.88/1.27 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 0.88/1.27 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.88/1.27 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 0.88/1.27 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'(
% 0.88/1.27 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ), Z, X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.27 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 0.88/1.27 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.88/1.27 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.88/1.27 ,
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.27 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.88/1.27 ,
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.88/1.27 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.27 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.88/1.27 ,
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.88/1.27 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.27 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 0.88/1.27 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.88/1.27 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.88/1.27 ,
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.27 'c_Polynomial_Osmult'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.88/1.27 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 0.88/1.27 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 0.88/1.27 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( 'c_Polynomial_Ocoeff'(
% 0.88/1.27 'c_Polynomial_Opoly__gcd'( Y, Z, X ), 'c_Polynomial_Odegree'(
% 0.88/1.27 'c_Polynomial_Opoly__gcd'( Y, Z, X ), X ), X ), 'c_HOL_Oone__class_Oone'(
% 0.88/1.27 X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ]
% 0.88/1.27 ,
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( 'c_Polynomial_Ocoeff'(
% 0.88/1.27 'c_Polynomial_Opoly__gcd'( Y, Z, X ), 'c_Polynomial_Odegree'(
% 0.88/1.27 'c_Polynomial_Opoly__gcd'( Y, Z, X ), X ), X ), 'c_HOL_Oone__class_Oone'(
% 0.88/1.27 X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ]
% 0.88/1.27 ,
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.88/1.27 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Otimes__class_Otimes'( Y,
% 0.88/1.27 'c_HOL_Osgn__class_Osgn'( Y, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.88/1.27 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.88/1.27 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ) ],
% 0.88/1.27 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.88/1.27 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.27 'tc_Polynomial_Opoly'( X ) ), Y, 'tc_Polynomial_Opoly'( X ) ),
% 0.88/1.27 'c_HOL_Ouminus__class_Ouminus'( Y, 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 0.88/1.27 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.27 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oone__class_Oone'( X ), X ), X ), Z
% 0.88/1.27 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'(
% 0.88/1.27 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.27 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oone__class_Oone'( X ), X ), X ), X
% 0.88/1.27 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.88/1.27 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.88/1.27 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 0.88/1.27 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), Z, X ) ), =( Z,
% 0.88/1.27 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.88/1.27 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.88/1.27 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 0.88/1.27 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Z,
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), T, X ) ), =( T,
% 0.88/1.27 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.27 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.88/1.27 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.27 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, U,
% 0.88/1.27 X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.88/1.27 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 0.88/1.27 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ominus__class_Ominus'(
% 0.88/1.27 Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 0.88/1.27 Z, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.88/1.27 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 0.88/1.27 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.88/1.27 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 0.88/1.27 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.88/1.27 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.88/1.27 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 0.88/1.27 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ), =( Z,
% 0.88/1.27 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.88/1.27 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.88/1.27 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.88/1.27 ,
% 0.88/1.27 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.88/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.88/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.88/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.88/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 0.88/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.88/1.27 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.88/1.27 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 0.88/1.27 , T, X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'(
% 0.88/1.27 Y, T, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 0.88/1.27 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 0.88/1.27 , T, X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'(
% 0.88/1.27 Y, T, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.88/1.27 'c_Polynomial_Opdivmod__rel'( 'c_Polynomial_Osmult'( Y, Z, X ), T,
% 0.88/1.27 'c_Polynomial_Osmult'( Y, U, X ), 'c_Polynomial_Osmult'( Y, W, X ), X ),
% 0.88/1.27 ~( 'c_Polynomial_Opdivmod__rel'( Z, T, U, W, X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.27 'c_HOL_Osgn__class_Osgn'( Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.27 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.88/1.27 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.27 'c_HOL_Osgn__class_Osgn'( Y, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 0.88/1.27 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ominus__class_Ominus'( Z
% 0.88/1.27 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 0.88/1.27 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 0.88/1.27 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.88/1.27 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 0.88/1.27 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.88/1.27 ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 0.88/1.27 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 0.88/1.27 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.88/1.27 ) ],
% 0.88/1.27 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 0.88/1.27 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 0.88/1.27 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 0.88/1.27 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.88/1.27 ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =(
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.88/1.27 , Z, X ) ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), =( Y, Z ) ]
% 0.88/1.27 ,
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.88/1.27 'c_Polynomial_Osynthetic__div'( 'c_Polynomial_OpCons'( Y, Z, X ), T, X )
% 0.88/1.27 , 'c_Polynomial_OpCons'( 'c_Polynomial_Opoly'( Z, T, X ),
% 0.88/1.27 'c_Polynomial_Osynthetic__div'( Z, T, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.88/1.27 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Osgn__class_Osgn'( Y, X ),
% 0.88/1.27 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), Y ) ],
% 0.88/1.27 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.88/1.27 'c_HOL_Ouminus__class_Ouminus'( 'c_Polynomial_OpCons'( Y, Z, X ),
% 0.88/1.27 'tc_Polynomial_Opoly'( X ) ), 'c_Polynomial_OpCons'(
% 0.88/1.27 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 0.88/1.27 , 'tc_Polynomial_Opoly'( X ) ), X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 0.88/1.27 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T,
% 0.88/1.27 'tc_Polynomial_Opoly'( X ) ), U, 'tc_Polynomial_Opoly'( X ) ) ), ~(
% 0.88/1.27 'c_Polynomial_Opdivmod__rel'( Y, T, Z, U, X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( 'c_Polynomial_Ocoeff'(
% 0.88/1.27 'c_Polynomial_Opoly__gcd'( 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.27 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.27 'tc_Polynomial_Opoly'( X ) ), X ), 'c_Polynomial_Odegree'(
% 0.88/1.27 'c_Polynomial_Opoly__gcd'( 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.27 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.27 'tc_Polynomial_Opoly'( X ) ), X ), X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.27 X ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.88/1.27 'c_Polynomial_Osmult'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X ),
% 0.88/1.27 'c_HOL_Oplus__class_Oplus'( 'c_Polynomial_Osmult'( Y, T, X ),
% 0.88/1.27 'c_Polynomial_Osmult'( Z, T, X ), 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.88/1.27 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.88/1.27 'c_Polynomial_Osmult'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T,
% 0.88/1.27 'tc_Polynomial_Opoly'( X ) ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.27 'c_Polynomial_Osmult'( Y, Z, X ), 'c_Polynomial_Osmult'( Y, T, X ),
% 0.88/1.27 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.88/1.27 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.88/1.27 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.88/1.27 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 0.88/1.27 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 0.88/1.27 , T, X ), X ) ) ],
% 0.88/1.27 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.88/1.27 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 0.88/1.27 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ), ~(
% 0.88/1.27 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 0.88/1.27 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.88/1.27 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.88/1.27 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 0.88/1.27 , T, X ), X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 0.88/1.27 ,
% 0.88/1.27 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 0.88/1.27 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 0.88/1.28 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 0.88/1.28 [ ~( 'class_HOL_Ozero'( X ) ), ~( 'class_HOL_Oeq'( X ) ),
% 0.88/1.28 'c_HOL_Oeq__class_Oeq'( 'c_Polynomial_OpCons'( Y, Z, X ),
% 0.88/1.28 'c_Polynomial_OpCons'( T, U, X ), 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.88/1.28 'c_HOL_Oeq__class_Oeq'( Z, U, 'tc_Polynomial_Opoly'( X ) ) ), ~(
% 0.88/1.28 'c_HOL_Oeq__class_Oeq'( Y, T, X ) ) ],
% 0.88/1.28 [ ~( 'class_RealVector_Oreal__vector'( X ) ), =(
% 0.88/1.28 'c_RealVector_OscaleR__class_OscaleR'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 0.88/1.28 Z, X ), X ), 'c_HOL_Ouminus__class_Ouminus'(
% 0.88/1.28 'c_RealVector_OscaleR__class_OscaleR'( Y, Z, X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 0.88/1.28 'c_RealVector_OscaleR__class_OscaleR'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 0.88/1.28 Z, X ), X ), 'c_HOL_Ouminus__class_Ouminus'(
% 0.88/1.28 'c_RealVector_OscaleR__class_OscaleR'( Y, Z, X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.28 'c_HOL_Ominus__class_Ominus'( T, Y, X ), Z, X ), U, X ), X ),
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 0.88/1.28 ) ) ],
% 0.88/1.28 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.88/1.28 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.28 'c_Polynomial_Odegree'( 'c_HOL_Oone__class_Oone'( 'tc_Polynomial_Opoly'(
% 0.88/1.28 X ) ), X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.88/1.28 'c_Polynomial_Opoly'(
% 0.88/1.28 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly'( Y, Z, X ), T
% 0.88/1.28 , X ), 'c_Polynomial_Opoly'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.88/1.28 ) ) ],
% 0.88/1.28 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z
% 0.88/1.28 , X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.88/1.28 'c_Polynomial_Odegree'(
% 0.88/1.28 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly'( Y, Z, X ), X
% 0.88/1.28 ), 'c_Polynomial_Odegree'( Y, X ) ) ],
% 0.88/1.28 [ ~( 'class_SEQ_Obanach'( X ) ), ~(
% 0.88/1.28 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 0.88/1.28 'c_Transcendental_Oexp'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ),
% 0.88/1.28 'c_HOL_Oinverse__class_Odivide'( 'c_Transcendental_Oexp'( Y, X ),
% 0.88/1.28 'c_Transcendental_Oexp'( Z, X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 0.88/1.28 ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.88/1.28 ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.88/1.28 ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.88/1.28 ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 0.88/1.28 ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 0.88/1.28 ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 0.88/1.28 , Y, X ), X ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 0.88/1.28 , Z, X ), X ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Odvd'( X ) ),
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 0.88/1.28 , Z, X ), X ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_Polynomial_Opoly'( X ) )
% 0.88/1.28 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_Osmult'( T, Y,
% 0.88/1.28 X ), Z, 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Polynomial_Osmult'( Z, T, X
% 0.88/1.28 ), 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, 'tc_Polynomial_Opoly'( X ) )
% 0.88/1.28 ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.88/1.28 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 0.88/1.28 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 0.88/1.28 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ), =( Z,
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.88/1.28 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.88/1.28 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.88/1.28 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.88/1.28 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.88/1.28 'c_Polynomial_Opoly__gcd'( Y, 'c_Polynomial_Opoly__gcd'( Z, T, X ), X ),
% 0.88/1.28 'c_Polynomial_Opoly__gcd'( Z, 'c_Polynomial_Opoly__gcd'( Y, T, X ), X ) )
% 0.88/1.28 ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.88/1.28 'c_Polynomial_Opoly__gcd'( 'c_Polynomial_Opoly__gcd'( Y, Z, X ), T, X ),
% 0.88/1.28 'c_Polynomial_Opoly__gcd'( Y, 'c_Polynomial_Opoly__gcd'( Z, T, X ), X ) )
% 0.88/1.28 ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.28 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Z, X ), U, X ) ),
% 0.88/1.28 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), T, X ) )
% 0.88/1.28 ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), Z, X
% 0.88/1.28 ), Y ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.88/1.28 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly'(
% 0.88/1.28 'c_Polynomial_OpCons'( Y, Z, X ), T, X ), 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.28 'c_Polynomial_Osmult'( T,
% 0.88/1.28 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly'( Z, T, X ), X
% 0.88/1.28 ), 'c_Polynomial_OpCons'( Y,
% 0.88/1.28 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly'( Z, T, X ), X
% 0.88/1.28 ), 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.88/1.28 'c_Polynomial_Opoly__gcd'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ), X ), 'c_Polynomial_Opoly__gcd'( Y, Z, X ) )
% 0.88/1.28 ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.88/1.28 'c_Polynomial_Opoly__gcd'( 'c_HOL_Ouminus__class_Ouminus'( Y,
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ), Z, X ), 'c_Polynomial_Opoly__gcd'( Y, Z, X
% 0.88/1.28 ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.88/1.28 , Y, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 0.88/1.28 , Y, X ) ) ],
% 0.88/1.28 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.88/1.28 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 0.88/1.28 , T, X ), X ), T, X ) ) ],
% 0.88/1.28 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.88/1.28 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.88/1.28 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.88/1.28 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.88/1.28 'c_Polynomial_Ocoeff'( 'c_Polynomial_Osmult'( Y, Z, X ), T, X ),
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Y, 'c_Polynomial_Ocoeff'( Z, T, X ), X ) )
% 0.88/1.28 ],
% 0.88/1.28 [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Ocoeff'(
% 0.88/1.28 'c_Polynomial_Omonom'( Y, Z, X ), T, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.88/1.28 ), =( Z, T ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.88/1.28 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.88/1.28 ) ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.88/1.28 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.88/1.28 ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.88/1.28 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.88/1.28 ) ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.88/1.28 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.88/1.28 ) ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.88/1.28 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.88/1.28 ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.88/1.28 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.88/1.28 ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.88/1.28 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 0.88/1.28 ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.88/1.28 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 0.88/1.28 ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 0.88/1.28 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 0.88/1.28 ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 0.88/1.28 , Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.88/1.28 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 0.88/1.28 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.88/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.88/1.28 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 0.88/1.28 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.28 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.88/1.28 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 0.88/1.28 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 0.88/1.28 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.88/1.28 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 0.88/1.28 , T, X ) ) ), =( Z, T ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.88/1.28 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 0.88/1.28 , T, X ) ) ), =( Y, Z ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.88/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.88/1.28 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.88/1.28 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 0.88/1.28 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ],
% 0.88/1.28 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 0.88/1.28 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.88/1.28 Z, X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'(
% 0.88/1.28 Y, Z, X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.88/1.28 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.28 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 0.88/1.28 , U, X ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'(
% 0.88/1.28 Y, T, X ), U, X ), X ), 'c_HOL_Otimes__class_Otimes'( T,
% 0.88/1.28 'c_HOL_Ominus__class_Ominus'( Z, U, X ), X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), =(
% 0.88/1.28 'c_Polynomial_Opoly'( 'c_HOL_Ouminus__class_Ouminus'( Y,
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ), Z, X ), 'c_HOL_Ouminus__class_Ouminus'(
% 0.88/1.28 'c_Polynomial_Opoly'( Y, Z, X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 0.88/1.28 ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ), U, X ) ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 0.88/1.28 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 0.88/1.28 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 0.88/1.28 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 0.88/1.28 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 0.88/1.28 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.88/1.28 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 0.88/1.28 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.88/1.28 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 0.88/1.28 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.88/1.28 X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 0.88/1.28 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.88/1.28 X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.88/1.28 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.28 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 0.88/1.28 , U, X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra__1'( X ) ), =(
% 0.88/1.28 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 0.88/1.28 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.28 'c_Polynomial_OpCons'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.88/1.28 'c_Polynomial_OpCons'( 'c_HOL_Oone__class_Oone'( X ),
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ), X ),
% 0.88/1.28 'c_Polynomial_Osynthetic__div'( Z, Y, X ), 'tc_Polynomial_Opoly'( X ) ),
% 0.88/1.28 'c_Polynomial_OpCons'( 'c_Polynomial_Opoly'( Z, Y, X ),
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ),
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ), Z ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 0.88/1.28 Z, X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 0.88/1.28 Z, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ouminus__class_Ouminus'( Y
% 0.88/1.28 , X ), Z, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ouminus__class_Ouminus'( Y
% 0.88/1.28 , X ), Z, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ]
% 0.88/1.28 ,
% 0.88/1.28 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( 'c_Polynomial_Omonom'( Y, Z, X ),
% 0.88/1.28 'c_Polynomial_Omonom'( T, Z, X ), 'tc_Polynomial_Opoly'( X ) ),
% 0.88/1.28 'c_Polynomial_Omonom'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ) ) ]
% 0.88/1.28 ,
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Osgn__class_Osgn'( Y, X ),
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Osgn__class_Osgn'( Y, X ),
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 0.88/1.28 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 0.88/1.28 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 0.88/1.28 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.88/1.28 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 0.88/1.28 , T, X ), X ), T, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.88/1.28 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y
% 0.88/1.28 ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.88/1.28 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ),
% 0.88/1.28 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.88/1.28 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 0.88/1.28 X ) ) ), =( Z, T ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 0.88/1.28 X ) ) ), =( Z, T ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 0.88/1.28 X ) ) ), =( Y, T ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.88/1.28 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 0.88/1.28 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.88/1.28 ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.88/1.28 'c_Polynomial_Opoly__gcd'( 'c_HOL_Oone__class_Oone'(
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ), Y, X ), 'c_HOL_Oone__class_Oone'(
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.88/1.28 'c_Polynomial_Opoly__gcd'( Y, 'c_HOL_Oone__class_Oone'(
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ), X ), 'c_HOL_Oone__class_Oone'(
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.28 'c_Polynomial_Opos__poly'( 'c_HOL_Ouminus__class_Ouminus'( Y,
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ), X ), 'c_Polynomial_Opos__poly'( Y, X ), =(
% 0.88/1.28 Y, 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.88/1.28 'c_Polynomial_Ocoeff'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ), T, X ), 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.28 'c_Polynomial_Ocoeff'( Y, T, X ), 'c_Polynomial_Ocoeff'( Z, T, X ), X ) )
% 0.88/1.28 ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.88/1.28 'c_HOL_Ouminus__class_Ouminus'( 'c_Polynomial_Omonom'( Y, Z, X ),
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ), 'c_Polynomial_Omonom'(
% 0.88/1.28 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ) ],
% 0.88/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( 'c_RealVector_OscaleR__class_OscaleR'( Y, Z
% 0.88/1.28 , X ), T, X ), 'c_RealVector_OscaleR__class_OscaleR'( Y,
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( 'c_RealVector_OscaleR__class_OscaleR'( Y, Z
% 0.88/1.28 , X ), T, X ), 'c_RealVector_OscaleR__class_OscaleR'( Y,
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Y, 'c_RealVector_OscaleR__class_OscaleR'( Z
% 0.88/1.28 , T, X ), X ), 'c_RealVector_OscaleR__class_OscaleR'( Z,
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Y, 'c_RealVector_OscaleR__class_OscaleR'( Z
% 0.88/1.28 , T, X ), X ), 'c_RealVector_OscaleR__class_OscaleR'( Z,
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_RealVector_Oreal__algebra'( X ) ), =(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( 'c_RealVector_OscaleR__class_OscaleR'( Y, Z
% 0.88/1.28 , X ), T, X ), 'c_RealVector_OscaleR__class_OscaleR'( Y,
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_RealVector_Oreal__algebra'( X ) ), =(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Y, 'c_RealVector_OscaleR__class_OscaleR'( Z
% 0.88/1.28 , T, X ), X ), 'c_RealVector_OscaleR__class_OscaleR'( Z,
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 0.88/1.28 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 0.88/1.28 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.88/1.28 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.28 X ) ) ],
% 0.88/1.28 [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Ocoeff'(
% 0.88/1.28 'c_Polynomial_Omonom'( Y, Z, X ), Z, X ), Y ) ],
% 0.88/1.28 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.88/1.28 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 0.88/1.28 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.88/1.28 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 0.88/1.28 [ ~( 'class_SEQ_Obanach'( X ) ), ~(
% 0.88/1.28 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( 'c_Transcendental_Oexp'( Y, X ),
% 0.88/1.28 'c_Transcendental_Oexp'( Z, X ), X ), 'c_Transcendental_Oexp'(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.88/1.28 , 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ), =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( Y, T, X ), U ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.28 'c_Polynomial_Opos__poly'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ), X ), ~( 'c_Polynomial_Opos__poly'( Z, X ) )
% 0.88/1.28 , ~( 'c_Polynomial_Opos__poly'( Y, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Osgn__if'( X ) ), =(
% 0.88/1.28 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'(
% 0.88/1.28 'c_HOL_Oone__class_Oone'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.28 X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.88/1.28 'c_Polynomial_Opdivmod__rel'( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ), Y, 'tc_Polynomial_Opoly'( X ) ),
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ),
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ), Y, 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ), X ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.88/1.28 'c_Polynomial_Opdivmod__rel'( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ), Y,
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ), Y, X ) ],
% 0.88/1.28 [ ~( 'class_SEQ_Obanach'( X ) ), ~(
% 0.88/1.28 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 0.88/1.28 'c_Transcendental_Oexp'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.88/1.28 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.88/1.28 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 0.88/1.28 'c_HOL_Oinverse__class_Odivide'( 'c_RealVector_OscaleR__class_OscaleR'( Y
% 0.88/1.28 , Z, X ), T, X ), 'c_RealVector_OscaleR__class_OscaleR'( Y,
% 0.88/1.28 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.88/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 0.88/1.28 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 0.88/1.28 ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.88/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 0.88/1.28 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 0.88/1.28 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.88/1.28 ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.88/1.28 'c_Polynomial_Opcompose'( 'c_Polynomial_OpCons'( Y, Z, X ), T, X ),
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( 'c_Polynomial_OpCons'( Y,
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ),
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( T, 'c_Polynomial_Opcompose'( Z, T, X ),
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.88/1.28 [ ~( 'class_RealVector_Oreal__field'( X ) ), =(
% 0.88/1.28 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.88/1.28 , U, X ), X ), W, X ), 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oinverse__class_Odivide'(
% 0.88/1.28 'c_HOL_Ominus__class_Ominus'( Z, U, X ), W, X ), X ),
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'(
% 0.88/1.28 'c_HOL_Ominus__class_Ominus'( Y, T, X ), W, X ), U, X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 0.88/1.28 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.88/1.28 'c_Polynomial_Opoly'( 'c_Polynomial_Opcompose'( Y, Z, X ), T, X ),
% 0.88/1.28 'c_Polynomial_Opoly'( Y, 'c_Polynomial_Opoly'( Z, T, X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), =(
% 0.88/1.28 'c_Polynomial_Osmult'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 0.88/1.28 'c_HOL_Ouminus__class_Ouminus'( 'c_Polynomial_Osmult'( Y, Z, X ),
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), =(
% 0.88/1.28 'c_Polynomial_Osmult'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ), X ), 'c_HOL_Ouminus__class_Ouminus'(
% 0.88/1.28 'c_Polynomial_Osmult'( Y, Z, X ), 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.88/1.28 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.28 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.88/1.28 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.88/1.28 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 0.88/1.28 [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Ocoeff'(
% 0.88/1.28 'c_Polynomial_OpCons'( Y, Z, X ), 'c_Suc'( T ), X ),
% 0.88/1.28 'c_Polynomial_Ocoeff'( Z, T, X ) ) ],
% 0.88/1.28 [ ~( 'class_HOL_Ozero'( X ) ), ~( 'class_HOL_Oeq'( X ) ),
% 0.88/1.28 'c_HOL_Oeq__class_Oeq'( Y, Z, X ), ~( 'c_HOL_Oeq__class_Oeq'(
% 0.88/1.28 'c_Polynomial_OpCons'( Y, T, X ), 'c_Polynomial_OpCons'( Z, U, X ),
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.88/1.28 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ),
% 0.88/1.28 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.88/1.28 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.88/1.28 W, X ) ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.28 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.88/1.28 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 0.88/1.28 W, X ) ) ), =( T, 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.88/1.28 , X ), W, X ) ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.28 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.28 X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.88/1.28 'c_Polynomial_Opoly'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ), T, X ), 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.28 'c_Polynomial_Opoly'( Y, T, X ), 'c_Polynomial_Opoly'( Z, T, X ), X ) ) ]
% 0.88/1.28 ,
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.28 'c_Polynomial_Ocoeff'( 'c_HOL_Oone__class_Oone'( 'tc_Polynomial_Opoly'( X
% 0.88/1.28 ) ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_Polynomial_Opoly'( X ) )
% 0.88/1.28 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Polynomial_Opoly__gcd'(
% 0.88/1.28 Z, T, X ), 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_Polynomial_Opoly'( X ) )
% 0.88/1.28 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Polynomial_Opoly__gcd'(
% 0.88/1.28 T, Z, X ), 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.88/1.28 'c_Polynomial_Opoly'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ), T, X ), 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.28 'c_Polynomial_Opoly'( Y, T, X ), 'c_Polynomial_Opoly'( Z, T, X ), X ) ) ]
% 0.88/1.28 ,
% 0.88/1.28 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 0.88/1.28 'c_RealVector_OscaleR__class_OscaleR'( Y,
% 0.88/1.28 'c_RealVector_OscaleR__class_OscaleR'( Z, T, X ), X ),
% 0.88/1.28 'c_RealVector_OscaleR__class_OscaleR'( Z,
% 0.88/1.28 'c_RealVector_OscaleR__class_OscaleR'( Y, T, X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_RealVector_Oreal__vector'( X ) ), =(
% 0.88/1.28 'c_RealVector_OscaleR__class_OscaleR'( Y,
% 0.88/1.28 'c_RealVector_OscaleR__class_OscaleR'( Z, T, X ), X ),
% 0.88/1.28 'c_RealVector_OscaleR__class_OscaleR'( Z,
% 0.88/1.28 'c_RealVector_OscaleR__class_OscaleR'( Y, T, X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 0.88/1.28 'c_RealVector_OscaleR__class_OscaleR'( Y,
% 0.88/1.28 'c_RealVector_OscaleR__class_OscaleR'( Z, T, X ), X ),
% 0.88/1.28 'c_RealVector_OscaleR__class_OscaleR'( Z,
% 0.88/1.28 'c_RealVector_OscaleR__class_OscaleR'( Y, T, X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.88/1.28 X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.88/1.28 X ) ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 0.88/1.28 X ) ) ],
% 0.88/1.28 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.88/1.28 , Z, X ) ) ), =( 'c_Divides_Odiv__class_Omod'(
% 0.88/1.28 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'( T, X ), Z,
% 0.88/1.28 X ) ) ],
% 0.88/1.28 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.88/1.28 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 0.88/1.28 , T, X ), X ), T, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.28 'c_Polynomial_Opos__poly'( Y, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), 'c_Polynomial_Ocoeff'( Y,
% 0.88/1.28 'c_Polynomial_Odegree'( Y, X ), X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.28 'c_Polynomial_Ocoeff'( Y, 'c_Polynomial_Odegree'( Y, X ), X ), X ), ~(
% 0.88/1.28 'c_Polynomial_Opos__poly'( Y, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.88/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 0.88/1.28 ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.88/1.28 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 0.88/1.28 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 0.88/1.28 , Y, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.88/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 0.88/1.28 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.28 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 0.88/1.28 X ), Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 0.88/1.28 , Z, X ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.88/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 0.88/1.28 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 0.88/1.28 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 0.88/1.28 X ), Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 0.88/1.28 , Z, X ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.88/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 0.88/1.28 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 0.88/1.28 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.88/1.28 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T, Z, X
% 0.88/1.28 ), X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.88/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X
% 0.88/1.28 ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.88/1.28 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ),
% 0.88/1.28 ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oinverse__class_Odivide'( Y, T, X
% 0.88/1.28 ), X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.88/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 0.88/1.28 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.28 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 0.88/1.28 T, X ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 0.88/1.28 , T, X ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.88/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 0.88/1.28 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.28 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 0.88/1.28 T, X ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 0.88/1.28 , T, X ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.88/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 0.88/1.28 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.28 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.88/1.28 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 0.88/1.28 Z, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 0.88/1.28 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ],
% 0.88/1.28 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.88/1.28 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( 'c_Polynomial_OpCons'( Y, Z, X ),
% 0.88/1.28 'c_Polynomial_OpCons'( T, U, X ), 'tc_Polynomial_Opoly'( X ) ),
% 0.88/1.28 'c_Polynomial_OpCons'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ),
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( Z, U, 'tc_Polynomial_Opoly'( X ) ), X ) ) ]
% 0.88/1.28 ,
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 0.88/1.28 , X ), U, X ), W, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), U, X
% 0.88/1.28 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, X ),
% 0.88/1.28 W, X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 0.88/1.28 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 0.88/1.28 , X ), T, X ), W, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 0.88/1.28 , X ), W, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X
% 0.88/1.28 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ),
% 0.88/1.28 W, X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 0.88/1.28 ), X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.88/1.28 , X ), W, X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.88/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 0.88/1.28 , X ) ) ],
% 0.88/1.28 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.88/1.28 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( U, Y, X ), Z, X
% 0.88/1.28 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( W, T, X ),
% 0.88/1.28 Z, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), =(
% 0.88/1.28 'c_Polynomial_Osmult'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 0.88/1.28 'c_HOL_Ominus__class_Ominus'( 'c_Polynomial_Osmult'( Y, T, X ),
% 0.88/1.28 'c_Polynomial_Osmult'( Z, T, X ), 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), =(
% 0.88/1.28 'c_Polynomial_Osmult'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T,
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ), X ), 'c_HOL_Ominus__class_Ominus'(
% 0.88/1.28 'c_Polynomial_Osmult'( Y, Z, X ), 'c_Polynomial_Osmult'( Y, T, X ),
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.88/1.28 ), =( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.88/1.28 ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.28 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.88/1.28 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 0.88/1.28 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 0.88/1.28 ,
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.88/1.28 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 0.88/1.28 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 0.88/1.28 ,
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X
% 0.88/1.28 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 0.88/1.28 'c_HOL_Ominus__class_Ominus'( T, Y, X ), X ), Z, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ), ~(
% 0.88/1.28 'c_Polynomial_Opdivmod__rel'( Z, Y, T, U, X ) ),
% 0.88/1.28 'c_Polynomial_Opdivmod__rel'( 'c_Polynomial_OpCons'( W, Z, X ), Y,
% 0.88/1.28 'c_Polynomial_OpCons'( 'c_HOL_Oinverse__class_Odivide'(
% 0.88/1.28 'c_Polynomial_Ocoeff'( 'c_Polynomial_OpCons'( W, U, X ),
% 0.88/1.28 'c_Polynomial_Odegree'( Y, X ), X ), 'c_Polynomial_Ocoeff'( Y,
% 0.88/1.28 'c_Polynomial_Odegree'( Y, X ), X ), X ), T, X ),
% 0.88/1.28 'c_HOL_Ominus__class_Ominus'( 'c_Polynomial_OpCons'( W, U, X ),
% 0.88/1.28 'c_Polynomial_Osmult'( 'c_HOL_Oinverse__class_Odivide'(
% 0.88/1.28 'c_Polynomial_Ocoeff'( 'c_Polynomial_OpCons'( W, U, X ),
% 0.88/1.28 'c_Polynomial_Odegree'( Y, X ), X ), 'c_Polynomial_Ocoeff'( Y,
% 0.88/1.28 'c_Polynomial_Odegree'( Y, X ), X ), X ), Y, X ), 'tc_Polynomial_Opoly'(
% 0.88/1.28 X ) ), X ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.88/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.88/1.28 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 0.88/1.28 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.88/1.28 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.88/1.28 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.88/1.28 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.88/1.28 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y,
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 0.88/1.28 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 0.88/1.28 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Z,
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Y,
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.28 [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Odegree'(
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ),
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.28 [ ~( 'class_RealVector_Oreal__vector'( X ) ), =(
% 0.88/1.28 'c_RealVector_OscaleR__class_OscaleR'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 0.88/1.28 T, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.28 'c_RealVector_OscaleR__class_OscaleR'( Y, Z, X ),
% 0.88/1.28 'c_RealVector_OscaleR__class_OscaleR'( Y, T, X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 0.88/1.28 'c_RealVector_OscaleR__class_OscaleR'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 0.88/1.28 T, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.28 'c_RealVector_OscaleR__class_OscaleR'( Y, Z, X ),
% 0.88/1.28 'c_RealVector_OscaleR__class_OscaleR'( Y, T, X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.88/1.28 'c_Polynomial_Opoly'( 'c_Polynomial_Osmult'( Y, Z, X ), T, X ),
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Y, 'c_Polynomial_Opoly'( Z, T, X ), X ) ) ]
% 0.88/1.28 ,
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.88/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.88/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.88/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.88/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.88/1.28 'c_Polynomial_Opdivmod__rel'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T,
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ), U, 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Z, W, 'tc_Polynomial_Opoly'( X ) ), V0,
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ), X ), ~( 'c_Polynomial_Opdivmod__rel'( V1, T
% 0.88/1.28 , U, W, X ) ), ~( 'c_Polynomial_Opdivmod__rel'( Y, Z, V1, V0, X ) ) ]
% 0.88/1.28 ,
% 0.88/1.28 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.88/1.28 , Z ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( T, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.88/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.88/1.28 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.88/1.28 , 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 0.88/1.28 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ), =( Z,
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.88/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.88/1.28 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 0.88/1.28 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.88/1.28 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ), =( Y,
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.28 [ ~( 'class_SEQ_Obanach'( X ) ), ~(
% 0.88/1.28 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 0.88/1.28 'c_Transcendental_Oexp'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ),
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( 'c_Transcendental_Oexp'( Y, X ),
% 0.88/1.28 'c_Transcendental_Oexp'( Z, X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.88/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 0.88/1.28 , T, X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 0.88/1.28 Y, T, X ), Z, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Y, 'c_Polynomial_Osmult'( Z, T, X ),
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ), 'c_Polynomial_Osmult'( Z,
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_Polynomial_Opoly'( X ) ), X ) ) ]
% 0.88/1.28 ,
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( 'c_Polynomial_Osmult'( Y, Z, X ), T,
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ), 'c_Polynomial_Osmult'( Y,
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_Polynomial_Opoly'( X ) ), X ) ) ]
% 0.88/1.28 ,
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), =(
% 0.88/1.28 'c_Polynomial_Opoly'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ), T, X ), 'c_HOL_Ominus__class_Ominus'(
% 0.88/1.28 'c_Polynomial_Opoly'( Y, T, X ), 'c_Polynomial_Opoly'( Z, T, X ), X ) ) ]
% 0.88/1.28 ,
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.88/1.28 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.28 X ), T, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.88/1.28 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.88/1.28 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 0.88/1.28 X ), 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ],
% 0.88/1.28 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), Z, X ),
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 0.88/1.28 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), T, X ),
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.88/1.28 'c_Polynomial_Osmult'( Y, 'c_Polynomial_Osmult'( Z, T, X ), X ),
% 0.88/1.28 'c_Polynomial_Osmult'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ) )
% 0.88/1.28 ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 0.88/1.28 , X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 0.88/1.28 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( Y, 'c_Polynomial_Osmult'( Z,
% 0.88/1.28 'c_Polynomial_Osynthetic__div'( Y, Z, X ), X ), 'tc_Polynomial_Opoly'( X
% 0.88/1.28 ) ), 'c_Polynomial_OpCons'( 'c_Polynomial_Opoly'( Y, Z, X ),
% 0.88/1.28 'c_Polynomial_Osynthetic__div'( Y, Z, X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.88/1.28 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 0.88/1.28 ), Y ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.88/1.28 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 0.88/1.28 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, T
% 0.88/1.28 , X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 0.88/1.28 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 0.88/1.28 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, T
% 0.88/1.28 , X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 0.88/1.28 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), T, X ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.88/1.28 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 0.88/1.28 , Y, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.88/1.28 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 0.88/1.28 ), Y ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 0.88/1.28 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 0.88/1.28 ) ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 0.88/1.28 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 0.88/1.28 ) ) ],
% 0.88/1.28 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 0.88/1.28 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 0.88/1.28 ), Y ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.88/1.28 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 0.88/1.28 ), Y ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.88/1.28 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.88/1.28 X ), 'c_HOL_Ominus__class_Ominus'( Z, Y, X ) ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 0.88/1.28 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 0.88/1.28 , X ) ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 0.88/1.28 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 0.88/1.28 , X ) ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 0.88/1.28 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 0.88/1.28 , X ) ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 0.88/1.28 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 0.88/1.28 , X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( 'c_Polynomial_Opoly'( Y,
% 0.88/1.28 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_OpCons'(
% 0.88/1.28 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_Polynomial_OpCons'(
% 0.88/1.28 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ), X ), X ), Y, 'tc_Polynomial_Opoly'( X ) ) )
% 0.88/1.28 ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =( 'c_Polynomial_Opoly'(
% 0.88/1.28 Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_OpCons'(
% 0.88/1.28 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_Polynomial_OpCons'(
% 0.88/1.28 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ), X ), X ), Y, 'tc_Polynomial_Opoly'( X ) ) ]
% 0.88/1.28 ,
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =( 'c_Polynomial_Opoly'(
% 0.88/1.28 Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_OpCons'( Z,
% 0.88/1.28 'c_Polynomial_OpCons'( 'c_HOL_Oone__class_Oone'( X ),
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ), X ), Y,
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( 'c_Polynomial_Opoly'( Y,
% 0.88/1.28 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.28 X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_OpCons'( Z
% 0.88/1.28 , 'c_Polynomial_OpCons'( 'c_HOL_Oone__class_Oone'( X ),
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ), X ), Y,
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.88/1.28 [ ~( =( 'c_Polynomial_Opoly'( 'v_ds____',
% 0.88/1.28 'v_sko__local__XpCons__Xhyps__1'( 'v_ds____' ), 'tc_Complex_Ocomplex' ),
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Complex_Ocomplex' ) ) ), =( 'v_ds____',
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( 'tc_Complex_Ocomplex'
% 0.88/1.28 ) ) ) ],
% 0.88/1.28 [ ~( =( 'c_Polynomial_Opoly'( 'v_ds____', 'v_sko__local__XpCons__1__1'(
% 0.88/1.28 'v_ds____' ), 'tc_Complex_Ocomplex' ), 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.28 'tc_Complex_Ocomplex' ) ) ), =( 'v_ds____', 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.28 'tc_Polynomial_Opoly'( 'tc_Complex_Ocomplex' ) ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.88/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_RealVector_Oreal__vector'( X ) ), ~( =(
% 0.88/1.28 'c_RealVector_OscaleR__class_OscaleR'( Y, Z, X ),
% 0.88/1.28 'c_RealVector_OscaleR__class_OscaleR'( T, Z, X ) ) ), =( Z,
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, T ) ],
% 0.88/1.28 [ ~( 'class_RealVector_Oreal__vector'( X ) ), =(
% 0.88/1.28 'c_RealVector_OscaleR__class_OscaleR'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 0.88/1.28 , X ), 'c_RealVector_OscaleR__class_OscaleR'( Z,
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~( =(
% 0.88/1.28 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 0.88/1.28 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), =(
% 0.88/1.28 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.88/1.28 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.88/1.28 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Osgn__if'( X ) ), =(
% 0.88/1.28 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.28 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 0.88/1.28 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 0.88/1.28 , X ) ],
% 0.88/1.28 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.88/1.28 ) ],
% 0.88/1.28 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 0.88/1.28 ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( Y,
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 0.88/1.28 , X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.88/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.88/1.28 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.88/1.28 ,
% 0.88/1.28 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), ~( =(
% 0.88/1.28 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y ) ), =( Y,
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.88/1.28 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.88/1.28 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.88/1.28 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.88/1.28 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.88/1.28 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.88/1.28 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.88/1.28 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.88/1.28 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), 'c_HOL_Otimes__class_Otimes'( Y, Y
% 0.88/1.28 , X ) ) ],
% 0.88/1.28 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.88/1.28 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( U, Y, X ), Z
% 0.88/1.28 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( W, T,
% 0.88/1.28 X ), Z, X ) ) ],
% 0.88/1.28 [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Odegree'(
% 0.88/1.28 'c_Polynomial_Omonom'( Y, Z, X ), X ), Z ), =( Y,
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 0.88/1.28 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 0.88/1.28 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.88/1.28 , Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ), =( U,
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 0.88/1.28 ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.88/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 0.88/1.28 , Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.88/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 0.88/1.28 , Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z, X
% 0.88/1.28 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y,
% 0.88/1.28 'c_HOL_Oone__class_Oone'( X ), X ), Z, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X
% 0.88/1.28 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Z,
% 0.88/1.28 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( 'c_Polynomial_OpCons'( Y, Z, X ), T,
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.28 'c_Polynomial_Osmult'( Y, T, X ), 'c_Polynomial_OpCons'(
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, T,
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ), X ), 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Y, 'c_Polynomial_OpCons'( Z, T, X ),
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.28 'c_Polynomial_Osmult'( Z, Y, X ), 'c_Polynomial_OpCons'(
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, T,
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ), X ), 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), ~( =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( Y, 'c_Polynomial_Osmult'( Z, T, X ),
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ), 'c_Polynomial_OpCons'( U, T, X ) ) ), =( U
% 0.88/1.28 , 'c_Polynomial_Opoly'( Y, Z, X ) ) ],
% 0.88/1.28 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.88/1.28 Z, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.88/1.28 Z, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 0.88/1.28 ), X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 0.88/1.28 ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 0.88/1.28 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.88/1.28 , Y, X ) ) ],
% 0.88/1.28 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 0.88/1.28 , X ) ) ],
% 0.88/1.28 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.88/1.28 , Y, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), ~( =(
% 0.88/1.28 'c_Polynomial_Osynthetic__div'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ) ) ), =( 'c_Polynomial_Odegree'( Y, X ),
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), ~( =(
% 0.88/1.28 'c_Polynomial_Odegree'( Y, X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 0.88/1.28 ), =( 'c_Polynomial_Osynthetic__div'( Y, Z, X ),
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.88/1.28 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 0.88/1.28 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 0.88/1.28 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 0.88/1.28 X ), Z, X ) ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.28 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( Z, Y, X ), X ), Z ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), Z ) ],
% 0.88/1.28 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.88/1.28 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.88/1.28 [ ~( 'class_HOL_Ozero'( X ) ), ~( 'class_HOL_Oeq'( X ) ), =( Y, Z ), ~(
% 0.88/1.28 'c_HOL_Oeq__class_Oeq'( Y, Z, 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.88/1.28 [ ~( 'class_HOL_Oeq'( X ) ), =( Y, Z ), ~( 'c_HOL_Oeq__class_Oeq'( Y, Z
% 0.88/1.28 , X ) ) ],
% 0.88/1.28 [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Ocoeff'(
% 0.88/1.28 'c_Polynomial_OpCons'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.88/1.28 , X ), Y ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.88/1.28 , X ) ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.88/1.28 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.88/1.28 , X ) ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.28 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 0.88/1.28 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 0.88/1.28 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.88/1.28 'c_Polynomial_Opoly__gcd'( Y, Z, X ), 'c_Polynomial_Opoly__gcd'( Z, Y, X
% 0.88/1.28 ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.88/1.28 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'(
% 0.88/1.28 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 0.88/1.28 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'(
% 0.88/1.28 'c_HOL_Oone__class_Oone'( X ), X ) ) ), 'c_HOL_Oord__class_Oless'( Y,
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.88/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 0.88/1.28 X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 0.88/1.28 X ), X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_Opoly__gcd'( Y, Z, X
% 0.88/1.28 ), Z, 'tc_Polynomial_Opoly'( X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_Opoly__gcd'( Y, Z, X
% 0.88/1.28 ), Y, 'tc_Polynomial_Opoly'( X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Polynomial_Opoly__gcd'( Z, T
% 0.88/1.28 , X ), 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, 'tc_Polynomial_Opoly'( X ) )
% 0.88/1.28 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_Polynomial_Opoly'(
% 0.88/1.28 X ) ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Polynomial_Opoly__gcd'( Z, T
% 0.88/1.28 , X ), 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, 'tc_Polynomial_Opoly'( X ) )
% 0.88/1.28 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_Polynomial_Opoly'(
% 0.88/1.28 X ) ) ) ],
% 0.88/1.28 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.88/1.28 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T
% 0.88/1.28 , X ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), ~(
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), ~( =(
% 0.88/1.28 'c_HOL_Oplus__class_Oplus'( Y, 'c_Polynomial_Osmult'( Z, T, X ),
% 0.88/1.28 'tc_Polynomial_Opoly'( X ) ), 'c_Polynomial_OpCons'( U, T, X ) ) ), =( T
% 0.88/1.28 , 'c_Polynomial_Osynthetic__div'( Y, Z, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.88/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.28 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 0.88/1.28 ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.88/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.88/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.88/1.28 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 0.88/1.28 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.88/1.28 ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =( 'c_Polynomial_Ocoeff'(
% 0.88/1.28 Y, 'c_Polynomial_Odegree'( Y, X ), X ), 'c_Polynomial_Ocoeff'( Z,
% 0.88/1.28 'c_Polynomial_Odegree'( Z, X ), X ) ) ), =( Y, Z ), ~(
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_Polynomial_Opoly'( X ) )
% 0.88/1.28 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_Polynomial_Opoly'(
% 0.88/1.28 X ) ) ) ],
% 0.88/1.28 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 0.88/1.28 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 0.88/1.28 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 0.88/1.28 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 0.88/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.88/1.28 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.88/1.28 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 0.88/1.28 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.88/1.28 X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 0.88/1.28 , X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Z, U, X ) ), ~(
% 0.88/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 0.88/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.88/1.28 'c_Polynomial_Opoly'( 'c_HOL_Oone__class_Oone'( 'tc_Polynomial_Opoly'( X
% 0.88/1.28 ) ), Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.88/1.28 'c_HOL_Ominus__class_Ominus'( 'c_Polynomial_Omonom'( Y, Z, X ),
% 0.88/1.28 'c_Polynomial_Omonom'( T, Z, X ), 'tc_Polynomial_Opoly'( X ) ),
% 0.88/1.28 'c_Polynomial_Omonom'( 'c_HOL_Ominus__class_Ominus'( Y, T, X ), Z, X ) )
% 0.88/1.28 ],
% 0.88/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.88/1.28 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oplus__class_Oplus'(
% 0.88/1.28 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 0.91/1.28 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 0.91/1.28 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 0.91/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 0.91/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.91/1.28 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ) ]
% 0.91/1.28 ,
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.91/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.28 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 0.91/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.91/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.91/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 0.91/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 0.91/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.28 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.91/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.91/1.28 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.28 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 0.91/1.28 X ), X ) ) ],
% 0.91/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.91/1.28 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.91/1.28 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.28 Z, T, X ) ) ],
% 0.91/1.28 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.91/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.91/1.28 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.28 Z, T, X ) ) ],
% 0.91/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.91/1.28 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.28 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 0.91/1.28 X ), X ) ) ],
% 0.91/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.91/1.28 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.91/1.28 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.28 Y, T, X ) ) ],
% 0.91/1.28 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.91/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 0.91/1.28 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.28 Y, T, X ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.91/1.28 'c_Polynomial_Opoly'( 'c_Polynomial_OpCons'( Y, Z, X ), T, X ),
% 0.91/1.28 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 0.91/1.28 'c_Polynomial_Opoly'( Z, T, X ), X ), X ) ) ],
% 0.91/1.28 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.28 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 0.91/1.28 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.28 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.28 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 0.91/1.28 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =(
% 0.91/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.91/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 0.91/1.28 ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ),
% 0.91/1.28 'c_Polynomial_Opdivmod__rel'( 'c_HOL_Oplus__class_Oplus'(
% 0.91/1.28 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_Polynomial_Opoly'( X ) ),
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ),
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), Y, Z, 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), X ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.28 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.28 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.91/1.28 , Y, X ), X ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.91/1.28 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.28 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.91/1.28 , T, X ), X ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.28 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.28 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 0.91/1.28 , T, X ), X ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.91/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.91/1.28 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.28 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.91/1.28 , Y, X ), X ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.91/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 0.91/1.28 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 0.91/1.28 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), T, X ) ) ],
% 0.91/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.91/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.91/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.91/1.28 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 0.91/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.91/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.91/1.28 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.91/1.28 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.28 'c_Polynomial_Ocoeff'( 'c_HOL_Oone__class_Oone'( 'tc_Polynomial_Opoly'( X
% 0.91/1.28 ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X ),
% 0.91/1.28 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 0.91/1.28 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 0.91/1.28 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ) ), =( U,
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 0.91/1.28 ), =( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 0.91/1.28 'c_HOL_Otimes__class_Otimes'( T, Z, X ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 0.91/1.28 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 0.91/1.28 , U, X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( U,
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 0.91/1.28 , U, X ), 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ],
% 0.91/1.28 [ ~( 'class_RealVector_Oreal__normed__div__algebra'( X ) ), =(
% 0.91/1.28 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 0.91/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Osgn__class_Osgn'( Y, X ),
% 0.91/1.28 'c_HOL_Osgn__class_Osgn'( Z, X ), X ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.91/1.28 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 0.91/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Osgn__class_Osgn'( Y, X ),
% 0.91/1.28 'c_HOL_Osgn__class_Osgn'( Z, X ), X ) ) ],
% 0.91/1.28 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.28 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.28 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 0.91/1.28 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Omod'( Z, T, X )
% 0.91/1.28 , X ) ) ],
% 0.91/1.28 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.28 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 0.91/1.28 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 0.91/1.28 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z
% 0.91/1.28 , X ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.91/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.91/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 0.91/1.28 ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.91/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 0.91/1.28 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 0.91/1.28 ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.91/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.91/1.28 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y, X ),
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.28 [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_Omonom'( Y, Z, X ),
% 0.91/1.28 'c_Polynomial_Omonom'( T, Z, X ) ) ), =( Y, T ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.91/1.28 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ), ~(
% 0.91/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.91/1.28 ,
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 0.91/1.28 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 0.91/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 0.91/1.28 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) ),
% 0.91/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ],
% 0.91/1.28 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.91/1.28 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X
% 0.91/1.28 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 0.91/1.28 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 0.91/1.28 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.91/1.28 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X
% 0.91/1.28 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.91/1.28 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 0.91/1.28 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.91/1.28 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.91/1.28 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.91/1.28 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.91/1.28 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.91/1.28 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.91/1.28 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.91/1.28 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.91/1.28 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.91/1.28 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.91/1.28 ) ],
% 0.91/1.28 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.91/1.28 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.91/1.28 ) ],
% 0.91/1.28 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.91/1.28 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 0.91/1.28 ) ],
% 0.91/1.28 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.91/1.28 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.91/1.28 ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.91/1.28 X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y, X ),
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.91/1.28 X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ), =( Z,
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.28 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 0.91/1.28 'c_OrderedGroup_Olordered__ab__group__add__class_Opprt'(
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.91/1.28 ,
% 0.91/1.28 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 0.91/1.28 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.28 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 0.91/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.91/1.28 ,
% 0.91/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 0.91/1.28 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.28 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 0.91/1.28 ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ],
% 0.91/1.28 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 0.91/1.28 'c_RealVector_OscaleR__class_OscaleR'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 0.91/1.28 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.28 [ ~( 'class_RealVector_Oreal__vector'( X ) ), =(
% 0.91/1.28 'c_RealVector_OscaleR__class_OscaleR'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 0.91/1.28 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.28 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 0.91/1.28 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.91/1.28 ) ), =( Y, Z ) ],
% 0.91/1.28 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.91/1.28 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.91/1.28 ) ), =( Y, Z ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.91/1.28 X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.91/1.28 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.91/1.28 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.91/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.91/1.28 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.91/1.28 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.91/1.28 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 0.91/1.28 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.91/1.28 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.28 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 0.91/1.28 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.91/1.28 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 0.91/1.28 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 0.91/1.28 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.28 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~( =(
% 0.91/1.28 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 0.91/1.28 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.28 [ ~( 'class_SEQ_Obanach'( X ) ), ~(
% 0.91/1.28 'class_RealVector_Oreal__normed__field'( X ) ), ~( =(
% 0.91/1.28 'c_Transcendental_Oexp'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ]
% 0.91/1.28 ,
% 0.91/1.28 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.91/1.28 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.91/1.28 ],
% 0.91/1.28 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 0.91/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.91/1.28 ],
% 0.91/1.28 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.91/1.28 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.91/1.28 ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.91/1.28 X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.91/1.28 ), X ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.91/1.28 ],
% 0.91/1.28 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.91/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.91/1.28 ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.28 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 0.91/1.28 ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 0.91/1.28 ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.91/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_Osmult'(
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Z, 'tc_Polynomial_Opoly'( X ) )
% 0.91/1.28 ), =( Z, 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ]
% 0.91/1.28 ,
% 0.91/1.28 [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Ocoeff'(
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ),
% 0.91/1.28 'c_Polynomial_Odegree'( 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'(
% 0.91/1.28 X ) ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.91/1.28 'c_Polynomial_Osynthetic__divmod'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), Y, X ), 'c_Pair'(
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ),
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( X ), 'tc_Polynomial_Opoly'( X ), X ) ) ],
% 0.91/1.28 [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_Ocoeff'( Y,
% 0.91/1.28 'c_Polynomial_Odegree'( Y, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 0.91/1.28 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.91/1.28 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_Osmult'(
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ) ],
% 0.91/1.28 [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Omonom'( Y, 'c_Suc'( Z )
% 0.91/1.28 , X ), 'c_Polynomial_OpCons'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.91/1.28 'c_Polynomial_Omonom'( Y, Z, X ), X ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.91/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.91/1.28 'c_Polynomial_Opos__poly'( Z, X ), ~( 'c_Polynomial_Opos__poly'(
% 0.91/1.28 'c_Polynomial_OpCons'( Y, Z, X ), X ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.91/1.28 'c_Polynomial_Osmult'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( 'c_Polynomial_Osmult'( Y
% 0.91/1.28 , 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ),
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.91/1.28 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.91/1.28 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ),
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.91/1.28 'c_Polynomial_Osynthetic__div'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 0.91/1.28 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ),
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.91/1.28 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ),
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.91/1.28 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), Y, 'tc_Polynomial_Opoly'( X ) ),
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.91/1.28 'c_Polynomial_Opdivmod__rel'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), Y, X ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), ~( =(
% 0.91/1.28 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly'( Y, Z, X ),
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ), =( Y,
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 0.91/1.28 'c_Polynomial_Opdivmod__rel'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), Y, 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), X ) ],
% 0.91/1.28 [ ~( 'class_HOL_Ozero'( X ) ), ~( 'class_HOL_Oeq'( X ) ),
% 0.91/1.28 'c_HOL_Oeq__class_Oeq'( 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'(
% 0.91/1.28 X ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ),
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 0.91/1.28 'c_Polynomial_Opoly__gcd'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 0.91/1.28 'c_Polynomial_Opoly__gcd'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ), ~(
% 0.91/1.28 'c_Polynomial_Opdivmod__rel'( Z, 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), Y, T, X ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ), ~(
% 0.91/1.28 'c_Polynomial_Opdivmod__rel'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), Z, T, Y, X ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ), ~(
% 0.91/1.28 'c_Polynomial_Opdivmod__rel'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), Z, Y, T, X ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 0.91/1.28 'c_Polynomial_Opdivmod__rel'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), Z, T, X ) ), =( Z,
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y, Z ), ~(
% 0.91/1.28 'c_Polynomial_Opdivmod__rel'( Z, 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), T, Y, X ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 0.91/1.28 'c_Polynomial_Opoly__gcd'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 0.91/1.28 'c_Polynomial_Opos__poly'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), X ) ) ],
% 0.91/1.28 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.91/1.28 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ), Y ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.91/1.28 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly'(
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), Y, X ),
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.91/1.28 'c_Polynomial_Opcompose'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.91/1.28 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.91/1.28 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), Y, 'tc_Polynomial_Opoly'( X ) ), Y ) ],
% 0.91/1.28 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 0.91/1.28 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ), Y ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( 'c_Polynomial_Opdivmod'(
% 0.91/1.28 'c_Polynomial_OpCons'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), X ), 'c_Pair'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), 'c_Polynomial_OpCons'( Y, Z, X ),
% 0.91/1.28 'tc_Polynomial_Opoly'( X ), 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.91/1.28 [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Odegree'(
% 0.91/1.28 'c_Polynomial_OpCons'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_nat' ) ) ],
% 0.91/1.28 [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Omonom'( Y,
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X ), 'c_Polynomial_OpCons'( Y,
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.91/1.28 'c_HOL_Oone__class_Oone'( 'tc_Polynomial_Opoly'( X ) ),
% 0.91/1.28 'c_Polynomial_OpCons'( 'c_HOL_Oone__class_Oone'( X ),
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), ~( =(
% 0.91/1.28 'c_HOL_Oplus__class_Oplus'( 'c_Polynomial_Osmult'( Y, Z, X ),
% 0.91/1.28 'c_Polynomial_OpCons'( T, Z, X ), 'tc_Polynomial_Opoly'( X ) ),
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ), =( Z,
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.91/1.28 [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Odegree'(
% 0.91/1.28 'c_Polynomial_OpCons'( Y, Z, X ), X ), 'c_Suc'( 'c_Polynomial_Odegree'( Z
% 0.91/1.28 , X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) )
% 0.91/1.28 ) ],
% 0.91/1.28 [ ~( 'class_HOL_Ozero'( X ) ), ~( 'class_HOL_Oeq'( X ) ),
% 0.91/1.28 'c_HOL_Oeq__class_Oeq'( Y, Z, 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.91/1.28 'c_HOL_Oeq__class_Oeq'( 'c_Polynomial_OpCons'( T, Y, X ),
% 0.91/1.28 'c_Polynomial_OpCons'( U, Z, X ), 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.91/1.28 'c_Polynomial_Opos__poly'( 'c_Polynomial_OpCons'( Y, Z, X ), X ), ~(
% 0.91/1.28 'c_Polynomial_Opos__poly'( Z, X ) ) ],
% 0.91/1.28 [ ~( =( 'v_sko__local__XpCons__Xhyps__1'( 'v_ds____' ),
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Complex_Ocomplex' ) ) ), =( 'v_ds____',
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( 'tc_Complex_Ocomplex'
% 0.91/1.28 ) ) ) ],
% 0.91/1.28 [ ~( =( 'v_sko__local__XpCons__1__1'( 'v_ds____' ),
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Complex_Ocomplex' ) ) ), =( 'v_ds____',
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( 'tc_Complex_Ocomplex'
% 0.91/1.28 ) ) ) ],
% 0.91/1.28 [ ~( =( 'v_d____', 'c_HOL_Ozero__class_Ozero'( 'tc_Complex_Ocomplex' ) )
% 0.91/1.28 ) ],
% 0.91/1.28 [ ~( 'class_HOL_Ozero'( X ) ), ~( 'class_HOL_Oeq'( X ) ),
% 0.91/1.28 'c_HOL_Oeq__class_Oeq'( 'c_Polynomial_OpCons'( Y, Z, X ),
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ),
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), ~( 'c_HOL_Oeq__class_Oeq'( Z,
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ),
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ) ), ~( 'c_HOL_Oeq__class_Oeq'( Y,
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.91/1.28 [ ~( 'class_HOL_Ozero'( X ) ), ~( 'class_HOL_Oeq'( X ) ),
% 0.91/1.28 'c_HOL_Oeq__class_Oeq'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.91/1.28 'c_HOL_Oeq__class_Oeq'( 'c_Polynomial_OpCons'( Y, Z, X ),
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ),
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.91/1.28 [ ~( 'class_HOL_Ozero'( X ) ), ~( 'class_HOL_Oeq'( X ) ),
% 0.91/1.28 'c_HOL_Oeq__class_Oeq'( 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'(
% 0.91/1.28 X ) ), 'c_Polynomial_OpCons'( Y, Z, X ), 'tc_Polynomial_Opoly'( X ) ),
% 0.91/1.28 ~( 'c_HOL_Oeq__class_Oeq'( 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), Z, 'tc_Polynomial_Opoly'( X ) ) ), ~(
% 0.91/1.28 'c_HOL_Oeq__class_Oeq'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.91/1.28 [ ~( 'class_HOL_Ozero'( X ) ), ~( 'class_HOL_Oeq'( X ) ),
% 0.91/1.28 'c_HOL_Oeq__class_Oeq'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.91/1.28 'c_HOL_Oeq__class_Oeq'( 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'(
% 0.91/1.28 X ) ), 'c_Polynomial_OpCons'( Y, Z, X ), 'tc_Polynomial_Opoly'( X ) ) ) ]
% 0.91/1.28 ,
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.91/1.28 'c_Polynomial_Opos__poly'( 'c_Polynomial_OpCons'( Y,
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ), X ), ~(
% 0.91/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.91/1.28 ,
% 0.91/1.28 [ ~( =( 'v_p', 'c_Polynomial_OpCons'( X, 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( 'tc_Complex_Ocomplex' ) ), 'tc_Complex_Ocomplex' )
% 0.91/1.28 ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_Complex_Ocomplex' ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.91/1.28 'c_Polynomial_Osmult'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( 'c_Polynomial_Osmult'(
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =( 'c_Polynomial_Osmult'(
% 0.91/1.28 Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ),
% 0.91/1.28 =( Z, 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ), =( Y,
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.91/1.28 'c_Polynomial_Opoly'( 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'(
% 0.91/1.28 X ) ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( 'c_Polynomial_Opoly'(
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), Y, X ),
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.28 [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_Omonom'( Y, Z, X ),
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ), =( Y,
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.28 [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Omonom'(
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.91/1.28 [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Ocoeff'(
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), Y, X ),
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.28 [ ~( 'class_HOL_Ozero'( X ) ), ~( 'class_HOL_Oeq'( X ) ),
% 0.91/1.28 'c_HOL_Oeq__class_Oeq'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.91/1.28 'c_HOL_Oeq__class_Oeq'( 'c_Polynomial_OpCons'( Z, Y, X ),
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ),
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ),
% 0.91/1.28 'c_Polynomial_Opos__poly'( Y, X ), ~( 'c_Polynomial_Opos__poly'(
% 0.91/1.28 'c_Polynomial_OpCons'( Z, Y, X ), X ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.91/1.28 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly'(
% 0.91/1.28 'c_Polynomial_OpCons'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), X ), Z, X ), 'c_Polynomial_OpCons'( Y,
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ) ) ],
% 0.91/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), ~( =(
% 0.91/1.28 'c_Polynomial_Osmult'( Y, Z, X ), 'c_Polynomial_OpCons'( T, Z, X ) ) ),
% 0.91/1.28 =( Z, 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.91/1.28 [ ~( 'class_HOL_Ozero'( X ) ), ~( 'class_HOL_Oeq'( X ) ),
% 0.91/1.28 'c_HOL_Oeq__class_Oeq'( 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'(
% 0.91/1.28 X ) ), Y, 'tc_Polynomial_Opoly'( X ) ), ~( 'c_HOL_Oeq__class_Oeq'(
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ),
% 0.91/1.28 'c_Polynomial_OpCons'( Z, Y, X ), 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.91/1.28 [ =( 'c_Polynomial_Opoly'( 'c_Polynomial_OpCons'( 'v_d____', 'v_ds____'
% 0.91/1.28 , 'tc_Complex_Ocomplex' ), X, 'tc_Complex_Ocomplex' ),
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Complex_Ocomplex' ) ), =( X,
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Complex_Ocomplex' ) ) ],
% 0.91/1.28 [ ~( =( 'v_d____', 'c_HOL_Ozero__class_Ozero'( 'tc_Complex_Ocomplex' ) )
% 0.91/1.28 ), =( 'c_Polynomial_OpCons'( 'v_d____', 'v_ds____',
% 0.91/1.28 'tc_Complex_Ocomplex' ), 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( 'tc_Complex_Ocomplex' ) ) ) ],
% 0.91/1.28 [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_OpCons'( Y, Z, X ),
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ), =( Y,
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.91/1.28 [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_OpCons'( Y, Z, X ),
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ), =( Z,
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.91/1.28 [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_OpCons'(
% 0.91/1.28 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.91/1.28 [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_OpCons'( Y, Z, X ),
% 0.91/1.28 'c_Polynomial_OpCons'( T, U, X ) ) ), =( Y, T ) ],
% 0.91/1.28 [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_OpCons'( Y, Z, X ),
% 0.91/1.28 'c_Polynomial_OpCons'( T, U, X ) ) ), =( Z, U ) ],
% 0.91/1.28 [ ~( =( 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.28 'c_RealVector_Oof__real'( 'v_x____', 'tc_Complex_Ocomplex' ),
% 0.91/1.28 'c_Polynomial_Opoly'( 'v_ds____', 'c_RealVector_Oof__real'( 'v_x____',
% 0.91/1.28 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' )
% 0.91/1.28 , 'tc_Complex_Ocomplex' ), 'c_RealVector_Onorm__class_Onorm'( 'v_d____',
% 0.91/1.28 'tc_Complex_Ocomplex' ) ) ) ],
% 0.91/1.28 [ =( 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Otimes__class_Otimes'(
% 0.91/1.28 'c_RealVector_Oof__real'( 'v_x____', 'tc_Complex_Ocomplex' ),
% 0.91/1.28 'c_Polynomial_Opoly'( 'v_ds____', 'c_RealVector_Oof__real'( 'v_x____',
% 0.91/1.28 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' )
% 0.91/1.28 , 'tc_Complex_Ocomplex' ), 'c_RealVector_Onorm__class_Onorm'( 'v_d____',
% 0.91/1.28 'tc_Complex_Ocomplex' ) ) ],
% 0.91/1.28 [ ~( =( 'c_Polynomial_OpCons'( 'v_d____', 'v_ds____',
% 0.91/1.28 'tc_Complex_Ocomplex' ), 'c_HOL_Ozero__class_Ozero'(
% 0.91/1.28 'tc_Polynomial_Opoly'( 'tc_Complex_Ocomplex' ) ) ) ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Ocancel__comm__monoid__add'( 'tc_Polynomial_Opoly'(
% 0.91/1.28 X ) ), ~( 'class_OrderedGroup_Ocancel__comm__monoid__add'( X ) ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Ocancel__comm__monoid__add'( 'tc_Complex_Ocomplex'
% 0.91/1.28 ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Ocancel__comm__monoid__add'( 'tc_RealDef_Oreal' )
% 0.91/1.28 ],
% 0.91/1.28 [ 'class_OrderedGroup_Ocancel__comm__monoid__add'( 'tc_nat' ) ],
% 0.91/1.28 [ 'class_HOL_Oeq'( 'tc_prod'( X, Y ) ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 0.91/1.28 ],
% 0.91/1.28 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 0.91/1.28 ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 0.91/1.28 ],
% 0.91/1.28 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_nat' ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 0.91/1.28 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Odvd'( 'tc_nat' ) ],
% 0.91/1.28 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 0.91/1.28 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 0.91/1.28 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 0.91/1.28 [ 'class_HOL_Ozero'( 'tc_nat' ) ],
% 0.91/1.28 [ 'class_HOL_Oeq'( 'tc_nat' ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 0.91/1.28 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 0.91/1.28 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 0.91/1.28 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 0.91/1.28 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 0.91/1.28 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Olordered__ab__group__add__abs'(
% 0.91/1.28 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_RealDef_Oreal'
% 0.91/1.28 ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_RealDef_Oreal'
% 0.91/1.28 ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_RealDef_Oreal' )
% 0.91/1.28 ],
% 0.91/1.28 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_RealDef_Oreal' )
% 0.91/1.28 ],
% 0.91/1.28 [ 'class_RealVector_Oreal__normed__div__algebra'( 'tc_RealDef_Oreal' ) ]
% 0.91/1.28 ,
% 0.91/1.28 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_RealDef_Oreal' ) ]
% 0.91/1.28 ,
% 0.91/1.28 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_RealDef_Oreal' ) ]
% 0.91/1.28 ,
% 0.91/1.28 [ 'class_OrderedGroup_Oordered__ab__group__add'( 'tc_RealDef_Oreal' ) ]
% 0.91/1.28 ,
% 0.91/1.28 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_RealDef_Oreal' ) ]
% 0.91/1.28 ,
% 0.91/1.28 [ 'class_RealVector_Oreal__normed__algebra__1'( 'tc_RealDef_Oreal' ) ]
% 0.91/1.28 ,
% 0.91/1.28 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_RealDef_Oreal' ) ]
% 0.91/1.28 ,
% 0.91/1.28 [ 'class_Ring__and__Field_Odivision__by__zero'( 'tc_RealDef_Oreal' ) ]
% 0.91/1.28 ,
% 0.91/1.28 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_RealDef_Oreal' ) ]
% 0.91/1.28 ,
% 0.91/1.28 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_RealDef_Oreal' ) ]
% 0.91/1.28 ,
% 0.91/1.28 [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_RealDef_Oreal' ) ]
% 0.91/1.28 ,
% 0.91/1.28 [ 'class_RealVector_Oreal__normed__algebra'( 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_RealVector_Oreal__normed__vector'( 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Oordered__field'( 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_RealVector_Oreal__normed__field'( 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Oab__group__add'( 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Omult__zero'( 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Osemiring'( 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_RealVector_Oreal__algebra'( 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Omonoid__add'( 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_RealVector_Oreal__vector'( 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Ogroup__add'( 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Osgn__if'( 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Oabs__if'( 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_RealVector_Oreal__field'( 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Ofield'( 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Oring'( 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Oidom'( 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Odvd'( 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_Orderings_Opreorder'( 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_Orderings_Olinorder'( 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_Orderings_Oorder'( 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_Int_Onumber__ring'( 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_SEQ_Obanach'( 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_HOL_Ozero'( 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_HOL_Oeq'( 'tc_RealDef_Oreal' ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 0.91/1.28 'tc_Complex_Ocomplex' ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 0.91/1.28 'tc_Complex_Ocomplex' ) ],
% 0.91/1.28 [ 'class_RealVector_Oreal__normed__div__algebra'( 'tc_Complex_Ocomplex'
% 0.91/1.28 ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Complex_Ocomplex' )
% 0.91/1.28 ],
% 0.91/1.28 [ 'class_RealVector_Oreal__normed__algebra__1'( 'tc_Complex_Ocomplex' )
% 0.91/1.28 ],
% 0.91/1.28 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Complex_Ocomplex' )
% 0.91/1.28 ],
% 0.91/1.28 [ 'class_Ring__and__Field_Odivision__by__zero'( 'tc_Complex_Ocomplex' )
% 0.91/1.28 ],
% 0.91/1.28 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Complex_Ocomplex' ) ]
% 0.91/1.28 ,
% 0.91/1.28 [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_Complex_Ocomplex' ) ]
% 0.91/1.28 ,
% 0.91/1.28 [ 'class_RealVector_Oreal__normed__algebra'( 'tc_Complex_Ocomplex' ) ]
% 0.91/1.28 ,
% 0.91/1.28 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Complex_Ocomplex' ) ]
% 0.91/1.28 ,
% 0.91/1.28 [ 'class_RealVector_Oreal__normed__vector'( 'tc_Complex_Ocomplex' ) ]
% 0.91/1.28 ,
% 0.91/1.28 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Complex_Ocomplex' ) ]
% 0.91/1.28 ,
% 0.91/1.28 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Complex_Ocomplex' ) ]
% 0.91/1.28 ,
% 0.91/1.28 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Complex_Ocomplex' ) ]
% 0.91/1.28 ,
% 0.91/1.28 [ 'class_RealVector_Oreal__normed__field'( 'tc_Complex_Ocomplex' ) ]
% 0.91/1.28 ,
% 0.91/1.28 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Complex_Ocomplex' ) ]
% 0.91/1.28 ,
% 0.91/1.28 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Complex_Ocomplex' ) ]
% 0.91/1.28 ,
% 0.91/1.28 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Complex_Ocomplex' ) ]
% 0.91/1.28 ,
% 0.91/1.28 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Complex_Ocomplex' ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Complex_Ocomplex' ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_Complex_Ocomplex' ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Complex_Ocomplex' ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Osemiring'( 'tc_Complex_Ocomplex' ) ],
% 0.91/1.28 [ 'class_RealVector_Oreal__algebra'( 'tc_Complex_Ocomplex' ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Complex_Ocomplex' ) ],
% 0.91/1.28 [ 'class_RealVector_Oreal__vector'( 'tc_Complex_Ocomplex' ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Complex_Ocomplex' ) ],
% 0.91/1.28 [ 'class_RealVector_Oreal__field'( 'tc_Complex_Ocomplex' ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Ofield'( 'tc_Complex_Ocomplex' ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Oring'( 'tc_Complex_Ocomplex' ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Oidom'( 'tc_Complex_Ocomplex' ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Odvd'( 'tc_Complex_Ocomplex' ) ],
% 0.91/1.28 [ 'class_Int_Onumber__ring'( 'tc_Complex_Ocomplex' ) ],
% 0.91/1.28 [ 'class_SEQ_Obanach'( 'tc_Complex_Ocomplex' ) ],
% 0.91/1.28 [ 'class_HOL_Ozero'( 'tc_Complex_Ocomplex' ) ],
% 0.91/1.28 [ 'class_HOL_Oeq'( 'tc_Complex_Ocomplex' ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 0.91/1.28 X ) ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 0.91/1.28 X ) ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 0.91/1.28 X ) ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 0.91/1.28 X ) ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 0.91/1.28 X ) ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 0.91/1.28 X ) ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oidom'( X ) ) ]
% 0.91/1.28 ,
% 0.91/1.28 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 0.91/1.28 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.91/1.28 'class_OrderedGroup_Ocancel__comm__monoid__add'( X ) ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_Polynomial_Opoly'(
% 0.91/1.28 X ) ), ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_Polynomial_Opoly'(
% 0.91/1.28 X ) ), ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Oordered__ab__group__add'( 'tc_Polynomial_Opoly'(
% 0.91/1.28 X ) ), ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Polynomial_Opoly'( X
% 0.91/1.28 ) ), ~( 'class_OrderedGroup_Ocancel__comm__monoid__add'( X ) ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Polynomial_Opoly'( X
% 0.91/1.28 ) ), ~( 'class_Ring__and__Field_Oidom'( X ) ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_Polynomial_Opoly'( X )
% 0.91/1.28 ), ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Polynomial_Opoly'( X
% 0.91/1.28 ) ), ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_Polynomial_Opoly'( X
% 0.91/1.28 ) ), ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Polynomial_Opoly'( X )
% 0.91/1.28 ), ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Polynomial_Opoly'( X ) )
% 0.91/1.28 , ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Polynomial_Opoly'( X ) )
% 0.91/1.28 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_Polynomial_Opoly'( X ) )
% 0.91/1.28 , ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Polynomial_Opoly'( X ) )
% 0.91/1.28 , ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Polynomial_Opoly'( X ) )
% 0.91/1.28 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Polynomial_Opoly'( X ) )
% 0.91/1.28 , ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Polynomial_Opoly'( X ) )
% 0.91/1.28 , ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Polynomial_Opoly'( X ) )
% 0.91/1.28 , ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Polynomial_Opoly'( X ) ),
% 0.91/1.28 ~( 'class_OrderedGroup_Oab__group__add'( X ) ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Polynomial_Opoly'( X ) ),
% 0.91/1.28 ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_Polynomial_Opoly'( X ) ),
% 0.91/1.28 ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.91/1.28 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Osemiring'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.91/1.28 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.91/1.28 'class_OrderedGroup_Ocomm__monoid__add'( X ) ) ],
% 0.91/1.28 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.91/1.28 'class_OrderedGroup_Oab__group__add'( X ) ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Osgn__if'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.91/1.28 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Oabs__if'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.91/1.28 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.91/1.28 [ 'class_Divides_Osemiring__div'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.91/1.28 'class_Ring__and__Field_Ofield'( X ) ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Oring'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.91/1.28 'class_Ring__and__Field_Ocomm__ring'( X ) ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Oidom'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.91/1.28 'class_Ring__and__Field_Oidom'( X ) ) ],
% 0.91/1.28 [ 'class_Ring__and__Field_Odvd'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.91/1.28 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ) ],
% 0.91/1.28 [ 'class_Orderings_Opreorder'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.91/1.28 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.91/1.28 [ 'class_Orderings_Olinorder'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.91/1.28 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.91/1.28 [ 'class_Divides_Oring__div'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.91/1.28 'class_Ring__and__Field_Ofield'( X ) ) ],
% 0.91/1.28 [ 'class_Orderings_Oorder'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.91/1.28 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.91/1.28 [ 'class_Int_Onumber__ring'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.91/1.28 'class_Ring__and__Field_Ocomm__ring__1'( X ) ) ],
% 0.91/1.28 [ 'class_HOL_Ozero'( 'tc_Polynomial_Opoly'( X ) ), ~( 'class_HOL_Ozero'(
% 0.91/1.28 X ) ) ],
% 0.91/1.28 [ 'class_HOL_Oeq'( 'tc_Polynomial_Opoly'( X ) ), ~( 'class_HOL_Ozero'( X
% 0.91/1.28 ) ), ~( 'class_HOL_Oeq'( X ) ) ]
% 0.91/1.28 ] .
% 0.91/1.28
% 0.91/1.28
% 0.91/1.28 percentage equality = 0.270047, percentage horn = 0.897304
% 0.91/1.28 This is a problem with some equality
% 0.91/1.28
% 0.91/1.28
% 0.91/1.28
% 0.91/1.28 Options Used:
% 0.91/1.28
% 0.91/1.28 useres = 1
% 0.91/1.28 useparamod = 1
% 0.91/1.28 useeqrefl = 1
% 0.91/1.28 useeqfact = 1
% 0.91/1.28 usefactor = 1
% 0.91/1.28 usesimpsplitting = 0
% 0.91/1.28 usesimpdemod = 5
% 0.91/1.28 usesimpres = 3
% 0.91/1.28
% 0.91/1.28 resimpinuse = 1000
% 0.91/1.28 resimpclauses = 20000
% 0.91/1.28 substype = eqrewr
% 0.91/1.28 backwardsubs = 1
% 0.91/1.28 selectoldest = 5
% 0.91/1.28
% 0.91/1.28 litorderings [0] = split
% 0.91/1.28 litorderings [1] = extend the termordering, first sorting on arguments
% 0.91/1.28
% 0.91/1.28 termordering = kbo
% 0.91/1.28
% 0.91/1.28 litapriori = 0
% 0.91/1.28 termapriori = 1
% 0.91/1.28 litaposteriori = 0
% 0.91/1.28 termaposteriori = 0
% 0.91/1.28 demodaposteriori = 0
% 0.91/1.28 ordereqreflfact = 0
% 0.91/1.28
% 0.91/1.28 litselect = negord
% 0.91/1.28
% 0.91/1.28 maxweight = 15
% 0.91/1.28 maxdepth = 30000
% 0.91/1.28 maxlength = 115
% 0.91/1.28 maxnrvars = 195
% 0.91/1.28 excuselevel = 1
% 0.91/1.28 increasemaxweight = 1
% 0.91/1.28
% 0.91/1.28 maxselected = 10000000
% 0.91/1.28 maxnrclauses = 10000000
% 0.91/1.28
% 0.91/1.28 showgenerated = 0
% 0.91/1.28 showkept = 0
% 0.91/1.28 showselected = 0
% 0.91/1.28 showdeleted = 0
% 0.91/1.28 showresimp = 1
% 0.91/1.28 showstatus = 2000
% 0.91/1.28
% 0.91/1.28 prologoutput = 1
% 0.91/1.28 nrgoals = 5000000
% 0.91/1.28 totalproof = 1
% 0.91/1.28
% 0.91/1.28 Symbols occurring in the translation:
% 0.91/1.28
% 0.91/1.28 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.91/1.28 . [1, 2] (w:1, o:132, a:1, s:1, b:0),
% 0.91/1.28 ! [4, 1] (w:0, o:59, a:1, s:1, b:0),
% 0.91/1.28 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.91/1.28 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.91/1.28 'class_Ring__and__Field_Oordered__field' [40, 1] (w:1, o:65, a:1, s:1
% 0.91/1.28 , b:0),
% 0.91/1.28 'class_Ring__and__Field_Odivision__by__zero' [41, 1] (w:1, o:71, a:1
% 0.91/1.28 , s:1, b:0),
% 0.91/1.28 'c_HOL_Otimes__class_Otimes' [45, 3] (w:1, o:167, a:1, s:1, b:0),
% 0.91/1.28 'c_HOL_Oord__class_Oless' [46, 3] (w:1, o:168, a:1, s:1, b:0),
% 0.91/1.28 'c_HOL_Ozero__class_Ozero' [47, 1] (w:1, o:72, a:1, s:1, b:0),
% 0.91/1.28 'c_HOL_Oinverse__class_Odivide' [48, 3] (w:1, o:169, a:1, s:1, b:0),
% 0.91/1.28
% 0.91/1.28 'c_Suc' [50, 1] (w:1, o:73, a:1, s:1, b:0),
% 0.91/1.28 'class_Ring__and__Field_Oordered__ring__strict' [51, 1] (w:1, o:74
% 0.91/1.28 , a:1, s:1, b:0),
% 0.91/1.28 'c_HOL_Oplus__class_Oplus' [54, 3] (w:1, o:170, a:1, s:1, b:0),
% 0.91/1.28 'class_Ring__and__Field_Oidom' [55, 1] (w:1, o:75, a:1, s:1, b:0),
% 0.91/1.28 'class_Int_Onumber__ring' [56, 1] (w:1, o:78, a:1, s:1, b:0),
% 0.91/1.28 'class_Ring__and__Field_Oordered__semidom' [59, 1] (w:1, o:79, a:1
% 0.91/1.28 , s:1, b:0),
% 0.91/1.28 'class_Ring__and__Field_Ocomm__semiring__1' [60, 1] (w:1, o:69, a:1
% 0.91/1.28 , s:1, b:0),
% 0.91/1.28 'c_Ring__and__Field_Odvd__class_Odvd' [61, 3] (w:1, o:171, a:1, s:1
% 0.91/1.28 , b:0),
% 0.91/1.28 'class_OrderedGroup_Oab__group__add' [62, 1] (w:1, o:80, a:1, s:1, b:
% 0.91/1.28 0),
% 0.91/1.28 'tc_Polynomial_Opoly' [64, 1] (w:1, o:81, a:1, s:1, b:0),
% 0.91/1.28 'c_HOL_Ouminus__class_Ouminus' [65, 2] (w:1, o:157, a:1, s:1, b:0),
% 0.91/1.28 'c_Polynomial_Odegree' [66, 2] (w:1, o:159, a:1, s:1, b:0),
% 0.91/1.28 'class_OrderedGroup_Ogroup__add' [67, 1] (w:1, o:82, a:1, s:1, b:0),
% 0.91/1.28
% 0.91/1.28 'class_Ring__and__Field_Oordered__semiring__strict' [68, 1] (w:1, o:
% 0.91/1.28 83, a:1, s:1, b:0),
% 0.91/1.28 'class_Divides_Osemiring__div' [69, 1] (w:1, o:85, a:1, s:1, b:0),
% 0.91/1.28 'c_Divides_Odiv__class_Omod' [70, 3] (w:1, o:172, a:1, s:1, b:0),
% 0.91/1.28 'class_Ring__and__Field_Oordered__idom' [71, 1] (w:1, o:86, a:1, s:1
% 0.91/1.28 , b:0),
% 0.91/1.28 'c_HOL_Oabs__class_Oabs' [72, 2] (w:1, o:160, a:1, s:1, b:0),
% 0.91/1.28 'c_HOL_Oone__class_Oone' [73, 1] (w:1, o:87, a:1, s:1, b:0),
% 0.91/1.28 'class_OrderedGroup_Oab__semigroup__idem__mult' [74, 1] (w:1, o:88
% 0.91/1.28 , a:1, s:1, b:0),
% 0.91/1.28 'class_Ring__and__Field_Oring' [75, 1] (w:1, o:89, a:1, s:1, b:0),
% 0.91/1.28 'class_RealVector_Oreal__normed__vector' [76, 1] (w:1, o:90, a:1, s:1
% 0.91/1.28 , b:0),
% 0.91/1.28 'c_HOL_Osgn__class_Osgn' [77, 2] (w:1, o:161, a:1, s:1, b:0),
% 0.91/1.28 'class_Ring__and__Field_Ofield' [78, 1] (w:1, o:91, a:1, s:1, b:0),
% 0.91/1.28 'class_RealVector_Oreal__vector' [81, 1] (w:1, o:92, a:1, s:1, b:0),
% 0.91/1.28
% 0.91/1.28 'c_HOL_Ominus__class_Ominus' [82, 3] (w:1, o:173, a:1, s:1, b:0),
% 0.91/1.28 'c_RealVector_OscaleR__class_OscaleR' [83, 3] (w:1, o:174, a:1, s:1
% 0.91/1.28 , b:0),
% 0.91/1.28 'c_Polynomial_Ocoeff' [86, 3] (w:1, o:175, a:1, s:1, b:0),
% 0.91/1.28 'class_Orderings_Olinorder' [87, 1] (w:1, o:93, a:1, s:1, b:0),
% 0.91/1.28 'c_Polynomial_Opdivmod__rel' [91, 5] (w:1, o:188, a:1, s:1, b:0),
% 1.97/2.39 'class_Lattices_Oboolean__algebra' [93, 1] (w:1, o:94, a:1, s:1, b:0)
% 1.97/2.39 ,
% 1.97/2.39 'class_OrderedGroup_Opordered__ab__group__add' [98, 1] (w:1, o:96, a:
% 1.97/2.39 1, s:1, b:0),
% 1.97/2.39 'c_Polynomial_Opdivmod' [99, 3] (w:1, o:177, a:1, s:1, b:0),
% 1.97/2.39 'c_Pair' [100, 4] (w:1, o:187, a:1, s:1, b:0),
% 1.97/2.39 'class_Ring__and__Field_Osgn__if' [101, 1] (w:1, o:98, a:1, s:1, b:0)
% 1.97/2.39 ,
% 1.97/2.39 'c_Polynomial_Osmult' [102, 3] (w:1, o:178, a:1, s:1, b:0),
% 1.97/2.39 'tc_nat' [103, 0] (w:1, o:40, a:1, s:1, b:0),
% 1.97/2.39 'c_Polynomial_Opos__poly' [104, 2] (w:1, o:162, a:1, s:1, b:0),
% 1.97/2.39 'class_Ring__and__Field_Ocomm__semiring__0' [105, 1] (w:1, o:68, a:1
% 1.97/2.39 , s:1, b:0),
% 1.97/2.39 'c_Polynomial_OpCons' [106, 3] (w:1, o:179, a:1, s:1, b:0),
% 1.97/2.39 'class_Ring__and__Field_Odvd' [111, 1] (w:1, o:99, a:1, s:1, b:0),
% 1.97/2.39 'class_Ring__and__Field_Ocomm__ring' [112, 1] (w:1, o:66, a:1, s:1
% 1.97/2.39 , b:0),
% 1.97/2.39 'class_OrderedGroup_Oab__semigroup__mult' [116, 1] (w:1, o:100, a:1
% 1.97/2.39 , s:1, b:0),
% 1.97/2.39 'class_RealVector_Oreal__normed__algebra' [117, 1] (w:1, o:101, a:1
% 1.97/2.39 , s:1, b:0),
% 1.97/2.39 'class_Ring__and__Field_Ocomm__semiring' [120, 1] (w:1, o:70, a:1, s:
% 1.97/2.39 1, b:0),
% 1.97/2.39 'class_OrderedGroup_Olordered__ab__group__add' [121, 1] (w:1, o:102
% 1.97/2.39 , a:1, s:1, b:0),
% 1.97/2.39 'class_OrderedGroup_Opordered__ab__group__add__abs' [122, 1] (w:1, o:
% 1.97/2.39 103, a:1, s:1, b:0),
% 1.97/2.39 'class_HOL_Ozero' [123, 1] (w:1, o:76, a:1, s:1, b:0),
% 1.97/2.39 'class_HOL_Oeq' [124, 1] (w:1, o:77, a:1, s:1, b:0),
% 1.97/2.39 'c_HOL_Oeq__class_Oeq' [125, 3] (w:1, o:180, a:1, s:1, b:0),
% 1.97/2.39 'c_Polynomial_Omonom' [127, 3] (w:1, o:181, a:1, s:1, b:0),
% 1.97/2.39 'class_Divides_Oring__div' [128, 1] (w:1, o:84, a:1, s:1, b:0),
% 1.97/2.39 'c_Polynomial_Opoly__gcd' [129, 3] (w:1, o:182, a:1, s:1, b:0),
% 1.97/2.39 'class_RealVector_Oreal__normed__field' [130, 1] (w:1, o:104, a:1, s:
% 1.97/2.39 1, b:0),
% 1.97/2.39 'class_Ring__and__Field_Ocomm__ring__1' [131, 1] (w:1, o:67, a:1, s:1
% 1.97/2.39 , b:0),
% 1.97/2.39 'class_Ring__and__Field_Oabs__if' [132, 1] (w:1, o:105, a:1, s:1, b:0
% 1.97/2.39 ),
% 1.97/2.39 'class_OrderedGroup_Olordered__ab__group__add__abs' [133, 1] (w:1, o:
% 1.97/2.39 106, a:1, s:1, b:0),
% 1.97/2.39 'c_Polynomial_Osynthetic__div' [134, 3] (w:1, o:183, a:1, s:1, b:0),
% 1.97/2.39
% 1.97/2.39 'c_Polynomial_Opoly' [135, 3] (w:1, o:184, a:1, s:1, b:0),
% 1.97/2.39 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly' [139, 3]
% 1.97/2.39 (w:1, o:185, a:1, s:1, b:0),
% 1.97/2.39 'class_SEQ_Obanach' [140, 1] (w:1, o:116, a:1, s:1, b:0),
% 1.97/2.39 'c_Transcendental_Oexp' [141, 2] (w:1, o:163, a:1, s:1, b:0),
% 1.97/2.39 'class_OrderedGroup_Omonoid__mult' [142, 1] (w:1, o:117, a:1, s:1, b:
% 1.97/2.39 0),
% 1.97/2.39 'class_OrderedGroup_Ocomm__monoid__mult' [143, 1] (w:1, o:118, a:1
% 1.97/2.39 , s:1, b:0),
% 1.97/2.39 'class_Orderings_Oorder' [144, 1] (w:1, o:119, a:1, s:1, b:0),
% 1.97/2.39 'class_Orderings_Opreorder' [145, 1] (w:1, o:120, a:1, s:1, b:0),
% 1.97/2.39 'class_OrderedGroup_Ocomm__monoid__add' [146, 1] (w:1, o:121, a:1, s:
% 1.97/2.39 1, b:0),
% 1.97/2.39 'class_OrderedGroup_Oab__semigroup__add' [147, 1] (w:1, o:122, a:1
% 1.97/2.39 , s:1, b:0),
% 1.97/2.39 'class_Ring__and__Field_Osemiring' [148, 1] (w:1, o:107, a:1, s:1, b:
% 1.97/2.39 0),
% 1.97/2.39 'class_OrderedGroup_Opordered__comm__monoid__add' [149, 1] (w:1, o:
% 1.97/2.39 123, a:1, s:1, b:0),
% 1.97/2.39 'class_RealVector_Oreal__normed__algebra__1' [150, 1] (w:1, o:108, a:
% 1.97/2.39 1, s:1, b:0),
% 1.97/2.39 'class_OrderedGroup_Ocancel__ab__semigroup__add' [151, 1] (w:1, o:124
% 1.97/2.39 , a:1, s:1, b:0),
% 1.97/2.39 'class_OrderedGroup_Ocancel__semigroup__add' [152, 1] (w:1, o:125, a:
% 1.97/2.39 1, s:1, b:0),
% 1.97/2.39 'class_RealVector_Oreal__algebra' [153, 1] (w:1, o:109, a:1, s:1, b:0
% 1.97/2.39 ),
% 1.97/2.39 'c_Polynomial_Opcompose' [155, 3] (w:1, o:176, a:1, s:1, b:0),
% 1.97/2.39 'class_RealVector_Oreal__field' [156, 1] (w:1, o:110, a:1, s:1, b:0)
% 1.97/2.39 ,
% 1.97/2.39 'class_Ring__and__Field_Opordered__ring' [159, 1] (w:1, o:112, a:1
% 1.97/2.39 , s:1, b:0),
% 1.97/2.39 'class_Ring__and__Field_Oordered__comm__semiring__strict' [162, 1]
% 1.97/2.39 (w:1, o:111, a:1, s:1, b:0),
% 1.97/2.39 'v_ds____' [163, 0] (w:1, o:51, a:1, s:1, b:0),
% 1.97/2.39 'v_sko__local__XpCons__Xhyps__1' [164, 1] (w:1, o:126, a:1, s:1, b:0)
% 1.97/2.39 ,
% 1.97/2.39 'tc_Complex_Ocomplex' [165, 0] (w:1, o:52, a:1, s:1, b:0),
% 1.97/2.39 'v_sko__local__XpCons__1__1' [166, 1] (w:1, o:127, a:1, s:1, b:0),
% 1.97/2.39 'class_OrderedGroup_Oordered__ab__group__add' [167, 1] (w:1, o:95, a:
% 1.97/2.39 1, s:1, b:0),
% 1.97/2.39 'class_Ring__and__Field_Oring__no__zero__divisors' [168, 1] (w:1, o:
% 1.97/2.39 97, a:1, s:1, b:0),
% 1.97/2.39 'class_Ring__and__Field_Omult__zero' [169, 1] (w:1, o:113, a:1, s:1
% 1.97/2.39 , b:0),
% 1.97/2.39 'class_Ring__and__Field_Ozero__neq__one' [170, 1] (w:1, o:114, a:1
% 1.97/2.39 , s:1, b:0),
% 1.97/2.39 'class_Ring__and__Field_Ono__zero__divisors' [171, 1] (w:1, o:64, a:1
% 1.97/2.39 , s:1, b:0),
% 1.97/2.39 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [172, 1]
% 1.97/2.39 (w:1, o:128, a:1, s:1, b:0),
% 1.97/2.39 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [173, 1]
% 1.97/2.39 (w:1, o:129, a:1, s:1, b:0),
% 1.97/2.39 'class_RealVector_Oreal__normed__div__algebra' [174, 1] (w:1, o:115
% 1.97/2.39 , a:1, s:1, b:0),
% 1.97/2.39 'c_OrderedGroup_Olordered__ab__group__add__class_Opprt' [176, 2] (w:1
% 1.97/2.39 , o:158, a:1, s:1, b:0),
% 1.97/2.39 'class_OrderedGroup_Omonoid__add' [177, 1] (w:1, o:130, a:1, s:1, b:0
% 1.97/2.39 ),
% 1.97/2.39 'c_Polynomial_Osynthetic__divmod' [178, 3] (w:1, o:186, a:1, s:1, b:0
% 1.97/2.39 ),
% 1.97/2.39 'v_d____' [179, 0] (w:1, o:53, a:1, s:1, b:0),
% 1.97/2.39 'v_p' [180, 0] (w:1, o:54, a:1, s:1, b:0),
% 1.97/2.39 'v_x____' [181, 0] (w:1, o:55, a:1, s:1, b:0),
% 1.97/2.39 'c_RealVector_Oof__real' [182, 2] (w:1, o:165, a:1, s:1, b:0),
% 1.97/2.39 'c_RealVector_Onorm__class_Onorm' [183, 2] (w:1, o:164, a:1, s:1, b:0
% 1.97/2.39 ),
% 1.97/2.39 'class_OrderedGroup_Ocancel__comm__monoid__add' [185, 1] (w:1, o:131
% 1.97/2.39 , a:1, s:1, b:0),
% 1.97/2.39 'tc_RealDef_Oreal' [186, 0] (w:1, o:57, a:1, s:1, b:0),
% 1.97/2.39 'tc_prod' [188, 2] (w:1, o:166, a:1, s:1, b:0).
% 1.97/2.39
% 1.97/2.39
% 1.97/2.39 Starting Search:
% 1.97/2.39
% 1.97/2.39 Resimplifying inuse:
% 1.97/2.39 Done
% 1.97/2.39
% 1.97/2.39
% 1.97/2.39 Intermediate Status:
% 1.97/2.39 Generated: 4604
% 1.97/2.39 Kept: 2019
% 1.97/2.39 Inuse: 166
% 1.97/2.39 Deleted: 1
% 1.97/2.39 Deletedinuse: 0
% 1.97/2.39
% 1.97/2.39 Resimplifying inuse:
% 1.97/2.39 Done
% 1.97/2.39
% 1.97/2.39 Resimplifying inuse:
% 1.97/2.39 Done
% 1.97/2.39
% 1.97/2.39
% 1.97/2.39 Intermediate Status:
% 1.97/2.39 Generated: 11706
% 1.97/2.39 Kept: 4030
% 1.97/2.39 Inuse: 230
% 1.97/2.39 Deleted: 4
% 1.97/2.39 Deletedinuse: 0
% 1.97/2.39
% 1.97/2.39 Resimplifying inuse:
% 1.97/2.39 Done
% 1.97/2.39
% 1.97/2.39 Resimplifying inuse:
% 1.97/2.39 Done
% 1.97/2.39
% 1.97/2.39
% 1.97/2.39 Intermediate Status:
% 1.97/2.39 Generated: 18795
% 1.97/2.39 Kept: 6035
% 1.97/2.39 Inuse: 318
% 1.97/2.39 Deleted: 7
% 1.97/2.39 Deletedinuse: 0
% 1.97/2.39
% 1.97/2.39 Resimplifying inuse:
% 1.97/2.39 Done
% 1.97/2.39
% 1.97/2.39 Resimplifying inuse:
% 1.97/2.39 Done
% 1.97/2.39
% 1.97/2.39
% 1.97/2.39 Intermediate Status:
% 1.97/2.39 Generated: 26124
% 1.97/2.39 Kept: 8058
% 1.97/2.39 Inuse: 349
% 1.97/2.39 Deleted: 7
% 1.97/2.39 Deletedinuse: 0
% 1.97/2.39
% 1.97/2.39 Resimplifying inuse:
% 1.97/2.39 Done
% 1.97/2.39
% 1.97/2.39
% 1.97/2.39 Intermediate Status:
% 1.97/2.39 Generated: 34335
% 1.97/2.39 Kept: 10064
% 1.97/2.39 Inuse: 393
% 1.97/2.39 Deleted: 7
% 1.97/2.39 Deletedinuse: 0
% 1.97/2.39
% 1.97/2.39 Resimplifying inuse:
% 1.97/2.39 Done
% 1.97/2.39
% 1.97/2.39 Resimplifying inuse:
% 1.97/2.39 Done
% 1.97/2.39
% 1.97/2.39
% 1.97/2.39 Intermediate Status:
% 1.97/2.39 Generated: 43042
% 1.97/2.39 Kept: 12238
% 1.97/2.39 Inuse: 449
% 1.97/2.39 Deleted: 7
% 1.97/2.39 Deletedinuse: 0
% 1.97/2.39
% 1.97/2.39 Resimplifying inuse:
% 1.97/2.39 Done
% 1.97/2.39
% 1.97/2.39
% 1.97/2.39 Intermediate Status:
% 1.97/2.39 Generated: 58625
% 1.97/2.39 Kept: 14661
% 1.97/2.39 Inuse: 498
% 1.97/2.39 Deleted: 8
% 1.97/2.39 Deletedinuse: 0
% 1.97/2.39
% 1.97/2.39 Resimplifying inuse:
% 1.97/2.39 Done
% 1.97/2.39
% 1.97/2.39 Resimplifying inuse:
% 1.97/2.39 Done
% 1.97/2.39
% 1.97/2.39
% 1.97/2.39 Intermediate Status:
% 1.97/2.39 Generated: 71687
% 1.97/2.39 Kept: 16726
% 1.97/2.39 Inuse: 568
% 1.97/2.39 Deleted: 8
% 1.97/2.39 Deletedinuse: 0
% 1.97/2.39
% 1.97/2.39 Resimplifying inuse:
% 1.97/2.39 Done
% 1.97/2.39
% 1.97/2.39 Resimplifying inuse:
% 1.97/2.39 Done
% 1.97/2.39
% 1.97/2.39
% 1.97/2.39 Intermediate Status:
% 1.97/2.39 Generated: 82870
% 1.97/2.39 Kept: 19061
% 1.97/2.39 Inuse: 628
% 1.97/2.39 Deleted: 8
% 1.97/2.39 Deletedinuse: 0
% 1.97/2.39
% 1.97/2.39 Resimplifying inuse:
% 1.97/2.39 Done
% 1.97/2.39
% 1.97/2.39 Resimplifying clauses:
% 1.97/2.39
% 1.97/2.39 Bliksems!, er is een bewijs:
% 1.97/2.39 % SZS status Unsatisfiable
% 1.97/2.39 % SZS output start Refutation
% 1.97/2.39
% 1.97/2.39 clause( 578, [ ~( =( 'c_RealVector_Onorm__class_Onorm'(
% 1.97/2.39 'c_HOL_Otimes__class_Otimes'( 'c_RealVector_Oof__real'( 'v_x____',
% 1.97/2.39 'tc_Complex_Ocomplex' ), 'c_Polynomial_Opoly'( 'v_ds____',
% 1.97/2.39 'c_RealVector_Oof__real'( 'v_x____', 'tc_Complex_Ocomplex' ),
% 1.97/2.39 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' )
% 1.97/2.39 , 'c_RealVector_Onorm__class_Onorm'( 'v_d____', 'tc_Complex_Ocomplex' ) )
% 1.97/2.39 ) ] )
% 1.97/2.39 .
% 1.97/2.39 clause( 579, [ =( 'c_RealVector_Onorm__class_Onorm'(
% 1.97/2.39 'c_HOL_Otimes__class_Otimes'( 'c_RealVector_Oof__real'( 'v_x____',
% 1.97/2.39 'tc_Complex_Ocomplex' ), 'c_Polynomial_Opoly'( 'v_ds____',
% 1.97/2.39 'c_RealVector_Oof__real'( 'v_x____', 'tc_Complex_Ocomplex' ),
% 1.97/2.39 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' )
% 1.97/2.39 , 'c_RealVector_Onorm__class_Onorm'( 'v_d____', 'tc_Complex_Ocomplex' ) )
% 1.97/2.39 ] )
% 1.97/2.39 .
% 1.97/2.39 clause( 20018, [] )
% 1.97/2.39 .
% 1.97/2.39
% 1.97/2.39
% 1.97/2.39 % SZS output end Refutation
% 1.97/2.39 found a proof!
% 1.97/2.39
% 1.97/2.39 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 1.97/2.39
% 1.97/2.39 initialclauses(
% 1.97/2.39 [ clause( 20020, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.97/2.39 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.97/2.39 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X
% 1.97/2.39 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.97/2.39 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, T,
% 1.97/2.39 X ), Z, X ) ) ] )
% 1.97/2.39 , clause( 20021, [ ~( =( 'c_Suc'( X ), X ) ) ] )
% 1.97/2.39 , clause( 20022, [ ~( =( X, 'c_Suc'( X ) ) ) ] )
% 1.97/2.39 , clause( 20023, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.97/2.39 ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y
% 1.97/2.39 , X ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ),
% 1.97/2.39 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.97/2.39 ) ) ] )
% 1.97/2.39 , clause( 20024, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.97/2.39 ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y
% 1.97/2.39 , X ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ),
% 1.97/2.39 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.97/2.39 ) ) ] )
% 1.97/2.39 , clause( 20025, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.97/2.39 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.97/2.39 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.97/2.39 Y, 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ), =( T, U ), =( Z,
% 1.97/2.39 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.97/2.39 , clause( 20026, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.97/2.39 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.97/2.39 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.97/2.39 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 1.97/2.39 , clause( 20027, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.97/2.39 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.97/2.39 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 1.97/2.39 , X ), Z, X ) ) ] )
% 1.97/2.39 , clause( 20028, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.97/2.39 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.97/2.39 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 1.97/2.39 , X ), Z, X ) ) ] )
% 1.97/2.39 , clause( 20029, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.97/2.39 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 1.97/2.39 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 1.97/2.39 , clause( 20030, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.97/2.39 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 1.97/2.39 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 1.97/2.39 , clause( 20031, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.97/2.39 'c_Polynomial_Odegree'( 'c_HOL_Ouminus__class_Ouminus'( Y,
% 1.97/2.39 'tc_Polynomial_Opoly'( X ) ), X ), 'c_Polynomial_Odegree'( Y, X ) ) ] )
% 1.97/2.39 , clause( 20032, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.97/2.39 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'(
% 1.97/2.39 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), X ), Z ) ] )
% 1.97/2.39 , clause( 20033, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 1.97/2.39 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.97/2.39 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.97/2.39 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.97/2.39 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 1.97/2.39 , clause( 20034, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 1.97/2.39 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.97/2.39 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.97/2.39 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.97/2.39 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.97/2.39 , clause( 20035, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 1.97/2.39 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.97/2.39 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.97/2.39 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.97/2.39 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.97/2.39 , clause( 20036, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.97/2.39 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 1.97/2.39 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 1.97/2.39 , clause( 20037, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.97/2.39 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Y, X
% 1.97/2.39 ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ] )
% 1.97/2.39 , clause( 20038, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.97/2.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.97/2.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.97/2.39 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 1.97/2.39 , clause( 20039, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.97/2.39 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 1.97/2.39 X ) ] )
% 1.97/2.39 , clause( 20040, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X )
% 1.97/2.39 ), =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.97/2.39 Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ] )
% 1.97/2.39 , clause( 20041, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.97/2.39 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Y,
% 1.97/2.39 'c_HOL_Oone__class_Oone'( X ), X ), X ) ] )
% 1.97/2.39 , clause( 20042, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.97/2.39 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.97/2.39 X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 1.97/2.39 X ), X ) ) ] )
% 1.97/2.39 , clause( 20043, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.97/2.39 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.97/2.39 X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.97/2.39 , Z, X ) ) ] )
% 1.97/2.39 , clause( 20044, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 1.97/2.39 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ),
% 1.97/2.39 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Osgn__class_Osgn'( Y, X ), X ) ) ]
% 1.97/2.39 )
% 1.97/2.39 , clause( 20045, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.97/2.39 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.97/2.39 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.97/2.39 , 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 1.97/2.39 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, T, X )
% 1.97/2.39 , 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ] )
% 1.97/2.39 , clause( 20046, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.97/2.39 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.97/2.39 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.97/2.39 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ] )
% 1.97/2.39 , clause( 20047, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.97/2.39 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.97/2.39 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Otimes__class_Otimes'( Z,
% 1.97/2.39 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ] )
% 1.97/2.39 , clause( 20048, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.97/2.39 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'(
% 1.97/2.39 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 1.97/2.39 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), X ) ] )
% 1.97/2.39 , clause( 20049, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.97/2.39 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.97/2.39 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 1.97/2.39 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 1.97/2.39 , clause( 20050, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.97/2.39 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Y, X ) ] )
% 1.97/2.39 , clause( 20051, [ ~( 'class_RealVector_Oreal__vector'( X ) ), =(
% 1.97/2.39 'c_RealVector_OscaleR__class_OscaleR'( Y, 'c_HOL_Ominus__class_Ominus'( Z
% 1.97/2.39 , T, X ), X ), 'c_HOL_Ominus__class_Ominus'(
% 1.97/2.39 'c_RealVector_OscaleR__class_OscaleR'( Y, Z, X ),
% 1.97/2.39 'c_RealVector_OscaleR__class_OscaleR'( Y, T, X ), X ) ) ] )
% 1.97/2.39 , clause( 20052, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 1.97/2.39 'c_RealVector_OscaleR__class_OscaleR'( Y, 'c_HOL_Ominus__class_Ominus'( Z
% 1.97/2.39 , T, X ), X ), 'c_HOL_Ominus__class_Ominus'(
% 1.97/2.39 'c_RealVector_OscaleR__class_OscaleR'( Y, Z, X ),
% 1.97/2.39 'c_RealVector_OscaleR__class_OscaleR'( Y, T, X ), X ) ) ] )
% 1.97/2.39 , clause( 20053, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.97/2.39 'c_Polynomial_Ocoeff'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.97/2.39 'tc_Polynomial_Opoly'( X ) ), T, X ), 'c_HOL_Ominus__class_Ominus'(
% 1.97/2.39 'c_Polynomial_Ocoeff'( Y, T, X ), 'c_Polynomial_Ocoeff'( Z, T, X ), X ) )
% 1.97/2.39 ] )
% 1.97/2.39 , clause( 20054, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.97/2.39 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.97/2.39 ), =( Z, Y ) ] )
% 1.97/2.39 , clause( 20055, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.97/2.39 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.97/2.39 ) ] )
% 1.97/2.39 , clause( 20056, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.97/2.39 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.97/2.39 ) ] )
% 1.97/2.39 , clause( 20057, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.97/2.39 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ),
% 1.97/2.39 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 1.97/2.39 , clause( 20058, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y, Z ),
% 1.97/2.39 ~( 'c_Polynomial_Opdivmod__rel'( T, U, W, Z, X ) ), ~(
% 1.97/2.39 'c_Polynomial_Opdivmod__rel'( T, U, V0, Y, X ) ) ] )
% 1.97/2.39 , clause( 20059, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y, Z ),
% 1.97/2.39 ~( 'c_Polynomial_Opdivmod__rel'( T, U, Z, W, X ) ), ~(
% 1.97/2.39 'c_Polynomial_Opdivmod__rel'( T, U, Y, V0, X ) ) ] )
% 1.97/2.39 , clause( 20060, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 1.97/2.39 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.97/2.39 ), =( Z, Y ) ] )
% 1.97/2.39 , clause( 20061, [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =(
% 1.97/2.39 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.97/2.39 , X ) ) ), =( Y, Z ) ] )
% 1.97/2.39 , clause( 20062, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.97/2.39 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.97/2.39 , X ) ) ), =( Y, Z ) ] )
% 1.97/2.39 , clause( 20063, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.97/2.39 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Oinverse__class_Odivide'(
% 1.97/2.39 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), Y, X ) ) ] )
% 1.97/2.39 , clause( 20064, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.97/2.39 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.97/2.39 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), Y, X ), Z ) ] )
% 1.97/2.39 , clause( 20065, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.97/2.39 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 1.97/2.39 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.97/2.39 , Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.97/2.39 , clause( 20066, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.97/2.39 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.97/2.39 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.97/2.39 , Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.97/2.39 , clause( 20067, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.97/2.39 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.97/2.39 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.97/2.39 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 1.97/2.39 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ] )
% 1.97/2.39 , clause( 20068, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.97/2.39 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.97/2.39 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.97/2.39 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 1.97/2.39 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ] )
% 1.97/2.39 , clause( 20069, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.97/2.39 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.97/2.39 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.97/2.39 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.97/2.39 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ] )
% 1.97/2.39 , clause( 20070, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.97/2.39 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.97/2.39 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.97/2.39 Z, Y, X ) ) ] )
% 1.97/2.39 , clause( 20071, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.97/2.39 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.97/2.39 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.97/2.39 , X ), X ) ) ] )
% 1.97/2.39 , clause( 20072, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.97/2.39 'c_Polynomial_Opdivmod'( 'c_HOL_Ozero__class_Ozero'(
% 1.97/2.39 'tc_Polynomial_Opoly'( X ) ), Y, X ), 'c_Pair'(
% 1.97/2.39 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ),
% 1.97/2.39 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ),
% 1.97/2.39 'tc_Polynomial_Opoly'( X ), 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 1.97/2.39 , clause( 20073, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.97/2.39 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.97/2.39 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.97/2.39 , 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.97/2.39 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X
% 1.97/2.39 ) ) ] )
% 1.97/2.39 , clause( 20074, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.97/2.39 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.97/2.39 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.97/2.39 , Z, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.97/2.39 , clause( 20075, [ ~( 'class_Ring__and__Field_Osgn__if'( X ) ), =(
% 1.97/2.39 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ), ~(
% 1.97/2.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =(
% 1.97/2.39 Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.97/2.39 , clause( 20076, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.97/2.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.97/2.39 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.97/2.39 ) ] )
% 1.97/2.39 , clause( 20077, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =(
% 1.97/2.39 'c_Polynomial_Odegree'( 'c_Polynomial_Osmult'( 'c_HOL_Ozero__class_Ozero'(
% 1.97/2.39 X ), Y, X ), X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.97/2.39 , clause( 20078, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 1.97/2.39 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.97/2.39 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.97/2.39 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.97/2.39 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 1.97/2.39 , clause( 20079, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 1.97/2.39 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.97/2.39 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.97/2.39 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.97/2.39 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ] )
% 1.97/2.39 , clause( 20080, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 1.97/2.39 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.97/2.39 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 1.97/2.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.97/2.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.97/2.39 , clause( 20081, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.97/2.39 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.97/2.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.97/2.39 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.97/2.39 X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.97/2.39 Z, X ), X ) ) ] )
% 1.97/2.39 , clause( 20082, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.97/2.39 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.97/2.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.97/2.39 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.97/2.39 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.97/2.39 Z, X ), X ) ) ] )
% 1.97/2.39 , clause( 20083, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.97/2.39 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.97/2.39 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.97/2.39 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.97/2.39 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.97/2.39 X ), Z, X ) ) ] )
% 1.97/2.39 , clause( 20084, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.97/2.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.97/2.39 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.97/2.39 Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.97/2.39 X ), Z, X ) ) ] )
% 1.97/2.39 , clause( 20085, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.97/2.39 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.97/2.39 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.97/2.39 X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.97/2.39 X ), T, X ) ) ] )
% 1.97/2.39 , clause( 20086, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.97/2.39 'c_Polynomial_Opos__poly'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.97/2.39 'tc_Polynomial_Opoly'( X ) ), X ), ~( 'c_Polynomial_Opos__poly'( Z, X ) )
% 1.97/2.39 , ~( 'c_Polynomial_Opos__poly'( Y, X ) ) ] )
% 1.97/2.39 , clause( 20087, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 1.97/2.39 =( 'c_Polynomial_Osmult'( Y, 'c_Polynomial_OpCons'( Z, T, X ), X ),
% 1.97/2.39 'c_Polynomial_OpCons'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.97/2.39 'c_Polynomial_Osmult'( Y, T, X ), X ) ) ] )
% 1.97/2.39 , clause( 20088, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.97/2.39 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.97/2.39 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.97/2.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.97/2.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.97/2.39 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ] )
% 1.97/2.39 , clause( 20089, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.97/2.39 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.97/2.39 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.97/2.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.97/2.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.97/2.39 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ] )
% 1.97/2.39 , clause( 20090, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.97/2.39 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.97/2.39 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.97/2.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.97/2.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.97/2.39 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ] )
% 1.97/2.39 , clause( 20091, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.97/2.39 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.97/2.39 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.97/2.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.97/2.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.97/2.39 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ] )
% 1.97/2.39 , clause( 20092, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X )
% 1.97/2.39 ), =( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ] )
% 1.97/2.39 , clause( 20093, [ ~( =( 'c_Pair'( X, Y, Z, T ), 'c_Pair'( U, W, Z, T ) ) )
% 1.97/2.39 , =( Y, W ) ] )
% 1.97/2.39 , clause( 20094, [ ~( =( 'c_Pair'( X, Y, Z, T ), 'c_Pair'( U, W, Z, T ) ) )
% 1.97/2.39 , =( X, U ) ] )
% 1.97/2.39 , clause( 20095, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.97/2.39 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.97/2.39 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y
% 1.97/2.39 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, U, X ) ) ] )
% 1.97/2.39 , clause( 20096, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.97/2.39 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.97/2.39 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_HOL_Oord__class_Oless'( T
% 1.97/2.39 , U, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 1.97/2.39 , clause( 20097, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =(
% 1.97/2.39 'c_Polynomial_Odegree'( 'c_Polynomial_Osmult'( Y, Z, X ), X ),
% 1.97/2.39 'c_Polynomial_Odegree'( Z, X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.97/2.39 ] )
% 1.97/2.39 , clause( 20098, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.97/2.39 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.97/2.39 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ),
% 1.97/2.39 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.97/2.39 ) ) ] )
% 1.97/2.39 , clause( 20099, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.97/2.39 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.97/2.39 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 1.97/2.39 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 1.97/2.39 ) ) ] )
% 1.97/2.39 , clause( 20100, [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 1.97/2.39 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 1.97/2.39 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'(
% 1.97/2.39 'c_HOL_Ominus__class_Ominus'( Z, 'c_HOL_Otimes__class_Otimes'( T, U, X )
% 1.97/2.39 , X ), W, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 1.97/2.39 'c_HOL_Oplus__class_Oplus'( Z, W, X ), X ) ), ~(
% 1.97/2.39 'c_Ring__and__Field_Odvd__class_Odvd'( Y, U, X ) ) ] )
% 1.97/2.39 , clause( 20101, [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 1.97/2.39 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 1.97/2.39 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 1.97/2.39 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 1.97/2.39 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Z,
% 1.97/2.39 'c_HOL_Otimes__class_Otimes'( U, W, X ), X ), T, X ), X ) ), ~(
% 1.97/2.39 'c_Ring__and__Field_Odvd__class_Odvd'( Y, W, X ) ) ] )
% 1.97/2.39 , clause( 20102, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.97/2.39 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_Osmult'( Y, Z, X ),
% 1.97/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ),
% 1.97/2.40 'tc_Polynomial_Opoly'( X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z
% 1.97/2.40 , 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ),
% 1.97/2.40 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 1.97/2.40 , clause( 20103, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.97/2.40 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.97/2.40 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ] )
% 1.97/2.40 , clause( 20104, [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.97/2.40 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 1.97/2.40 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oone__class_Oone'( X ), X ), Y, X
% 1.97/2.40 ) ) ] )
% 1.97/2.40 , clause( 20105, [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.97/2.40 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 1.97/2.40 T, X ), X ) ) ] )
% 1.97/2.40 , clause( 20106, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.97/2.40 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.97/2.40 , T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.97/2.40 T, X ), Z, X ) ) ] )
% 1.97/2.40 , clause( 20107, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.97/2.40 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.97/2.40 , T, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.97/2.40 Z, T, X ), X ) ) ] )
% 1.97/2.40 , clause( 20108, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.97/2.40 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 1.97/2.40 ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.97/2.40 , X ), T, X ) ) ] )
% 1.97/2.40 , clause( 20109, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.97/2.40 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 1.97/2.40 ), X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y
% 1.97/2.40 , T, X ), X ) ) ] )
% 1.97/2.40 , clause( 20110, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.97/2.40 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 1.97/2.40 ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.97/2.40 , X ), T, X ) ) ] )
% 1.97/2.40 , clause( 20111, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.97/2.40 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 1.97/2.40 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X
% 1.97/2.40 ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 1.97/2.40 , clause( 20112, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.97/2.40 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 1.97/2.40 , clause( 20113, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.97/2.40 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 1.97/2.40 , clause( 20114, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.97/2.40 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 1.97/2.40 , clause( 20115, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.97/2.40 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 1.97/2.40 , clause( 20116, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 1.97/2.40 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.97/2.40 'tc_Polynomial_Opoly'( X ) ), T, 'tc_Polynomial_Opoly'( X ) ),
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.97/2.40 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Otimes__class_Otimes'( Z, T,
% 1.97/2.40 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 1.97/2.40 , clause( 20117, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.97/2.40 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X )
% 1.97/2.40 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X
% 1.97/2.40 ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 1.97/2.40 , clause( 20118, [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.97/2.40 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 1.97/2.40 , clause( 20119, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.97/2.40 'c_Polynomial_Ocoeff'( 'c_HOL_Ouminus__class_Ouminus'( Y,
% 1.97/2.40 'tc_Polynomial_Opoly'( X ) ), Z, X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.97/2.40 'c_Polynomial_Ocoeff'( Y, Z, X ), X ) ) ] )
% 1.97/2.40 , clause( 20120, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.97/2.40 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ] )
% 1.97/2.40 , clause( 20121, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.97/2.40 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.97/2.40 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.97/2.40 , clause( 20122, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.97/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_Osmult'( Y, Z, X ),
% 1.97/2.40 T, 'tc_Polynomial_Opoly'( X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'(
% 1.97/2.40 Z, T, 'tc_Polynomial_Opoly'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.97/2.40 ) ) ] )
% 1.97/2.40 , clause( 20123, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.97/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_Polynomial_Opoly'( X ) )
% 1.97/2.40 , =( T, 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.97/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_Osmult'( T, Y, X ),
% 1.97/2.40 Z, 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 1.97/2.40 , clause( 20124, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.97/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Polynomial_Osmult'( Z, T, X
% 1.97/2.40 ), 'tc_Polynomial_Opoly'( X ) ), ~(
% 1.97/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, 'tc_Polynomial_Opoly'( X ) )
% 1.97/2.40 ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.97/2.40 , clause( 20125, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.97/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_Polynomial_Opoly'( X ) )
% 1.97/2.40 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Polynomial_Osmult'( T,
% 1.97/2.40 Z, X ), 'tc_Polynomial_Opoly'( X ) ) ), =( T, 'c_HOL_Ozero__class_Ozero'(
% 1.97/2.40 X ) ) ] )
% 1.97/2.40 , clause( 20126, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.97/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_Osmult'( Y, Z, X ),
% 1.97/2.40 T, 'tc_Polynomial_Opoly'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.97/2.40 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, 'tc_Polynomial_Opoly'(
% 1.97/2.40 X ) ) ) ] )
% 1.97/2.40 , clause( 20127, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.97/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_Polynomial_Opoly'( X ) )
% 1.97/2.40 , =( T, 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.97/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Polynomial_Osmult'( T, Z, X
% 1.97/2.40 ), 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 1.97/2.40 , clause( 20128, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 1.97/2.40 X ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 1.97/2.40 ), X ), 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Z, Y, X
% 1.97/2.40 ), X ) ) ] )
% 1.97/2.40 , clause( 20129, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.97/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.97/2.40 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.97/2.40 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.97/2.40 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ] )
% 1.97/2.40 , clause( 20130, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.97/2.40 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.97/2.40 ), X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.97/2.40 Y, X ), Z, X ) ) ] )
% 1.97/2.40 , clause( 20131, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.97/2.40 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.97/2.40 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.97/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), X ) ) ] )
% 1.97/2.40 , clause( 20132, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.97/2.40 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.97/2.40 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 1.97/2.40 , clause( 20133, [ ~( 'class_HOL_Ozero'( X ) ), ~( 'class_HOL_Oeq'( X ) ),
% 1.97/2.40 'c_HOL_Oeq__class_Oeq'( Y, Y, 'tc_Polynomial_Opoly'( X ) ) ] )
% 1.97/2.40 , clause( 20134, [ ~( 'class_HOL_Oeq'( X ) ), 'c_HOL_Oeq__class_Oeq'( Y, Y
% 1.97/2.40 , X ) ] )
% 1.97/2.40 , clause( 20135, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.97/2.40 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 1.97/2.40 ) ) ] )
% 1.97/2.40 , clause( 20136, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.97/2.40 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.97/2.40 , 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 1.97/2.40 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'(
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.97/2.40 , Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ), =( U,
% 1.97/2.40 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.97/2.40 ) ] )
% 1.97/2.40 , clause( 20137, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 1.97/2.40 'c_HOL_Oone__class_Oone'( X ), X ), X ) ] )
% 1.97/2.40 , clause( 20138, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 1.97/2.40 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.97/2.40 X ), X ) ) ] )
% 1.97/2.40 , clause( 20139, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 1.97/2.40 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.97/2.40 X ), X ) ) ] )
% 1.97/2.40 , clause( 20140, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 1.97/2.40 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.97/2.40 X ), X ) ) ] )
% 1.97/2.40 , clause( 20141, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 1.97/2.40 X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.97/2.40 X ), X ) ) ] )
% 1.97/2.40 , clause( 20142, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =(
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.97/2.40 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.97/2.40 Y, Y, X ) ) ] )
% 1.97/2.40 , clause( 20143, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.97/2.40 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.97/2.40 Y, Z, X ) ) ] )
% 1.97/2.40 , clause( 20144, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.97/2.40 'c_HOL_Ominus__class_Ominus'( 'c_Polynomial_OpCons'( Y, Z, X ),
% 1.97/2.40 'c_Polynomial_OpCons'( T, U, X ), 'tc_Polynomial_Opoly'( X ) ),
% 1.97/2.40 'c_Polynomial_OpCons'( 'c_HOL_Ominus__class_Ominus'( Y, T, X ),
% 1.97/2.40 'c_HOL_Ominus__class_Ominus'( Z, U, 'tc_Polynomial_Opoly'( X ) ), X ) ) ]
% 1.97/2.40 )
% 1.97/2.40 , clause( 20145, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.97/2.40 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Osgn__class_Osgn'( Y, X ), X ),
% 1.97/2.40 'c_HOL_Osgn__class_Osgn'( Y, X ) ) ] )
% 1.97/2.40 , clause( 20146, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.97/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y
% 1.97/2.40 , X ) ) ] )
% 1.97/2.40 , clause( 20147, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.97/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.97/2.40 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.97/2.40 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.97/2.40 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ] )
% 1.97/2.40 , clause( 20148, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.97/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.97/2.40 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.97/2.40 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.97/2.40 X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ] )
% 1.97/2.40 , clause( 20149, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.97/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.97/2.40 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.97/2.40 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.97/2.40 X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ] )
% 1.97/2.40 , clause( 20150, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.97/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.97/2.40 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.97/2.40 , X ) ) ] )
% 1.97/2.40 , clause( 20151, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.97/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.97/2.40 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.97/2.40 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.97/2.40 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ] )
% 1.97/2.40 , clause( 20152, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.97/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.97/2.40 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.97/2.40 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.97/2.40 T, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.97/2.40 Y, T, X ), Z, X ) ) ] )
% 1.97/2.40 , clause( 20153, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.97/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.97/2.40 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.97/2.40 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.97/2.40 T, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.97/2.40 Y, T, X ), Z, X ) ) ] )
% 1.97/2.40 , clause( 20154, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 1.97/2.40 =( 'c_Polynomial_Osmult'( Y, 'c_Polynomial_Omonom'( Z, T, X ), X ),
% 1.97/2.40 'c_Polynomial_Omonom'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ) )
% 1.97/2.40 ] )
% 1.97/2.40 , clause( 20155, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.97/2.40 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 1.97/2.40 , clause( 20156, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.97/2.40 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y
% 1.97/2.40 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.97/2.40 X ), 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ] )
% 1.97/2.40 , clause( 20157, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.97/2.40 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ] )
% 1.97/2.40 , clause( 20158, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.97/2.40 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y
% 1.97/2.40 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T,
% 1.97/2.40 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 1.97/2.40 , clause( 20159, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 1.97/2.40 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 1.97/2.40 X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.97/2.40 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ), Z, X ) ) ] )
% 1.97/2.40 , clause( 20160, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.97/2.40 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.97/2.40 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.97/2.40 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.97/2.40 , clause( 20161, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.97/2.40 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.97/2.40 , clause( 20162, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.97/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.97/2.40 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.97/2.40 , clause( 20163, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.97/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.97/2.40 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.97/2.40 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.97/2.40 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.97/2.40 , clause( 20164, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.97/2.40 =( 'c_Polynomial_Osmult'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y ) ] )
% 1.97/2.40 , clause( 20165, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.97/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 1.97/2.40 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.97/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 1.97/2.40 , clause( 20166, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.97/2.40 'c_Polynomial_Ocoeff'( 'c_Polynomial_Opoly__gcd'( Y, Z, X ),
% 1.97/2.40 'c_Polynomial_Odegree'( 'c_Polynomial_Opoly__gcd'( Y, Z, X ), X ), X ),
% 1.97/2.40 'c_HOL_Oone__class_Oone'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.97/2.40 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 1.97/2.40 , clause( 20167, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.97/2.40 'c_Polynomial_Ocoeff'( 'c_Polynomial_Opoly__gcd'( Y, Z, X ),
% 1.97/2.40 'c_Polynomial_Odegree'( 'c_Polynomial_Opoly__gcd'( Y, Z, X ), X ), X ),
% 1.97/2.40 'c_HOL_Oone__class_Oone'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.97/2.40 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 1.97/2.40 , clause( 20168, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.97/2.40 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Otimes__class_Otimes'( Y,
% 1.97/2.40 'c_HOL_Osgn__class_Osgn'( Y, X ), X ) ) ] )
% 1.97/2.40 , clause( 20169, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.97/2.40 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.97/2.40 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ) ] )
% 1.97/2.40 , clause( 20170, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.97/2.40 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'(
% 1.97/2.40 'tc_Polynomial_Opoly'( X ) ), Y, 'tc_Polynomial_Opoly'( X ) ),
% 1.97/2.40 'c_HOL_Ouminus__class_Ouminus'( Y, 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 1.97/2.40 , clause( 20171, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.97/2.40 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oone__class_Oone'( X ), X ), X ), Z
% 1.97/2.40 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 1.97/2.40 , clause( 20172, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'(
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.97/2.40 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oone__class_Oone'( X ), X ), X ), X
% 1.97/2.40 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 1.97/2.40 , clause( 20173, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.97/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.97/2.40 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), Z, X ) ), =( Z,
% 1.97/2.40 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.97/2.40 , clause( 20174, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.97/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.97/2.40 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Z,
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), T, X ) ), =( T,
% 1.97/2.40 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.97/2.40 , clause( 20175, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.97/2.40 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, U,
% 1.97/2.40 X ), X ) ) ] )
% 1.97/2.40 , clause( 20176, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.97/2.40 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.97/2.40 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ] )
% 1.97/2.40 , clause( 20177, [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.97/2.40 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.97/2.40 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ] )
% 1.97/2.40 , clause( 20178, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.97/2.40 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.97/2.40 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ] )
% 1.97/2.40 , clause( 20179, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.97/2.40 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.97/2.40 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ] )
% 1.97/2.40 , clause( 20180, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.97/2.40 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.97/2.40 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.97/2.40 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ), =( Z,
% 1.97/2.40 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.97/2.40 , clause( 20181, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.97/2.40 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 1.97/2.40 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.97/2.40 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.97/2.40 , clause( 20182, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.97/2.40 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.97/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.97/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.97/2.40 , clause( 20183, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 1.97/2.40 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.97/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.97/2.40 , clause( 20184, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.97/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.97/2.40 , clause( 20185, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.97/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.97/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.97/2.40 , clause( 20186, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.97/2.40 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.97/2.40 , T, X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.97/2.40 Y, T, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ] )
% 1.97/2.40 , clause( 20187, [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.97/2.40 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.97/2.40 , T, X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.97/2.40 Y, T, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ] )
% 1.97/2.40 , clause( 20188, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.97/2.40 'c_Polynomial_Opdivmod__rel'( 'c_Polynomial_Osmult'( Y, Z, X ), T,
% 1.97/2.40 'c_Polynomial_Osmult'( Y, U, X ), 'c_Polynomial_Osmult'( Y, W, X ), X ),
% 1.97/2.40 ~( 'c_Polynomial_Opdivmod__rel'( Z, T, U, W, X ) ) ] )
% 1.97/2.40 , clause( 20189, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.97/2.40 'c_HOL_Osgn__class_Osgn'( Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.97/2.40 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.97/2.40 , clause( 20190, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.97/2.40 'c_HOL_Osgn__class_Osgn'( Y, X ), X ) ) ] )
% 1.97/2.40 , clause( 20191, [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.97/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ominus__class_Ominus'( Z
% 1.97/2.40 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.97/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 1.97/2.40 , clause( 20192, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 1.97/2.40 X ) ), =( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.97/2.40 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.97/2.40 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.97/2.40 , clause( 20193, [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 1.97/2.40 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.97/2.40 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.97/2.40 ) ] )
% 1.97/2.40 , clause( 20194, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.97/2.40 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 1.97/2.40 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.97/2.40 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.97/2.40 ) ] )
% 1.97/2.40 , clause( 20195, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =(
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.97/2.40 , Z, X ) ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), =( Y, Z ) ]
% 1.97/2.40 )
% 1.97/2.40 , clause( 20196, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 1.97/2.40 =( 'c_Polynomial_Osynthetic__div'( 'c_Polynomial_OpCons'( Y, Z, X ), T, X
% 1.97/2.40 ), 'c_Polynomial_OpCons'( 'c_Polynomial_Opoly'( Z, T, X ),
% 1.97/2.40 'c_Polynomial_Osynthetic__div'( Z, T, X ), X ) ) ] )
% 1.97/2.40 , clause( 20197, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Osgn__class_Osgn'( Y, X ),
% 1.97/2.40 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), Y ) ] )
% 1.97/2.40 , clause( 20198, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.97/2.40 'c_HOL_Ouminus__class_Ouminus'( 'c_Polynomial_OpCons'( Y, Z, X ),
% 1.97/2.40 'tc_Polynomial_Opoly'( X ) ), 'c_Polynomial_OpCons'(
% 1.97/2.40 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.97/2.40 , 'tc_Polynomial_Opoly'( X ) ), X ) ) ] )
% 1.97/2.40 , clause( 20199, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T,
% 1.97/2.40 'tc_Polynomial_Opoly'( X ) ), U, 'tc_Polynomial_Opoly'( X ) ) ), ~(
% 1.97/2.40 'c_Polynomial_Opdivmod__rel'( Y, T, Z, U, X ) ) ] )
% 1.97/2.40 , clause( 20200, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.97/2.40 'c_Polynomial_Ocoeff'( 'c_Polynomial_Opoly__gcd'(
% 1.97/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ),
% 1.97/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ),
% 1.97/2.40 'c_Polynomial_Odegree'( 'c_Polynomial_Opoly__gcd'(
% 1.97/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ),
% 1.97/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ), X ), X ),
% 1.97/2.40 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.97/2.40 , clause( 20201, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 1.97/2.40 =( 'c_Polynomial_Osmult'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X ),
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( 'c_Polynomial_Osmult'( Y, T, X ),
% 1.97/2.40 'c_Polynomial_Osmult'( Z, T, X ), 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 1.97/2.40 , clause( 20202, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 1.97/2.40 =( 'c_Polynomial_Osmult'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T,
% 1.97/2.40 'tc_Polynomial_Opoly'( X ) ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.97/2.40 'c_Polynomial_Osmult'( Y, Z, X ), 'c_Polynomial_Osmult'( Y, T, X ),
% 1.97/2.40 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 1.97/2.40 , clause( 20203, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.97/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.97/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.97/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.97/2.40 , T, X ), X ) ) ] )
% 1.97/2.40 , clause( 20204, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.97/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.97/2.40 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ), ~(
% 1.97/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 1.97/2.40 , clause( 20205, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.97/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.97/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.97/2.40 , T, X ), X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 1.97/2.40 )
% 1.97/2.40 , clause( 20206, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.97/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.97/2.40 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.97/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 1.97/2.40 , clause( 20207, [ ~( 'class_HOL_Ozero'( X ) ), ~( 'class_HOL_Oeq'( X ) ),
% 1.97/2.40 'c_HOL_Oeq__class_Oeq'( 'c_Polynomial_OpCons'( Y, Z, X ),
% 1.97/2.40 'c_Polynomial_OpCons'( T, U, X ), 'tc_Polynomial_Opoly'( X ) ), ~(
% 1.97/2.40 'c_HOL_Oeq__class_Oeq'( Z, U, 'tc_Polynomial_Opoly'( X ) ) ), ~(
% 1.97/2.40 'c_HOL_Oeq__class_Oeq'( Y, T, X ) ) ] )
% 1.97/2.40 , clause( 20208, [ ~( 'class_RealVector_Oreal__vector'( X ) ), =(
% 1.97/2.40 'c_RealVector_OscaleR__class_OscaleR'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 1.97/2.40 Z, X ), X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.97/2.40 'c_RealVector_OscaleR__class_OscaleR'( Y, Z, X ), X ) ) ] )
% 1.97/2.40 , clause( 20209, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 1.97/2.40 'c_RealVector_OscaleR__class_OscaleR'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 1.97/2.40 Z, X ), X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.97/2.40 'c_RealVector_OscaleR__class_OscaleR'( Y, Z, X ), X ) ) ] )
% 1.97/2.40 , clause( 20210, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.97/2.40 'c_HOL_Ominus__class_Ominus'( T, Y, X ), Z, X ), U, X ), X ),
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 1.97/2.40 ) ) ] )
% 1.97/2.40 , clause( 20211, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X
% 1.97/2.40 ) ) ) ] )
% 1.97/2.40 , clause( 20212, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X
% 1.97/2.40 ) ) ) ] )
% 1.97/2.40 , clause( 20213, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.97/2.40 =( 'c_Polynomial_Odegree'( 'c_HOL_Oone__class_Oone'(
% 1.97/2.40 'tc_Polynomial_Opoly'( X ) ), X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.97/2.40 ) ] )
% 1.97/2.40 , clause( 20214, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 1.97/2.40 =( 'c_Polynomial_Opoly'(
% 1.97/2.40 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly'( Y, Z, X ), T
% 1.97/2.40 , X ), 'c_Polynomial_Opoly'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.97/2.40 ) ) ] )
% 1.97/2.40 , clause( 20215, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.97/2.40 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 1.97/2.40 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 1.97/2.40 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z
% 1.97/2.40 , X ) ) ] )
% 1.97/2.40 , clause( 20216, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 1.97/2.40 =( 'c_Polynomial_Odegree'(
% 1.97/2.40 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly'( Y, Z, X ), X
% 1.97/2.40 ), 'c_Polynomial_Odegree'( Y, X ) ) ] )
% 1.97/2.40 , clause( 20217, [ ~( 'class_SEQ_Obanach'( X ) ), ~(
% 1.97/2.40 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.97/2.40 'c_Transcendental_Oexp'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ),
% 1.97/2.40 'c_HOL_Oinverse__class_Odivide'( 'c_Transcendental_Oexp'( Y, X ),
% 1.97/2.40 'c_Transcendental_Oexp'( Z, X ), X ) ) ] )
% 1.97/2.40 , clause( 20218, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.97/2.40 ] )
% 1.97/2.40 , clause( 20219, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 1.97/2.40 ] )
% 1.97/2.40 , clause( 20220, [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 1.97/2.40 ] )
% 1.97/2.40 , clause( 20221, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.97/2.40 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y
% 1.97/2.40 ) ] )
% 1.97/2.40 , clause( 20222, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.97/2.40 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y
% 1.97/2.40 ) ] )
% 1.97/2.40 , clause( 20223, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.97/2.40 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y
% 1.97/2.40 ) ] )
% 1.97/2.40 , clause( 20224, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.97/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 1.97/2.40 , Y, X ), X ) ] )
% 1.97/2.40 , clause( 20225, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.97/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 1.97/2.40 , Z, X ), X ) ] )
% 1.97/2.40 , clause( 20226, [ ~( 'class_Ring__and__Field_Odvd'( X ) ),
% 1.97/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 1.97/2.40 , Z, X ), X ) ] )
% 1.97/2.40 , clause( 20227, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.97/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_Polynomial_Opoly'( X ) )
% 1.97/2.40 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_Osmult'( T, Y,
% 1.97/2.40 X ), Z, 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 1.97/2.40 , clause( 20228, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.97/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Polynomial_Osmult'( Z, T, X
% 1.97/2.40 ), 'tc_Polynomial_Opoly'( X ) ), ~(
% 1.97/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, 'tc_Polynomial_Opoly'( X ) )
% 1.97/2.40 ) ] )
% 1.97/2.40 , clause( 20229, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.97/2.40 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.97/2.40 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.97/2.40 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ), =( Z,
% 1.97/2.40 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.97/2.40 , clause( 20230, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.97/2.40 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.97/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.97/2.40 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 1.97/2.40 , clause( 20231, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 1.97/2.40 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.97/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.97/2.40 , clause( 20232, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.97/2.40 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.97/2.40 , T, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.97/2.40 Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 1.97/2.40 , clause( 20233, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.97/2.40 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.97/2.40 , T, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.97/2.40 Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 1.97/2.40 , clause( 20234, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.97/2.40 'c_Polynomial_Opoly__gcd'( Y, 'c_Polynomial_Opoly__gcd'( Z, T, X ), X ),
% 1.97/2.40 'c_Polynomial_Opoly__gcd'( Z, 'c_Polynomial_Opoly__gcd'( Y, T, X ), X ) )
% 1.97/2.40 ] )
% 1.97/2.40 , clause( 20235, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.97/2.40 'c_Polynomial_Opoly__gcd'( 'c_Polynomial_Opoly__gcd'( Y, Z, X ), T, X ),
% 1.97/2.40 'c_Polynomial_Opoly__gcd'( Y, 'c_Polynomial_Opoly__gcd'( Z, T, X ), X ) )
% 1.97/2.40 ] )
% 1.97/2.40 , clause( 20236, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.97/2.40 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Z, X ), U, X ) ),
% 1.97/2.40 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), T, X ) )
% 1.97/2.40 ] )
% 1.97/2.40 , clause( 20237, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), Z, X
% 1.97/2.40 ), Y ) ] )
% 1.97/2.40 , clause( 20238, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 1.97/2.40 =( 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly'(
% 1.97/2.40 'c_Polynomial_OpCons'( Y, Z, X ), T, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.97/2.40 'c_Polynomial_Osmult'( T,
% 1.97/2.40 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly'( Z, T, X ), X
% 1.97/2.40 ), 'c_Polynomial_OpCons'( Y,
% 1.97/2.40 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly'( Z, T, X ), X
% 1.97/2.40 ), 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 1.97/2.40 , clause( 20239, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.97/2.40 'c_Polynomial_Opoly__gcd'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 1.97/2.40 'tc_Polynomial_Opoly'( X ) ), X ), 'c_Polynomial_Opoly__gcd'( Y, Z, X ) )
% 1.97/2.40 ] )
% 1.97/2.40 , clause( 20240, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.97/2.40 'c_Polynomial_Opoly__gcd'( 'c_HOL_Ouminus__class_Ouminus'( Y,
% 1.97/2.40 'tc_Polynomial_Opoly'( X ) ), Z, X ), 'c_Polynomial_Opoly__gcd'( Y, Z, X
% 1.97/2.40 ) ) ] )
% 1.97/2.40 , clause( 20241, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.97/2.40 =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'(
% 1.97/2.40 Z, Y, X ) ) ] )
% 1.97/2.40 , clause( 20242, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.97/2.40 =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'(
% 1.97/2.40 Z, Y, X ) ) ] )
% 1.97/2.40 , clause( 20243, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.97/2.40 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.97/2.40 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.97/2.40 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.97/2.40 , T, X ), X ), T, X ) ) ] )
% 1.97/2.40 , clause( 20244, [ ~( 'class_Orderings_Oorder'( X ) ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.97/2.40 , X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 1.97/2.40 , clause( 20245, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 1.97/2.40 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 1.97/2.40 , clause( 20246, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 1.97/2.40 =( 'c_Polynomial_Ocoeff'( 'c_Polynomial_Osmult'( Y, Z, X ), T, X ),
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( Y, 'c_Polynomial_Ocoeff'( Z, T, X ), X ) )
% 1.97/2.40 ] )
% 1.97/2.40 , clause( 20247, [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Ocoeff'(
% 1.97/2.40 'c_Polynomial_Omonom'( Y, Z, X ), T, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.97/2.40 ), =( Z, T ) ] )
% 1.97/2.40 , clause( 20248, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.97/2.40 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 1.97/2.40 ) ) ] )
% 1.97/2.40 , clause( 20249, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.97/2.40 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.97/2.40 ) ) ] )
% 1.97/2.40 , clause( 20250, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.97/2.40 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 1.97/2.40 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 1.97/2.40 , X ) ) ] )
% 1.97/2.40 , clause( 20251, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.97/2.40 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 1.97/2.40 ) ) ] )
% 1.97/2.40 , clause( 20252, [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.97/2.40 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.97/2.40 ) ) ] )
% 1.97/2.40 , clause( 20253, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.97/2.40 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 1.97/2.40 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 1.97/2.40 , X ) ) ] )
% 1.97/2.40 , clause( 20254, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.97/2.40 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T,
% 1.97/2.40 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z
% 1.97/2.40 , X ) ) ] )
% 1.97/2.40 , clause( 20255, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.97/2.40 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 1.97/2.40 X ), 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X )
% 1.97/2.40 , X ) ) ] )
% 1.97/2.40 , clause( 20256, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.97/2.40 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T,
% 1.97/2.40 X ), 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X )
% 1.97/2.40 , X ) ) ] )
% 1.97/2.40 , clause( 20257, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.97/2.40 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 1.97/2.40 , Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 1.97/2.40 , clause( 20258, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.97/2.40 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.97/2.40 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.97/2.40 , clause( 20259, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.97/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.97/2.40 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.97/2.40 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.97/2.40 , clause( 20260, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.97/2.40 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.97/2.40 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.97/2.40 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ] )
% 1.97/2.40 , clause( 20261, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.97/2.40 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.97/2.40 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.97/2.40 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ] )
% 1.97/2.40 , clause( 20262, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.97/2.40 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.97/2.40 , T, X ) ) ), =( Z, T ) ] )
% 1.97/2.40 , clause( 20263, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.97/2.40 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.97/2.40 , T, X ) ) ), =( Y, Z ) ] )
% 1.97/2.40 , clause( 20264, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.97/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.97/2.40 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.97/2.40 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.97/2.40 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ] )
% 1.97/2.40 , clause( 20265, [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.97/2.40 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.97/2.40 Z, X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.97/2.40 Y, Z, X ), X ) ) ] )
% 1.97/2.40 , clause( 20266, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.97/2.40 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.97/2.40 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.97/2.40 , U, X ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'(
% 1.97/2.40 Y, T, X ), U, X ), X ), 'c_HOL_Otimes__class_Otimes'( T,
% 1.97/2.40 'c_HOL_Ominus__class_Ominus'( Z, U, X ), X ), X ) ) ] )
% 1.97/2.40 , clause( 20267, [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), =(
% 1.97/2.40 'c_Polynomial_Opoly'( 'c_HOL_Ouminus__class_Ouminus'( Y,
% 1.97/2.40 'tc_Polynomial_Opoly'( X ) ), Z, X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.97/2.40 'c_Polynomial_Opoly'( Y, Z, X ), X ) ) ] )
% 1.97/2.40 , clause( 20268, [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =(
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 1.97/2.40 ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ), U, X ) ) ] )
% 1.97/2.40 , clause( 20269, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 1.97/2.40 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.97/2.40 , clause( 20270, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 1.97/2.40 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.97/2.40 , clause( 20271, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.97/2.40 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.97/2.40 , clause( 20272, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 1.97/2.40 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 1.97/2.40 , clause( 20273, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 1.97/2.40 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.97/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.97/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.97/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.97/2.40 , clause( 20274, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 1.97/2.40 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.97/2.40 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 1.97/2.40 , clause( 20275, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 1.97/2.40 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.97/2.40 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 1.97/2.40 , clause( 20276, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.97/2.40 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.97/2.40 X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 1.97/2.40 , clause( 20277, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.97/2.40 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.97/2.40 X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 1.97/2.40 , clause( 20278, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.97/2.40 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.97/2.40 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.97/2.40 , U, X ), X ) ) ] )
% 1.97/2.40 , clause( 20279, [ ~( 'class_RealVector_Oreal__normed__algebra__1'( X ) ),
% 1.97/2.40 =( 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.97/2.40 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 1.97/2.40 , clause( 20280, [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =(
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.97/2.40 'c_Polynomial_OpCons'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.97/2.40 'c_Polynomial_OpCons'( 'c_HOL_Oone__class_Oone'( X ),
% 1.97/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ), X ),
% 1.97/2.40 'c_Polynomial_Osynthetic__div'( Z, Y, X ), 'tc_Polynomial_Opoly'( X ) ),
% 1.97/2.40 'c_Polynomial_OpCons'( 'c_Polynomial_Opoly'( Z, Y, X ),
% 1.97/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ),
% 1.97/2.40 'tc_Polynomial_Opoly'( X ) ), Z ) ] )
% 1.97/2.40 , clause( 20281, [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.97/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.97/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 1.97/2.40 Z, X ), X ) ) ] )
% 1.97/2.40 , clause( 20282, [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.97/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 1.97/2.40 Z, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 1.97/2.40 , clause( 20283, [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.97/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.97/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.97/2.40 , X ), Z, X ) ) ] )
% 1.97/2.40 , clause( 20284, [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.97/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.97/2.40 , X ), Z, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 1.97/2.40 , clause( 20285, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( 'c_Polynomial_Omonom'( Y, Z, X ),
% 1.97/2.40 'c_Polynomial_Omonom'( T, Z, X ), 'tc_Polynomial_Opoly'( X ) ),
% 1.97/2.40 'c_Polynomial_Omonom'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ) ) ]
% 1.97/2.40 )
% 1.97/2.40 , clause( 20286, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Osgn__class_Osgn'( Y, X ),
% 1.97/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.97/2.40 , clause( 20287, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Osgn__class_Osgn'( Y, X ),
% 1.97/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.97/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.97/2.40 , clause( 20288, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.97/2.40 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.97/2.40 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 1.97/2.40 , clause( 20289, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.97/2.40 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.97/2.40 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.97/2.40 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ] )
% 1.97/2.40 , clause( 20290, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 1.97/2.40 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.97/2.40 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.97/2.40 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.97/2.40 , T, X ), X ), T, X ) ) ] )
% 1.97/2.40 , clause( 20291, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.97/2.40 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y
% 1.97/2.40 ) ] )
% 1.97/2.40 , clause( 20292, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 1.97/2.40 X ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 1.97/2.40 ), X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ] )
% 1.97/2.40 , clause( 20293, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 1.97/2.40 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z
% 1.97/2.40 , X ), 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ] )
% 1.97/2.40 , clause( 20294, [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X )
% 1.97/2.40 ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ] )
% 1.97/2.40 , clause( 20295, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 1.97/2.40 ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.97/2.40 Y, T, X ) ) ), =( Z, T ) ] )
% 1.97/2.40 , clause( 20296, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 1.97/2.40 ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.97/2.40 T, Z, X ) ) ), =( Y, T ) ] )
% 1.97/2.40 , clause( 20297, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 1.97/2.40 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X )
% 1.97/2.40 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 1.97/2.40 , clause( 20298, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.97/2.40 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.97/2.40 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ] )
% 1.97/2.40 , clause( 20299, [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.97/2.40 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.97/2.40 ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ] )
% 1.97/2.40 , clause( 20300, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.97/2.40 'c_Polynomial_Opoly__gcd'( 'c_HOL_Oone__class_Oone'(
% 1.97/2.40 'tc_Polynomial_Opoly'( X ) ), Y, X ), 'c_HOL_Oone__class_Oone'(
% 1.97/2.40 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 1.97/2.40 , clause( 20301, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.97/2.40 'c_Polynomial_Opoly__gcd'( Y, 'c_HOL_Oone__class_Oone'(
% 1.97/2.40 'tc_Polynomial_Opoly'( X ) ), X ), 'c_HOL_Oone__class_Oone'(
% 1.97/2.40 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 1.97/2.40 , clause( 20302, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.97/2.40 'c_Polynomial_Opos__poly'( 'c_HOL_Ouminus__class_Ouminus'( Y,
% 1.97/2.40 'tc_Polynomial_Opoly'( X ) ), X ), 'c_Polynomial_Opos__poly'( Y, X ), =(
% 1.97/2.40 Y, 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 1.97/2.40 , clause( 20303, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.97/2.40 'c_Polynomial_Ocoeff'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.97/2.40 'tc_Polynomial_Opoly'( X ) ), T, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.97/2.40 'c_Polynomial_Ocoeff'( Y, T, X ), 'c_Polynomial_Ocoeff'( Z, T, X ), X ) )
% 1.97/2.40 ] )
% 1.97/2.40 , clause( 20304, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.97/2.40 'c_HOL_Ouminus__class_Ouminus'( 'c_Polynomial_Omonom'( Y, Z, X ),
% 1.97/2.40 'tc_Polynomial_Opoly'( X ) ), 'c_Polynomial_Omonom'(
% 1.97/2.40 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ) ] )
% 1.97/2.40 , clause( 20305, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( 'c_RealVector_OscaleR__class_OscaleR'( Y, Z
% 1.97/2.40 , X ), T, X ), 'c_RealVector_OscaleR__class_OscaleR'( Y,
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 1.97/2.40 , clause( 20306, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( 'c_RealVector_OscaleR__class_OscaleR'( Y, Z
% 1.97/2.40 , X ), T, X ), 'c_RealVector_OscaleR__class_OscaleR'( Y,
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 1.97/2.40 , clause( 20307, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( Y, 'c_RealVector_OscaleR__class_OscaleR'( Z
% 1.97/2.40 , T, X ), X ), 'c_RealVector_OscaleR__class_OscaleR'( Z,
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 1.97/2.40 , clause( 20308, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( Y, 'c_RealVector_OscaleR__class_OscaleR'( Z
% 1.97/2.40 , T, X ), X ), 'c_RealVector_OscaleR__class_OscaleR'( Z,
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 1.97/2.40 , clause( 20309, [ ~( 'class_RealVector_Oreal__algebra'( X ) ), =(
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( 'c_RealVector_OscaleR__class_OscaleR'( Y, Z
% 1.97/2.40 , X ), T, X ), 'c_RealVector_OscaleR__class_OscaleR'( Y,
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 1.97/2.40 , clause( 20310, [ ~( 'class_RealVector_Oreal__algebra'( X ) ), =(
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( Y, 'c_RealVector_OscaleR__class_OscaleR'( Z
% 1.97/2.40 , T, X ), X ), 'c_RealVector_OscaleR__class_OscaleR'( Z,
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 1.97/2.40 , clause( 20311, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 1.97/2.40 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 1.97/2.40 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.97/2.40 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.97/2.40 X ) ) ] )
% 1.97/2.40 , clause( 20312, [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Ocoeff'(
% 1.97/2.40 'c_Polynomial_Omonom'( Y, Z, X ), Z, X ), Y ) ] )
% 1.97/2.40 , clause( 20313, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 1.97/2.40 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.97/2.40 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.97/2.40 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ] )
% 1.97/2.40 , clause( 20314, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 1.97/2.40 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.97/2.40 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 1.97/2.40 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ] )
% 1.97/2.40 , clause( 20315, [ ~( 'class_SEQ_Obanach'( X ) ), ~(
% 1.97/2.40 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( 'c_Transcendental_Oexp'( Y, X ),
% 1.97/2.40 'c_Transcendental_Oexp'( Z, X ), X ), 'c_Transcendental_Oexp'(
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ) ) ] )
% 1.97/2.40 , clause( 20316, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.97/2.40 , 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ), =(
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( Y, T, X ), U ) ] )
% 1.97/2.40 , clause( 20317, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.97/2.40 'c_Polynomial_Opos__poly'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.97/2.40 'tc_Polynomial_Opoly'( X ) ), X ), ~( 'c_Polynomial_Opos__poly'( Z, X ) )
% 1.97/2.40 , ~( 'c_Polynomial_Opos__poly'( Y, X ) ) ] )
% 1.97/2.40 , clause( 20318, [ ~( 'class_Ring__and__Field_Osgn__if'( X ) ), =(
% 1.97/2.40 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.97/2.40 'c_HOL_Oone__class_Oone'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.97/2.40 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.97/2.40 X ) ) ] )
% 1.97/2.40 , clause( 20319, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.97/2.40 'c_Polynomial_Opdivmod__rel'( 'c_HOL_Oplus__class_Oplus'(
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'(
% 1.97/2.40 'tc_Polynomial_Opoly'( X ) ), Y, 'tc_Polynomial_Opoly'( X ) ),
% 1.97/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ),
% 1.97/2.40 'tc_Polynomial_Opoly'( X ) ), Y, 'c_HOL_Ozero__class_Ozero'(
% 1.97/2.40 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.97/2.40 'tc_Polynomial_Opoly'( X ) ), X ) ] )
% 1.97/2.40 , clause( 20320, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.97/2.40 'c_Polynomial_Opdivmod__rel'( 'c_HOL_Oplus__class_Oplus'(
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'(
% 1.97/2.40 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.97/2.40 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ), Y,
% 1.97/2.40 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.97/2.40 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.97/2.40 'tc_Polynomial_Opoly'( X ) ), Y, X ) ] )
% 1.97/2.40 , clause( 20321, [ ~( 'class_SEQ_Obanach'( X ) ), ~(
% 1.97/2.40 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.97/2.40 'c_Transcendental_Oexp'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.97/2.40 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 1.97/2.40 , clause( 20322, [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.97/2.40 'c_HOL_Oinverse__class_Odivide'( 'c_RealVector_OscaleR__class_OscaleR'( Y
% 1.97/2.40 , Z, X ), T, X ), 'c_RealVector_OscaleR__class_OscaleR'( Y,
% 1.97/2.40 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ] )
% 1.97/2.40 , clause( 20323, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.97/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.97/2.40 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.97/2.40 ) ) ] )
% 1.97/2.40 , clause( 20324, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.97/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.97/2.40 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.97/2.40 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.97/2.40 ) ] )
% 1.97/2.40 , clause( 20325, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 1.97/2.40 =( 'c_Polynomial_Opcompose'( 'c_Polynomial_OpCons'( Y, Z, X ), T, X ),
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( 'c_Polynomial_OpCons'( Y,
% 1.97/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ),
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( T, 'c_Polynomial_Opcompose'( Z, T, X ),
% 1.97/2.40 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 1.97/2.40 , clause( 20326, [ ~( 'class_RealVector_Oreal__field'( X ) ), =(
% 1.97/2.40 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'(
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.97/2.40 , U, X ), X ), W, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oinverse__class_Odivide'(
% 1.97/2.40 'c_HOL_Ominus__class_Ominus'( Z, U, X ), W, X ), X ),
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'(
% 1.97/2.40 'c_HOL_Ominus__class_Ominus'( Y, T, X ), W, X ), U, X ), X ) ) ] )
% 1.97/2.40 , clause( 20327, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.97/2.40 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.97/2.40 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 1.97/2.40 , clause( 20328, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 1.97/2.40 =( 'c_Polynomial_Opoly'( 'c_Polynomial_Opcompose'( Y, Z, X ), T, X ),
% 1.97/2.40 'c_Polynomial_Opoly'( Y, 'c_Polynomial_Opoly'( Z, T, X ), X ) ) ] )
% 1.97/2.40 , clause( 20329, [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), =(
% 1.97/2.40 'c_Polynomial_Osmult'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 1.97/2.40 'c_HOL_Ouminus__class_Ouminus'( 'c_Polynomial_Osmult'( Y, Z, X ),
% 1.97/2.40 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 1.97/2.40 , clause( 20330, [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), =(
% 1.97/2.40 'c_Polynomial_Osmult'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 1.97/2.40 'tc_Polynomial_Opoly'( X ) ), X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.97/2.40 'c_Polynomial_Osmult'( Y, Z, X ), 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 1.97/2.40 , clause( 20331, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.97/2.40 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.97/2.40 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), X ) ) ] )
% 1.97/2.40 , clause( 20332, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.97/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.97/2.40 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.97/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ) ] )
% 1.97/2.40 , clause( 20333, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.97/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.97/2.40 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.97/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 1.97/2.40 , clause( 20334, [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Ocoeff'(
% 1.97/2.40 'c_Polynomial_OpCons'( Y, Z, X ), 'c_Suc'( T ), X ),
% 1.97/2.40 'c_Polynomial_Ocoeff'( Z, T, X ) ) ] )
% 1.97/2.40 , clause( 20335, [ ~( 'class_HOL_Ozero'( X ) ), ~( 'class_HOL_Oeq'( X ) ),
% 1.97/2.40 'c_HOL_Oeq__class_Oeq'( Y, Z, X ), ~( 'c_HOL_Oeq__class_Oeq'(
% 1.97/2.40 'c_Polynomial_OpCons'( Y, T, X ), 'c_Polynomial_OpCons'( Z, U, X ),
% 1.97/2.40 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 1.97/2.40 , clause( 20336, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 1.97/2.40 X ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X )
% 1.97/2.40 , 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ] )
% 1.97/2.40 , clause( 20337, [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.97/2.40 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.97/2.40 W, X ) ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.97/2.40 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W ) ] )
% 1.97/2.40 , clause( 20338, [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.97/2.40 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.97/2.40 W, X ) ) ), =( T, 'c_HOL_Oplus__class_Oplus'(
% 1.97/2.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.97/2.40 , X ), W, X ) ) ] )
% 1.97/2.40 , clause( 20339, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 1.97/2.40 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.97/2.40 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.97/2.40 X ) ) ] )
% 1.97/2.40 , clause( 20340, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 1.97/2.40 =( 'c_Polynomial_Opoly'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.97/2.40 'tc_Polynomial_Opoly'( X ) ), T, X ), 'c_HOL_Otimes__class_Otimes'(
% 1.97/2.40 'c_Polynomial_Opoly'( Y, T, X ), 'c_Polynomial_Opoly'( Z, T, X ), X ) ) ]
% 1.97/2.40 )
% 1.97/2.40 , clause( 20341, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.97/2.40 =( 'c_Polynomial_Ocoeff'( 'c_HOL_Oone__class_Oone'( 'tc_Polynomial_Opoly'(
% 1.97/2.40 X ) ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.97/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 1.97/2.40 , clause( 20342, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.97/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_Polynomial_Opoly'( X ) )
% 1.97/2.40 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Polynomial_Opoly__gcd'(
% 1.97/2.40 Z, T, X ), 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 1.97/2.40 , clause( 20343, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 1.97/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_Polynomial_Opoly'( X ) )
% 1.97/2.40 , ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Polynomial_Opoly__gcd'(
% 1.97/2.40 T, Z, X ), 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 1.97/2.40 , clause( 20344, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 1.97/2.40 =( 'c_Polynomial_Opoly'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.97/2.40 'tc_Polynomial_Opoly'( X ) ), T, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.97/2.40 'c_Polynomial_Opoly'( Y, T, X ), 'c_Polynomial_Opoly'( Z, T, X ), X ) ) ]
% 1.97/2.40 )
% 1.97/2.40 , clause( 20345, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 1.97/2.40 'c_RealVector_OscaleR__class_OscaleR'( Y,
% 1.97/2.40 'c_RealVector_OscaleR__class_OscaleR'( Z, T, X ), X ),
% 1.97/2.40 'c_RealVector_OscaleR__class_OscaleR'( Z,
% 1.97/2.40 'c_RealVector_OscaleR__class_OscaleR'( Y, T, X ), X ) ) ] )
% 1.97/2.40 , clause( 20346, [ ~( 'class_RealVector_Oreal__vector'( X ) ), =(
% 1.97/2.40 'c_RealVector_OscaleR__class_OscaleR'( Y,
% 1.97/2.40 'c_RealVector_OscaleR__class_OscaleR'( Z, T, X ), X ),
% 1.97/2.40 'c_RealVector_OscaleR__class_OscaleR'( Z,
% 1.97/2.40 'c_RealVector_OscaleR__class_OscaleR'( Y, T, X ), X ) ) ] )
% 1.97/2.40 , clause( 20347, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 1.97/2.40 'c_RealVector_OscaleR__class_OscaleR'( Y,
% 1.97/2.40 'c_RealVector_OscaleR__class_OscaleR'( Z, T, X ), X ),
% 1.97/2.40 'c_RealVector_OscaleR__class_OscaleR'( Z,
% 1.97/2.40 'c_RealVector_OscaleR__class_OscaleR'( Y, T, X ), X ) ) ] )
% 1.97/2.40 , clause( 20348, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.97/2.40 =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z,
% 1.97/2.40 Y, X ) ) ] )
% 1.97/2.40 , clause( 20349, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.97/2.40 =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z,
% 1.97/2.40 Y, X ) ) ] )
% 1.97/2.40 , clause( 20350, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.97/2.40 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 1.97/2.40 X ) ) ] )
% 1.97/2.40 , clause( 20351, [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.97/2.40 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.97/2.40 , Z, X ) ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.97/2.40 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 1.97/2.40 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'( T, X ), Z,
% 1.97/2.40 X ) ) ] )
% 1.97/2.40 , clause( 20352, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.97/2.40 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.97/2.40 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 1.97/2.40 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.97/2.40 , T, X ), X ), T, X ) ) ] )
% 1.97/2.40 , clause( 20353, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.97/2.40 'c_Polynomial_Opos__poly'( Y, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.97/2.40 'c_HOL_Ozero__class_Ozero'( X ), 'c_Polynomial_Ocoeff'( Y,
% 1.97/2.40 'c_Polynomial_Odegree'( Y, X ), X ), X ) ) ] )
% 1.97/2.40 , clause( 20354, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.97/2.40 'c_Polynomial_Ocoeff'( Y, 'c_Polynomial_Odegree'( Y, X ), X ), X ), ~(
% 1.97/2.40 'c_Polynomial_Opos__poly'( Y, X ) ) ] )
% 1.97/2.40 , clause( 20355, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.97/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.97/2.40 ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.97/2.40 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.97/2.40 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.97/2.40 , Y, X ) ) ] )
% 1.97/2.40 , clause( 20356, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.97/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.97/2.40 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.97/2.40 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.97/2.40 X ), Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.97/2.40 , Z, X ) ] )
% 1.97/2.40 , clause( 20357, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.97/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.97/2.40 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.97/2.40 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.97/2.40 X ), Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.97/2.40 , Z, X ) ] )
% 1.97/2.40 , clause( 20358, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.97/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.97/2.40 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.97/2.40 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.97/2.40 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T, Z, X
% 1.97/2.40 ), X ) ) ] )
% 1.97/2.40 , clause( 20359, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.97/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X
% 1.97/2.40 ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.97/2.40 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ),
% 1.97/2.40 ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oinverse__class_Odivide'( Y, T, X
% 1.97/2.40 ), X ) ) ] )
% 1.97/2.40 , clause( 20360, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.97/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.97/2.40 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.97/2.40 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.97/2.40 T, X ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.97/2.40 , T, X ) ] )
% 1.97/2.40 , clause( 20361, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.97/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.97/2.40 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.97/2.40 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.97/2.40 T, X ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.97/2.40 , T, X ) ] )
% 1.97/2.40 , clause( 20362, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.97/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.97/2.40 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.97/2.40 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.97/2.40 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.97/2.40 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 2.05/2.40 Z, X ) ) ] )
% 2.05/2.40 , clause( 20363, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.05/2.40 =( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 2.05/2.40 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 2.05/2.40 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ] )
% 2.05/2.40 , clause( 20364, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 2.05/2.40 , clause( 20365, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 2.05/2.40 , clause( 20366, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 2.05/2.40 'c_HOL_Oplus__class_Oplus'( 'c_Polynomial_OpCons'( Y, Z, X ),
% 2.05/2.40 'c_Polynomial_OpCons'( T, U, X ), 'tc_Polynomial_Opoly'( X ) ),
% 2.05/2.40 'c_Polynomial_OpCons'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ),
% 2.05/2.40 'c_HOL_Oplus__class_Oplus'( Z, U, 'tc_Polynomial_Opoly'( X ) ), X ) ) ]
% 2.05/2.40 )
% 2.05/2.40 , clause( 20367, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 2.05/2.40 , X ), U, X ), W, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.05/2.40 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), U, X
% 2.05/2.40 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, X ),
% 2.05/2.40 W, X ), X ) ) ] )
% 2.05/2.40 , clause( 20368, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 2.05/2.40 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 2.05/2.40 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 2.05/2.40 , X ), T, X ), W, X ) ) ] )
% 2.05/2.40 , clause( 20369, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.05/2.40 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'(
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 2.05/2.40 , X ), W, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.05/2.40 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X
% 2.05/2.40 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ),
% 2.05/2.40 W, X ), X ) ) ] )
% 2.05/2.40 , clause( 20370, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 2.05/2.40 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 2.05/2.40 ), X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Oplus__class_Oplus'(
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 2.05/2.40 , X ), W, X ), X ) ) ] )
% 2.05/2.40 , clause( 20371, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.05/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 2.05/2.40 , X ) ) ] )
% 2.05/2.40 , clause( 20372, [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 2.05/2.40 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 2.05/2.40 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 2.05/2.40 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 2.05/2.40 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( U, Y, X ), Z, X
% 2.05/2.40 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( W, T, X ),
% 2.05/2.40 Z, X ) ) ] )
% 2.05/2.40 , clause( 20373, [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), =(
% 2.05/2.40 'c_Polynomial_Osmult'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 2.05/2.40 'c_HOL_Ominus__class_Ominus'( 'c_Polynomial_Osmult'( Y, T, X ),
% 2.05/2.40 'c_Polynomial_Osmult'( Z, T, X ), 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 2.05/2.40 , clause( 20374, [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), =(
% 2.05/2.40 'c_Polynomial_Osmult'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T,
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), X ), 'c_HOL_Ominus__class_Ominus'(
% 2.05/2.40 'c_Polynomial_Osmult'( Y, Z, X ), 'c_Polynomial_Osmult'( Y, T, X ),
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 2.05/2.40 , clause( 20375, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 2.05/2.40 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 2.05/2.40 ), =( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z ) ] )
% 2.05/2.40 , clause( 20376, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 2.05/2.40 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 2.05/2.40 ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ] )
% 2.05/2.40 , clause( 20377, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.05/2.40 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.05/2.40 , clause( 20378, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.05/2.40 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.05/2.40 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ] )
% 2.05/2.40 , clause( 20379, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 2.05/2.40 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.05/2.40 , U, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.05/2.40 Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ),
% 2.05/2.40 =( Y, T ) ] )
% 2.05/2.40 , clause( 20380, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 2.05/2.40 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.05/2.40 , U, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.05/2.40 Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ),
% 2.05/2.40 =( Y, T ) ] )
% 2.05/2.40 , clause( 20381, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X
% 2.05/2.40 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 2.05/2.40 'c_HOL_Ominus__class_Ominus'( T, Y, X ), X ), Z, X ) ) ] )
% 2.05/2.40 , clause( 20382, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ), ~(
% 2.05/2.40 'c_Polynomial_Opdivmod__rel'( Z, Y, T, U, X ) ),
% 2.05/2.40 'c_Polynomial_Opdivmod__rel'( 'c_Polynomial_OpCons'( W, Z, X ), Y,
% 2.05/2.40 'c_Polynomial_OpCons'( 'c_HOL_Oinverse__class_Odivide'(
% 2.05/2.40 'c_Polynomial_Ocoeff'( 'c_Polynomial_OpCons'( W, U, X ),
% 2.05/2.40 'c_Polynomial_Odegree'( Y, X ), X ), 'c_Polynomial_Ocoeff'( Y,
% 2.05/2.40 'c_Polynomial_Odegree'( Y, X ), X ), X ), T, X ),
% 2.05/2.40 'c_HOL_Ominus__class_Ominus'( 'c_Polynomial_OpCons'( W, U, X ),
% 2.05/2.40 'c_Polynomial_Osmult'( 'c_HOL_Oinverse__class_Odivide'(
% 2.05/2.40 'c_Polynomial_Ocoeff'( 'c_Polynomial_OpCons'( W, U, X ),
% 2.05/2.40 'c_Polynomial_Odegree'( Y, X ), X ), 'c_Polynomial_Ocoeff'( Y,
% 2.05/2.40 'c_Polynomial_Odegree'( Y, X ), X ), X ), Y, X ), 'tc_Polynomial_Opoly'(
% 2.05/2.40 X ) ), X ) ] )
% 2.05/2.40 , clause( 20383, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.05/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.05/2.40 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 2.05/2.40 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 2.05/2.40 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ] )
% 2.05/2.40 , clause( 20384, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.05/2.40 X ) ), =( 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.05/2.40 , clause( 20385, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.05/2.40 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 2.05/2.40 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y,
% 2.05/2.40 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ] )
% 2.05/2.40 , clause( 20386, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.05/2.40 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 2.05/2.40 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 2.05/2.40 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ] )
% 2.05/2.40 , clause( 20387, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.05/2.40 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.05/2.40 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Z,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20388, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.05/2.40 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.05/2.40 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Y,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20389, [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Odegree'(
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.05/2.40 , clause( 20390, [ ~( 'class_RealVector_Oreal__vector'( X ) ), =(
% 2.05/2.40 'c_RealVector_OscaleR__class_OscaleR'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 2.05/2.40 T, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 2.05/2.40 'c_RealVector_OscaleR__class_OscaleR'( Y, Z, X ),
% 2.05/2.40 'c_RealVector_OscaleR__class_OscaleR'( Y, T, X ), X ) ) ] )
% 2.05/2.40 , clause( 20391, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 2.05/2.40 'c_RealVector_OscaleR__class_OscaleR'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 2.05/2.40 T, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 2.05/2.40 'c_RealVector_OscaleR__class_OscaleR'( Y, Z, X ),
% 2.05/2.40 'c_RealVector_OscaleR__class_OscaleR'( Y, T, X ), X ) ) ] )
% 2.05/2.40 , clause( 20392, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 2.05/2.40 =( 'c_Polynomial_Opoly'( 'c_Polynomial_Osmult'( Y, Z, X ), T, X ),
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( Y, 'c_Polynomial_Opoly'( Z, T, X ), X ) ) ]
% 2.05/2.40 )
% 2.05/2.40 , clause( 20393, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.05/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 2.05/2.40 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.05/2.40 , clause( 20394, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.05/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.05/2.40 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.05/2.40 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.05/2.40 , clause( 20395, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.05/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.05/2.40 , clause( 20396, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.05/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.05/2.40 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.05/2.40 , clause( 20397, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 2.05/2.40 'c_Polynomial_Opdivmod__rel'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T,
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), U, 'c_HOL_Oplus__class_Oplus'(
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( Z, W, 'tc_Polynomial_Opoly'( X ) ), V0,
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), X ), ~( 'c_Polynomial_Opdivmod__rel'( V1, T
% 2.05/2.40 , U, W, X ) ), ~( 'c_Polynomial_Opdivmod__rel'( Y, Z, V1, V0, X ) ) ] )
% 2.05/2.40 , clause( 20398, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 2.05/2.40 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 2.05/2.40 , Z ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( T, X ) ) ] )
% 2.05/2.40 , clause( 20399, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.05/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.05/2.40 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.05/2.40 , 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 2.05/2.40 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ), =( Z,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20400, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.05/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.05/2.40 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.05/2.40 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 2.05/2.40 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ), =( Y,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20401, [ ~( 'class_SEQ_Obanach'( X ) ), ~(
% 2.05/2.40 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 2.05/2.40 'c_Transcendental_Oexp'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ),
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( 'c_Transcendental_Oexp'( Y, X ),
% 2.05/2.40 'c_Transcendental_Oexp'( Z, X ), X ) ) ] )
% 2.05/2.40 , clause( 20402, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.05/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 2.05/2.40 , T, X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 2.05/2.40 Y, T, X ), Z, X ) ) ] )
% 2.05/2.40 , clause( 20403, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 2.05/2.40 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_Polynomial_Osmult'( Z, T, X ),
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), 'c_Polynomial_Osmult'( Z,
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_Polynomial_Opoly'( X ) ), X ) ) ]
% 2.05/2.40 )
% 2.05/2.40 , clause( 20404, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 2.05/2.40 =( 'c_HOL_Otimes__class_Otimes'( 'c_Polynomial_Osmult'( Y, Z, X ), T,
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), 'c_Polynomial_Osmult'( Y,
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_Polynomial_Opoly'( X ) ), X ) ) ]
% 2.05/2.40 )
% 2.05/2.40 , clause( 20405, [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), =(
% 2.05/2.40 'c_Polynomial_Opoly'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), T, X ), 'c_HOL_Ominus__class_Ominus'(
% 2.05/2.40 'c_Polynomial_Opoly'( Y, T, X ), 'c_Polynomial_Opoly'( Z, T, X ), X ) ) ]
% 2.05/2.40 )
% 2.05/2.40 , clause( 20406, [ ~(
% 2.05/2.40 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 2.05/2.40 , clause( 20407, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.05/2.40 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.05/2.40 , clause( 20408, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.05/2.40 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 2.05/2.40 , clause( 20409, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.05/2.40 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.05/2.40 , 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 2.05/2.40 , clause( 20410, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.05/2.40 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ] )
% 2.05/2.40 , clause( 20411, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.05/2.40 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.05/2.40 , clause( 20412, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.05/2.40 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.05/2.40 , clause( 20413, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.05/2.40 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.05/2.40 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 2.05/2.40 , clause( 20414, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.05/2.40 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 2.05/2.40 , clause( 20415, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.05/2.40 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.05/2.40 , clause( 20416, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.05/2.40 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.05/2.40 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 X ), T, X ) ) ] )
% 2.05/2.40 , clause( 20417, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.05/2.40 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.05/2.40 , clause( 20418, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.05/2.40 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.05/2.40 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.05/2.40 , clause( 20419, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.05/2.40 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 2.05/2.40 X ), 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ] )
% 2.05/2.40 , clause( 20420, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.05/2.40 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), Z, X ),
% 2.05/2.40 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 2.05/2.40 , clause( 20421, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.05/2.40 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), T, X ),
% 2.05/2.40 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ] )
% 2.05/2.40 , clause( 20422, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 2.05/2.40 =( 'c_Polynomial_Osmult'( Y, 'c_Polynomial_Osmult'( Z, T, X ), X ),
% 2.05/2.40 'c_Polynomial_Osmult'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ) )
% 2.05/2.40 ] )
% 2.05/2.40 , clause( 20423, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 2.05/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 2.05/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 2.05/2.40 , X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 2.05/2.40 , clause( 20424, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 2.05/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 2.05/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 2.05/2.40 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ] )
% 2.05/2.40 , clause( 20425, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 2.05/2.40 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_Polynomial_Osmult'( Z,
% 2.05/2.40 'c_Polynomial_Osynthetic__div'( Y, Z, X ), X ), 'tc_Polynomial_Opoly'( X
% 2.05/2.40 ) ), 'c_Polynomial_OpCons'( 'c_Polynomial_Opoly'( Y, Z, X ),
% 2.05/2.40 'c_Polynomial_Osynthetic__div'( Y, Z, X ), X ) ) ] )
% 2.05/2.40 , clause( 20426, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.05/2.40 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 2.05/2.40 ), Y ) ] )
% 2.05/2.40 , clause( 20427, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 2.05/2.40 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 2.05/2.40 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, T
% 2.05/2.40 , X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ] )
% 2.05/2.40 , clause( 20428, [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 2.05/2.40 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 2.05/2.40 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, T
% 2.05/2.40 , X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ] )
% 2.05/2.40 , clause( 20429, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 2.05/2.40 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), T, X ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 2.05/2.40 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 2.05/2.40 , Y, X ) ) ] )
% 2.05/2.40 , clause( 20430, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 2.05/2.40 , clause( 20431, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.05/2.40 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 2.05/2.40 ), Y ) ] )
% 2.05/2.40 , clause( 20432, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 2.05/2.40 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 2.05/2.40 ) ) ] )
% 2.05/2.40 , clause( 20433, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 2.05/2.40 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 2.05/2.40 ) ) ] )
% 2.05/2.40 , clause( 20434, [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 2.05/2.40 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 2.05/2.40 ), Y ) ] )
% 2.05/2.40 , clause( 20435, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.05/2.40 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 2.05/2.40 ), Y ) ] )
% 2.05/2.40 , clause( 20436, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 2.05/2.40 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 2.05/2.40 X ), 'c_HOL_Ominus__class_Ominus'( Z, Y, X ) ) ] )
% 2.05/2.40 , clause( 20437, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.05/2.40 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X
% 2.05/2.40 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X )
% 2.05/2.40 , Y, X ) ) ] )
% 2.05/2.40 , clause( 20438, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.05/2.40 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X
% 2.05/2.40 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X )
% 2.05/2.40 , Y, X ) ) ] )
% 2.05/2.40 , clause( 20439, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.05/2.40 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X
% 2.05/2.40 ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 2.05/2.40 ), X ) ) ] )
% 2.05/2.40 , clause( 20440, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.05/2.40 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X
% 2.05/2.40 ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 2.05/2.40 ), X ) ) ] )
% 2.05/2.40 , clause( 20441, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =(
% 2.05/2.40 'c_Polynomial_Opoly'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 2.05/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_OpCons'(
% 2.05/2.40 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_Polynomial_OpCons'(
% 2.05/2.40 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), X ), X ), Y, 'tc_Polynomial_Opoly'( X ) ) )
% 2.05/2.40 ] )
% 2.05/2.40 , clause( 20442, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =(
% 2.05/2.40 'c_Polynomial_Opoly'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 2.05/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_OpCons'(
% 2.05/2.40 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_Polynomial_OpCons'(
% 2.05/2.40 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), X ), X ), Y, 'tc_Polynomial_Opoly'( X ) ) ]
% 2.05/2.40 )
% 2.05/2.40 , clause( 20443, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =(
% 2.05/2.40 'c_Polynomial_Opoly'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 2.05/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_OpCons'( Z,
% 2.05/2.40 'c_Polynomial_OpCons'( 'c_HOL_Oone__class_Oone'( X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ), X ), Y,
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ) ] )
% 2.05/2.40 , clause( 20444, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =(
% 2.05/2.40 'c_Polynomial_Opoly'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 2.05/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_OpCons'( Z,
% 2.05/2.40 'c_Polynomial_OpCons'( 'c_HOL_Oone__class_Oone'( X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ), X ), Y,
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 2.05/2.40 , clause( 20445, [ ~( =( 'c_Polynomial_Opoly'( 'v_ds____',
% 2.05/2.40 'v_sko__local__XpCons__Xhyps__1'( 'v_ds____' ), 'tc_Complex_Ocomplex' ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Complex_Ocomplex' ) ) ), =( 'v_ds____',
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( 'tc_Complex_Ocomplex'
% 2.05/2.40 ) ) ) ] )
% 2.05/2.40 , clause( 20446, [ ~( =( 'c_Polynomial_Opoly'( 'v_ds____',
% 2.05/2.40 'v_sko__local__XpCons__1__1'( 'v_ds____' ), 'tc_Complex_Ocomplex' ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Complex_Ocomplex' ) ) ), =( 'v_ds____',
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( 'tc_Complex_Ocomplex'
% 2.05/2.40 ) ) ) ] )
% 2.05/2.40 , clause( 20447, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.05/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.05/2.40 , clause( 20448, [ ~( 'class_RealVector_Oreal__vector'( X ) ), ~( =(
% 2.05/2.40 'c_RealVector_OscaleR__class_OscaleR'( Y, Z, X ),
% 2.05/2.40 'c_RealVector_OscaleR__class_OscaleR'( T, Z, X ) ) ), =( Z,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, T ) ] )
% 2.05/2.40 , clause( 20449, [ ~( 'class_RealVector_Oreal__vector'( X ) ), =(
% 2.05/2.40 'c_RealVector_OscaleR__class_OscaleR'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 2.05/2.40 , X ), 'c_RealVector_OscaleR__class_OscaleR'( Z,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.05/2.40 , clause( 20450, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.05/2.40 X ) ), ~( =( 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20451, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) )
% 2.05/2.40 , =( 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X )
% 2.05/2.40 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20452, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.05/2.40 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20453, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.05/2.40 , clause( 20454, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 2.05/2.40 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20455, [ ~( 'class_Ring__and__Field_Osgn__if'( X ) ), =(
% 2.05/2.40 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20456, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 2.05/2.40 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20457, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 2.05/2.40 ) ), =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 2.05/2.40 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20458, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 2.05/2.40 ) ), =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 2.05/2.40 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20459, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20460, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20461, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.05/2.40 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 2.05/2.40 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20462, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20463, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20464, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20465, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20466, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.05/2.40 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 2.05/2.40 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20467, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.05/2.40 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 2.05/2.40 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20468, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.05/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 2.05/2.40 , X ) ] )
% 2.05/2.40 , clause( 20469, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.05/2.40 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.05/2.40 ) ] )
% 2.05/2.40 , clause( 20470, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.05/2.40 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 2.05/2.40 ) ] )
% 2.05/2.40 , clause( 20471, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 2.05/2.40 =( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ]
% 2.05/2.40 )
% 2.05/2.40 , clause( 20472, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.05/2.40 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 2.05/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 2.05/2.40 , X ) ) ] )
% 2.05/2.40 , clause( 20473, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.05/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.05/2.40 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 2.05/2.40 )
% 2.05/2.40 , clause( 20474, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) )
% 2.05/2.40 , ~( =( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y ) ), =( Y,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20475, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 2.05/2.40 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 2.05/2.40 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20476, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 2.05/2.40 =( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ]
% 2.05/2.40 )
% 2.05/2.40 , clause( 20477, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 2.05/2.40 ) ), ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 2.05/2.40 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20478, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 2.05/2.40 ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20479, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 2.05/2.40 ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20480, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.05/2.40 , ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20481, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 2.05/2.40 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), 'c_HOL_Otimes__class_Otimes'( Y, Y
% 2.05/2.40 , X ) ) ] )
% 2.05/2.40 , clause( 20482, [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 2.05/2.40 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 2.05/2.40 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 2.05/2.40 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 2.05/2.40 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( U, Y, X ), Z
% 2.05/2.40 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( W, T,
% 2.05/2.40 X ), Z, X ) ) ] )
% 2.05/2.40 , clause( 20483, [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Odegree'(
% 2.05/2.40 'c_Polynomial_Omonom'( Y, Z, X ), X ), Z ), =( Y,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20484, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 2.05/2.40 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 2.05/2.40 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 2.05/2.40 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'(
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.05/2.40 , Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ), =( U,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 2.05/2.40 ) ] )
% 2.05/2.40 , clause( 20485, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.05/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 2.05/2.40 , Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20486, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.05/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 2.05/2.40 , Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20487, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.05/2.40 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 2.05/2.40 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y,
% 2.05/2.40 'c_HOL_Oone__class_Oone'( X ), X ), Z, X ) ) ] )
% 2.05/2.40 , clause( 20488, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.05/2.40 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 2.05/2.40 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Z,
% 2.05/2.40 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ] )
% 2.05/2.40 , clause( 20489, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 2.05/2.40 =( 'c_HOL_Otimes__class_Otimes'( 'c_Polynomial_OpCons'( Y, Z, X ), T,
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Oplus__class_Oplus'(
% 2.05/2.40 'c_Polynomial_Osmult'( Y, T, X ), 'c_Polynomial_OpCons'(
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, T,
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), X ), 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 2.05/2.40 , clause( 20490, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 2.05/2.40 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_Polynomial_OpCons'( Z, T, X ),
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Oplus__class_Oplus'(
% 2.05/2.40 'c_Polynomial_Osmult'( Z, Y, X ), 'c_Polynomial_OpCons'(
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, T,
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), X ), 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 2.05/2.40 , clause( 20491, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 2.05/2.40 ~( =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_Polynomial_Osmult'( Z, T, X ),
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), 'c_Polynomial_OpCons'( U, T, X ) ) ), =( U
% 2.05/2.40 , 'c_Polynomial_Opoly'( Y, Z, X ) ) ] )
% 2.05/2.40 , clause( 20492, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.05/2.40 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20493, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.05/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 2.05/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 2.05/2.40 Z, X ) ) ] )
% 2.05/2.40 , clause( 20494, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.05/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 2.05/2.40 Z, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 2.05/2.40 , clause( 20495, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.05/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 2.05/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 2.05/2.40 ), X ) ) ] )
% 2.05/2.40 , clause( 20496, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.05/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 2.05/2.40 ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 2.05/2.40 , clause( 20497, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 2.05/2.40 , clause( 20498, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 2.05/2.40 , clause( 20499, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 2.05/2.40 , clause( 20500, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 2.05/2.40 ~( =( 'c_Polynomial_Osynthetic__div'( Y, Z, X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ), =(
% 2.05/2.40 'c_Polynomial_Odegree'( Y, X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 2.05/2.40 ] )
% 2.05/2.40 , clause( 20501, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 2.05/2.40 ~( =( 'c_Polynomial_Odegree'( Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_nat' ) ) ), =( 'c_Polynomial_Osynthetic__div'( Y, Z, X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 2.05/2.40 , clause( 20502, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 2.05/2.40 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.05/2.40 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.05/2.40 , clause( 20503, [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 2.05/2.40 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 2.05/2.40 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 2.05/2.40 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 2.05/2.40 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 2.05/2.40 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 2.05/2.40 X ), Z, X ) ) ] )
% 2.05/2.40 , clause( 20504, [ ~(
% 2.05/2.40 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.05/2.40 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.05/2.40 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 2.05/2.40 , clause( 20505, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 2.05/2.40 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 2.05/2.40 'c_HOL_Oplus__class_Oplus'( Z, Y, X ), X ), Z ) ] )
% 2.05/2.40 , clause( 20506, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.05/2.40 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 2.05/2.40 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), Z ) ] )
% 2.05/2.40 , clause( 20507, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 2.05/2.40 ) ) ) ] )
% 2.05/2.40 , clause( 20508, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 2.05/2.40 ) ) ) ] )
% 2.05/2.40 , clause( 20509, [ ~( 'class_HOL_Ozero'( X ) ), ~( 'class_HOL_Oeq'( X ) ),
% 2.05/2.40 =( Y, Z ), ~( 'c_HOL_Oeq__class_Oeq'( Y, Z, 'tc_Polynomial_Opoly'( X ) )
% 2.05/2.40 ) ] )
% 2.05/2.40 , clause( 20510, [ ~( 'class_HOL_Oeq'( X ) ), =( Y, Z ), ~(
% 2.05/2.40 'c_HOL_Oeq__class_Oeq'( Y, Z, X ) ) ] )
% 2.05/2.40 , clause( 20511, [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Ocoeff'(
% 2.05/2.40 'c_Polynomial_OpCons'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 2.05/2.40 , X ), Y ) ] )
% 2.05/2.40 , clause( 20512, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.05/2.40 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 2.05/2.40 , X ) ) ] )
% 2.05/2.40 , clause( 20513, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.05/2.40 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.05/2.40 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.05/2.40 , X ) ) ] )
% 2.05/2.40 , clause( 20514, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.05/2.40 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.05/2.40 , clause( 20515, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.05/2.40 'c_HOL_Oone__class_Oone'( X ), X ) ] )
% 2.05/2.40 , clause( 20516, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 2.05/2.40 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 2.05/2.40 , clause( 20517, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 2.05/2.40 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 2.05/2.40 , clause( 20518, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 2.05/2.40 'c_Polynomial_Opoly__gcd'( Y, Z, X ), 'c_Polynomial_Opoly__gcd'( Z, Y, X
% 2.05/2.40 ) ) ] )
% 2.05/2.40 , clause( 20519, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 2.05/2.40 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'(
% 2.05/2.40 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.05/2.40 , clause( 20520, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 2.05/2.40 =( 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'(
% 2.05/2.40 'c_HOL_Oone__class_Oone'( X ), X ) ) ), 'c_HOL_Oord__class_Oless'( Y,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ) ] )
% 2.05/2.40 , clause( 20521, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 2.05/2.40 X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 2.05/2.40 X ), X ) ) ] )
% 2.05/2.40 , clause( 20522, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 2.05/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_Opoly__gcd'( Y, Z, X
% 2.05/2.40 ), Z, 'tc_Polynomial_Opoly'( X ) ) ] )
% 2.05/2.40 , clause( 20523, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 2.05/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_Opoly__gcd'( Y, Z, X
% 2.05/2.40 ), Y, 'tc_Polynomial_Opoly'( X ) ) ] )
% 2.05/2.40 , clause( 20524, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 2.05/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Polynomial_Opoly__gcd'( Z, T
% 2.05/2.40 , X ), 'tc_Polynomial_Opoly'( X ) ), ~(
% 2.05/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, 'tc_Polynomial_Opoly'( X ) )
% 2.05/2.40 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_Polynomial_Opoly'(
% 2.05/2.40 X ) ) ) ] )
% 2.05/2.40 , clause( 20525, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 2.05/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Polynomial_Opoly__gcd'( Z, T
% 2.05/2.40 , X ), 'tc_Polynomial_Opoly'( X ) ), ~(
% 2.05/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, 'tc_Polynomial_Opoly'( X ) )
% 2.05/2.40 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_Polynomial_Opoly'(
% 2.05/2.40 X ) ) ) ] )
% 2.05/2.40 , clause( 20526, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.05/2.40 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T
% 2.05/2.40 , X ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), ~(
% 2.05/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ) ] )
% 2.05/2.40 , clause( 20527, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 2.05/2.40 ~( =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_Polynomial_Osmult'( Z, T, X ),
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), 'c_Polynomial_OpCons'( U, T, X ) ) ), =( T
% 2.05/2.40 , 'c_Polynomial_Osynthetic__div'( Y, Z, X ) ) ] )
% 2.05/2.40 , clause( 20528, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.05/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.05/2.40 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 2.05/2.40 ) ) ] )
% 2.05/2.40 , clause( 20529, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.05/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.05/2.40 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 2.05/2.40 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 2.05/2.40 ) ] )
% 2.05/2.40 , clause( 20530, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =(
% 2.05/2.40 'c_Polynomial_Ocoeff'( Y, 'c_Polynomial_Odegree'( Y, X ), X ),
% 2.05/2.40 'c_Polynomial_Ocoeff'( Z, 'c_Polynomial_Odegree'( Z, X ), X ) ) ), =( Y,
% 2.05/2.40 Z ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y,
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'(
% 2.05/2.40 Y, Z, 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 2.05/2.40 , clause( 20531, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 2.05/2.40 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 2.05/2.40 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ) ] )
% 2.05/2.40 , clause( 20532, [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 2.05/2.40 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ) ] )
% 2.05/2.40 , clause( 20533, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 2.05/2.40 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 2.05/2.40 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 2.05/2.40 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 2.05/2.40 X ) ) ] )
% 2.05/2.40 , clause( 20534, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.05/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 2.05/2.40 , X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 2.05/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Z, U, X ) ), ~(
% 2.05/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 2.05/2.40 , clause( 20535, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.05/2.40 =( 'c_Polynomial_Opoly'( 'c_HOL_Oone__class_Oone'( 'tc_Polynomial_Opoly'(
% 2.05/2.40 X ) ), Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 2.05/2.40 , clause( 20536, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 2.05/2.40 'c_HOL_Ominus__class_Ominus'( 'c_Polynomial_Omonom'( Y, Z, X ),
% 2.05/2.40 'c_Polynomial_Omonom'( T, Z, X ), 'tc_Polynomial_Opoly'( X ) ),
% 2.05/2.40 'c_Polynomial_Omonom'( 'c_HOL_Ominus__class_Ominus'( Y, T, X ), Z, X ) )
% 2.05/2.40 ] )
% 2.05/2.40 , clause( 20537, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.05/2.40 X ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oplus__class_Oplus'(
% 2.05/2.40 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 2.05/2.40 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 2.05/2.40 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ] )
% 2.05/2.40 , clause( 20538, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.05/2.40 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.05/2.40 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ) ]
% 2.05/2.40 )
% 2.05/2.40 , clause( 20539, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.05/2.40 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.05/2.40 , clause( 20540, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.05/2.40 , clause( 20541, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.05/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.05/2.40 , clause( 20542, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.05/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.05/2.40 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.05/2.40 , clause( 20543, [ ~(
% 2.05/2.40 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 2.05/2.40 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.05/2.40 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 2.05/2.40 X ), X ) ) ] )
% 2.05/2.40 , clause( 20544, [ ~(
% 2.05/2.40 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.05/2.40 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.05/2.40 Z, T, X ) ) ] )
% 2.05/2.40 , clause( 20545, [ ~(
% 2.05/2.40 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.05/2.40 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.05/2.40 Z, T, X ) ) ] )
% 2.05/2.40 , clause( 20546, [ ~(
% 2.05/2.40 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 2.05/2.40 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.05/2.40 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 2.05/2.40 X ), X ) ) ] )
% 2.05/2.40 , clause( 20547, [ ~(
% 2.05/2.40 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.05/2.40 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.05/2.40 Y, T, X ) ) ] )
% 2.05/2.40 , clause( 20548, [ ~(
% 2.05/2.40 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.05/2.40 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.05/2.40 Y, T, X ) ) ] )
% 2.05/2.40 , clause( 20549, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 2.05/2.40 =( 'c_Polynomial_Opoly'( 'c_Polynomial_OpCons'( Y, Z, X ), T, X ),
% 2.05/2.40 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 2.05/2.40 'c_Polynomial_Opoly'( Z, T, X ), X ), X ) ) ] )
% 2.05/2.40 , clause( 20550, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.05/2.40 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 2.05/2.40 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20551, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.05/2.40 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 2.05/2.40 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20552, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.05/2.40 ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 2.05/2.40 ) ) ] )
% 2.05/2.40 , clause( 20553, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ),
% 2.05/2.40 'c_Polynomial_Opdivmod__rel'( 'c_HOL_Oplus__class_Oplus'(
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_Polynomial_Opoly'( X ) ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ),
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), Y, Z, 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), X ) ] )
% 2.05/2.40 , clause( 20554, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.05/2.40 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.05/2.40 , Y, X ), X ) ) ] )
% 2.05/2.40 , clause( 20555, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.05/2.40 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.05/2.40 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 2.05/2.40 , T, X ), X ) ) ] )
% 2.05/2.40 , clause( 20556, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.05/2.40 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 2.05/2.40 , T, X ), X ) ) ] )
% 2.05/2.40 , clause( 20557, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.05/2.40 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.05/2.40 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.05/2.40 , Y, X ), X ) ) ] )
% 2.05/2.40 , clause( 20558, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.05/2.40 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 2.05/2.40 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 2.05/2.40 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), T, X ) ) ] )
% 2.05/2.40 , clause( 20559, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.05/2.40 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.05/2.40 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 2.05/2.40 , clause( 20560, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.05/2.40 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.05/2.40 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.05/2.40 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.05/2.40 , clause( 20561, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.05/2.40 =( 'c_Polynomial_Ocoeff'( 'c_HOL_Oone__class_Oone'( 'tc_Polynomial_Opoly'(
% 2.05/2.40 X ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X ),
% 2.05/2.40 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 2.05/2.40 , clause( 20562, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 2.05/2.40 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 2.05/2.40 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ) ), =( U,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 2.05/2.40 ), =( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( T, Z, X ) ) ] )
% 2.05/2.40 , clause( 20563, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.05/2.40 , U, X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( U,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 2.05/2.40 , U, X ), 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ] )
% 2.05/2.40 , clause( 20564, [ ~( 'class_RealVector_Oreal__normed__div__algebra'( X ) )
% 2.05/2.40 , =( 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X
% 2.05/2.40 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Osgn__class_Osgn'( Y, X ),
% 2.05/2.40 'c_HOL_Osgn__class_Osgn'( Z, X ), X ) ) ] )
% 2.05/2.40 , clause( 20565, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 2.05/2.40 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Osgn__class_Osgn'( Y, X ),
% 2.05/2.40 'c_HOL_Osgn__class_Osgn'( Z, X ), X ) ) ] )
% 2.05/2.40 , clause( 20566, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.05/2.40 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Omod'( Z, T, X )
% 2.05/2.40 , X ) ) ] )
% 2.05/2.40 , clause( 20567, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.05/2.40 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z
% 2.05/2.40 , X ) ) ] )
% 2.05/2.40 , clause( 20568, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.05/2.40 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 2.05/2.40 ) ] )
% 2.05/2.40 , clause( 20569, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.05/2.40 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 2.05/2.40 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 2.05/2.40 ] )
% 2.05/2.40 , clause( 20570, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.05/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.05/2.40 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y, X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20571, [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_Omonom'(
% 2.05/2.40 Y, Z, X ), 'c_Polynomial_Omonom'( T, Z, X ) ) ), =( Y, T ) ] )
% 2.05/2.40 , clause( 20572, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 2.05/2.40 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.05/2.40 , clause( 20573, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 2.05/2.40 =( 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ] )
% 2.05/2.40 , clause( 20574, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 2.05/2.40 =( 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 2.05/2.40 , 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ] )
% 2.05/2.40 , clause( 20575, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.05/2.40 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X
% 2.05/2.40 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 2.05/2.40 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 2.05/2.40 , clause( 20576, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 2.05/2.40 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X
% 2.05/2.40 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 2.05/2.40 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ] )
% 2.05/2.40 , clause( 20577, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 2.05/2.40 Y, X ) ) ] )
% 2.05/2.40 , clause( 20578, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 2.05/2.40 Y, X ) ) ] )
% 2.05/2.40 , clause( 20579, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 2.05/2.40 Y, X ) ) ] )
% 2.05/2.40 , clause( 20580, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 2.05/2.40 Y, X ) ) ] )
% 2.05/2.40 , clause( 20581, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 2.05/2.40 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.05/2.40 ) ] )
% 2.05/2.40 , clause( 20582, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.05/2.40 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.05/2.40 ) ] )
% 2.05/2.40 , clause( 20583, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.05/2.40 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 2.05/2.40 ) ] )
% 2.05/2.40 , clause( 20584, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.05/2.40 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.05/2.40 ) ] )
% 2.05/2.40 , clause( 20585, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 2.05/2.40 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y,
% 2.05/2.40 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20586, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 2.05/2.40 'class_Int_Onumber__ring'( X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y
% 2.05/2.40 , Z, X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20587, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.05/2.40 , =( 'c_OrderedGroup_Olordered__ab__group__add__class_Opprt'(
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 2.05/2.40 )
% 2.05/2.40 , clause( 20588, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.05/2.40 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20589, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.05/2.40 , =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 2.05/2.40 )
% 2.05/2.40 , clause( 20590, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.05/2.40 X ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X )
% 2.05/2.40 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20591, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 2.05/2.40 ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ] )
% 2.05/2.40 , clause( 20592, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 2.05/2.40 'c_RealVector_OscaleR__class_OscaleR'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 2.05/2.40 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20593, [ ~( 'class_RealVector_Oreal__vector'( X ) ), =(
% 2.05/2.40 'c_RealVector_OscaleR__class_OscaleR'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 2.05/2.40 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20594, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 2.05/2.40 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.05/2.40 ) ), =( Y, Z ) ] )
% 2.05/2.40 , clause( 20595, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 2.05/2.40 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.05/2.40 ) ), =( Y, Z ) ] )
% 2.05/2.40 , clause( 20596, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 2.05/2.40 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y,
% 2.05/2.40 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ] )
% 2.05/2.40 , clause( 20597, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 2.05/2.40 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 2.05/2.40 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20598, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.05/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.05/2.40 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 2.05/2.40 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20599, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.05/2.40 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.05/2.40 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 2.05/2.40 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20600, [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 2.05/2.40 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 2.05/2.40 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20601, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 2.05/2.40 =( 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 2.05/2.40 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20602, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 2.05/2.40 =( 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 2.05/2.40 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20603, [ ~( 'class_SEQ_Obanach'( X ) ), ~(
% 2.05/2.40 'class_RealVector_Oreal__normed__field'( X ) ), ~( =(
% 2.05/2.40 'c_Transcendental_Oexp'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ] )
% 2.05/2.40 , clause( 20604, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 2.05/2.40 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 2.05/2.40 ] )
% 2.05/2.40 , clause( 20605, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 2.05/2.40 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 2.05/2.40 ] )
% 2.05/2.40 , clause( 20606, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 2.05/2.40 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 2.05/2.40 ] )
% 2.05/2.40 , clause( 20607, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 2.05/2.40 'class_Int_Onumber__ring'( X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.05/2.40 , clause( 20608, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.05/2.40 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 2.05/2.40 ) ] )
% 2.05/2.40 , clause( 20609, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 2.05/2.40 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 2.05/2.40 ] )
% 2.05/2.40 , clause( 20610, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.05/2.40 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 2.05/2.40 ) ] )
% 2.05/2.40 , clause( 20611, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.05/2.40 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 2.05/2.40 ) ] )
% 2.05/2.40 , clause( 20612, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.05/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_Osmult'(
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Z, 'tc_Polynomial_Opoly'( X ) )
% 2.05/2.40 ), =( Z, 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 2.05/2.40 , clause( 20613, [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Ocoeff'(
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ),
% 2.05/2.40 'c_Polynomial_Odegree'( 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'(
% 2.05/2.40 X ) ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20614, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 2.05/2.40 =( 'c_Polynomial_Osynthetic__divmod'( 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), Y, X ), 'c_Pair'(
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), 'tc_Polynomial_Opoly'( X ), X ) ) ] )
% 2.05/2.40 , clause( 20615, [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_Ocoeff'(
% 2.05/2.40 Y, 'c_Polynomial_Odegree'( Y, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 2.05/2.40 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 2.05/2.40 , clause( 20616, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 2.05/2.40 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Polynomial_Osmult'(
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ) ] )
% 2.05/2.40 , clause( 20617, [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Omonom'( Y
% 2.05/2.40 , 'c_Suc'( Z ), X ), 'c_Polynomial_OpCons'( 'c_HOL_Ozero__class_Ozero'( X
% 2.05/2.40 ), 'c_Polynomial_Omonom'( Y, Z, X ), X ) ) ] )
% 2.05/2.40 , clause( 20618, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 2.05/2.40 'c_Polynomial_Opos__poly'( Z, X ), ~( 'c_Polynomial_Opos__poly'(
% 2.05/2.40 'c_Polynomial_OpCons'( Y, Z, X ), X ) ) ] )
% 2.05/2.40 , clause( 20619, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 2.05/2.40 =( 'c_Polynomial_Osmult'( Y, 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 2.05/2.40 , clause( 20620, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =(
% 2.05/2.40 'c_Polynomial_Osmult'( Y, 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 2.05/2.40 , clause( 20621, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 2.05/2.40 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 2.05/2.40 , clause( 20622, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 2.05/2.40 =( 'c_Polynomial_Osynthetic__div'( 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 2.05/2.40 , clause( 20623, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 2.05/2.40 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 2.05/2.40 , clause( 20624, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 2.05/2.40 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 2.05/2.40 , clause( 20625, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 2.05/2.40 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), Y, 'tc_Polynomial_Opoly'( X ) ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 2.05/2.40 , clause( 20626, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 2.05/2.40 'c_Polynomial_Opdivmod__rel'( Y, 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), Y, X ) ] )
% 2.05/2.40 , clause( 20627, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 2.05/2.40 ~( =( 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly'( Y, Z, X
% 2.05/2.40 ), 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ), =( Y,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 2.05/2.40 , clause( 20628, [ ~( 'class_Ring__and__Field_Ofield'( X ) ),
% 2.05/2.40 'c_Polynomial_Opdivmod__rel'( 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), Y, 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), X ) ] )
% 2.05/2.40 , clause( 20629, [ ~( 'class_HOL_Ozero'( X ) ), ~( 'class_HOL_Oeq'( X ) ),
% 2.05/2.40 'c_HOL_Oeq__class_Oeq'( 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'(
% 2.05/2.40 X ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ),
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ) ] )
% 2.05/2.40 , clause( 20630, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 2.05/2.40 'c_Polynomial_Opoly__gcd'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 2.05/2.40 , clause( 20631, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 2.05/2.40 'c_Polynomial_Opoly__gcd'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 2.05/2.40 , clause( 20632, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ), ~(
% 2.05/2.40 'c_Polynomial_Opdivmod__rel'( Z, 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), Y, T, X ) ) ] )
% 2.05/2.40 , clause( 20633, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ), ~(
% 2.05/2.40 'c_Polynomial_Opdivmod__rel'( 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), Z, T, Y, X ) ) ] )
% 2.05/2.40 , clause( 20634, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ), ~(
% 2.05/2.40 'c_Polynomial_Opdivmod__rel'( 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), Z, Y, T, X ) ) ] )
% 2.05/2.40 , clause( 20635, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.05/2.40 'c_Polynomial_Opdivmod__rel'( Y, 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), Z, T, X ) ), =( Z,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 2.05/2.40 , clause( 20636, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y, Z ),
% 2.05/2.40 ~( 'c_Polynomial_Opdivmod__rel'( Z, 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), T, Y, X ) ) ] )
% 2.05/2.40 , clause( 20637, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 2.05/2.40 'c_Polynomial_Opoly__gcd'( 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 2.05/2.40 , clause( 20638, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 2.05/2.40 'c_Polynomial_Opos__poly'( 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), X ) ) ] )
% 2.05/2.40 , clause( 20639, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 2.05/2.40 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ), Y ) ] )
% 2.05/2.40 , clause( 20640, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 2.05/2.40 =( 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly'(
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), Y, X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 2.05/2.40 , clause( 20641, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 2.05/2.40 =( 'c_Polynomial_Opcompose'( 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 2.05/2.40 , clause( 20642, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 2.05/2.40 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), Y, 'tc_Polynomial_Opoly'( X ) ), Y ) ] )
% 2.05/2.40 , clause( 20643, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 2.05/2.40 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ), Y ) ] )
% 2.05/2.40 , clause( 20644, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 2.05/2.40 'c_Polynomial_Opdivmod'( 'c_Polynomial_OpCons'( Y, Z, X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ), 'c_Pair'(
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ),
% 2.05/2.40 'c_Polynomial_OpCons'( Y, Z, X ), 'tc_Polynomial_Opoly'( X ),
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 2.05/2.40 , clause( 20645, [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Odegree'(
% 2.05/2.40 'c_Polynomial_OpCons'( Y, 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_nat' ) ) ] )
% 2.05/2.40 , clause( 20646, [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Omonom'( Y
% 2.05/2.40 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X ), 'c_Polynomial_OpCons'( Y,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ) ) ] )
% 2.05/2.40 , clause( 20647, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.05/2.40 =( 'c_HOL_Oone__class_Oone'( 'tc_Polynomial_Opoly'( X ) ),
% 2.05/2.40 'c_Polynomial_OpCons'( 'c_HOL_Oone__class_Oone'( X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ) ) ] )
% 2.05/2.40 , clause( 20648, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 2.05/2.40 ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_Polynomial_Osmult'( Y, Z, X ),
% 2.05/2.40 'c_Polynomial_OpCons'( T, Z, X ), 'tc_Polynomial_Opoly'( X ) ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ), =( Z,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 2.05/2.40 , clause( 20649, [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Odegree'(
% 2.05/2.40 'c_Polynomial_OpCons'( Y, Z, X ), X ), 'c_Suc'( 'c_Polynomial_Odegree'( Z
% 2.05/2.40 , X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) )
% 2.05/2.40 ) ] )
% 2.05/2.40 , clause( 20650, [ ~( 'class_HOL_Ozero'( X ) ), ~( 'class_HOL_Oeq'( X ) ),
% 2.05/2.40 'c_HOL_Oeq__class_Oeq'( Y, Z, 'tc_Polynomial_Opoly'( X ) ), ~(
% 2.05/2.40 'c_HOL_Oeq__class_Oeq'( 'c_Polynomial_OpCons'( T, Y, X ),
% 2.05/2.40 'c_Polynomial_OpCons'( U, Z, X ), 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 2.05/2.40 , clause( 20651, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.05/2.40 'c_Polynomial_Opos__poly'( 'c_Polynomial_OpCons'( Y, Z, X ), X ), ~(
% 2.05/2.40 'c_Polynomial_Opos__poly'( Z, X ) ) ] )
% 2.05/2.40 , clause( 20652, [ ~( =( 'v_sko__local__XpCons__Xhyps__1'( 'v_ds____' ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Complex_Ocomplex' ) ) ), =( 'v_ds____',
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( 'tc_Complex_Ocomplex'
% 2.05/2.40 ) ) ) ] )
% 2.05/2.40 , clause( 20653, [ ~( =( 'v_sko__local__XpCons__1__1'( 'v_ds____' ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Complex_Ocomplex' ) ) ), =( 'v_ds____',
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( 'tc_Complex_Ocomplex'
% 2.05/2.40 ) ) ) ] )
% 2.05/2.40 , clause( 20654, [ ~( =( 'v_d____', 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Complex_Ocomplex' ) ) ) ] )
% 2.05/2.40 , clause( 20655, [ ~( 'class_HOL_Ozero'( X ) ), ~( 'class_HOL_Oeq'( X ) ),
% 2.05/2.40 'c_HOL_Oeq__class_Oeq'( 'c_Polynomial_OpCons'( Y, Z, X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ),
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), ~( 'c_HOL_Oeq__class_Oeq'( Z,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ),
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ) ), ~( 'c_HOL_Oeq__class_Oeq'( Y,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.05/2.40 , clause( 20656, [ ~( 'class_HOL_Ozero'( X ) ), ~( 'class_HOL_Oeq'( X ) ),
% 2.05/2.40 'c_HOL_Oeq__class_Oeq'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.05/2.40 'c_HOL_Oeq__class_Oeq'( 'c_Polynomial_OpCons'( Y, Z, X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ),
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 2.05/2.40 , clause( 20657, [ ~( 'class_HOL_Ozero'( X ) ), ~( 'class_HOL_Oeq'( X ) ),
% 2.05/2.40 'c_HOL_Oeq__class_Oeq'( 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'(
% 2.05/2.40 X ) ), 'c_Polynomial_OpCons'( Y, Z, X ), 'tc_Polynomial_Opoly'( X ) ),
% 2.05/2.40 ~( 'c_HOL_Oeq__class_Oeq'( 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), Z, 'tc_Polynomial_Opoly'( X ) ) ), ~(
% 2.05/2.40 'c_HOL_Oeq__class_Oeq'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.05/2.40 , clause( 20658, [ ~( 'class_HOL_Ozero'( X ) ), ~( 'class_HOL_Oeq'( X ) ),
% 2.05/2.40 'c_HOL_Oeq__class_Oeq'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.05/2.40 'c_HOL_Oeq__class_Oeq'( 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'(
% 2.05/2.40 X ) ), 'c_Polynomial_OpCons'( Y, Z, X ), 'tc_Polynomial_Opoly'( X ) ) ) ]
% 2.05/2.40 )
% 2.05/2.40 , clause( 20659, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.05/2.40 'c_Polynomial_Opos__poly'( 'c_Polynomial_OpCons'( Y,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ), X ), ~(
% 2.05/2.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.05/2.40 , clause( 20660, [ ~( =( 'v_p', 'c_Polynomial_OpCons'( X,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( 'tc_Complex_Ocomplex'
% 2.05/2.40 ) ), 'tc_Complex_Ocomplex' ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Complex_Ocomplex' ) ) ] )
% 2.05/2.40 , clause( 20661, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 2.05/2.40 =( 'c_Polynomial_Osmult'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 2.05/2.40 , clause( 20662, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =(
% 2.05/2.40 'c_Polynomial_Osmult'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 2.05/2.40 , clause( 20663, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =(
% 2.05/2.40 'c_Polynomial_Osmult'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 2.05/2.40 )
% 2.05/2.40 , clause( 20664, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 2.05/2.40 =( 'c_Polynomial_Opoly'( 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 2.05/2.40 )
% 2.05/2.40 , clause( 20665, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =(
% 2.05/2.40 'c_Polynomial_Opoly'( 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'(
% 2.05/2.40 X ) ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20666, [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_Omonom'(
% 2.05/2.40 Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ),
% 2.05/2.40 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20667, [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Omonom'(
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 2.05/2.40 , clause( 20668, [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Ocoeff'(
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), Y, X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20669, [ ~( 'class_HOL_Ozero'( X ) ), ~( 'class_HOL_Oeq'( X ) ),
% 2.05/2.40 'c_HOL_Oeq__class_Oeq'( Y, 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ), ~(
% 2.05/2.40 'c_HOL_Oeq__class_Oeq'( 'c_Polynomial_OpCons'( Z, Y, X ),
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ),
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 2.05/2.40 , clause( 20670, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y
% 2.05/2.40 , 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ),
% 2.05/2.40 'c_Polynomial_Opos__poly'( Y, X ), ~( 'c_Polynomial_Opos__poly'(
% 2.05/2.40 'c_Polynomial_OpCons'( Z, Y, X ), X ) ) ] )
% 2.05/2.40 , clause( 20671, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 2.05/2.40 =( 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly'(
% 2.05/2.40 'c_Polynomial_OpCons'( Y, 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), X ), Z, X ), 'c_Polynomial_OpCons'( Y,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ) ) ] )
% 2.05/2.40 , clause( 20672, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ),
% 2.05/2.40 ~( =( 'c_Polynomial_Osmult'( Y, Z, X ), 'c_Polynomial_OpCons'( T, Z, X )
% 2.05/2.40 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ]
% 2.05/2.40 )
% 2.05/2.40 , clause( 20673, [ ~( 'class_HOL_Ozero'( X ) ), ~( 'class_HOL_Oeq'( X ) ),
% 2.05/2.40 'c_HOL_Oeq__class_Oeq'( 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'(
% 2.05/2.40 X ) ), Y, 'tc_Polynomial_Opoly'( X ) ), ~( 'c_HOL_Oeq__class_Oeq'(
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ),
% 2.05/2.40 'c_Polynomial_OpCons'( Z, Y, X ), 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 2.05/2.40 , clause( 20674, [ =( 'c_Polynomial_Opoly'( 'c_Polynomial_OpCons'(
% 2.05/2.40 'v_d____', 'v_ds____', 'tc_Complex_Ocomplex' ), X, 'tc_Complex_Ocomplex'
% 2.05/2.40 ), 'c_HOL_Ozero__class_Ozero'( 'tc_Complex_Ocomplex' ) ), =( X,
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( 'tc_Complex_Ocomplex' ) ) ] )
% 2.05/2.40 , clause( 20675, [ ~( =( 'v_d____', 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Complex_Ocomplex' ) ) ), =( 'c_Polynomial_OpCons'( 'v_d____',
% 2.05/2.40 'v_ds____', 'tc_Complex_Ocomplex' ), 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( 'tc_Complex_Ocomplex' ) ) ) ] )
% 2.05/2.40 , clause( 20676, [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_OpCons'(
% 2.05/2.40 Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ),
% 2.05/2.40 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.05/2.40 , clause( 20677, [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_OpCons'(
% 2.05/2.40 Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ),
% 2.05/2.40 =( Z, 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 2.05/2.40 , clause( 20678, [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_OpCons'(
% 2.05/2.40 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 2.05/2.40 , clause( 20679, [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_OpCons'(
% 2.05/2.40 Y, Z, X ), 'c_Polynomial_OpCons'( T, U, X ) ) ), =( Y, T ) ] )
% 2.05/2.40 , clause( 20680, [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_OpCons'(
% 2.05/2.40 Y, Z, X ), 'c_Polynomial_OpCons'( T, U, X ) ) ), =( Z, U ) ] )
% 2.05/2.40 , clause( 20681, [ ~( =( 'c_RealVector_Onorm__class_Onorm'(
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( 'c_RealVector_Oof__real'( 'v_x____',
% 2.05/2.40 'tc_Complex_Ocomplex' ), 'c_Polynomial_Opoly'( 'v_ds____',
% 2.05/2.40 'c_RealVector_Oof__real'( 'v_x____', 'tc_Complex_Ocomplex' ),
% 2.05/2.40 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' )
% 2.05/2.40 , 'c_RealVector_Onorm__class_Onorm'( 'v_d____', 'tc_Complex_Ocomplex' ) )
% 2.05/2.40 ) ] )
% 2.05/2.40 , clause( 20682, [ =( 'c_RealVector_Onorm__class_Onorm'(
% 2.05/2.40 'c_HOL_Otimes__class_Otimes'( 'c_RealVector_Oof__real'( 'v_x____',
% 2.05/2.40 'tc_Complex_Ocomplex' ), 'c_Polynomial_Opoly'( 'v_ds____',
% 2.05/2.40 'c_RealVector_Oof__real'( 'v_x____', 'tc_Complex_Ocomplex' ),
% 2.05/2.40 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' )
% 2.05/2.40 , 'c_RealVector_Onorm__class_Onorm'( 'v_d____', 'tc_Complex_Ocomplex' ) )
% 2.05/2.40 ] )
% 2.05/2.40 , clause( 20683, [ ~( =( 'c_Polynomial_OpCons'( 'v_d____', 'v_ds____',
% 2.05/2.40 'tc_Complex_Ocomplex' ), 'c_HOL_Ozero__class_Ozero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( 'tc_Complex_Ocomplex' ) ) ) ) ] )
% 2.05/2.40 , clause( 20684, [ 'class_OrderedGroup_Ocancel__comm__monoid__add'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), ~(
% 2.05/2.40 'class_OrderedGroup_Ocancel__comm__monoid__add'( X ) ) ] )
% 2.05/2.40 , clause( 20685, [ 'class_OrderedGroup_Ocancel__comm__monoid__add'(
% 2.05/2.40 'tc_Complex_Ocomplex' ) ] )
% 2.05/2.40 , clause( 20686, [ 'class_OrderedGroup_Ocancel__comm__monoid__add'(
% 2.05/2.40 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20687, [ 'class_OrderedGroup_Ocancel__comm__monoid__add'(
% 2.05/2.40 'tc_nat' ) ] )
% 2.05/2.40 , clause( 20688, [ 'class_HOL_Oeq'( 'tc_prod'( X, Y ) ) ] )
% 2.05/2.40 , clause( 20689, [
% 2.05/2.40 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' ) ]
% 2.05/2.40 )
% 2.05/2.40 , clause( 20690, [
% 2.05/2.40 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat' ) ]
% 2.05/2.40 )
% 2.05/2.40 , clause( 20691, [
% 2.05/2.40 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' ) ]
% 2.05/2.40 )
% 2.05/2.40 , clause( 20692, [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.05/2.40 'tc_nat' ) ] )
% 2.05/2.40 , clause( 20693, [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 2.05/2.40 'tc_nat' ) ] )
% 2.05/2.40 , clause( 20694, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 2.05/2.40 'tc_nat' ) ] )
% 2.05/2.40 , clause( 20695, [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' )
% 2.05/2.40 ] )
% 2.05/2.40 , clause( 20696, [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' )
% 2.05/2.40 ] )
% 2.05/2.40 , clause( 20697, [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ]
% 2.05/2.40 )
% 2.05/2.40 , clause( 20698, [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' )
% 2.05/2.40 ] )
% 2.05/2.40 , clause( 20699, [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_nat' )
% 2.05/2.40 ] )
% 2.05/2.40 , clause( 20700, [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ]
% 2.05/2.40 )
% 2.05/2.40 , clause( 20701, [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ]
% 2.05/2.40 )
% 2.05/2.40 , clause( 20702, [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ]
% 2.05/2.40 )
% 2.05/2.40 , clause( 20703, [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ]
% 2.05/2.40 )
% 2.05/2.40 , clause( 20704, [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ] )
% 2.05/2.40 , clause( 20705, [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ]
% 2.05/2.40 )
% 2.05/2.40 , clause( 20706, [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ] )
% 2.05/2.40 , clause( 20707, [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ] )
% 2.05/2.40 , clause( 20708, [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ] )
% 2.05/2.40 , clause( 20709, [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ] )
% 2.05/2.40 , clause( 20710, [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ] )
% 2.05/2.40 , clause( 20711, [ 'class_Ring__and__Field_Odvd'( 'tc_nat' ) ] )
% 2.05/2.40 , clause( 20712, [ 'class_Orderings_Opreorder'( 'tc_nat' ) ] )
% 2.05/2.40 , clause( 20713, [ 'class_Orderings_Olinorder'( 'tc_nat' ) ] )
% 2.05/2.40 , clause( 20714, [ 'class_Orderings_Oorder'( 'tc_nat' ) ] )
% 2.05/2.40 , clause( 20715, [ 'class_HOL_Ozero'( 'tc_nat' ) ] )
% 2.05/2.40 , clause( 20716, [ 'class_HOL_Oeq'( 'tc_nat' ) ] )
% 2.05/2.40 , clause( 20717, [
% 2.05/2.40 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 2.05/2.40 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20718, [
% 2.05/2.40 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 2.05/2.40 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20719, [
% 2.05/2.40 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 2.05/2.40 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20720, [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.05/2.40 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20721, [ 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.05/2.40 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20722, [ 'class_OrderedGroup_Olordered__ab__group__add__abs'(
% 2.05/2.40 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20723, [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 2.05/2.40 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20724, [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 2.05/2.40 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20725, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 2.05/2.40 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20726, [ 'class_Ring__and__Field_Oordered__ring__strict'(
% 2.05/2.40 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20727, [ 'class_RealVector_Oreal__normed__div__algebra'(
% 2.05/2.40 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20728, [ 'class_OrderedGroup_Opordered__ab__group__add'(
% 2.05/2.40 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20729, [ 'class_OrderedGroup_Olordered__ab__group__add'(
% 2.05/2.40 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20730, [ 'class_OrderedGroup_Oordered__ab__group__add'(
% 2.05/2.40 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20731, [ 'class_OrderedGroup_Ocancel__semigroup__add'(
% 2.05/2.40 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20732, [ 'class_RealVector_Oreal__normed__algebra__1'(
% 2.05/2.40 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20733, [ 'class_Ring__and__Field_Ono__zero__divisors'(
% 2.05/2.40 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20734, [ 'class_Ring__and__Field_Odivision__by__zero'(
% 2.05/2.40 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20735, [ 'class_Ring__and__Field_Oordered__semidom'(
% 2.05/2.40 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20736, [ 'class_Ring__and__Field_Ocomm__semiring__1'(
% 2.05/2.40 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20737, [ 'class_Ring__and__Field_Ocomm__semiring__0'(
% 2.05/2.40 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20738, [ 'class_RealVector_Oreal__normed__algebra'(
% 2.05/2.40 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20739, [ 'class_OrderedGroup_Oab__semigroup__mult'(
% 2.05/2.40 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20740, [ 'class_RealVector_Oreal__normed__vector'(
% 2.05/2.40 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20741, [ 'class_OrderedGroup_Ocomm__monoid__mult'(
% 2.05/2.40 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20742, [ 'class_OrderedGroup_Oab__semigroup__add'(
% 2.05/2.40 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20743, [ 'class_Ring__and__Field_Opordered__ring'(
% 2.05/2.40 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20744, [ 'class_Ring__and__Field_Oordered__field'(
% 2.05/2.40 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20745, [ 'class_Ring__and__Field_Ocomm__semiring'(
% 2.05/2.40 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20746, [ 'class_RealVector_Oreal__normed__field'(
% 2.05/2.40 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20747, [ 'class_OrderedGroup_Ocomm__monoid__add'(
% 2.05/2.40 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20748, [ 'class_Ring__and__Field_Ozero__neq__one'(
% 2.05/2.40 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20749, [ 'class_Ring__and__Field_Oordered__idom'(
% 2.05/2.40 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20750, [ 'class_Ring__and__Field_Ocomm__ring__1'(
% 2.05/2.40 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20751, [ 'class_OrderedGroup_Oab__group__add'( 'tc_RealDef_Oreal'
% 2.05/2.40 ) ] )
% 2.05/2.40 , clause( 20752, [ 'class_Ring__and__Field_Omult__zero'( 'tc_RealDef_Oreal'
% 2.05/2.40 ) ] )
% 2.05/2.40 , clause( 20753, [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_RealDef_Oreal'
% 2.05/2.40 ) ] )
% 2.05/2.40 , clause( 20754, [ 'class_OrderedGroup_Omonoid__mult'( 'tc_RealDef_Oreal' )
% 2.05/2.40 ] )
% 2.05/2.40 , clause( 20755, [ 'class_Ring__and__Field_Osemiring'( 'tc_RealDef_Oreal' )
% 2.05/2.40 ] )
% 2.05/2.40 , clause( 20756, [ 'class_RealVector_Oreal__algebra'( 'tc_RealDef_Oreal' )
% 2.05/2.40 ] )
% 2.05/2.40 , clause( 20757, [ 'class_OrderedGroup_Omonoid__add'( 'tc_RealDef_Oreal' )
% 2.05/2.40 ] )
% 2.05/2.40 , clause( 20758, [ 'class_RealVector_Oreal__vector'( 'tc_RealDef_Oreal' ) ]
% 2.05/2.40 )
% 2.05/2.40 , clause( 20759, [ 'class_OrderedGroup_Ogroup__add'( 'tc_RealDef_Oreal' ) ]
% 2.05/2.40 )
% 2.05/2.40 , clause( 20760, [ 'class_Ring__and__Field_Osgn__if'( 'tc_RealDef_Oreal' )
% 2.05/2.40 ] )
% 2.05/2.40 , clause( 20761, [ 'class_Ring__and__Field_Oabs__if'( 'tc_RealDef_Oreal' )
% 2.05/2.40 ] )
% 2.05/2.40 , clause( 20762, [ 'class_RealVector_Oreal__field'( 'tc_RealDef_Oreal' ) ]
% 2.05/2.40 )
% 2.05/2.40 , clause( 20763, [ 'class_Ring__and__Field_Ofield'( 'tc_RealDef_Oreal' ) ]
% 2.05/2.40 )
% 2.05/2.40 , clause( 20764, [ 'class_Ring__and__Field_Oring'( 'tc_RealDef_Oreal' ) ]
% 2.05/2.40 )
% 2.05/2.40 , clause( 20765, [ 'class_Ring__and__Field_Oidom'( 'tc_RealDef_Oreal' ) ]
% 2.05/2.40 )
% 2.05/2.40 , clause( 20766, [ 'class_Ring__and__Field_Odvd'( 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20767, [ 'class_Orderings_Opreorder'( 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20768, [ 'class_Orderings_Olinorder'( 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20769, [ 'class_Orderings_Oorder'( 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20770, [ 'class_Int_Onumber__ring'( 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20771, [ 'class_SEQ_Obanach'( 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20772, [ 'class_HOL_Ozero'( 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20773, [ 'class_HOL_Oeq'( 'tc_RealDef_Oreal' ) ] )
% 2.05/2.40 , clause( 20774, [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 2.05/2.40 'tc_Complex_Ocomplex' ) ] )
% 2.05/2.40 , clause( 20775, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 2.05/2.40 'tc_Complex_Ocomplex' ) ] )
% 2.05/2.40 , clause( 20776, [ 'class_RealVector_Oreal__normed__div__algebra'(
% 2.05/2.40 'tc_Complex_Ocomplex' ) ] )
% 2.05/2.40 , clause( 20777, [ 'class_OrderedGroup_Ocancel__semigroup__add'(
% 2.05/2.40 'tc_Complex_Ocomplex' ) ] )
% 2.05/2.40 , clause( 20778, [ 'class_RealVector_Oreal__normed__algebra__1'(
% 2.05/2.40 'tc_Complex_Ocomplex' ) ] )
% 2.05/2.40 , clause( 20779, [ 'class_Ring__and__Field_Ono__zero__divisors'(
% 2.05/2.40 'tc_Complex_Ocomplex' ) ] )
% 2.05/2.40 , clause( 20780, [ 'class_Ring__and__Field_Odivision__by__zero'(
% 2.05/2.40 'tc_Complex_Ocomplex' ) ] )
% 2.05/2.40 , clause( 20781, [ 'class_Ring__and__Field_Ocomm__semiring__1'(
% 2.05/2.40 'tc_Complex_Ocomplex' ) ] )
% 2.05/2.40 , clause( 20782, [ 'class_Ring__and__Field_Ocomm__semiring__0'(
% 2.05/2.40 'tc_Complex_Ocomplex' ) ] )
% 2.05/2.40 , clause( 20783, [ 'class_RealVector_Oreal__normed__algebra'(
% 2.05/2.40 'tc_Complex_Ocomplex' ) ] )
% 2.05/2.40 , clause( 20784, [ 'class_OrderedGroup_Oab__semigroup__mult'(
% 2.05/2.40 'tc_Complex_Ocomplex' ) ] )
% 2.05/2.40 , clause( 20785, [ 'class_RealVector_Oreal__normed__vector'(
% 2.05/2.40 'tc_Complex_Ocomplex' ) ] )
% 2.05/2.40 , clause( 20786, [ 'class_OrderedGroup_Ocomm__monoid__mult'(
% 2.05/2.40 'tc_Complex_Ocomplex' ) ] )
% 2.05/2.40 , clause( 20787, [ 'class_OrderedGroup_Oab__semigroup__add'(
% 2.05/2.40 'tc_Complex_Ocomplex' ) ] )
% 2.05/2.40 , clause( 20788, [ 'class_Ring__and__Field_Ocomm__semiring'(
% 2.05/2.40 'tc_Complex_Ocomplex' ) ] )
% 2.05/2.40 , clause( 20789, [ 'class_RealVector_Oreal__normed__field'(
% 2.05/2.40 'tc_Complex_Ocomplex' ) ] )
% 2.05/2.40 , clause( 20790, [ 'class_OrderedGroup_Ocomm__monoid__add'(
% 2.05/2.40 'tc_Complex_Ocomplex' ) ] )
% 2.05/2.40 , clause( 20791, [ 'class_Ring__and__Field_Ozero__neq__one'(
% 2.05/2.40 'tc_Complex_Ocomplex' ) ] )
% 2.05/2.40 , clause( 20792, [ 'class_Ring__and__Field_Ocomm__ring__1'(
% 2.05/2.40 'tc_Complex_Ocomplex' ) ] )
% 2.05/2.40 , clause( 20793, [ 'class_OrderedGroup_Oab__group__add'(
% 2.05/2.40 'tc_Complex_Ocomplex' ) ] )
% 2.05/2.40 , clause( 20794, [ 'class_Ring__and__Field_Omult__zero'(
% 2.05/2.40 'tc_Complex_Ocomplex' ) ] )
% 2.05/2.40 , clause( 20795, [ 'class_Ring__and__Field_Ocomm__ring'(
% 2.05/2.40 'tc_Complex_Ocomplex' ) ] )
% 2.05/2.40 , clause( 20796, [ 'class_OrderedGroup_Omonoid__mult'(
% 2.05/2.40 'tc_Complex_Ocomplex' ) ] )
% 2.05/2.40 , clause( 20797, [ 'class_Ring__and__Field_Osemiring'(
% 2.05/2.40 'tc_Complex_Ocomplex' ) ] )
% 2.05/2.40 , clause( 20798, [ 'class_RealVector_Oreal__algebra'( 'tc_Complex_Ocomplex'
% 2.05/2.40 ) ] )
% 2.05/2.40 , clause( 20799, [ 'class_OrderedGroup_Omonoid__add'( 'tc_Complex_Ocomplex'
% 2.05/2.40 ) ] )
% 2.05/2.40 , clause( 20800, [ 'class_RealVector_Oreal__vector'( 'tc_Complex_Ocomplex'
% 2.05/2.40 ) ] )
% 2.05/2.40 , clause( 20801, [ 'class_OrderedGroup_Ogroup__add'( 'tc_Complex_Ocomplex'
% 2.05/2.40 ) ] )
% 2.05/2.40 , clause( 20802, [ 'class_RealVector_Oreal__field'( 'tc_Complex_Ocomplex' )
% 2.05/2.40 ] )
% 2.05/2.40 , clause( 20803, [ 'class_Ring__and__Field_Ofield'( 'tc_Complex_Ocomplex' )
% 2.05/2.40 ] )
% 2.05/2.40 , clause( 20804, [ 'class_Ring__and__Field_Oring'( 'tc_Complex_Ocomplex' )
% 2.05/2.40 ] )
% 2.05/2.40 , clause( 20805, [ 'class_Ring__and__Field_Oidom'( 'tc_Complex_Ocomplex' )
% 2.05/2.40 ] )
% 2.05/2.40 , clause( 20806, [ 'class_Ring__and__Field_Odvd'( 'tc_Complex_Ocomplex' ) ]
% 2.05/2.40 )
% 2.05/2.40 , clause( 20807, [ 'class_Int_Onumber__ring'( 'tc_Complex_Ocomplex' ) ] )
% 2.05/2.40 , clause( 20808, [ 'class_SEQ_Obanach'( 'tc_Complex_Ocomplex' ) ] )
% 2.05/2.40 , clause( 20809, [ 'class_HOL_Ozero'( 'tc_Complex_Ocomplex' ) ] )
% 2.05/2.40 , clause( 20810, [ 'class_HOL_Oeq'( 'tc_Complex_Ocomplex' ) ] )
% 2.05/2.40 , clause( 20811, [
% 2.05/2.40 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 2.05/2.40 X ) ) ] )
% 2.05/2.40 , clause( 20812, [
% 2.05/2.40 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 2.05/2.40 X ) ) ] )
% 2.05/2.40 , clause( 20813, [
% 2.05/2.40 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 2.05/2.40 X ) ) ] )
% 2.05/2.40 , clause( 20814, [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 2.05/2.40 X ) ) ] )
% 2.05/2.40 , clause( 20815, [ 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 2.05/2.40 X ) ) ] )
% 2.05/2.40 , clause( 20816, [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 2.05/2.40 X ) ) ] )
% 2.05/2.40 , clause( 20817, [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oidom'( X ) ) ]
% 2.05/2.40 )
% 2.05/2.40 , clause( 20818, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), ~(
% 2.05/2.40 'class_OrderedGroup_Ocancel__comm__monoid__add'( X ) ) ] )
% 2.05/2.40 , clause( 20819, [ 'class_Ring__and__Field_Oordered__ring__strict'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 2.05/2.40 X ) ) ] )
% 2.05/2.40 , clause( 20820, [ 'class_OrderedGroup_Opordered__ab__group__add'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 2.05/2.40 X ) ) ] )
% 2.05/2.40 , clause( 20821, [ 'class_OrderedGroup_Oordered__ab__group__add'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 2.05/2.40 X ) ) ] )
% 2.05/2.40 , clause( 20822, [ 'class_OrderedGroup_Ocancel__semigroup__add'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), ~(
% 2.05/2.40 'class_OrderedGroup_Ocancel__comm__monoid__add'( X ) ) ] )
% 2.05/2.40 , clause( 20823, [ 'class_Ring__and__Field_Ono__zero__divisors'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oidom'( X ) ) ]
% 2.05/2.40 )
% 2.05/2.40 , clause( 20824, [ 'class_Ring__and__Field_Oordered__semidom'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 2.05/2.40 X ) ) ] )
% 2.05/2.40 , clause( 20825, [ 'class_Ring__and__Field_Ocomm__semiring__1'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), ~(
% 2.05/2.40 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ) ] )
% 2.05/2.40 , clause( 20826, [ 'class_Ring__and__Field_Ocomm__semiring__0'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), ~(
% 2.05/2.40 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ] )
% 2.05/2.40 , clause( 20827, [ 'class_OrderedGroup_Oab__semigroup__mult'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), ~(
% 2.05/2.40 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ] )
% 2.05/2.40 , clause( 20828, [ 'class_OrderedGroup_Ocomm__monoid__mult'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), ~(
% 2.05/2.40 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ) ] )
% 2.05/2.40 , clause( 20829, [ 'class_OrderedGroup_Oab__semigroup__add'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), ~( 'class_OrderedGroup_Ocomm__monoid__add'(
% 2.05/2.40 X ) ) ] )
% 2.05/2.40 , clause( 20830, [ 'class_Ring__and__Field_Opordered__ring'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 2.05/2.40 X ) ) ] )
% 2.05/2.40 , clause( 20831, [ 'class_Ring__and__Field_Ocomm__semiring'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), ~(
% 2.05/2.40 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ] )
% 2.05/2.40 , clause( 20832, [ 'class_OrderedGroup_Ocomm__monoid__add'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), ~( 'class_OrderedGroup_Ocomm__monoid__add'(
% 2.05/2.40 X ) ) ] )
% 2.05/2.40 , clause( 20833, [ 'class_Ring__and__Field_Ozero__neq__one'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), ~(
% 2.05/2.40 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ) ] )
% 2.05/2.40 , clause( 20834, [ 'class_Ring__and__Field_Oordered__idom'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 2.05/2.40 X ) ) ] )
% 2.05/2.40 , clause( 20835, [ 'class_Ring__and__Field_Ocomm__ring__1'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Ocomm__ring__1'(
% 2.05/2.40 X ) ) ] )
% 2.05/2.40 , clause( 20836, [ 'class_OrderedGroup_Oab__group__add'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), ~( 'class_OrderedGroup_Oab__group__add'( X
% 2.05/2.40 ) ) ] )
% 2.05/2.40 , clause( 20837, [ 'class_Ring__and__Field_Omult__zero'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), ~(
% 2.05/2.40 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ] )
% 2.05/2.40 , clause( 20838, [ 'class_Ring__and__Field_Ocomm__ring'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Ocomm__ring'( X
% 2.05/2.40 ) ) ] )
% 2.05/2.40 , clause( 20839, [ 'class_OrderedGroup_Omonoid__mult'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), ~(
% 2.05/2.40 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ) ] )
% 2.05/2.40 , clause( 20840, [ 'class_Ring__and__Field_Osemiring'(
% 2.05/2.40 'tc_Polynomial_Opoly'( X ) ), ~(
% 2.05/2.40 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ] )
% 2.05/2.40 , clause( 20841, [ 'class_OrderedGroup_Omonoid__add'( 'tc_Polynomial_Opoly'(
% 2.05/2.40 X ) ), ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ) ] )
% 2.05/2.40 , clause( 20842, [ 'class_OrderedGroup_Ogroup__add'( 'tc_Polynomial_Opoly'(
% 2.05/2.40 X ) ), ~( 'class_OrderedGroup_Oab__group__add'( X ) ) ] )
% 2.05/2.40 , clause( 20843, [ 'class_Ring__and__Field_Osgn__if'( 'tc_Polynomial_Opoly'(
% 2.05/2.40 X ) ), ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ] )
% 2.05/2.40 , clause( 20844, [ 'class_Ring__and__Field_Oabs__if'( 'tc_Polynomial_Opoly'(
% 2.05/2.40 X ) ), ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ] )
% 2.05/2.40 , clause( 20845, [ 'class_Divides_Osemiring__div'( 'tc_Polynomial_Opoly'( X
% 2.05/2.40 ) ), ~( 'class_Ring__and__Field_Ofield'( X ) ) ] )
% 2.05/2.40 , clause( 20846, [ 'class_Ring__and__Field_Oring'( 'tc_Polynomial_Opoly'( X
% 2.05/2.40 ) ), ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ) ] )
% 2.05/2.40 , clause( 20847, [ 'class_Ring__and__Field_Oidom'( 'tc_Polynomial_Opoly'( X
% 2.05/2.40 ) ), ~( 'class_Ring__and__Field_Oidom'( X ) ) ] )
% 2.05/2.40 , clause( 20848, [ 'class_Ring__and__Field_Odvd'( 'tc_Polynomial_Opoly'( X
% 2.05/2.40 ) ), ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ) ] )
% 2.05/2.40 , clause( 20849, [ 'class_Orderings_Opreorder'( 'tc_Polynomial_Opoly'( X )
% 2.05/2.40 ), ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ] )
% 2.05/2.40 , clause( 20850, [ 'class_Orderings_Olinorder'( 'tc_Polynomial_Opoly'( X )
% 2.05/2.40 ), ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ] )
% 2.05/2.40 , clause( 20851, [ 'class_Divides_Oring__div'( 'tc_Polynomial_Opoly'( X ) )
% 2.05/2.40 , ~( 'class_Ring__and__Field_Ofield'( X ) ) ] )
% 2.05/2.40 , clause( 20852, [ 'class_Orderings_Oorder'( 'tc_Polynomial_Opoly'( X ) ),
% 2.05/2.40 ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ] )
% 2.05/2.40 , clause( 20853, [ 'class_Int_Onumber__ring'( 'tc_Polynomial_Opoly'( X ) )
% 2.05/2.40 , ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ) ] )
% 2.05/2.41 , clause( 20854, [ 'class_HOL_Ozero'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 2.05/2.41 'class_HOL_Ozero'( X ) ) ] )
% 2.05/2.41 , clause( 20855, [ 'class_HOL_Oeq'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 2.05/2.41 'class_HOL_Ozero'( X ) ), ~( 'class_HOL_Oeq'( X ) ) ] )
% 2.05/2.41 ] ).
% 2.05/2.41
% 2.05/2.41
% 2.05/2.41
% 2.05/2.41 subsumption(
% 2.05/2.41 clause( 578, [ ~( =( 'c_RealVector_Onorm__class_Onorm'(
% 2.05/2.41 'c_HOL_Otimes__class_Otimes'( 'c_RealVector_Oof__real'( 'v_x____',
% 2.05/2.41 'tc_Complex_Ocomplex' ), 'c_Polynomial_Opoly'( 'v_ds____',
% 2.05/2.41 'c_RealVector_Oof__real'( 'v_x____', 'tc_Complex_Ocomplex' ),
% 2.05/2.41 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' )
% 2.05/2.41 , 'c_RealVector_Onorm__class_Onorm'( 'v_d____', 'tc_Complex_Ocomplex' ) )
% 2.05/2.41 ) ] )
% 2.05/2.41 , clause( 20681, [ ~( =( 'c_RealVector_Onorm__class_Onorm'(
% 2.05/2.41 'c_HOL_Otimes__class_Otimes'( 'c_RealVector_Oof__real'( 'v_x____',
% 2.05/2.41 'tc_Complex_Ocomplex' ), 'c_Polynomial_Opoly'( 'v_ds____',
% 2.05/2.41 'c_RealVector_Oof__real'( 'v_x____', 'tc_Complex_Ocomplex' ),
% 2.05/2.41 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' )
% 2.05/2.41 , 'c_RealVector_Onorm__class_Onorm'( 'v_d____', 'tc_Complex_Ocomplex' ) )
% 2.05/2.41 ) ] )
% 2.05/2.41 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.05/2.41
% 2.05/2.41
% 2.05/2.41 subsumption(
% 2.05/2.41 clause( 579, [ =( 'c_RealVector_Onorm__class_Onorm'(
% 2.05/2.41 'c_HOL_Otimes__class_Otimes'( 'c_RealVector_Oof__real'( 'v_x____',
% 2.05/2.41 'tc_Complex_Ocomplex' ), 'c_Polynomial_Opoly'( 'v_ds____',
% 2.05/2.41 'c_RealVector_Oof__real'( 'v_x____', 'tc_Complex_Ocomplex' ),
% 2.05/2.41 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' )
% 2.05/2.41 , 'c_RealVector_Onorm__class_Onorm'( 'v_d____', 'tc_Complex_Ocomplex' ) )
% 2.05/2.41 ] )
% 2.05/2.41 , clause( 20682, [ =( 'c_RealVector_Onorm__class_Onorm'(
% 2.05/2.41 'c_HOL_Otimes__class_Otimes'( 'c_RealVector_Oof__real'( 'v_x____',
% 2.05/2.41 'tc_Complex_Ocomplex' ), 'c_Polynomial_Opoly'( 'v_ds____',
% 2.05/2.41 'c_RealVector_Oof__real'( 'v_x____', 'tc_Complex_Ocomplex' ),
% 2.05/2.41 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' )
% 2.05/2.41 , 'c_RealVector_Onorm__class_Onorm'( 'v_d____', 'tc_Complex_Ocomplex' ) )
% 2.05/2.41 ] )
% 2.05/2.41 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.05/2.41
% 2.05/2.41
% 2.05/2.41 resolution(
% 2.05/2.41 clause( 22437, [] )
% 2.05/2.41 , clause( 578, [ ~( =( 'c_RealVector_Onorm__class_Onorm'(
% 2.05/2.41 'c_HOL_Otimes__class_Otimes'( 'c_RealVector_Oof__real'( 'v_x____',
% 2.05/2.41 'tc_Complex_Ocomplex' ), 'c_Polynomial_Opoly'( 'v_ds____',
% 2.05/2.41 'c_RealVector_Oof__real'( 'v_x____', 'tc_Complex_Ocomplex' ),
% 2.05/2.41 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' )
% 2.05/2.41 , 'c_RealVector_Onorm__class_Onorm'( 'v_d____', 'tc_Complex_Ocomplex' ) )
% 2.05/2.41 ) ] )
% 2.05/2.41 , 0, clause( 579, [ =( 'c_RealVector_Onorm__class_Onorm'(
% 2.05/2.41 'c_HOL_Otimes__class_Otimes'( 'c_RealVector_Oof__real'( 'v_x____',
% 2.05/2.41 'tc_Complex_Ocomplex' ), 'c_Polynomial_Opoly'( 'v_ds____',
% 2.05/2.41 'c_RealVector_Oof__real'( 'v_x____', 'tc_Complex_Ocomplex' ),
% 2.05/2.41 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex' )
% 2.05/2.41 , 'c_RealVector_Onorm__class_Onorm'( 'v_d____', 'tc_Complex_Ocomplex' ) )
% 2.05/2.41 ] )
% 2.05/2.41 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 2.05/2.41
% 2.05/2.41
% 2.05/2.41 subsumption(
% 2.05/2.41 clause( 20018, [] )
% 2.05/2.41 , clause( 22437, [] )
% 2.05/2.41 , substitution( 0, [] ), permutation( 0, [] ) ).
% 2.05/2.41
% 2.05/2.41
% 2.05/2.41 end.
% 2.05/2.41
% 2.05/2.41 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 2.05/2.41
% 2.05/2.41 Memory use:
% 2.05/2.41
% 2.05/2.41 space for terms: 588541
% 2.05/2.41 space for clauses: 956335
% 2.05/2.41
% 2.05/2.41
% 2.05/2.41 clauses generated: 89206
% 2.05/2.41 clauses kept: 20019
% 2.05/2.41 clauses selected: 648
% 2.05/2.41 clauses deleted: 66
% 2.05/2.41 clauses inuse deleted: 0
% 2.05/2.41
% 2.05/2.41 subsentry: 173161
% 2.05/2.41 literals s-matched: 116952
% 2.05/2.41 literals matched: 114549
% 2.05/2.41 full subsumption: 65736
% 2.05/2.41
% 2.05/2.41 checksum: 1172882096
% 2.05/2.41
% 2.05/2.41
% 2.05/2.41 Bliksem ended
%------------------------------------------------------------------------------