TSTP Solution File: ALG397-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : ALG397-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n027.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 12:10:43 EDT 2022
% Result : Unsatisfiable 0.90s 1.30s
% Output : Refutation 0.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ALG397-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13 % Command : bliksem %s
% 0.14/0.34 % Computer : n027.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % DateTime : Thu Jun 9 05:37:57 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.90/1.28 *** allocated 10000 integers for termspace/termends
% 0.90/1.28 *** allocated 10000 integers for clauses
% 0.90/1.28 *** allocated 10000 integers for justifications
% 0.90/1.28 *** allocated 15000 integers for termspace/termends
% 0.90/1.28 Bliksem 1.12
% 0.90/1.28
% 0.90/1.28
% 0.90/1.28 Automatic Strategy Selection
% 0.90/1.28
% 0.90/1.28 Clauses:
% 0.90/1.28 [
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), X ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.28 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 0.90/1.28 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.90/1.28 ,
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.28 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 0.90/1.28 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.90/1.28 ,
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.28 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 0.90/1.28 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.90/1.28 ,
% 0.90/1.28 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.90/1.28 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.90/1.28 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.90/1.28 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 0.90/1.28 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.90/1.28 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 0.90/1.28 ,
% 0.90/1.28 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 0.90/1.28 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 0.90/1.28 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.90/1.28 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 0.90/1.28 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.90/1.28 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.90/1.28 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 0.90/1.28 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 0.90/1.28 ,
% 0.90/1.28 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.90/1.28 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.90/1.28 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.90/1.28 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.90/1.28 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.90/1.28 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.28 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 0.90/1.28 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.28 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 0.90/1.28 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'( Z,
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.90/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.90/1.28 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ouminus__class_Ouminus'(
% 0.90/1.28 Y, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 0.90/1.28 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oone__class_Oone'( X ), X ) ), Y )
% 0.90/1.28 ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 0.90/1.28 [ ~( 'class_HOL_Ozero'( X ) ), ~( =( hAPP( hAPP( hAPP( Y,
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.28 'tc_Polynomial_Opoly'( X ) ) ), Z ), Z ) ), =( 'c_Polynomial_Opoly__rec'(
% 0.90/1.28 Z, Y, 'c_Polynomial_OpCons'( T, U, X ), W, X ), hAPP( hAPP( hAPP( Y, T )
% 0.90/1.28 , U ), 'c_Polynomial_Opoly__rec'( Z, Y, U, W, X ) ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.28 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 0.90/1.28 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 0.90/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.28 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 0.90/1.28 ) ) ],
% 0.90/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.28 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 0.90/1.28 ) ) ],
% 0.90/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.28 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 0.90/1.28 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 0.90/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.28 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 0.90/1.28 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.28 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 0.90/1.28 ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.28 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 0.90/1.28 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.28 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.28 X ), Y ), Z ), X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.28 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.28 X ), Z ), Y ), X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.28 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.28 X ), Y ), Z ), X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.28 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.28 X ), Z ), Y ), X ) ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), ~( =(
% 0.90/1.28 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y ) ), =( Y,
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), ~( =(
% 0.90/1.28 'c_Polynomial_Osmult'( Y, Z, X ), 'c_Polynomial_OpCons'( T, Z, X ) ) ),
% 0.90/1.28 =( Z, 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.90/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.28 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.28 'tc_nat' ) ), X ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.90/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.28 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.90/1.28 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), X
% 0.90/1.28 ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.28 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 0.90/1.28 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 0.90/1.28 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 0.90/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 0.90/1.28 ), Z ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 0.90/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 0.90/1.28 ), Z ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 0.90/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 0.90/1.28 , X ) ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 0.90/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 0.90/1.28 , X ) ), 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 0.90/1.28 ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 0.90/1.28 ), 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 0.90/1.28 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 0.90/1.28 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 0.90/1.28 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 0.90/1.28 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 0.90/1.28 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 0.90/1.28 'c_Power_Opower__class_Opower'( X ), T ), 'c_Suc'( Z ) ) ) ), =( Y, T ),
% 0.90/1.28 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 0.90/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.90/1.28 'c_Polynomial_Osmult'( Y, 'c_Polynomial_Omonom'( Z, T, X ), X ),
% 0.90/1.28 'c_Polynomial_Omonom'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 0.90/1.28 , Z ), T, X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.28 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.90/1.28 , Y ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP(
% 0.90/1.28 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 0.90/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 0.90/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.90/1.28 ,
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.90/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.90/1.28 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.90/1.28 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 0.90/1.28 ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.28 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.90/1.28 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.90/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.90/1.28 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.90/1.28 , Z ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X )
% 0.90/1.28 ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.28 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.90/1.28 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.28 'c_Polynomial_Osmult'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.90/1.28 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly'(
% 0.90/1.28 'c_Polynomial_OpCons'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.28 'tc_Polynomial_Opoly'( X ) ), X ), Z, X ), 'c_Polynomial_OpCons'( Y,
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ) ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Oplus__class_Oplus'( 'tc_Polynomial_Opoly'( X ) ),
% 0.90/1.28 'c_Polynomial_Omonom'( Y, Z, X ) ), 'c_Polynomial_Omonom'( T, Z, X ) ),
% 0.90/1.28 'c_Polynomial_Omonom'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.90/1.28 T ), Z, X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 0.90/1.28 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Z, X ), ~(
% 0.90/1.28 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 0.90/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.90/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 0.90/1.28 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Y, X ), ~(
% 0.90/1.28 'c_lessequals'( Z, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 0.90/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.90/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.90/1.28 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.90/1.28 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 0.90/1.28 ) ],
% 0.90/1.28 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.90/1.28 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 0.90/1.28 ) ],
% 0.90/1.28 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.90/1.28 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 0.90/1.28 ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.90/1.28 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.90/1.28 , Y ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.28 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.28 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.90/1.28 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.90/1.28 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.90/1.28 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.90/1.28 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 0.90/1.28 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.90/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 0.90/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.90/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.90/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.90/1.28 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 0.90/1.28 , Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'(
% 0.90/1.28 Y ) ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.90/1.28 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Suc'( Y ), X ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 0.90/1.28 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ) ],
% 0.90/1.28 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.90/1.28 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.90/1.28 'c_Polynomial_Ocoeff'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.28 'tc_Polynomial_Opoly'( X ) ), Y ), Z ), X ), T ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_Polynomial_Ocoeff'( Y, X ), T )
% 0.90/1.28 ), hAPP( 'c_Polynomial_Ocoeff'( Z, X ), T ) ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.90/1.28 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 0.90/1.28 ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.90/1.28 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.28 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ]
% 0.90/1.28 ,
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), ~( =(
% 0.90/1.28 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly'( Y, Z, X ),
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ), =( Y,
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.28 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.90/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.28 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.28 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_lessequals'( Y,
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y )
% 0.90/1.28 , 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.90/1.28 [ ~( 'class_HOL_Ozero'( X ) ), =( hAPP( 'c_Polynomial_Ocoeff'(
% 0.90/1.28 'c_Polynomial_Omonom'( Y, Z, X ), X ), Z ), Y ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.28 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 0.90/1.28 ), Y ), 'c_Suc'( Z ) ), 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 0.90/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 0.90/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.90/1.28 ,
% 0.90/1.28 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.28 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 0.90/1.28 ), Z ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 0.90/1.28 ), T ) ) ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.90/1.28 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.90/1.28 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 0.90/1.28 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.90/1.28 [ ~( 'class_HOL_Ozero'( X ) ), =( hAPP( 'c_Polynomial_Ocoeff'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ),
% 0.90/1.28 'c_Polynomial_Odegree'( 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'(
% 0.90/1.28 X ) ), X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 0.90/1.28 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) )
% 0.90/1.28 ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.90/1.28 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 0.90/1.28 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.90/1.28 , Z ), T ), X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 0.90/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 0.90/1.28 ,
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.28 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.28 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.28 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.90/1.28 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.28 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 0.90/1.28 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.90/1.28 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.28 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 0.90/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 0.90/1.28 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.90/1.28 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 0.90/1.28 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 0.90/1.28 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 0.90/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.90/1.28 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 0.90/1.28 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 0.90/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.90/1.28 [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Odegree'(
% 0.90/1.28 'c_Polynomial_OpCons'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.28 'tc_Polynomial_Opoly'( X ) ), X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.28 'tc_nat' ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.90/1.28 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 0.90/1.28 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 0.90/1.28 X ) ) ],
% 0.90/1.28 [ ~( 'class_HOL_Ozero'( X ) ), =( hAPP( 'c_Polynomial_Ocoeff'(
% 0.90/1.28 'c_Polynomial_OpCons'( Y, Z, X ), X ), 'c_Suc'( T ) ), hAPP(
% 0.90/1.28 'c_Polynomial_Ocoeff'( Z, X ), T ) ) ],
% 0.90/1.28 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 0.90/1.28 , Y ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.90/1.28 Y ) ) ) ],
% 0.90/1.28 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'( Y
% 0.90/1.28 ) ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y
% 0.90/1.28 ) ) ) ],
% 0.90/1.28 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 0.90/1.28 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 0.90/1.28 , X ), 'c_RealVector_Onorm__class_Onorm'( Y, X ) ) ],
% 0.90/1.28 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 0.90/1.28 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Osemigroup__add'( X ) ), =( 'c_List_Ofoldl'(
% 0.90/1.28 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.28 X ), Y ), Z ), T, X, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.90/1.28 ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Z, T, X, X ) ) ) ]
% 0.90/1.28 ,
% 0.90/1.28 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), 'c_Suc'( U ) )
% 0.90/1.28 , hAPP( hAPP( Y, T ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T )
% 0.90/1.28 , U ) ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 0.90/1.28 ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.28 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 0.90/1.28 'c_HOL_Oone__class_Oone'( X ), X ) ), Z ) ), hAPP( hAPP(
% 0.90/1.28 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( 'c_Polynomial_Odegree'(
% 0.90/1.28 'c_Polynomial_Osmult'( Y, Z, X ), X ), 'c_Polynomial_Odegree'( Z, X ) ),
% 0.90/1.28 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.90/1.28 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Oplus__class_Oplus'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 0.90/1.28 , X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ],
% 0.90/1.28 [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_Ocoeff'( Y, X ),
% 0.90/1.28 'c_Polynomial_Ocoeff'( Z, X ) ) ), =( Y, Z ) ],
% 0.90/1.28 [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Omonom'( Y,
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X ), 'c_Polynomial_OpCons'( Y,
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.90/1.28 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.90/1.28 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 0.90/1.28 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.90/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.90/1.28 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.90/1.28 T, X ) ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 0.90/1.28 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), Y ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.90/1.28 'c_Polynomial_Osmult'( Y, 'c_Polynomial_OpCons'( Z, T, X ), X ),
% 0.90/1.28 'c_Polynomial_OpCons'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 0.90/1.28 , Z ), 'c_Polynomial_Osmult'( Y, T, X ), X ) ) ],
% 0.90/1.28 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 0.90/1.28 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.90/1.28 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'( Z,
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 0.90/1.28 ,
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 0.90/1.28 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'( Y,
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 0.90/1.28 ,
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 0.90/1.28 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 0.90/1.28 ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 0.90/1.28 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 0.90/1.28 ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'( hAPP(
% 0.90/1.28 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 0.90/1.28 ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.28 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 0.90/1.28 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 0.90/1.28 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 0.90/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 0.90/1.28 [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_OpCons'( Y, Z, X ),
% 0.90/1.28 'c_Polynomial_OpCons'( T, U, X ) ) ), =( Y, T ) ],
% 0.90/1.28 [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_OpCons'( Y, Z, X ),
% 0.90/1.28 'c_Polynomial_OpCons'( T, U, X ) ) ), =( Z, U ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 0.90/1.28 , Z ) ), Z ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.90/1.28 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.90/1.28 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.90/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.90/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 0.90/1.28 ,
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.90/1.28 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.90/1.28 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.90/1.28 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.90/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.90/1.28 ,
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.90/1.28 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.90/1.28 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.90/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.90/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.90/1.28 ,
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 0.90/1.28 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.28 X ), X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.28 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.90/1.28 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.28 X ), X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.28 X ), X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.28 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.28 X ), X ) ) ],
% 0.90/1.28 [ ~( 'class_HOL_Ozero'( X ) ), =(
% 0.90/1.28 'c_Fundamental__Theorem__Algebra__Mirabelle_Opsize'( Y, X ), 'c_Suc'(
% 0.90/1.28 'c_Polynomial_Odegree'( Y, X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.28 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.28 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.90/1.28 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.28 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.28 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.90/1.28 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 0.90/1.28 =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.90/1.28 ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.90/1.28 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.90/1.28 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.90/1.28 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.90/1.28 ) ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 0.90/1.28 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.28 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.90/1.28 , Y ), 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.28 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 0.90/1.28 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.28 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 0.90/1.28 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.90/1.28 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.28 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 0.90/1.28 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.90/1.28 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.28 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 0.90/1.28 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), Z ) ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.90/1.28 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.90/1.28 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 0.90/1.28 'c_lessequals'( Y, T, X ) ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.90/1.28 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.90/1.28 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.90/1.28 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 0.90/1.28 'c_lessequals'( Z, T, X ) ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.90/1.28 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.90/1.28 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.90/1.28 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 0.90/1.28 'c_lessequals'( Y, T, X ) ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 0.90/1.28 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.90/1.28 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 0.90/1.28 'c_lessequals'( Z, T, X ) ) ],
% 0.90/1.28 [ ~( 'class_HOL_Ozero'( X ) ), ~( =( hAPP( 'c_Polynomial_Ocoeff'( Y, X )
% 0.90/1.28 , 'c_Polynomial_Odegree'( Y, X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 0.90/1.28 =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.90/1.28 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.90/1.28 ), =( Z, Y ) ],
% 0.90/1.28 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.90/1.28 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.90/1.28 ) ],
% 0.90/1.28 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.90/1.28 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.90/1.28 ) ],
% 0.90/1.28 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.90/1.28 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 0.90/1.28 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 0.90/1.28 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 0.90/1.28 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 0.90/1.28 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.90/1.28 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.90/1.28 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 0.90/1.28 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 0.90/1.28 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.90/1.28 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_RealDef_Oreal' ) ), ~(
% 0.90/1.28 'c_lessequals'( X, Y, 'tc_RealDef_Oreal' ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.90/1.28 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 0.90/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 0.90/1.28 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =(
% 0.90/1.28 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 0.90/1.28 , X ) ) ), =( Y, Z ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.90/1.28 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 0.90/1.28 , X ) ) ), =( Y, Z ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), U ) ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.90/1.28 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.90/1.28 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.28 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.90/1.28 ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.90/1.28 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.90/1.28 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.90/1.28 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.90/1.28 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.90/1.28 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.90/1.28 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.90/1.28 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.28 Z, Y, X ) ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.28 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.28 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 0.90/1.28 , X ), X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 0.90/1.28 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.90/1.28 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.28 X ), X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.90/1.28 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( 'c_Polynomial_Odegree'(
% 0.90/1.28 'c_Polynomial_Osmult'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), X ),
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.28 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.28 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 0.90/1.28 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.90/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.90/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.90/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.90/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.90/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.90/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.90/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 0.90/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.90/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.90/1.28 ,
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 0.90/1.28 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.90/1.28 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.90/1.28 ,
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 0.90/1.28 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 0.90/1.28 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 0.90/1.28 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 0.90/1.28 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 0.90/1.28 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.90/1.28 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), ~( =( hAPP(
% 0.90/1.28 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Polynomial_Opoly'( X ) ),
% 0.90/1.28 'c_Polynomial_Osmult'( Y, Z, X ) ), 'c_Polynomial_OpCons'( T, Z, X ) ),
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ), =( Z,
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.90/1.28 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.90/1.28 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.28 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 0.90/1.28 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 0.90/1.28 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ), =( Y,
% 0.90/1.28 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), =( Y, Z ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.90/1.28 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.28 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.90/1.28 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.28 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 0.90/1.28 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.28 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 0.90/1.28 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.28 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 0.90/1.28 [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 0.90/1.28 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.90/1.28 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 0.90/1.28 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.90/1.28 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 0.90/1.28 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.90/1.28 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ],
% 0.90/1.28 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( X )
% 0.90/1.28 , 'c_Power_Opower_Opower'( 'c_HOL_Oone__class_Oone'( X ),
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.28 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.28 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 0.90/1.28 ), X ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.90/1.28 'c_Polynomial_Osmult'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.90/1.28 Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.28 'tc_Polynomial_Opoly'( X ) ), 'c_Polynomial_Osmult'( Y, T, X ) ),
% 0.90/1.28 'c_Polynomial_Osmult'( Z, T, X ) ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.90/1.28 'c_Polynomial_Osmult'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.28 'tc_Polynomial_Opoly'( X ) ), Z ), T ), X ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Oplus__class_Oplus'( 'tc_Polynomial_Opoly'( X ) ),
% 0.90/1.28 'c_Polynomial_Osmult'( Y, Z, X ) ), 'c_Polynomial_Osmult'( Y, T, X ) ) )
% 0.90/1.28 ],
% 0.90/1.28 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.90/1.28 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.28 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 0.90/1.28 , X ), X ) ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.28 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.90/1.28 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_lessequals'( Z, Y, X )
% 0.90/1.28 ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 0.90/1.28 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.90/1.28 'c_Suc'( Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.90/1.28 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.90/1.28 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 0.90/1.28 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.90/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 0.90/1.28 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.90/1.28 T, X ) ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.28 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Oone__class_Oone'(
% 0.90/1.28 'tc_nat' ) ), Y ) ],
% 0.90/1.28 [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_OpCons'( Y, Z, X ),
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ), =( Z,
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.28 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.90/1.28 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.28 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 0.90/1.28 Y ) ) ],
% 0.90/1.28 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.90/1.28 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Oplus__class_Oplus'( 'tc_Polynomial_Opoly'( X ) ),
% 0.90/1.28 'c_Polynomial_OpCons'( Y, Z, X ) ), 'c_Polynomial_OpCons'( T, U, X ) ),
% 0.90/1.28 'c_Polynomial_OpCons'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.90/1.28 T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Polynomial_Opoly'( X ) )
% 0.90/1.28 , Z ), U ), X ) ) ],
% 0.90/1.28 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_Suc'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 0.90/1.28 'tc_nat' ) ), Y ) ],
% 0.90/1.28 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 0.90/1.28 'tc_nat' ) ), Y ) ],
% 0.90/1.28 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.90/1.28 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.28 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 0.90/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.90/1.28 ,
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP(
% 0.90/1.28 'c_Polynomial_Opoly'( 'c_Polynomial_Omonom'( Y, Z, X ), X ), T ), hAPP(
% 0.90/1.28 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.90/1.28 'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.90/1.28 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.90/1.28 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.28 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 0.90/1.28 ) ) ), =( Z, U ), =( Y, T ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.90/1.28 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 0.90/1.28 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.28 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 0.90/1.28 ) ) ), =( Z, U ), =( Y, T ) ],
% 0.90/1.28 [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Odegree'(
% 0.90/1.28 'c_Polynomial_Omonom'( Y, Z, X ), X ), Z ), =( Y,
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.90/1.28 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 0.90/1.28 ,
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 0.90/1.28 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.90/1.28 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 0.90/1.28 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 0.90/1.28 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.90/1.28 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.28 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.90/1.28 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 0.90/1.28 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 0.90/1.28 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 0.90/1.28 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.28 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.90/1.29 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 0.90/1.29 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.90/1.29 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 0.90/1.29 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.29 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.29 X ), Y ), Z ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 0.90/1.29 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 0.90/1.29 ) ), Z ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.29 X ), Z ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), ~( =( hAPP(
% 0.90/1.29 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Polynomial_Opoly'( X ) ), Y ),
% 0.90/1.29 'c_Polynomial_Osmult'( Z, T, X ) ), 'c_Polynomial_OpCons'( U, T, X ) ) )
% 0.90/1.29 , =( U, hAPP( 'c_Polynomial_Opoly'( Y, X ), Z ) ) ],
% 0.90/1.29 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.29 'tc_nat' ) ) ) ],
% 0.90/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.90/1.29 , Y, X ) ) ],
% 0.90/1.29 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 0.90/1.29 , X ) ) ],
% 0.90/1.29 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.90/1.29 , Y, X ) ) ],
% 0.90/1.29 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.90/1.29 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.90/1.29 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.29 X ), X ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.90/1.29 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 0.90/1.29 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.90/1.29 T, X ) ) ],
% 0.90/1.29 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.90/1.29 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.90/1.29 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.90/1.29 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 0.90/1.29 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ), Z ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 0.90/1.29 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), Z ) ],
% 0.90/1.29 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.90/1.29 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 0.90/1.29 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), X ), ~(
% 0.90/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 0.90/1.29 [ ~( 'class_HOL_Ozero'( X ) ), =( hAPP( 'c_Polynomial_Ocoeff'(
% 0.90/1.29 'c_Polynomial_OpCons'( Y, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.29 'tc_nat' ) ), Y ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 'c_lessequals'(
% 0.90/1.29 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.90/1.29 , X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.29 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.90/1.29 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 0.90/1.29 ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 0.90/1.29 'c_Suc'( T ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Z ),
% 0.90/1.29 'c_Suc'( T ) ), X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.90/1.29 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 0.90/1.29 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.90/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.90/1.29 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.90/1.29 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 0.90/1.29 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 0.90/1.29 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.90/1.29 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 0.90/1.29 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 0.90/1.29 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~(
% 0.90/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Z
% 0.90/1.29 , T ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.90/1.29 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 0.90/1.29 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.29 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 0.90/1.29 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 0.90/1.29 ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 0.90/1.29 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.90/1.29 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), =(
% 0.90/1.29 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( 'c_Polynomial_Osmult'( Y
% 0.90/1.29 , 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ),
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.90/1.29 'c_Polynomial_Osmult'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.29 'tc_Polynomial_Opoly'( X ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.29 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.90/1.29 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.90/1.29 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.29 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.90/1.29 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.90/1.29 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ),
% 0.90/1.29 ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.90/1.29 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 0.90/1.29 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.90/1.29 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.29 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.90/1.29 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.90/1.29 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ),
% 0.90/1.29 ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.90/1.29 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 0.90/1.29 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.90/1.29 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 0.90/1.29 [ 'c_lessequals'( X, Y, 'tc_RealDef_Oreal' ), ~( 'c_lessequals'( Z, Y,
% 0.90/1.29 'tc_RealDef_Oreal' ) ), ~( 'c_lessequals'( X, Z, 'tc_RealDef_Oreal' ) ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ 'c_lessequals'( X, X, 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.90/1.29 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 0.90/1.29 , X ) ) ],
% 0.90/1.29 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.90/1.29 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 0.90/1.29 , X ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.29 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 0.90/1.29 , X ), ~( 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ), X ) ) ],
% 0.90/1.29 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.90/1.29 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 0.90/1.29 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.90/1.29 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 0.90/1.29 ) ) ],
% 0.90/1.29 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.90/1.29 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 0.90/1.29 ) ) ],
% 0.90/1.29 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 0.90/1.29 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 0.90/1.29 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =( hAPP(
% 0.90/1.29 'c_Polynomial_Opoly'( 'c_Polynomial_OpCons'( Y, Z, X ), X ), T ), hAPP(
% 0.90/1.29 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( 'c_Polynomial_Opoly'( Z, X
% 0.90/1.29 ), T ) ) ) ) ],
% 0.90/1.29 [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Opoly__rec'( Y, Z,
% 0.90/1.29 'c_Polynomial_OpCons'( T, U, X ), W, X ), hAPP( hAPP( hAPP( Z, T ), U ),
% 0.90/1.29 'c_HOL_OIf'( 'c_fequal'( U, 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.29 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ), Y,
% 0.90/1.29 'c_Polynomial_Opoly__rec'( Y, Z, U, W, X ), W ) ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.29 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 0.90/1.29 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.29 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 0.90/1.29 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 0.90/1.29 [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Omonom'( Y, 'c_Suc'( Z )
% 0.90/1.29 , X ), 'c_Polynomial_OpCons'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.29 'c_Polynomial_Omonom'( Y, Z, X ), X ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.90/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.29 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.29 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.29 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.90/1.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 0.90/1.29 ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 0.90/1.29 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 0.90/1.29 ],
% 0.90/1.29 [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_Omonom'( Y, Z, X ),
% 0.90/1.29 'c_Polynomial_Omonom'( T, Z, X ) ) ), =( Y, T ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.90/1.29 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 0.90/1.29 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.90/1.29 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), 'c_HOL_Ouminus__class_Ouminus'(
% 0.90/1.29 Y, X ) ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.90/1.29 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 0.90/1.29 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.90/1.29 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), 'c_HOL_Ouminus__class_Ouminus'(
% 0.90/1.29 Z, X ) ) ) ],
% 0.90/1.29 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.90/1.29 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.90/1.29 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.90/1.29 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.90/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.90/1.29 'c_lessequals'( Z, Y, X ) ],
% 0.90/1.29 [ 'c_lessequals'( X, Y, 'tc_RealDef_Oreal' ), 'c_lessequals'( Y, X,
% 0.90/1.29 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.90/1.29 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.90/1.29 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 0.90/1.29 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.90/1.29 [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Odegree'(
% 0.90/1.29 'c_Polynomial_OpCons'( Y, Z, X ), X ), 'c_Suc'( 'c_Polynomial_Odegree'( Z
% 0.90/1.29 , X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) )
% 0.90/1.29 ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.90/1.29 'c_Polynomial_Odegree'(
% 0.90/1.29 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly'( Y, Z, X ), X
% 0.90/1.29 ), 'c_Polynomial_Odegree'( Y, X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.90/1.29 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), Y, X ),
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 0.90/1.29 Y ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 0.90/1.29 Y ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 0.90/1.29 Y ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 0.90/1.29 Y ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 0.90/1.29 Y ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 0.90/1.29 Y ) ],
% 0.90/1.29 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.29 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.90/1.29 [ =( 'c_Suc'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.90/1.29 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ) ],
% 0.90/1.29 [ =( 'c_Suc'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 0.90/1.29 ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.90/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.90/1.29 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.29 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 0.90/1.29 ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.90/1.29 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.29 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 0.90/1.29 ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.90/1.29 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly'(
% 0.90/1.29 'c_Polynomial_OpCons'( Y, Z, X ), T, X ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( 'tc_Polynomial_Opoly'( X ) ),
% 0.90/1.29 'c_Polynomial_Osmult'( T,
% 0.90/1.29 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly'( Z, T, X ), X
% 0.90/1.29 ) ), 'c_Polynomial_OpCons'( Y,
% 0.90/1.29 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly'( Z, T, X ), X
% 0.90/1.29 ) ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.90/1.29 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.29 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ) ) ],
% 0.90/1.29 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.90/1.29 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.90/1.29 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 0.90/1.29 ), Z ) ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 0.90/1.29 ), Z ) ), Y ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 0.90/1.29 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.29 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.29 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 0.90/1.29 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 0.90/1.29 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.90/1.29 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.90/1.29 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.90/1.29 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.90/1.29 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 0.90/1.29 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =( hAPP(
% 0.90/1.29 'c_Polynomial_Ocoeff'( 'c_Polynomial_Osmult'( Y, Z, X ), X ), T ), hAPP(
% 0.90/1.29 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( 'c_Polynomial_Ocoeff'(
% 0.90/1.29 Z, X ), T ) ) ) ],
% 0.90/1.29 [ ~( 'class_HOL_Ozero'( X ) ), =( hAPP( 'c_Polynomial_Ocoeff'(
% 0.90/1.29 'c_Polynomial_Omonom'( Y, Z, X ), X ), T ), 'c_HOL_Ozero__class_Ozero'( X
% 0.90/1.29 ) ), =( Z, T ) ],
% 0.90/1.29 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 0.90/1.29 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 0.90/1.29 ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.29 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 0.90/1.29 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ) ],
% 0.90/1.29 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 0.90/1.29 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.90/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.90/1.29 , X ), 'c_lessequals'( Z, Y, X ) ],
% 0.90/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 0.90/1.29 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 0.90/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 0.90/1.29 , X ), 'c_lessequals'( Y, Y, X ) ],
% 0.90/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.90/1.29 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 0.90/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 0.90/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 0.90/1.29 , X ), 'c_lessequals'( Z, Y, X ) ],
% 0.90/1.29 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 0.90/1.29 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.90/1.29 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.90/1.29 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.90/1.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.90/1.29 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 0.90/1.29 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 0.90/1.29 ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.90/1.29 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 0.90/1.29 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.90/1.29 'c_Power_Opower__class_Opower'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.29 X ), X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.90/1.29 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.90/1.29 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.29 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 0.90/1.29 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 0.90/1.29 'c_lessequals'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.29 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 0.90/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.29 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 0.90/1.29 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 0.90/1.29 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.29 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 0.90/1.29 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.29 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.29 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), U )
% 0.90/1.29 ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.29 X ), Z ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y )
% 0.90/1.29 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.29 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 0.90/1.29 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.29 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.90/1.29 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.90/1.29 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 0.90/1.29 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.29 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 0.90/1.29 ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.29 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 0.90/1.29 ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =( hAPP(
% 0.90/1.29 'c_Polynomial_Opoly'( 'c_Polynomial_Osmult'( Y, Z, X ), X ), T ), hAPP(
% 0.90/1.29 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( 'c_Polynomial_Opoly'(
% 0.90/1.29 Z, X ), T ) ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.90/1.29 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), Z ) ), =( Y,
% 0.90/1.29 'c_HOL_Ouminus__class_Ouminus'( T, X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.90/1.29 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 0.90/1.29 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 0.90/1.29 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.90/1.29 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 0.90/1.29 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.29 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.90/1.29 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 0.90/1.29 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.90/1.29 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 0.90/1.29 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 0.90/1.29 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.90/1.29 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 0.90/1.29 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 0.90/1.29 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.90/1.29 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 0.90/1.29 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.29 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.90/1.29 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 0.90/1.29 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.90/1.29 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 0.90/1.29 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 0.90/1.29 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.90/1.29 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 0.90/1.29 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 0.90/1.29 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.90/1.29 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 0.90/1.29 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 0.90/1.29 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 0.90/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.90/1.29 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 0.90/1.29 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.29 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 0.90/1.29 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 0.90/1.29 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.90/1.29 'c_Polynomial_Osmult'( Y, 'c_Polynomial_Osmult'( Z, T, X ), X ),
% 0.90/1.29 'c_Polynomial_Osmult'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 0.90/1.29 , Z ), T, X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 0.90/1.29 , X ), X ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 0.90/1.29 , X ), X ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( 'tc_Polynomial_Opoly'( X ) ),
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ), Y ), Y ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( 'tc_Polynomial_Opoly'( X ) ), Y ),
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ), Y ) ],
% 0.90/1.29 [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 0.90/1.29 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 0.90/1.29 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 0.90/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 0.90/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.90/1.29 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 0.90/1.29 ), Y ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 0.90/1.29 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 0.90/1.29 ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 0.90/1.29 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 0.90/1.29 ) ) ],
% 0.90/1.29 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 0.90/1.29 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 0.90/1.29 ), Y ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.90/1.29 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 0.90/1.29 ), Y ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.90/1.29 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 0.90/1.29 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.90/1.29 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 0.90/1.29 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 0.90/1.29 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 0.90/1.29 , X ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 0.90/1.29 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 0.90/1.29 , X ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 0.90/1.29 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 0.90/1.29 , X ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 0.90/1.29 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 0.90/1.29 , X ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.29 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 0.90/1.29 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.29 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 0.90/1.29 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.29 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 0.90/1.29 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.29 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 0.90/1.29 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.90/1.29 Y ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.90/1.29 Y ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.90/1.29 Y ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.90/1.29 Y ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.90/1.29 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.90/1.29 Y ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.90/1.29 Y ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.90/1.29 Y ) ],
% 0.90/1.29 [ ~( =( hAPP( 'c_Polynomial_Opoly'( 'v_pa____', 'tc_Complex_Ocomplex' )
% 0.90/1.29 , 'v_c____' ), 'c_HOL_Ozero__class_Ozero'( 'tc_Complex_Ocomplex' ) ) ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ =( 'c_Fundamental__Theorem__Algebra__Mirabelle_Opsize'(
% 0.90/1.29 'v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1'( X, Y
% 0.90/1.29 ), 'tc_Complex_Ocomplex' ),
% 0.90/1.29 'c_Fundamental__Theorem__Algebra__Mirabelle_Opsize'( Y,
% 0.90/1.29 'tc_Complex_Ocomplex' ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oidom'( 't_a' ) ), ~( =(
% 0.90/1.29 'v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2'(
% 0.90/1.29 X ), 'c_HOL_Ozero__class_Ozero'( 't_a' ) ) ), =( hAPP(
% 0.90/1.29 'c_Polynomial_Opoly'( X, 't_a' ), Y ), 'c_HOL_Ozero__class_Ozero'( 't_a'
% 0.90/1.29 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 't_a' ) ) ],
% 0.90/1.29 [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Odegree'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ),
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.90/1.29 [ ~( 'class_HOL_Ozero'( X ) ), =( hAPP( 'c_Polynomial_Ocoeff'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ), Y ),
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.90/1.29 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.90/1.29 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.90/1.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 0.90/1.29 , Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Y,
% 0.90/1.29 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 0.90/1.29 , Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 0.90/1.29 , Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.90/1.29 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.90/1.29 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.90/1.29 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.90/1.29 ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.29 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.90/1.29 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.29 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 0.90/1.29 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.29 X ), Y ), Z ) ), T ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.29 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.90/1.29 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.29 X ), Y ), Z ) ), T ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.29 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.90/1.29 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 0.90/1.29 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.90/1.29 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 0.90/1.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 0.90/1.29 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.90/1.29 'c_Polynomial_Opcompose'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.29 'tc_Polynomial_Opoly'( X ) ), Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.29 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.90/1.29 [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Omonom'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.29 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =( hAPP(
% 0.90/1.29 'c_Polynomial_Opoly'(
% 0.90/1.29 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly'( Y, Z, X ), X
% 0.90/1.29 ), T ), hAPP( 'c_Polynomial_Opoly'( Y, X ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.90/1.29 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 0.90/1.29 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 0.90/1.29 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 0.90/1.29 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 0.90/1.29 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 0.90/1.29 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.90/1.29 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 0.90/1.29 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 0.90/1.29 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.90/1.29 ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 0.90/1.29 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 0.90/1.29 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.90/1.29 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.90/1.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.90/1.29 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.90/1.29 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.90/1.29 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.90/1.29 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.90/1.29 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.90/1.29 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ 'c_lessequals'( 'c_RealVector_Onorm__class_Onorm'( hAPP(
% 0.90/1.29 'c_Polynomial_Opoly'( 'v_pa____', 'tc_Complex_Ocomplex' ), 'v_c____' ),
% 0.90/1.29 'tc_Complex_Ocomplex' ), 'c_RealVector_Onorm__class_Onorm'( hAPP(
% 0.90/1.29 'c_Polynomial_Opoly'( 'v_pa____', 'tc_Complex_Ocomplex' ), X ),
% 0.90/1.29 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ ~( 'class_HOL_Ozero'( X ) ), ~( =( hAPP( hAPP( hAPP( Y,
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.29 'tc_Polynomial_Opoly'( X ) ) ), Z ), Z ) ), =( 'c_Polynomial_Opoly__rec'(
% 0.90/1.29 Z, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), T, X ), Z
% 0.90/1.29 ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( hAPP(
% 0.90/1.29 'c_Polynomial_Opoly'( Y, X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ), =(
% 0.90/1.29 'c_Polynomial_Oorder'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.90/1.29 ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.90/1.29 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.90/1.29 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.90/1.29 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.90/1.29 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 0.90/1.29 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 0.90/1.29 ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.29 'tc_nat' ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 0.90/1.29 ), Z ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 0.90/1.29 hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.90/1.29 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.90/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.90/1.29 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ), =( T, U ), =( Z,
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 0.90/1.29 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.29 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 0.90/1.29 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.29 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.29 [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_Omonom'( Y, Z, X ),
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ), =( Y,
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.90/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 0.90/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.29 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 0.90/1.29 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( hAPP(
% 0.90/1.29 'c_Polynomial_Opoly'( 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'(
% 0.90/1.29 X ) ), X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =( hAPP(
% 0.90/1.29 'c_Polynomial_Opoly'( 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'(
% 0.90/1.29 X ) ), X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 0.90/1.29 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 0.90/1.29 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 0.90/1.29 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 0.90/1.29 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 0.90/1.29 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 0.90/1.29 [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_OpCons'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.29 'tc_Polynomial_Opoly'( X ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.29 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.90/1.29 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.29 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =( 'c_Polynomial_Osmult'(
% 0.90/1.29 Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ),
% 0.90/1.29 =( Z, 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ), =( Y,
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 0.90/1.29 [ =( 'v_n____', 'c_Fundamental__Theorem__Algebra__Mirabelle_Opsize'(
% 0.90/1.29 'v_pa____', 'tc_Complex_Ocomplex' ) ) ],
% 0.90/1.29 [ ~( 'class_HOL_Ozero'( X ) ), =(
% 0.90/1.29 'c_Fundamental__Theorem__Algebra__Mirabelle_Opsize'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ),
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.90/1.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 0.90/1.29 ), T ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Z
% 0.90/1.29 ), T ) ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.90/1.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.29 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~( 'c_lessequals'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =( hAPP(
% 0.90/1.29 'c_Polynomial_Opoly'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.29 'tc_Polynomial_Opoly'( X ) ), Y ), Z ), X ), T ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_Polynomial_Opoly'( Y, X ), T )
% 0.90/1.29 ), hAPP( 'c_Polynomial_Opoly'( Z, X ), T ) ) ) ],
% 0.90/1.29 [ ~( 'class_HOL_Ozero'( X ) ), ~( =(
% 0.90/1.29 'c_Fundamental__Theorem__Algebra__Mirabelle_Opsize'( Y, X ),
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 0.90/1.29 [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_OpCons'( Y, Z, X ),
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ), =( Y,
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldl'(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ), Z, X, X
% 0.90/1.29 ) ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ) ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 0.90/1.29 ) ) ), =( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 0.90/1.29 ) ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ],
% 0.90/1.29 [ ~( =( hAPP( 'c_Polynomial_Opoly'( 'v_pa____', 'tc_Complex_Ocomplex' )
% 0.90/1.29 , 'v_c____' ), 'c_HOL_Ozero__class_Ozero'( 'tc_Complex_Ocomplex' ) ) ),
% 0.90/1.29 =( hAPP( 'c_Polynomial_Opoly'( 'v_pa____', 'tc_Complex_Ocomplex' ),
% 0.90/1.29 'v_sko__unknown__thm__rrS__1'( 'v_pa____' ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.29 'tc_Complex_Ocomplex' ) ) ],
% 0.90/1.29 [ ~( 'class_HOL_Ozero'( 't_a' ) ), =(
% 0.90/1.29 'c_Fundamental__Theorem__Algebra__Mirabelle_Opsize'( 'v_p', 't_a' ),
% 0.90/1.29 'c_HOL_OIf'( 'c_fequal'( 'v_p', 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.29 'tc_Polynomial_Opoly'( 't_a' ) ), 'tc_Polynomial_Opoly'( 't_a' ) ),
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( 'c_Polynomial_Odegree'(
% 0.90/1.29 'v_p', 't_a' ) ), 'tc_nat' ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.90/1.29 Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.29 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.90/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 0.90/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.90/1.29 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oidom'( 't_a' ) ), =( hAPP(
% 0.90/1.29 'c_Polynomial_Opoly'( X, 't_a' ), Y ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( 't_a' ), hAPP( 'c_Polynomial_Opoly'( X, 't_a'
% 0.90/1.29 ), 'c_HOL_Ozero__class_Ozero'( 't_a' ) ) ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( 't_a' ), hAPP( hAPP(
% 0.90/1.29 'c_Power_Opower__class_Opower'( 't_a' ), Y ),
% 0.90/1.29 'v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1'( X
% 0.90/1.29 ) ) ), hAPP( 'c_Polynomial_Opoly'( 'c_Polynomial_OpCons'(
% 0.90/1.29 'v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__2'( X
% 0.90/1.29 ),
% 0.90/1.29 'v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__3'( X
% 0.90/1.29 ), 't_a' ), 't_a' ), Y ) ) ) ),
% 0.90/1.29 'c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant'(
% 0.90/1.29 'c_Polynomial_Opoly'( X, 't_a' ), 't_a', 't_a' ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 0.90/1.29 'c_OrderedGroup_Ocomm__monoid__add__axioms'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.29 X ), 'c_HOL_Oplus__class_Oplus'( X ), X ) ],
% 0.90/1.29 [ =( hAPP( 'c_Polynomial_Opoly'(
% 0.90/1.29 'v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1'( X, Y
% 0.90/1.29 ), 'tc_Complex_Ocomplex' ), Z ), hAPP( 'c_Polynomial_Opoly'( Y,
% 0.90/1.29 'tc_Complex_Ocomplex' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.29 'tc_Complex_Ocomplex' ), X ), Z ) ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ),
% 0.90/1.29 'c_OrderedGroup_Omonoid__add__axioms'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( X ), X ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oidom'( 't_a' ) ), =( hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.90/1.29 'c_Fundamental__Theorem__Algebra__Mirabelle_Opsize'(
% 0.90/1.29 'v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__3'( X
% 0.90/1.29 ), 't_a' ) ),
% 0.90/1.29 'v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1'( X
% 0.90/1.29 ) ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ),
% 0.90/1.29 'c_Fundamental__Theorem__Algebra__Mirabelle_Opsize'( X, 't_a' ) ),
% 0.90/1.29 'c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant'(
% 0.90/1.29 'c_Polynomial_Opoly'( X, 't_a' ), 't_a', 't_a' ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =( 'c_Polynomial_Oorder'(
% 0.90/1.29 Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Z,
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ), ~( =( hAPP(
% 0.90/1.29 'c_Polynomial_Opoly'( Z, X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( 'c_Polynomial_Osmult'(
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.29 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.90/1.29 'c_Polynomial_Osmult'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.29 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.90/1.29 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.29 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.29 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 0.90/1.29 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( hAPP(
% 0.90/1.29 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 0.90/1.29 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.90/1.29 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.90/1.29 'class_Int_Oring__char__0'( X ) ), ~( =( 'c_Polynomial_Opoly'( Y, X ),
% 0.90/1.29 'c_Polynomial_Opoly'( 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'(
% 0.90/1.29 X ) ), X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'(
% 0.90/1.29 X ) ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.90/1.29 'class_Int_Oring__char__0'( X ) ), ~( =( 'c_Polynomial_Opoly'( Y, X ),
% 0.90/1.29 'c_Polynomial_Opoly'( Z, X ) ) ), =( Y, Z ) ],
% 0.90/1.29 [ =( hAPP( X, Y ), hAPP( X, Z ) ), ~(
% 0.90/1.29 'c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant'( X, 't_a', 't_b' )
% 0.90/1.29 ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oidom'( 't_a' ) ), ~( =(
% 0.90/1.29 'v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1'( X
% 0.90/1.29 ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 0.90/1.29 'c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant'(
% 0.90/1.29 'c_Polynomial_Opoly'( X, 't_a' ), 't_a', 't_a' ) ],
% 0.90/1.29 [ ~( 'c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant'(
% 0.90/1.29 'c_Polynomial_Opoly'( 'v_p', 'tc_Complex_Ocomplex' ),
% 0.90/1.29 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =( hAPP(
% 0.90/1.29 'c_Polynomial_Opoly'( 'c_Polynomial_Opcompose'( Y, Z, X ), X ), T ), hAPP(
% 0.90/1.29 'c_Polynomial_Opoly'( Y, X ), hAPP( 'c_Polynomial_Opoly'( Z, X ), T ) ) )
% 0.90/1.29 ],
% 0.90/1.29 [ =( 'c_Fundamental__Theorem__Algebra__Mirabelle_Opsize'( 'v_q____',
% 0.90/1.29 'tc_Complex_Ocomplex' ),
% 0.90/1.29 'c_Fundamental__Theorem__Algebra__Mirabelle_Opsize'( 'v_pa____',
% 0.90/1.29 'tc_Complex_Ocomplex' ) ) ],
% 0.90/1.29 [ =( hAPP( 'c_Polynomial_Opoly'( 'v_q____', 'tc_Complex_Ocomplex' ), X )
% 0.90/1.29 , hAPP( 'c_Polynomial_Opoly'( 'v_pa____', 'tc_Complex_Ocomplex' ), hAPP(
% 0.90/1.29 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Complex_Ocomplex' ), 'v_c____' ), X
% 0.90/1.29 ) ) ) ],
% 0.90/1.29 [ ~( 'c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant'(
% 0.90/1.29 'c_Polynomial_Opoly'( 'v_pa____', 'tc_Complex_Ocomplex' ),
% 0.90/1.29 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ) ) ],
% 0.90/1.29 [ ~( 'class_Ring__and__Field_Oidom'( 't_a' ) ), ~( =(
% 0.90/1.29 'v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__2'( X
% 0.90/1.29 ), 'c_HOL_Ozero__class_Ozero'( 't_a' ) ) ),
% 0.90/1.29 'c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant'(
% 0.90/1.29 'c_Polynomial_Opoly'( X, 't_a' ), 't_a', 't_a' ) ],
% 0.90/1.29 [ ~( 'c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant'(
% 0.90/1.29 'c_Polynomial_Opoly'( 'v_q____', 'tc_Complex_Ocomplex' ),
% 0.90/1.29 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ) ) ],
% 0.90/1.29 [ 'c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant'(
% 0.90/1.29 'c_Polynomial_Opoly'( 'v_q____', 'tc_Complex_Ocomplex' ),
% 0.90/1.29 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Ocancel__comm__monoid__add'( 'tc_Polynomial_Opoly'(
% 0.90/1.29 X ) ), ~( 'class_OrderedGroup_Ocancel__comm__monoid__add'( X ) ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Polynomial_Opoly'( X ) )
% 0.90/1.29 , ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_Polynomial_Opoly'( X ) ),
% 0.90/1.29 ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Ocancel__comm__monoid__add'( 'tc_Complex_Ocomplex'
% 0.90/1.29 ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Complex_Ocomplex' ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_Complex_Ocomplex' ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Ocancel__comm__monoid__add'( 'tc_RealDef_Oreal' )
% 0.90/1.29 ],
% 0.90/1.29 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Ocancel__comm__monoid__add'( 'tc_nat' ) ],
% 0.90/1.29 [ 'class_Lattices_Oboolean__algebra'( 'tc_fun'( X, Y ) ), ~(
% 0.90/1.29 'class_Lattices_Oboolean__algebra'( Y ) ) ],
% 0.90/1.29 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 0.90/1.29 'class_Orderings_Opreorder'( Y ) ) ],
% 0.90/1.29 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 0.90/1.29 'class_Orderings_Oorder'( Y ) ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 0.90/1.29 ],
% 0.90/1.29 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 0.90/1.29 ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 0.90/1.29 ],
% 0.90/1.29 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_nat' ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Osemigroup__add'( 'tc_nat' ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 0.90/1.29 [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ],
% 0.90/1.29 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 0.90/1.29 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 0.90/1.29 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 0.90/1.29 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 0.90/1.29 [ 'class_HOL_Ozero'( 'tc_nat' ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 0.90/1.29 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 0.90/1.29 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 0.90/1.29 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 0.90/1.29 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 0.90/1.29 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 0.90/1.29 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_RealDef_Oreal'
% 0.90/1.29 ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_RealDef_Oreal'
% 0.90/1.29 ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_RealDef_Oreal'
% 0.90/1.29 ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_RealDef_Oreal' )
% 0.90/1.29 ],
% 0.90/1.29 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_RealDef_Oreal' )
% 0.90/1.29 ],
% 0.90/1.29 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_RealDef_Oreal' ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_RealDef_Oreal' ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ 'class_OrderedGroup_Oordered__ab__group__add'( 'tc_RealDef_Oreal' ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_RealDef_Oreal' ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_RealDef_Oreal' ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_RealDef_Oreal' ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_RealDef_Oreal' ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_RealDef_Oreal' ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_RealDef_Oreal' ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_RealDef_Oreal' ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ 'class_RealVector_Oreal__normed__algebra'( 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ 'class_RealVector_Oreal__normed__vector'( 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Osemigroup__add'( 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Oab__group__add'( 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Omult__zero'( 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Omult__mono'( 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Osemiring'( 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Omonoid__add'( 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Ogroup__add'( 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Oring__1'( 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Oring'( 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Oidom'( 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ 'class_Nat_Osemiring__char__0'( 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ 'class_Orderings_Opreorder'( 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ 'class_Orderings_Olinorder'( 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ 'class_Orderings_Oorder'( 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ 'class_Int_Oring__char__0'( 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ 'class_Int_Onumber__ring'( 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ 'class_Power_Opower'( 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ 'class_HOL_Ozero'( 'tc_RealDef_Oreal' ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 0.90/1.29 'tc_Complex_Ocomplex' ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 0.90/1.29 'tc_Complex_Ocomplex' ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 0.90/1.29 'tc_Complex_Ocomplex' ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Complex_Ocomplex' )
% 0.90/1.29 ],
% 0.90/1.29 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Complex_Ocomplex' )
% 0.90/1.29 ],
% 0.90/1.29 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Complex_Ocomplex' ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_Complex_Ocomplex' ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ 'class_RealVector_Oreal__normed__algebra'( 'tc_Complex_Ocomplex' ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Complex_Ocomplex' ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ 'class_RealVector_Oreal__normed__vector'( 'tc_Complex_Ocomplex' ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Complex_Ocomplex' ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Complex_Ocomplex' ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Complex_Ocomplex' ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Complex_Ocomplex' ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Complex_Ocomplex' ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ 'class_OrderedGroup_Osemigroup__add'( 'tc_Complex_Ocomplex' ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Complex_Ocomplex' ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Complex_Ocomplex' ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Complex_Ocomplex' ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Complex_Ocomplex' ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Complex_Ocomplex' ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Osemiring'( 'tc_Complex_Ocomplex' ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Complex_Ocomplex' ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Complex_Ocomplex' ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Oring__1'( 'tc_Complex_Ocomplex' ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Oring'( 'tc_Complex_Ocomplex' ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Oidom'( 'tc_Complex_Ocomplex' ) ],
% 0.90/1.29 [ 'class_Nat_Osemiring__char__0'( 'tc_Complex_Ocomplex' ) ],
% 0.90/1.29 [ 'class_Int_Oring__char__0'( 'tc_Complex_Ocomplex' ) ],
% 0.90/1.29 [ 'class_Int_Onumber__ring'( 'tc_Complex_Ocomplex' ) ],
% 0.90/1.29 [ 'class_Power_Opower'( 'tc_Complex_Ocomplex' ) ],
% 0.90/1.29 [ 'class_HOL_Ozero'( 'tc_Complex_Ocomplex' ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 0.90/1.29 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 0.90/1.29 X ) ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 0.90/1.29 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 0.90/1.29 X ) ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 0.90/1.29 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 0.90/1.29 X ) ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 0.90/1.29 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 0.90/1.29 X ) ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 0.90/1.29 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oidom'( X ) ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 0.90/1.29 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 0.90/1.29 X ) ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 0.90/1.29 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 0.90/1.29 X ) ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 0.90/1.29 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 0.90/1.29 X ) ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 0.90/1.29 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oidom'( X ) ) ]
% 0.90/1.29 ,
% 0.90/1.29 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 0.90/1.29 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.90/1.29 'class_OrderedGroup_Ocancel__comm__monoid__add'( X ) ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_Polynomial_Opoly'(
% 0.90/1.29 X ) ), ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_Polynomial_Opoly'(
% 0.90/1.29 X ) ), ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Oordered__ab__group__add'( 'tc_Polynomial_Opoly'(
% 0.90/1.29 X ) ), ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Polynomial_Opoly'( X
% 0.90/1.29 ) ), ~( 'class_OrderedGroup_Ocancel__comm__monoid__add'( X ) ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_Polynomial_Opoly'( X
% 0.90/1.29 ) ), ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_Polynomial_Opoly'( X
% 0.90/1.29 ) ), ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Polynomial_Opoly'( X
% 0.90/1.29 ) ), ~( 'class_Ring__and__Field_Oidom'( X ) ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_Polynomial_Opoly'( X )
% 0.90/1.29 ), ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Polynomial_Opoly'( X
% 0.90/1.29 ) ), ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_Polynomial_Opoly'( X
% 0.90/1.29 ) ), ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Polynomial_Opoly'( X )
% 0.90/1.29 ), ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Polynomial_Opoly'( X ) )
% 0.90/1.29 , ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Polynomial_Opoly'( X ) )
% 0.90/1.29 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_Polynomial_Opoly'( X ) )
% 0.90/1.29 , ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Polynomial_Opoly'( X ) )
% 0.90/1.29 , ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Polynomial_Opoly'( X ) )
% 0.90/1.29 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Polynomial_Opoly'( X ) )
% 0.90/1.29 , ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Polynomial_Opoly'( X ) )
% 0.90/1.29 , ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Osemigroup__add'( 'tc_Polynomial_Opoly'( X ) ),
% 0.90/1.29 ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Polynomial_Opoly'( X ) ),
% 0.90/1.29 ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Polynomial_Opoly'( X ) ),
% 0.90/1.29 ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_Polynomial_Opoly'( X ) ),
% 0.90/1.29 ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Polynomial_Opoly'( X ) ),
% 0.90/1.29 ~( 'class_OrderedGroup_Oab__group__add'( X ) ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Polynomial_Opoly'( X ) ),
% 0.90/1.29 ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Omult__mono'( 'tc_Polynomial_Opoly'( X ) ),
% 0.90/1.29 ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.90/1.29 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Osemiring'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.90/1.29 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.90/1.29 'class_OrderedGroup_Ocomm__monoid__add'( X ) ) ],
% 0.90/1.29 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.90/1.29 'class_OrderedGroup_Oab__group__add'( X ) ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Oring__1'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.90/1.29 'class_Ring__and__Field_Ocomm__ring__1'( X ) ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Oring'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.90/1.29 'class_Ring__and__Field_Ocomm__ring'( X ) ) ],
% 0.90/1.29 [ 'class_Ring__and__Field_Oidom'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.90/1.29 'class_Ring__and__Field_Oidom'( X ) ) ],
% 0.90/1.29 [ 'class_Nat_Osemiring__char__0'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.90/1.29 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.90/1.29 [ 'class_Orderings_Opreorder'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.90/1.29 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.90/1.29 [ 'class_Orderings_Olinorder'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.90/1.29 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.90/1.29 [ 'class_Orderings_Oorder'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.90/1.29 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.90/1.29 [ 'class_Int_Oring__char__0'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.90/1.29 'class_Ring__and__Field_Oordered__idom'( X ) ) ],
% 0.90/1.29 [ 'class_Int_Onumber__ring'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.90/1.29 'class_Ring__and__Field_Ocomm__ring__1'( X ) ) ],
% 0.90/1.29 [ 'class_Power_Opower'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.90/1.29 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ) ],
% 0.90/1.29 [ 'class_HOL_Ozero'( 'tc_Polynomial_Opoly'( X ) ), ~( 'class_HOL_Ozero'(
% 0.90/1.29 X ) ) ],
% 0.90/1.29 [ hBOOL( 'c_fequal'( X, X, Y ) ) ],
% 0.90/1.29 [ =( X, Y ), ~( hBOOL( 'c_fequal'( X, Y, Z ) ) ) ]
% 0.90/1.29 ] .
% 0.90/1.29
% 0.90/1.29
% 0.90/1.29 percentage equality = 0.234345, percentage horn = 0.917431
% 0.90/1.29 This is a problem with some equality
% 0.90/1.29
% 0.90/1.29
% 0.90/1.29
% 0.90/1.29 Options Used:
% 0.90/1.29
% 0.90/1.29 useres = 1
% 0.90/1.29 useparamod = 1
% 0.90/1.29 useeqrefl = 1
% 0.90/1.29 useeqfact = 1
% 0.90/1.29 usefactor = 1
% 0.90/1.29 usesimpsplitting = 0
% 0.90/1.29 usesimpdemod = 5
% 0.90/1.29 usesimpres = 3
% 0.90/1.29
% 0.90/1.29 resimpinuse = 1000
% 0.90/1.29 resimpclauses = 20000
% 0.90/1.29 substype = eqrewr
% 0.90/1.29 backwardsubs = 1
% 0.90/1.29 selectoldest = 5
% 0.90/1.29
% 0.90/1.29 litorderings [0] = split
% 0.90/1.29 litorderings [1] = extend the termordering, first sorting on arguments
% 0.90/1.29
% 0.90/1.29 termordering = kbo
% 0.90/1.29
% 0.90/1.29 litapriori = 0
% 0.90/1.29 termapriori = 1
% 0.90/1.29 litaposteriori = 0
% 0.90/1.29 termaposteriori = 0
% 0.90/1.29 demodaposteriori = 0
% 0.90/1.29 ordereqreflfact = 0
% 0.90/1.29
% 0.90/1.29 litselect = negord
% 0.90/1.29
% 0.90/1.29 maxweight = 15
% 0.90/1.29 maxdepth = 30000
% 0.90/1.29 maxlength = 115
% 0.90/1.29 maxnrvars = 195
% 0.90/1.29 excuselevel = 1
% 0.90/1.29 increasemaxweight = 1
% 0.90/1.29
% 0.90/1.29 maxselected = 10000000
% 0.90/1.29 maxnrclauses = 10000000
% 0.90/1.29
% 0.90/1.29 showgenerated = 0
% 0.90/1.29 showkept = 0
% 0.90/1.29 showselected = 0
% 0.90/1.29 showdeleted = 0
% 0.90/1.29 showresimp = 1
% 0.90/1.29 showstatus = 2000
% 0.90/1.29
% 0.90/1.29 prologoutput = 1
% 0.90/1.29 nrgoals = 5000000
% 0.90/1.29 totalproof = 1
% 0.90/1.29
% 0.90/1.29 Symbols occurring in the translation:
% 0.90/1.29
% 0.90/1.29 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 0.90/1.29 . [1, 2] (w:1, o:134, a:1, s:1, b:0),
% 0.90/1.29 ! [4, 1] (w:0, o:58, a:1, s:1, b:0),
% 0.90/1.29 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.90/1.29 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 0.90/1.29 'class_Ring__and__Field_Oordered__ring__strict' [40, 1] (w:1, o:65
% 0.90/1.29 , a:1, s:1, b:0),
% 0.90/1.29 'c_HOL_Ozero__class_Ozero' [41, 1] (w:1, o:66, a:1, s:1, b:0),
% 0.90/1.29 'c_HOL_Otimes__class_Otimes' [42, 1] (w:1, o:67, a:1, s:1, b:0),
% 0.90/1.29 hAPP [44, 2] (w:1, o:159, a:1, s:1, b:0),
% 0.90/1.29 'c_lessequals' [45, 3] (w:1, o:169, a:1, s:1, b:0),
% 0.90/1.29 'class_Ring__and__Field_Opordered__ring' [46, 1] (w:1, o:73, a:1, s:1
% 0.90/1.29 , b:0),
% 0.90/1.29 'class_Orderings_Oorder' [48, 1] (w:1, o:75, a:1, s:1, b:0),
% 0.90/1.29 'c_HOL_Oord__class_Oless' [49, 3] (w:1, o:170, a:1, s:1, b:0),
% 0.90/1.29 'class_Orderings_Olinorder' [50, 1] (w:1, o:76, a:1, s:1, b:0),
% 0.90/1.29 'tc_nat' [53, 0] (w:1, o:17, a:1, s:1, b:0),
% 0.90/1.29 'c_HOL_Oplus__class_Oplus' [54, 1] (w:1, o:78, a:1, s:1, b:0),
% 0.90/1.29 'c_Suc' [57, 1] (w:1, o:79, a:1, s:1, b:0),
% 0.90/1.29 'class_OrderedGroup_Ocomm__monoid__mult' [58, 1] (w:1, o:80, a:1, s:1
% 0.90/1.29 , b:0),
% 0.90/1.29 'c_Power_Opower__class_Opower' [59, 1] (w:1, o:81, a:1, s:1, b:0),
% 0.90/1.29 'class_Ring__and__Field_Ocomm__semiring__1' [60, 1] (w:1, o:85, a:1
% 0.90/1.29 , s:1, b:0),
% 0.90/1.29 'class_Ring__and__Field_Opordered__cancel__semiring' [62, 1] (w:1, o:
% 0.90/1.29 86, a:1, s:1, b:0),
% 0.90/1.29 'class_Int_Onumber__ring' [63, 1] (w:1, o:88, a:1, s:1, b:0),
% 0.90/1.29 'c_HOL_Ouminus__class_Ouminus' [64, 2] (w:1, o:160, a:1, s:1, b:0),
% 0.90/1.29 'c_HOL_Oone__class_Oone' [65, 1] (w:1, o:77, a:1, s:1, b:0),
% 0.90/1.29 'class_OrderedGroup_Oab__semigroup__mult' [66, 1] (w:1, o:89, a:1, s:
% 0.90/1.29 1, b:0),
% 0.90/1.29 'class_HOL_Ozero' [74, 1] (w:1, o:87, a:1, s:1, b:0),
% 0.90/1.29 'tc_Polynomial_Opoly' [76, 1] (w:1, o:90, a:1, s:1, b:0),
% 0.90/1.29 'c_Polynomial_OpCons' [78, 3] (w:1, o:174, a:1, s:1, b:0),
% 0.90/1.29 'c_Polynomial_Opoly__rec' [79, 5] (w:1, o:183, a:1, s:1, b:0),
% 0.90/1.29 'class_RealVector_Oreal__normed__algebra' [80, 1] (w:1, o:91, a:1, s:
% 0.90/1.29 1, b:0),
% 0.90/1.29 'class_Ring__and__Field_Ocomm__semiring' [85, 1] (w:1, o:92, a:1, s:1
% 0.90/1.29 , b:0),
% 0.90/1.29 'class_OrderedGroup_Oordered__ab__group__add' [86, 1] (w:1, o:93, a:1
% 0.90/1.29 , s:1, b:0),
% 0.90/1.29 'class_Ring__and__Field_Ocomm__semiring__0' [87, 1] (w:1, o:84, a:1
% 0.90/1.29 , s:1, b:0),
% 0.90/1.29 'c_Polynomial_Osmult' [88, 3] (w:1, o:175, a:1, s:1, b:0),
% 0.90/1.29 'class_Ring__and__Field_Oordered__idom' [89, 1] (w:1, o:68, a:1, s:1
% 0.90/1.29 , b:0),
% 0.90/1.29 'class_Ring__and__Field_Oordered__semidom' [90, 1] (w:1, o:69, a:1
% 0.90/1.29 , s:1, b:0),
% 0.90/1.29 'class_Ring__and__Field_Oidom' [91, 1] (w:1, o:94, a:1, s:1, b:0),
% 0.90/1.29 'class_Ring__and__Field_Oring' [92, 1] (w:1, o:95, a:1, s:1, b:0),
% 0.90/1.29 'class_Ring__and__Field_Opordered__semiring' [93, 1] (w:1, o:96, a:1
% 0.90/1.29 , s:1, b:0),
% 0.90/1.29 'c_Polynomial_Omonom' [95, 3] (w:1, o:176, a:1, s:1, b:0),
% 0.90/1.29 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly' [97, 3]
% 0.90/1.29 (w:1, o:177, a:1, s:1, b:0),
% 0.90/1.29 'class_OrderedGroup_Ocomm__monoid__add' [98, 1] (w:1, o:97, a:1, s:1
% 0.90/1.29 , b:0),
% 0.90/1.29 'class_OrderedGroup_Opordered__comm__monoid__add' [100, 1] (w:1, o:98
% 0.90/1.29 , a:1, s:1, b:0),
% 0.90/1.29 'class_Ring__and__Field_Osemiring__1' [101, 1] (w:1, o:103, a:1, s:1
% 0.90/1.29 , b:0),
% 0.90/1.29 'c_Nat_Osemiring__1__class_Oof__nat' [102, 2] (w:1, o:161, a:1, s:1
% 0.90/1.29 , b:0),
% 0.90/1.29 'c_Polynomial_Ocoeff' [103, 2] (w:1, o:162, a:1, s:1, b:0),
% 0.90/1.29 'class_Ring__and__Field_Ozero__neq__one' [104, 1] (w:1, o:104, a:1
% 0.90/1.29 , s:1, b:0),
% 0.90/1.29 'class_OrderedGroup_Opordered__ab__group__add' [105, 1] (w:1, o:105
% 0.90/1.29 , a:1, s:1, b:0),
% 0.90/1.29 'class_OrderedGroup_Omonoid__mult' [106, 1] (w:1, o:107, a:1, s:1, b:
% 0.90/1.29 0),
% 0.90/1.29 'c_Power_Opower_Opower' [107, 3] (w:1, o:178, a:1, s:1, b:0),
% 0.90/1.29 'class_OrderedGroup_Opordered__ab__semigroup__add' [108, 1] (w:1, o:
% 0.90/1.29 108, a:1, s:1, b:0),
% 0.90/1.30 'c_Polynomial_Odegree' [109, 2] (w:1, o:163, a:1, s:1, b:0),
% 0.90/1.30 'class_Ring__and__Field_Osemiring__0' [110, 1] (w:1, o:102, a:1, s:1
% 0.90/1.30 , b:0),
% 0.90/1.30 'class_Power_Opower' [111, 1] (w:1, o:121, a:1, s:1, b:0),
% 0.90/1.30 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [112, 1]
% 0.90/1.30 (w:1, o:109, a:1, s:1, b:0),
% 0.90/1.30 'class_OrderedGroup_Olordered__ab__group__add' [113, 1] (w:1, o:106
% 0.90/1.30 , a:1, s:1, b:0),
% 0.90/1.30 'class_RealVector_Oreal__normed__vector' [114, 1] (w:1, o:122, a:1
% 0.90/1.30 , s:1, b:0),
% 0.90/1.30 'c_RealVector_Onorm__class_Onorm' [115, 2] (w:1, o:164, a:1, s:1, b:0
% 0.90/1.30 ),
% 0.90/1.30 'class_OrderedGroup_Osemigroup__add' [116, 1] (w:1, o:110, a:1, s:1
% 0.90/1.30 , b:0),
% 0.90/1.30 'c_List_Ofoldl' [118, 5] (w:1, o:184, a:1, s:1, b:0),
% 0.90/1.30 'class_Ring__and__Field_Oring__1' [121, 1] (w:1, o:99, a:1, s:1, b:0)
% 0.90/1.30 ,
% 0.90/1.30 'class_Ring__and__Field_Oordered__semiring__strict' [122, 1] (w:1, o:
% 0.90/1.30 70, a:1, s:1, b:0),
% 0.90/1.30 'class_OrderedGroup_Oab__semigroup__idem__mult' [123, 1] (w:1, o:111
% 0.90/1.30 , a:1, s:1, b:0),
% 0.90/1.30 'class_Ring__and__Field_Omult__mono' [124, 1] (w:1, o:123, a:1, s:1
% 0.90/1.30 , b:0),
% 0.90/1.30 'class_Ring__and__Field_Omult__mono1' [125, 1] (w:1, o:124, a:1, s:1
% 0.90/1.30 , b:0),
% 0.90/1.30 'class_OrderedGroup_Ogroup__add' [126, 1] (w:1, o:112, a:1, s:1, b:0)
% 0.90/1.30 ,
% 0.90/1.30 'c_Fundamental__Theorem__Algebra__Mirabelle_Opsize' [127, 2] (w:1, o:
% 0.90/1.30 165, a:1, s:1, b:0),
% 0.90/1.30 'class_Ring__and__Field_Oring__1__no__zero__divisors' [128, 1] (w:1
% 0.90/1.30 , o:100, a:1, s:1, b:0),
% 0.90/1.30 'class_Ring__and__Field_Ono__zero__divisors' [129, 1] (w:1, o:64, a:1
% 0.90/1.30 , s:1, b:0),
% 0.90/1.30 'class_Ring__and__Field_Omult__zero' [130, 1] (w:1, o:63, a:1, s:1
% 0.90/1.30 , b:0),
% 0.90/1.30 'tc_RealDef_Oreal' [132, 0] (w:1, o:42, a:1, s:1, b:0),
% 0.90/1.30 'class_Lattices_Oboolean__algebra' [133, 1] (w:1, o:125, a:1, s:1, b:
% 0.90/1.30 0),
% 0.90/1.30 'class_Ring__and__Field_Oring__no__zero__divisors' [134, 1] (w:1, o:
% 0.90/1.30 101, a:1, s:1, b:0),
% 0.90/1.30 'class_Ring__and__Field_Oordered__semiring' [135, 1] (w:1, o:71, a:1
% 0.90/1.30 , s:1, b:0),
% 0.90/1.30 'class_Nat_Osemiring__char__0' [136, 1] (w:1, o:74, a:1, s:1, b:0),
% 0.90/1.30 'c_Polynomial_Opoly' [139, 2] (w:1, o:166, a:1, s:1, b:0),
% 0.90/1.30 'class_Orderings_Opreorder' [141, 1] (w:1, o:113, a:1, s:1, b:0),
% 0.90/1.30 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [142, 1]
% 0.90/1.30 (w:1, o:114, a:1, s:1, b:0),
% 0.90/1.30 'class_OrderedGroup_Oab__group__add' [143, 1] (w:1, o:115, a:1, s:1
% 0.90/1.30 , b:0),
% 0.90/1.30 'c_fequal' [146, 3] (w:1, o:179, a:1, s:1, b:0),
% 0.90/1.30 'c_HOL_OIf' [147, 4] (w:1, o:182, a:1, s:1, b:0),
% 0.90/1.30 'class_Ring__and__Field_Osemiring' [148, 1] (w:1, o:126, a:1, s:1, b:
% 0.90/1.30 0),
% 0.90/1.30 'class_Ring__and__Field_Oordered__comm__semiring__strict' [150, 1]
% 0.90/1.30 (w:1, o:72, a:1, s:1, b:0),
% 0.90/1.30 'class_OrderedGroup_Omonoid__add' [151, 1] (w:1, o:116, a:1, s:1, b:0
% 0.90/1.30 ),
% 0.90/1.30 'v_pa____' [152, 0] (w:1, o:45, a:1, s:1, b:0),
% 0.90/1.30 'tc_Complex_Ocomplex' [153, 0] (w:1, o:46, a:1, s:1, b:0),
% 0.90/1.30 'v_c____' [154, 0] (w:1, o:47, a:1, s:1, b:0),
% 0.90/1.30 'v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1' [155,
% 0.90/1.30 2] (w:1, o:167, a:1, s:1, b:0),
% 0.90/1.30 't_a' [156, 0] (w:1, o:48, a:1, s:1, b:0),
% 0.90/1.30
% 0.90/1.30 'v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2'
% 0.90/1.30 [157, 1] (w:1, o:127, a:1, s:1, b:0),
% 0.90/1.30 'class_OrderedGroup_Oab__semigroup__add' [158, 1] (w:1, o:117, a:1
% 0.90/1.30 , s:1, b:0),
% 0.90/1.30 'c_Polynomial_Opcompose' [159, 3] (w:1, o:180, a:1, s:1, b:0),
% 0.90/1.30 'c_Polynomial_Oorder' [160, 3] (w:1, o:173, a:1, s:1, b:0),
% 0.90/1.30 'class_OrderedGroup_Ocancel__ab__semigroup__add' [161, 1] (w:1, o:118
% 0.90/1.30 , a:1, s:1, b:0),
% 0.90/1.30 'class_OrderedGroup_Ocancel__semigroup__add' [162, 1] (w:1, o:119, a:
% 0.90/1.30 1, s:1, b:0),
% 0.90/1.30 'v_n____' [164, 0] (w:1, o:50, a:1, s:1, b:0),
% 0.90/1.30 'v_sko__unknown__thm__rrS__1' [165, 1] (w:1, o:128, a:1, s:1, b:0),
% 0.90/1.30 'v_p' [166, 0] (w:1, o:51, a:1, s:1, b:0),
% 0.90/1.30 'v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1' [
% 0.90/1.30 167, 1] (w:1, o:129, a:1, s:1, b:0),
% 0.90/1.30 'v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__2' [
% 0.90/1.30 168, 1] (w:1, o:130, a:1, s:1, b:0),
% 0.90/1.30 'v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__3' [
% 0.90/1.30 169, 1] (w:1, o:131, a:1, s:1, b:0),
% 0.90/1.30 'c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant' [170, 3] (w:1
% 0.90/1.30 , o:181, a:1, s:1, b:0),
% 0.90/1.30 'c_OrderedGroup_Ocomm__monoid__add__axioms' [171, 3] (w:1, o:171, a:1
% 0.90/1.30 , s:1, b:0),
% 0.90/1.30 'c_OrderedGroup_Omonoid__add__axioms' [172, 3] (w:1, o:172, a:1, s:1
% 0.90/1.30 , b:0),
% 0.90/1.30 'class_Int_Oring__char__0' [173, 1] (w:1, o:132, a:1, s:1, b:0),
% 0.90/1.30 't_b' [174, 0] (w:1, o:52, a:1, s:1, b:0),
% 0.90/1.30 'v_q____' [175, 0] (w:1, o:53, a:1, s:1, b:0),
% 0.90/1.30 'class_OrderedGroup_Ocancel__comm__monoid__add' [177, 1] (w:1, o:120
% 0.90/1.30 , a:1, s:1, b:0),
% 0.90/1.30 'class_Ring__and__Field_Ocomm__ring__1' [178, 1] (w:1, o:82, a:1, s:1
% 0.90/1.30 , b:0),
% 0.90/1.30 'class_Ring__and__Field_Ocomm__ring' [179, 1] (w:1, o:83, a:1, s:1
% 0.90/1.30 , b:0),
% 0.90/1.30 'tc_fun' [181, 2] (w:1, o:168, a:1, s:1, b:0),
% 0.90/1.30 hBOOL [182, 1] (w:1, o:133, a:1, s:1, b:0).
% 0.90/1.30
% 0.90/1.30
% 0.90/1.30 Starting Search:
% 0.90/1.30
% 0.90/1.30
% 0.90/1.30 Bliksems!, er is een bewijs:
% 0.90/1.30 % SZS status Unsatisfiable
% 0.90/1.30 % SZS output start Refutation
% 0.90/1.30
% 0.90/1.30 clause( 448, [ ~( 'c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant'(
% 0.90/1.30 'c_Polynomial_Opoly'( 'v_q____', 'tc_Complex_Ocomplex' ),
% 0.90/1.30 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ) ) ] )
% 0.90/1.30 .
% 0.90/1.30 clause( 449, [] )
% 0.90/1.30 .
% 0.90/1.30
% 0.90/1.30
% 0.90/1.30 % SZS output end Refutation
% 0.90/1.30 found a proof!
% 0.90/1.30
% 0.90/1.30 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.90/1.30
% 0.90/1.30 initialclauses(
% 0.90/1.30 [ clause( 451, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), X ) ] )
% 0.90/1.30 , clause( 452, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'( Z,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.30 , clause( 453, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'( Z,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.30 , clause( 454, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.30 , clause( 455, [ ~( 'class_Orderings_Oorder'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ), ~( 'c_lessequals'( Y, Z
% 0.90/1.30 , X ) ) ] )
% 0.90/1.30 , clause( 456, [ ~( 'class_Orderings_Oorder'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ), =(
% 0.90/1.30 Z, Y ) ] )
% 0.90/1.30 , clause( 457, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 0.90/1.30 , clause( 458, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~(
% 0.90/1.30 'c_lessequals'( Y, Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ] )
% 0.90/1.30 , clause( 459, [ ~( 'class_Orderings_Oorder'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ), =(
% 0.90/1.30 Y, Z ) ] )
% 0.90/1.30 , clause( 460, [ ~( 'class_Orderings_Oorder'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 0.90/1.30 , X ) ) ] )
% 0.90/1.30 , clause( 461, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 0.90/1.30 , clause( 462, [ ~( 'class_Orderings_Oorder'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 0.90/1.30 , X ) ) ] )
% 0.90/1.30 , clause( 463, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.90/1.30 X ), Y ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y,
% 0.90/1.30 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.90/1.30 , clause( 464, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.90/1.30 X ), Y ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.90/1.30 , clause( 465, [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ] )
% 0.90/1.30 , clause( 466, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ] )
% 0.90/1.30 , clause( 467, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.30 , clause( 468, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'( Z,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.30 , clause( 469, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X
% 0.90/1.30 ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.30 , clause( 470, [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 0.90/1.30 'c_HOL_Ouminus__class_Ouminus'( Y, X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 0.90/1.30 'c_HOL_Oone__class_Oone'( X ), X ) ), Y ) ) ] )
% 0.90/1.30 , clause( 471, [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ] )
% 0.90/1.30 , clause( 472, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ] )
% 0.90/1.30 , clause( 473, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ] )
% 0.90/1.30 , clause( 474, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ] )
% 0.90/1.30 , clause( 475, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ] )
% 0.90/1.30 , clause( 476, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ] )
% 0.90/1.30 , clause( 477, [ ~( 'class_HOL_Ozero'( X ) ), ~( =( hAPP( hAPP( hAPP( Y,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ) ), Z ), Z ) ), =( 'c_Polynomial_Opoly__rec'(
% 0.90/1.30 Z, Y, 'c_Polynomial_OpCons'( T, U, X ), W, X ), hAPP( hAPP( hAPP( Y, T )
% 0.90/1.30 , U ), 'c_Polynomial_Opoly__rec'( Z, Y, U, W, X ) ) ) ] )
% 0.90/1.30 , clause( 478, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T )
% 0.90/1.30 ) ) ] )
% 0.90/1.30 , clause( 479, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 0.90/1.30 ) ) ] )
% 0.90/1.30 , clause( 480, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 0.90/1.30 ) ) ] )
% 0.90/1.30 , clause( 481, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T )
% 0.90/1.30 ) ) ] )
% 0.90/1.30 , clause( 482, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T )
% 0.90/1.30 ) ) ] )
% 0.90/1.30 , clause( 483, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 0.90/1.30 ) ) ] )
% 0.90/1.30 , clause( 484, [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T )
% 0.90/1.30 ) ) ] )
% 0.90/1.30 , clause( 485, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 X ), Y ), Z ), X ) ) ] )
% 0.90/1.30 , clause( 486, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 X ), Z ), Y ), X ) ) ] )
% 0.90/1.30 , clause( 487, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 X ), Y ), Z ), X ) ) ] )
% 0.90/1.30 , clause( 488, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 X ), Z ), Y ), X ) ) ] )
% 0.90/1.30 , clause( 489, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 0.90/1.30 ~( =( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y ) ), =( Y,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.30 , clause( 490, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), ~(
% 0.90/1.30 =( 'c_Polynomial_Osmult'( Y, Z, X ), 'c_Polynomial_OpCons'( T, Z, X ) ) )
% 0.90/1.30 , =( Z, 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 0.90/1.30 , clause( 491, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_nat' ) ), X ) ] )
% 0.90/1.30 , clause( 492, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ) ), X ) ) ] )
% 0.90/1.30 , clause( 493, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.30 X ), Y ), T ) ), Z ) ) ] )
% 0.90/1.30 , clause( 494, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 0.90/1.30 'c_HOL_Oone__class_Oone'( X ) ), X ) ] )
% 0.90/1.30 , clause( 495, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 0.90/1.30 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), Z ),
% 0.90/1.30 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 X ), Y ), Z ), X ) ) ] )
% 0.90/1.30 , clause( 496, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 0.90/1.30 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), Z ),
% 0.90/1.30 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 X ), Y ), Z ), X ) ) ] )
% 0.90/1.30 , clause( 497, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 0.90/1.30 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), 'c_HOL_Ouminus__class_Ouminus'(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ] )
% 0.90/1.30 , clause( 498, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 0.90/1.30 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), 'c_HOL_Ouminus__class_Ouminus'(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ] )
% 0.90/1.30 , clause( 499, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 0.90/1.30 ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ] )
% 0.90/1.30 , clause( 500, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 0.90/1.30 ), 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ] )
% 0.90/1.30 , clause( 501, [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ),
% 0.90/1.30 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~(
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 0.90/1.30 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 0.90/1.30 , clause( 502, [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ),
% 0.90/1.30 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~(
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.90/1.30 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 0.90/1.30 , clause( 503, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.90/1.30 =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ),
% 0.90/1.30 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), 'c_Suc'( Z ) ) ) )
% 0.90/1.30 , =( Y, T ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) )
% 0.90/1.30 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.30 , clause( 504, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.90/1.30 'c_Polynomial_Osmult'( Y, 'c_Polynomial_Omonom'( Z, T, X ), X ),
% 0.90/1.30 'c_Polynomial_Omonom'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 0.90/1.30 , Z ), T, X ) ) ] )
% 0.90/1.30 , clause( 505, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.90/1.30 , Y ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP(
% 0.90/1.30 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.30 , clause( 506, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.90/1.30 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 0.90/1.30 ) ] )
% 0.90/1.30 , clause( 507, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y,
% 0.90/1.30 X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ] )
% 0.90/1.30 , clause( 508, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.90/1.30 , Z ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X )
% 0.90/1.30 ) ] )
% 0.90/1.30 , clause( 509, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y,
% 0.90/1.30 X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ] )
% 0.90/1.30 , clause( 510, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 'c_Polynomial_Osmult'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y ) ] )
% 0.90/1.30 , clause( 511, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.90/1.30 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly'(
% 0.90/1.30 'c_Polynomial_OpCons'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), X ), Z, X ), 'c_Polynomial_OpCons'( Y,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ) ) ] )
% 0.90/1.30 , clause( 512, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Polynomial_Opoly'( X ) ),
% 0.90/1.30 'c_Polynomial_Omonom'( Y, Z, X ) ), 'c_Polynomial_Omonom'( T, Z, X ) ),
% 0.90/1.30 'c_Polynomial_Omonom'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.90/1.30 T ), Z, X ) ) ] )
% 0.90/1.30 , clause( 513, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.90/1.30 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 0.90/1.30 Z, X ), ~( 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 0.90/1.30 , clause( 514, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.90/1.30 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 0.90/1.30 Y, X ), ~( 'c_lessequals'( Z, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.30 , clause( 515, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.90/1.30 X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) )
% 0.90/1.30 ), =( X, Z ) ] )
% 0.90/1.30 , clause( 516, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.90/1.30 X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) )
% 0.90/1.30 ), =( Y, Z ) ] )
% 0.90/1.30 , clause( 517, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.90/1.30 X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) )
% 0.90/1.30 ), =( Y, Z ) ] )
% 0.90/1.30 , clause( 518, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.30 , clause( 519, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 0.90/1.30 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.30 , clause( 520, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 0.90/1.30 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.30 , clause( 521, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X
% 0.90/1.30 ) ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 0.90/1.30 , Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.30 , clause( 522, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X
% 0.90/1.30 ) ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 0.90/1.30 , Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.30 , clause( 523, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X
% 0.90/1.30 ) ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 0.90/1.30 , Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.30 , clause( 524, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X
% 0.90/1.30 ) ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 0.90/1.30 , Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.30 , clause( 525, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X
% 0.90/1.30 ) ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 0.90/1.30 , Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 0.90/1.30 , clause( 526, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.90/1.30 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.30 , clause( 527, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.90/1.30 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.30 , clause( 528, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.90/1.30 'c_Suc'( X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.90/1.30 X ), 'c_Suc'( Y ) ) ) ] )
% 0.90/1.30 , clause( 529, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.90/1.30 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Suc'( Y ), X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 0.90/1.30 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ) ] )
% 0.90/1.30 , clause( 530, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y,
% 0.90/1.30 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.90/1.30 , clause( 531, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.90/1.30 , clause( 532, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.90/1.30 'c_Polynomial_Ocoeff'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), Y ), Z ), X ), T ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_Polynomial_Ocoeff'( Y, X ), T )
% 0.90/1.30 ), hAPP( 'c_Polynomial_Ocoeff'( Z, X ), T ) ) ) ] )
% 0.90/1.30 , clause( 533, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ] )
% 0.90/1.30 , clause( 534, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.90/1.30 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 0.90/1.30 ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 0.90/1.30 , clause( 535, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 0.90/1.30 , clause( 536, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), ~(
% 0.90/1.30 =( 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly'( Y, Z, X )
% 0.90/1.30 , 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ), =( Y,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 0.90/1.30 , clause( 537, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.30 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.30 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 0.90/1.30 , clause( 538, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.30 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_lessequals'( Y,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.30 , clause( 539, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP(
% 0.90/1.30 hAPP( 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X )
% 0.90/1.30 ), Y ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 0.90/1.30 , clause( 540, [ ~( 'class_HOL_Ozero'( X ) ), =( hAPP(
% 0.90/1.30 'c_Polynomial_Ocoeff'( 'c_Polynomial_Omonom'( Y, Z, X ), X ), Z ), Y ) ]
% 0.90/1.30 )
% 0.90/1.30 , clause( 541, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 0.90/1.30 ), Y ), 'c_Suc'( Z ) ), 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.30 , clause( 542, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.90/1.30 hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 0.90/1.30 ), Z ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 0.90/1.30 ), T ) ) ) ] )
% 0.90/1.30 , clause( 543, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X )
% 0.90/1.30 ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z )
% 0.90/1.30 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 0.90/1.30 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 0.90/1.30 , clause( 544, [ ~( 'class_HOL_Ozero'( X ) ), =( hAPP(
% 0.90/1.30 'c_Polynomial_Ocoeff'( 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'(
% 0.90/1.30 X ) ), X ), 'c_Polynomial_Odegree'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.90/1.30 )
% 0.90/1.30 , clause( 545, [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 0.90/1.30 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) )
% 0.90/1.30 ] )
% 0.90/1.30 , clause( 546, [ ~(
% 0.90/1.30 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 0.90/1.30 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.90/1.30 Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 0.90/1.30 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 0.90/1.30 , clause( 547, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.30 , clause( 548, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.30 , clause( 549, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.30 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.90/1.30 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 0.90/1.30 , clause( 550, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.30 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 0.90/1.30 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.30 , clause( 551, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ] )
% 0.90/1.30 , clause( 552, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.30 , clause( 553, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 0.90/1.30 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.90/1.30 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 0.90/1.30 , clause( 554, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 0.90/1.30 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 0.90/1.30 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.30 , clause( 555, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ] )
% 0.90/1.30 , clause( 556, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.30 , clause( 557, [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Odegree'(
% 0.90/1.30 'c_Polynomial_OpCons'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_nat' ) ) ] )
% 0.90/1.30 , clause( 558, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.30 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 0.90/1.30 , clause( 559, [ ~( 'class_HOL_Ozero'( X ) ), =( hAPP(
% 0.90/1.30 'c_Polynomial_Ocoeff'( 'c_Polynomial_OpCons'( Y, Z, X ), X ), 'c_Suc'( T
% 0.90/1.30 ) ), hAPP( 'c_Polynomial_Ocoeff'( Z, X ), T ) ) ] )
% 0.90/1.30 , clause( 560, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.90/1.30 'c_Suc'( X ) ), Y ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.30 'tc_nat' ), X ), Y ) ) ) ] )
% 0.90/1.30 , clause( 561, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X )
% 0.90/1.30 , 'c_Suc'( Y ) ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.30 'tc_nat' ), X ), Y ) ) ) ] )
% 0.90/1.30 , clause( 562, [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 0.90/1.30 'c_RealVector_Onorm__class_Onorm'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 0.90/1.30 , X ), 'c_RealVector_Onorm__class_Onorm'( Y, X ) ) ] )
% 0.90/1.30 , clause( 563, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X )
% 0.90/1.30 , Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ]
% 0.90/1.30 )
% 0.90/1.30 , clause( 564, [ ~( 'class_OrderedGroup_Osemigroup__add'( X ) ), =(
% 0.90/1.30 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), T, X, X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldl'(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Z, T, X, X ) ) ) ] )
% 0.90/1.30 , clause( 565, [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 0.90/1.30 'c_Suc'( U ) ), hAPP( hAPP( Y, T ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 0.90/1.30 X, Y, Z ), T ), U ) ) ) ] )
% 0.90/1.30 , clause( 566, [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =( hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 0.90/1.30 ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 0.90/1.30 'c_HOL_Oone__class_Oone'( X ), X ) ), Z ) ), hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ] )
% 0.90/1.30 , clause( 567, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =(
% 0.90/1.30 'c_Polynomial_Odegree'( 'c_Polynomial_Osmult'( Y, Z, X ), X ),
% 0.90/1.30 'c_Polynomial_Odegree'( Z, X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.90/1.30 ] )
% 0.90/1.30 , clause( 568, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.90/1.30 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 0.90/1.30 , X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ] )
% 0.90/1.30 , clause( 569, [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_Ocoeff'(
% 0.90/1.30 Y, X ), 'c_Polynomial_Ocoeff'( Z, X ) ) ), =( Y, Z ) ] )
% 0.90/1.30 , clause( 570, [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Omonom'( Y,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X ), 'c_Polynomial_OpCons'( Y,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ) ) ] )
% 0.90/1.30 , clause( 571, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.90/1.30 ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 X ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X
% 0.90/1.30 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.90/1.30 T, X ) ) ] )
% 0.90/1.30 , clause( 572, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) )
% 0.90/1.30 , =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), Y ) ] )
% 0.90/1.30 , clause( 573, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.90/1.30 'c_Polynomial_Osmult'( Y, 'c_Polynomial_OpCons'( Z, T, X ), X ),
% 0.90/1.30 'c_Polynomial_OpCons'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 0.90/1.30 , Z ), 'c_Polynomial_Osmult'( Y, T, X ), X ) ) ] )
% 0.90/1.30 , clause( 574, [ ~( =( 'c_Suc'( X ), X ) ) ] )
% 0.90/1.30 , clause( 575, [ ~( =( X, 'c_Suc'( X ) ) ) ] )
% 0.90/1.30 , clause( 576, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.90/1.30 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~(
% 0.90/1.30 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.90/1.30 'c_lessequals'( T, Y, X ) ) ] )
% 0.90/1.30 , clause( 577, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 0.90/1.30 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 0.90/1.30 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.90/1.30 'c_lessequals'( T, Z, X ) ) ] )
% 0.90/1.30 , clause( 578, [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ),
% 0.90/1.30 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~(
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.90/1.30 'c_lessequals'( Y, T, X ) ) ] )
% 0.90/1.30 , clause( 579, [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ),
% 0.90/1.30 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.90/1.30 'c_lessequals'( Z, T, X ) ) ] )
% 0.90/1.30 , clause( 580, [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ),
% 0.90/1.30 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.90/1.30 'c_lessequals'( Z, T, X ) ) ] )
% 0.90/1.30 , clause( 581, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 0.90/1.30 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 0.90/1.30 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 0.90/1.30 , clause( 582, [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_OpCons'(
% 0.90/1.30 Y, Z, X ), 'c_Polynomial_OpCons'( T, U, X ) ) ), =( Y, T ) ] )
% 0.90/1.30 , clause( 583, [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_OpCons'(
% 0.90/1.30 Y, Z, X ), 'c_Polynomial_OpCons'( T, U, X ) ) ), =( Z, U ) ] )
% 0.90/1.30 , clause( 584, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 0.90/1.30 , Z ) ), Z ) ] )
% 0.90/1.30 , clause( 585, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.90/1.30 ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 0.90/1.30 , clause( 586, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.90/1.30 ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.30 , clause( 587, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.90/1.30 ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.30 , clause( 588, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 0.90/1.30 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 X ), X ) ) ] )
% 0.90/1.30 , clause( 589, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.90/1.30 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 X ), X ) ) ] )
% 0.90/1.30 , clause( 590, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 X ), X ) ) ] )
% 0.90/1.30 , clause( 591, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 X ), X ) ) ] )
% 0.90/1.30 , clause( 592, [ ~( 'class_HOL_Ozero'( X ) ), =(
% 0.90/1.30 'c_Fundamental__Theorem__Algebra__Mirabelle_Opsize'( Y, X ), 'c_Suc'(
% 0.90/1.30 'c_Polynomial_Odegree'( Y, X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 0.90/1.30 , clause( 593, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) )
% 0.90/1.30 ] )
% 0.90/1.30 , clause( 594, [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 0.90/1.30 , clause( 595, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.30 , clause( 596, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.30 , clause( 597, [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 0.90/1.30 X ) ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.90/1.30 ) ) ] )
% 0.90/1.30 , clause( 598, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.90/1.30 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.90/1.30 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.90/1.30 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.90/1.30 ) ) ] )
% 0.90/1.30 , clause( 599, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) )
% 0.90/1.30 , =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ] )
% 0.90/1.30 , clause( 600, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.90/1.30 , Y ), 'c_HOL_Oone__class_Oone'( X ) ), X ) ] )
% 0.90/1.30 , clause( 601, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.30 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 0.90/1.30 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.30 , clause( 602, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.30 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 0.90/1.30 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ] )
% 0.90/1.30 , clause( 603, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.90/1.30 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 0.90/1.30 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ) ] )
% 0.90/1.30 , clause( 604, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 0.90/1.30 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 0.90/1.30 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), Z ) ) ] )
% 0.90/1.30 , clause( 605, [ ~(
% 0.90/1.30 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.90/1.30 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 0.90/1.30 'c_lessequals'( Y, T, X ) ) ] )
% 0.90/1.30 , clause( 606, [ ~(
% 0.90/1.30 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.90/1.30 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ] )
% 0.90/1.30 , clause( 607, [ ~(
% 0.90/1.30 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.90/1.30 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 0.90/1.30 'c_lessequals'( Z, T, X ) ) ] )
% 0.90/1.30 , clause( 608, [ ~(
% 0.90/1.30 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.90/1.30 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ] )
% 0.90/1.30 , clause( 609, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X )
% 0.90/1.30 ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z )
% 0.90/1.30 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 0.90/1.30 'c_lessequals'( Y, T, X ) ) ] )
% 0.90/1.30 , clause( 610, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X )
% 0.90/1.30 ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z )
% 0.90/1.30 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 0.90/1.30 'c_lessequals'( Z, T, X ) ) ] )
% 0.90/1.30 , clause( 611, [ ~( 'class_HOL_Ozero'( X ) ), ~( =( hAPP(
% 0.90/1.30 'c_Polynomial_Ocoeff'( Y, X ), 'c_Polynomial_Odegree'( Y, X ) ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 0.90/1.30 , clause( 612, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.90/1.30 ), =( Z, Y ) ] )
% 0.90/1.30 , clause( 613, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 0.90/1.30 ) ] )
% 0.90/1.30 , clause( 614, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.90/1.30 ) ] )
% 0.90/1.30 , clause( 615, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 0.90/1.30 , clause( 616, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 0.90/1.30 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ] )
% 0.90/1.30 , clause( 617, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 0.90/1.30 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 0.90/1.30 , clause( 618, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 0.90/1.30 ), =( Z, Y ) ] )
% 0.90/1.30 , clause( 619, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 0.90/1.30 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 0.90/1.30 , clause( 620, [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_RealDef_Oreal' ) )
% 0.90/1.30 , ~( 'c_lessequals'( X, Y, 'tc_RealDef_Oreal' ) ) ] )
% 0.90/1.30 , clause( 621, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 0.90/1.30 , clause( 622, [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =(
% 0.90/1.30 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 0.90/1.30 , X ) ) ), =( Y, Z ) ] )
% 0.90/1.30 , clause( 623, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.90/1.30 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 0.90/1.30 , X ) ) ), =( Y, Z ) ] )
% 0.90/1.30 , clause( 624, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), U ) ) ) ] )
% 0.90/1.30 , clause( 625, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ) ) ] )
% 0.90/1.30 , clause( 626, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ] )
% 0.90/1.30 , clause( 627, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.90/1.30 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.90/1.30 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.30 , clause( 628, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.90/1.30 ] )
% 0.90/1.30 , clause( 629, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.90/1.30 ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 0.90/1.30 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.90/1.30 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.30 , clause( 630, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.90/1.30 ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 0.90/1.30 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z
% 0.90/1.30 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 0.90/1.30 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.30 , clause( 631, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.90/1.30 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.30 Z, Y, X ) ) ] )
% 0.90/1.30 , clause( 632, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.30 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 0.90/1.30 , X ), X ) ) ] )
% 0.90/1.30 , clause( 633, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 0.90/1.30 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 X ), X ) ) ] )
% 0.90/1.30 , clause( 634, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 0.90/1.30 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ] )
% 0.90/1.30 , clause( 635, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =(
% 0.90/1.30 'c_Polynomial_Odegree'( 'c_Polynomial_Osmult'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 X ), Y, X ), X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.90/1.30 , clause( 636, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.30 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ) ] )
% 0.90/1.30 , clause( 637, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.90/1.30 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.90/1.30 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 0.90/1.30 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ] )
% 0.90/1.30 , clause( 638, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.90/1.30 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.90/1.30 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 0.90/1.30 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X ) ) ] )
% 0.90/1.30 , clause( 639, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.90/1.30 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.30 , clause( 640, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.30 , clause( 641, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X )
% 0.90/1.30 ), ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 0.90/1.30 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.30 , clause( 642, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 0.90/1.30 ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 0.90/1.30 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.30 , clause( 643, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 0.90/1.30 ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.90/1.30 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.30 , clause( 644, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), ~(
% 0.90/1.30 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Polynomial_Opoly'( X ) ),
% 0.90/1.30 'c_Polynomial_Osmult'( Y, Z, X ) ), 'c_Polynomial_OpCons'( T, Z, X ) ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ), =( Z,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 0.90/1.30 , clause( 645, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.90/1.30 X ), Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.90/1.30 , clause( 646, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.90/1.30 X ), Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.90/1.30 , clause( 647, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ) ] )
% 0.90/1.30 , clause( 648, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =( hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ), =( Y,
% 0.90/1.30 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), =( Y, Z ) ] )
% 0.90/1.30 , clause( 649, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.90/1.30 ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ] )
% 0.90/1.30 , clause( 650, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.90/1.30 ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ] )
% 0.90/1.30 , clause( 651, [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ] )
% 0.90/1.30 , clause( 652, [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ] )
% 0.90/1.30 , clause( 653, [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 0.90/1.30 ), X ), Y ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.90/1.30 , clause( 654, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.90/1.30 X ), Y ), X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.90/1.30 , clause( 655, [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 0.90/1.30 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.90/1.30 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ] )
% 0.90/1.30 , clause( 656, [ ~( 'class_Power_Opower'( X ) ), =(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), 'c_Power_Opower_Opower'(
% 0.90/1.30 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Otimes__class_Otimes'( X ), X ) ) ]
% 0.90/1.30 )
% 0.90/1.30 , clause( 657, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 0.90/1.30 ), X ) ] )
% 0.90/1.30 , clause( 658, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.90/1.30 'c_Polynomial_Osmult'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.90/1.30 Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), 'c_Polynomial_Osmult'( Y, T, X ) ),
% 0.90/1.30 'c_Polynomial_Osmult'( Z, T, X ) ) ) ] )
% 0.90/1.30 , clause( 659, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.90/1.30 'c_Polynomial_Osmult'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), Z ), T ), X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'tc_Polynomial_Opoly'( X ) ),
% 0.90/1.30 'c_Polynomial_Osmult'( Y, Z, X ) ), 'c_Polynomial_Osmult'( Y, T, X ) ) )
% 0.90/1.30 ] )
% 0.90/1.30 , clause( 660, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X )
% 0.90/1.30 ) ) ] )
% 0.90/1.30 , clause( 661, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X )
% 0.90/1.30 ) ) ] )
% 0.90/1.30 , clause( 662, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.30 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 0.90/1.30 , X ), X ) ) ] )
% 0.90/1.30 , clause( 663, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.90/1.30 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_lessequals'( Z, Y, X )
% 0.90/1.30 ) ] )
% 0.90/1.30 , clause( 664, [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 0.90/1.30 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.90/1.30 'c_Suc'( Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.30 , clause( 665, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.90/1.30 ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 X ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X
% 0.90/1.30 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.90/1.30 T, X ) ) ] )
% 0.90/1.30 , clause( 666, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.90/1.30 hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Oone__class_Oone'(
% 0.90/1.30 'tc_nat' ) ), Y ) ] )
% 0.90/1.30 , clause( 667, [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_OpCons'(
% 0.90/1.30 Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ),
% 0.90/1.30 =( Z, 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 0.90/1.30 , clause( 668, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ] )
% 0.90/1.30 , clause( 669, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.30 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 0.90/1.30 Y ) ) ] )
% 0.90/1.30 , clause( 670, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 0.90/1.30 , clause( 671, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 0.90/1.30 , clause( 672, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Polynomial_Opoly'( X ) ),
% 0.90/1.30 'c_Polynomial_OpCons'( Y, Z, X ) ), 'c_Polynomial_OpCons'( T, U, X ) ),
% 0.90/1.30 'c_Polynomial_OpCons'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.90/1.30 T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Polynomial_Opoly'( X ) )
% 0.90/1.30 , Z ), U ), X ) ) ] )
% 0.90/1.30 , clause( 673, [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_Suc'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.90/1.30 , clause( 674, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 0.90/1.30 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), Y ) ] )
% 0.90/1.30 , clause( 675, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP(
% 0.90/1.30 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 0.90/1.30 'tc_nat' ) ), Y ) ] )
% 0.90/1.30 , clause( 676, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.90/1.30 , clause( 677, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y,
% 0.90/1.30 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.90/1.30 , clause( 678, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.30 , clause( 679, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( 'c_Polynomial_Opoly'( 'c_Polynomial_Omonom'( Y, Z, X ), X ), T ),
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ) ] )
% 0.90/1.30 , clause( 680, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.30 , clause( 681, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.90/1.30 'class_Int_Onumber__ring'( X ) ), ~( =( hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U )
% 0.90/1.30 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ), =( Z, U ), =( Y, T ) ]
% 0.90/1.30 )
% 0.90/1.30 , clause( 682, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.90/1.30 'class_Int_Onumber__ring'( X ) ), ~( =( hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U )
% 0.90/1.30 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ), =( Z, U ), =( Y, T ) ]
% 0.90/1.30 )
% 0.90/1.30 , clause( 683, [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Odegree'(
% 0.90/1.30 'c_Polynomial_Omonom'( Y, Z, X ), X ), Z ), =( Y,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.30 , clause( 684, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'(
% 0.90/1.30 X ), X ) ] )
% 0.90/1.30 , clause( 685, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.30 , clause( 686, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.30 , clause( 687, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.30 , clause( 688, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.30 , clause( 689, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.30 , clause( 690, [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.30 , clause( 691, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.30 , clause( 692, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.90/1.30 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.30 , clause( 693, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.30 , clause( 694, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X )
% 0.90/1.30 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.90/1.30 ] )
% 0.90/1.30 , clause( 695, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X )
% 0.90/1.30 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.30 , clause( 696, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), Z ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.30 X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ) ), Z ) ) ] )
% 0.90/1.30 , clause( 697, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.30 X ), Z ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ] )
% 0.90/1.30 , clause( 698, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), ~(
% 0.90/1.30 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Polynomial_Opoly'( X ) ),
% 0.90/1.30 Y ), 'c_Polynomial_Osmult'( Z, T, X ) ), 'c_Polynomial_OpCons'( U, T, X )
% 0.90/1.30 ) ), =( U, hAPP( 'c_Polynomial_Opoly'( Y, X ), Z ) ) ] )
% 0.90/1.30 , clause( 699, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_nat' ) ) ) ] )
% 0.90/1.30 , clause( 700, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 0.90/1.30 , clause( 701, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 0.90/1.30 , clause( 702, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 0.90/1.30 , clause( 703, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ), ~(
% 0.90/1.30 'c_lessequals'( Y, Z, X ) ) ] )
% 0.90/1.30 , clause( 704, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.90/1.30 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 X ), X ) ) ] )
% 0.90/1.30 , clause( 705, [ ~(
% 0.90/1.30 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.90/1.30 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.90/1.30 T, X ) ) ] )
% 0.90/1.30 , clause( 706, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z,
% 0.90/1.30 X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 0.90/1.30 , clause( 707, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y,
% 0.90/1.30 Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 0.90/1.30 , clause( 708, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 0.90/1.30 , X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ), Z ) ]
% 0.90/1.30 )
% 0.90/1.30 , clause( 709, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 0.90/1.30 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), Z ) ] )
% 0.90/1.30 , clause( 710, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.90/1.30 ) ) ] )
% 0.90/1.30 , clause( 711, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.90/1.30 ) ) ] )
% 0.90/1.30 , clause( 712, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), X ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 0.90/1.30 , clause( 713, [ ~( 'class_HOL_Ozero'( X ) ), =( hAPP(
% 0.90/1.30 'c_Polynomial_Ocoeff'( 'c_Polynomial_OpCons'( Y, Z, X ), X ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y ) ] )
% 0.90/1.30 , clause( 714, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 0.90/1.30 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.90/1.30 , X ) ) ] )
% 0.90/1.30 , clause( 715, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.30 'c_HOL_Oone__class_Oone'( X ), X ) ] )
% 0.90/1.30 , clause( 716, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.30 , clause( 717, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.30 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 X ), Z, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( T ) ), hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), Z ), 'c_Suc'( T ) ), X ) ) ] )
% 0.90/1.30 , clause( 718, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.90/1.30 ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 X ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X
% 0.90/1.30 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 0.90/1.30 )
% 0.90/1.30 , clause( 719, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.90/1.30 ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 X ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X
% 0.90/1.30 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 0.90/1.30 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.90/1.30 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 0.90/1.30 )
% 0.90/1.30 , clause( 720, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.90/1.30 =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Z
% 0.90/1.30 , T ) ] )
% 0.90/1.30 , clause( 721, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ) ) ] )
% 0.90/1.30 , clause( 722, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ) ) ] )
% 0.90/1.30 , clause( 723, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 0.90/1.30 ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 0.90/1.30 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ) ] )
% 0.90/1.30 , clause( 724, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.90/1.30 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.30 , clause( 725, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 0.90/1.30 =( 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.30 , clause( 726, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =(
% 0.90/1.30 'c_Polynomial_Osmult'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 0.90/1.30 , clause( 727, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.90/1.30 'c_Polynomial_Osmult'( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 0.90/1.30 , clause( 728, [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ] )
% 0.90/1.30 , clause( 729, [ ~(
% 0.90/1.30 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ] )
% 0.90/1.30 , clause( 730, [ ~(
% 0.90/1.30 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.90/1.30 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 0.90/1.30 , clause( 731, [ ~(
% 0.90/1.30 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.90/1.30 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 0.90/1.30 , clause( 732, [ ~(
% 0.90/1.30 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ] )
% 0.90/1.30 , clause( 733, [ ~(
% 0.90/1.30 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.90/1.30 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 0.90/1.30 , clause( 734, [ ~(
% 0.90/1.30 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.90/1.30 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 0.90/1.30 , clause( 735, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y,
% 0.90/1.30 Y, X ) ] )
% 0.90/1.30 , clause( 736, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y,
% 0.90/1.30 X ) ] )
% 0.90/1.30 , clause( 737, [ 'c_lessequals'( X, Y, 'tc_RealDef_Oreal' ), ~(
% 0.90/1.30 'c_lessequals'( Z, Y, 'tc_RealDef_Oreal' ) ), ~( 'c_lessequals'( X, Z,
% 0.90/1.30 'tc_RealDef_Oreal' ) ) ] )
% 0.90/1.30 , clause( 738, [ 'c_lessequals'( X, X, 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 739, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 0.90/1.30 , X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 0.90/1.30 , clause( 740, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( T, Z, X ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 0.90/1.30 , clause( 741, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.30 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 0.90/1.30 , X ), ~( 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ), X ) ) ] )
% 0.90/1.30 , clause( 742, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y,
% 0.90/1.30 Z, X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 0.90/1.30 )
% 0.90/1.30 , clause( 743, [ ~( 'class_Orderings_Oorder'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 0.90/1.30 , X ) ), ~( 'c_lessequals'( T, Z, X ) ) ] )
% 0.90/1.30 , clause( 744, [ ~( 'class_Orderings_Oorder'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 0.90/1.30 , clause( 745, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z,
% 0.90/1.30 X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ] )
% 0.90/1.30 , clause( 746, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.90/1.30 , clause( 747, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.90/1.30 hAPP( 'c_Polynomial_Opoly'( 'c_Polynomial_OpCons'( Y, Z, X ), X ), T ),
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( 'c_Polynomial_Opoly'( Z, X
% 0.90/1.30 ), T ) ) ) ) ] )
% 0.90/1.30 , clause( 748, [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Opoly__rec'(
% 0.90/1.30 Y, Z, 'c_Polynomial_OpCons'( T, U, X ), W, X ), hAPP( hAPP( hAPP( Z, T )
% 0.90/1.30 , U ), 'c_HOL_OIf'( 'c_fequal'( U, 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), 'tc_Polynomial_Opoly'( X ) ), Y,
% 0.90/1.30 'c_Polynomial_Opoly__rec'( Y, Z, U, W, X ), W ) ) ) ] )
% 0.90/1.30 , clause( 749, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ] )
% 0.90/1.30 , clause( 750, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ] )
% 0.90/1.30 , clause( 751, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ] )
% 0.90/1.30 , clause( 752, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ] )
% 0.90/1.30 , clause( 753, [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Omonom'( Y,
% 0.90/1.30 'c_Suc'( Z ), X ), 'c_Polynomial_OpCons'( 'c_HOL_Ozero__class_Ozero'( X )
% 0.90/1.30 , 'c_Polynomial_Omonom'( Y, Z, X ), X ) ) ] )
% 0.90/1.30 , clause( 754, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.30 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 0.90/1.30 , clause( 755, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.30 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.30 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.30 , clause( 756, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 0.90/1.30 ) ] )
% 0.90/1.30 , clause( 757, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 0.90/1.30 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 0.90/1.30 ] )
% 0.90/1.30 , clause( 758, [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_Omonom'(
% 0.90/1.30 Y, Z, X ), 'c_Polynomial_Omonom'( T, Z, X ) ) ), =( Y, T ) ] )
% 0.90/1.30 , clause( 759, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.90/1.30 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 0.90/1.30 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.90/1.30 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), 'c_HOL_Ouminus__class_Ouminus'(
% 0.90/1.30 Y, X ) ) ) ] )
% 0.90/1.30 , clause( 760, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 0.90/1.30 'c_HOL_Ouminus__class_Ouminus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 0.90/1.30 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.90/1.30 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), 'c_HOL_Ouminus__class_Ouminus'(
% 0.90/1.30 Z, X ) ) ) ] )
% 0.90/1.30 , clause( 761, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.90/1.30 Y, X ) ) ] )
% 0.90/1.30 , clause( 762, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.90/1.30 Y, X ) ) ] )
% 0.90/1.30 , clause( 763, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.90/1.30 Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 0.90/1.30 , clause( 764, [ 'c_lessequals'( X, Y, 'tc_RealDef_Oreal' ), 'c_lessequals'(
% 0.90/1.30 Y, X, 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 765, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.90/1.30 Y, X ) ) ] )
% 0.90/1.30 , clause( 766, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 0.90/1.30 Y, X ) ) ] )
% 0.90/1.30 , clause( 767, [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Odegree'(
% 0.90/1.30 'c_Polynomial_OpCons'( Y, Z, X ), X ), 'c_Suc'( 'c_Polynomial_Odegree'( Z
% 0.90/1.30 , X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) )
% 0.90/1.30 ) ] )
% 0.90/1.30 , clause( 768, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.90/1.30 'c_Polynomial_Odegree'(
% 0.90/1.30 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly'( Y, Z, X ), X
% 0.90/1.30 ), 'c_Polynomial_Odegree'( Y, X ) ) ] )
% 0.90/1.30 , clause( 769, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.90/1.30 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), Y, X ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 0.90/1.30 , clause( 770, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X
% 0.90/1.30 ) ), Y ) ] )
% 0.90/1.30 , clause( 771, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) )
% 0.90/1.30 , Y ), Y ) ] )
% 0.90/1.30 , clause( 772, [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'(
% 0.90/1.30 X ) ), Y ), Y ) ] )
% 0.90/1.30 , clause( 773, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'(
% 0.90/1.30 X ) ), Y ), Y ) ] )
% 0.90/1.30 , clause( 774, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 0.90/1.30 'c_HOL_Oone__class_Oone'( X ) ), Y ) ] )
% 0.90/1.30 , clause( 775, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'(
% 0.90/1.30 X ) ), Y ), Y ) ] )
% 0.90/1.30 , clause( 776, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.90/1.30 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.90/1.30 , clause( 777, [ =( 'c_Suc'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.30 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ) ] )
% 0.90/1.30 , clause( 778, [ =( 'c_Suc'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.30 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ] )
% 0.90/1.30 , clause( 779, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.30 , clause( 780, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.30 , clause( 781, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.90/1.30 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 0.90/1.30 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ] )
% 0.90/1.30 , clause( 782, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.90/1.30 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 0.90/1.30 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ] )
% 0.90/1.30 , clause( 783, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.90/1.30 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly'(
% 0.90/1.30 'c_Polynomial_OpCons'( Y, Z, X ), T, X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'tc_Polynomial_Opoly'( X ) ),
% 0.90/1.30 'c_Polynomial_Osmult'( T,
% 0.90/1.30 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly'( Z, T, X ), X
% 0.90/1.30 ) ), 'c_Polynomial_OpCons'( Y,
% 0.90/1.30 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly'( Z, T, X ), X
% 0.90/1.30 ) ) ) ] )
% 0.90/1.30 , clause( 784, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ),
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ] )
% 0.90/1.30 , clause( 785, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP(
% 0.90/1.30 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ) ) ] )
% 0.90/1.30 , clause( 786, [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ] )
% 0.90/1.30 , clause( 787, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ),
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ] )
% 0.90/1.30 , clause( 788, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.90/1.30 hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 0.90/1.30 ), Z ) ) ) ] )
% 0.90/1.30 , clause( 789, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.90/1.30 hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 0.90/1.30 ), Z ) ), Y ) ) ] )
% 0.90/1.30 , clause( 790, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ] )
% 0.90/1.30 , clause( 791, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.90/1.30 , clause( 792, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ] )
% 0.90/1.30 , clause( 793, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 0.90/1.30 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ] )
% 0.90/1.30 , clause( 794, [ ~( 'class_Orderings_Oorder'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 0.90/1.30 , X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 0.90/1.30 , clause( 795, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 0.90/1.30 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 0.90/1.30 , clause( 796, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.90/1.30 hAPP( 'c_Polynomial_Ocoeff'( 'c_Polynomial_Osmult'( Y, Z, X ), X ), T ),
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 0.90/1.30 'c_Polynomial_Ocoeff'( Z, X ), T ) ) ) ] )
% 0.90/1.30 , clause( 797, [ ~( 'class_HOL_Ozero'( X ) ), =( hAPP(
% 0.90/1.30 'c_Polynomial_Ocoeff'( 'c_Polynomial_Omonom'( Y, Z, X ), X ), T ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, T ) ] )
% 0.90/1.30 , clause( 798, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ] )
% 0.90/1.30 , clause( 799, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X )
% 0.90/1.30 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ] )
% 0.90/1.30 , clause( 800, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 0.90/1.30 ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ] )
% 0.90/1.30 , clause( 801, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP(
% 0.90/1.30 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ) ] )
% 0.90/1.30 , clause( 802, [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'(
% 0.90/1.30 Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ] )
% 0.90/1.30 , clause( 803, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 0.90/1.30 , clause( 804, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'(
% 0.90/1.30 Y, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 0.90/1.30 , clause( 805, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, Y, X ), 'c_lessequals'( Y, Y, X ) ] )
% 0.90/1.30 , clause( 806, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 0.90/1.30 )
% 0.90/1.30 , clause( 807, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 0.90/1.30 Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 0.90/1.30 , clause( 808, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 0.90/1.30 , clause( 809, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'(
% 0.90/1.30 Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ] )
% 0.90/1.30 , clause( 810, [ ~(
% 0.90/1.30 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 0.90/1.30 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_HOL_Oord__class_Oless'(
% 0.90/1.30 Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 0.90/1.30 , clause( 811, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.30 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z )
% 0.90/1.30 , hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~(
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 0.90/1.30 'c_lessequals'( Y, T, X ) ) ] )
% 0.90/1.30 , clause( 812, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 0.90/1.30 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.30 , clause( 813, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 X ), X ) ) ] )
% 0.90/1.30 , clause( 814, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.90/1.30 ) ), 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ] )
% 0.90/1.30 , clause( 815, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.90/1.30 ) ), 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ] )
% 0.90/1.30 , clause( 816, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 0.90/1.30 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 0.90/1.30 'c_lessequals'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.30 , clause( 817, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ] )
% 0.90/1.30 , clause( 818, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 0.90/1.30 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 0.90/1.30 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.30 , clause( 819, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.30 , clause( 820, [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 X ), T ), Z ) ), U ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), U ) ) ] )
% 0.90/1.30 , clause( 821, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 X ), Z ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y )
% 0.90/1.30 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.30 , clause( 822, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 0.90/1.30 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.30 , clause( 823, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.90/1.30 X ), Y ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.90/1.30 , clause( 824, [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.90/1.30 X ), Y ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y,
% 0.90/1.30 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.90/1.30 , clause( 825, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 0.90/1.30 ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.30 , clause( 826, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 0.90/1.30 ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.30 , clause( 827, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.90/1.30 hAPP( 'c_Polynomial_Opoly'( 'c_Polynomial_Osmult'( Y, Z, X ), X ), T ),
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 0.90/1.30 'c_Polynomial_Opoly'( Z, X ), T ) ) ) ] )
% 0.90/1.30 , clause( 828, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.30 , clause( 829, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), Z ) ), =( Y,
% 0.90/1.30 'c_HOL_Ouminus__class_Ouminus'( T, X ) ) ] )
% 0.90/1.30 , clause( 830, [ ~(
% 0.90/1.30 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 0.90/1.30 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 0.90/1.30 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 0.90/1.30 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 0.90/1.30 , clause( 831, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 0.90/1.30 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 0.90/1.30 ), ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.30 , clause( 832, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 0.90/1.30 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 0.90/1.30 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 0.90/1.30 , clause( 833, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.90/1.30 ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 X ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 0.90/1.30 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 0.90/1.30 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 0.90/1.30 , clause( 834, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 0.90/1.30 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 0.90/1.30 ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.90/1.30 ), ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ] )
% 0.90/1.30 , clause( 835, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 0.90/1.30 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 0.90/1.30 ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.30 , clause( 836, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 0.90/1.30 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 0.90/1.30 ), ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.30 , clause( 837, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X
% 0.90/1.30 ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 0.90/1.30 X ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 0.90/1.30 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 0.90/1.30 ), ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 0.90/1.30 , clause( 838, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 0.90/1.30 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 0.90/1.30 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 0.90/1.30 ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 0.90/1.30 , clause( 839, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 0.90/1.30 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 0.90/1.30 ), ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.30 , clause( 840, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ] )
% 0.90/1.30 , clause( 841, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 0.90/1.30 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 0.90/1.30 ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.30 , clause( 842, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.30 , clause( 843, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.90/1.30 'c_Polynomial_Osmult'( Y, 'c_Polynomial_Osmult'( Z, T, X ), X ),
% 0.90/1.30 'c_Polynomial_Osmult'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 0.90/1.30 , Z ), T, X ) ) ] )
% 0.90/1.30 , clause( 844, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.30 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ] )
% 0.90/1.30 , clause( 845, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.30 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ] )
% 0.90/1.30 , clause( 846, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Polynomial_Opoly'( X ) ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ), Y ), Y ) ] )
% 0.90/1.30 , clause( 847, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Polynomial_Opoly'( X ) ), Y ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ), Y ) ] )
% 0.90/1.30 , clause( 848, [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.90/1.30 X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 0.90/1.30 , clause( 849, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X )
% 0.90/1.30 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ] )
% 0.90/1.30 , clause( 850, [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ] )
% 0.90/1.30 , clause( 851, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 0.90/1.30 , clause( 852, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.90/1.30 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 0.90/1.30 ), Y ) ] )
% 0.90/1.30 , clause( 853, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 0.90/1.30 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 0.90/1.30 ) ) ] )
% 0.90/1.30 , clause( 854, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 0.90/1.30 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 0.90/1.30 ) ) ] )
% 0.90/1.30 , clause( 855, [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 0.90/1.30 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 0.90/1.30 ), Y ) ] )
% 0.90/1.30 , clause( 856, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 0.90/1.30 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 0.90/1.30 ), Y ) ] )
% 0.90/1.30 , clause( 857, [ ~(
% 0.90/1.30 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.90/1.30 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 0.90/1.30 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 0.90/1.30 )
% 0.90/1.30 , clause( 858, [ ~(
% 0.90/1.30 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.90/1.30 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 0.90/1.30 )
% 0.90/1.30 , clause( 859, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 0.90/1.30 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 0.90/1.30 , X ) ) ] )
% 0.90/1.30 , clause( 860, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 0.90/1.30 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 0.90/1.30 , X ) ) ] )
% 0.90/1.30 , clause( 861, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 0.90/1.30 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 0.90/1.30 , X ) ) ] )
% 0.90/1.30 , clause( 862, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 0.90/1.30 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 0.90/1.30 , X ) ) ] )
% 0.90/1.30 , clause( 863, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ] )
% 0.90/1.30 , clause( 864, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ] )
% 0.90/1.30 , clause( 865, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.30 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 0.90/1.30 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 0.90/1.30 , clause( 866, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 0.90/1.30 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 0.90/1.30 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 0.90/1.30 , clause( 867, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 X ) ), Y ), Y ) ] )
% 0.90/1.30 , clause( 868, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ] )
% 0.90/1.30 , clause( 869, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.90/1.30 , Y ), Y ) ] )
% 0.90/1.30 , clause( 870, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 X ) ), Y ), Y ) ] )
% 0.90/1.30 , clause( 871, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.90/1.30 'class_Int_Onumber__ring'( X ) ), =( Y, hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 0.90/1.30 ] )
% 0.90/1.30 , clause( 872, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 0.90/1.30 ) ), Y ) ] )
% 0.90/1.30 , clause( 873, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 0.90/1.30 Y ) ] )
% 0.90/1.30 , clause( 874, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.90/1.30 Y ) ] )
% 0.90/1.30 , clause( 875, [ ~( =( hAPP( 'c_Polynomial_Opoly'( 'v_pa____',
% 0.90/1.30 'tc_Complex_Ocomplex' ), 'v_c____' ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_Complex_Ocomplex' ) ) ) ] )
% 0.90/1.30 , clause( 876, [ =( 'c_Fundamental__Theorem__Algebra__Mirabelle_Opsize'(
% 0.90/1.30 'v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1'( X, Y
% 0.90/1.30 ), 'tc_Complex_Ocomplex' ),
% 0.90/1.30 'c_Fundamental__Theorem__Algebra__Mirabelle_Opsize'( Y,
% 0.90/1.30 'tc_Complex_Ocomplex' ) ) ] )
% 0.90/1.30 , clause( 877, [ ~( 'class_Ring__and__Field_Oidom'( 't_a' ) ), ~( =(
% 0.90/1.30 'v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2'(
% 0.90/1.30 X ), 'c_HOL_Ozero__class_Ozero'( 't_a' ) ) ), =( hAPP(
% 0.90/1.30 'c_Polynomial_Opoly'( X, 't_a' ), Y ), 'c_HOL_Ozero__class_Ozero'( 't_a'
% 0.90/1.30 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 't_a' ) ) ] )
% 0.90/1.30 , clause( 878, [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Odegree'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.90/1.30 , clause( 879, [ ~( 'class_HOL_Ozero'( X ) ), =( hAPP(
% 0.90/1.30 'c_Polynomial_Ocoeff'( 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'(
% 0.90/1.30 X ) ), X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.30 , clause( 880, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.90/1.30 ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 0.90/1.30 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.30 , clause( 881, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 0.90/1.30 , Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.30 , clause( 882, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ouminus__class_Ouminus'( Y,
% 0.90/1.30 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.30 , clause( 883, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 0.90/1.30 , X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.30 , clause( 884, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 0.90/1.30 , Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.30 , clause( 885, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.90/1.30 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.90/1.30 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.90/1.30 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 0.90/1.30 ) ) ] )
% 0.90/1.30 , clause( 886, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 0.90/1.30 , clause( 887, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ] )
% 0.90/1.30 , clause( 888, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.30 X ), Y ), T ) ), Z ) ) ] )
% 0.90/1.30 , clause( 889, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.30 X ), Y ), Z ) ), T ) ) ] )
% 0.90/1.30 , clause( 890, [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 0.90/1.30 , clause( 891, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ] )
% 0.90/1.30 , clause( 892, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.30 X ), Y ), Z ) ), T ) ) ] )
% 0.90/1.30 , clause( 893, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 0.90/1.30 , clause( 894, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ] )
% 0.90/1.30 , clause( 895, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.30 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.30 , clause( 896, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.90/1.30 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 0.90/1.30 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.30 , clause( 897, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.90/1.30 'c_Polynomial_Opcompose'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 0.90/1.30 , clause( 898, [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_Omonom'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 0.90/1.30 , clause( 899, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.90/1.30 hAPP( 'c_Polynomial_Opoly'(
% 0.90/1.30 'c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly'( Y, Z, X ), X
% 0.90/1.30 ), T ), hAPP( 'c_Polynomial_Opoly'( Y, X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ] )
% 0.90/1.30 , clause( 900, [ ~(
% 0.90/1.30 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 0.90/1.30 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y, hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~( 'c_lessequals'(
% 0.90/1.30 Y, T, X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 0.90/1.30 ] )
% 0.90/1.30 , clause( 901, [ ~(
% 0.90/1.30 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 0.90/1.30 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y, hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~( 'c_lessequals'(
% 0.90/1.30 Y, Z, X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) )
% 0.90/1.30 ] )
% 0.90/1.30 , clause( 902, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.90/1.30 'class_Int_Onumber__ring'( X ) ), ~( =( Y, hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), =( Z,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.30 , clause( 903, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.30 ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 0.90/1.30 ) ) ] )
% 0.90/1.30 , clause( 904, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.90/1.30 ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.30 , clause( 905, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.90/1.30 ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.30 , clause( 906, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.90/1.30 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.30 , clause( 907, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.90/1.30 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.30 , clause( 908, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.90/1.30 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.30 , clause( 909, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 0.90/1.30 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.30 , clause( 910, [ 'c_lessequals'( 'c_RealVector_Onorm__class_Onorm'( hAPP(
% 0.90/1.30 'c_Polynomial_Opoly'( 'v_pa____', 'tc_Complex_Ocomplex' ), 'v_c____' ),
% 0.90/1.30 'tc_Complex_Ocomplex' ), 'c_RealVector_Onorm__class_Onorm'( hAPP(
% 0.90/1.30 'c_Polynomial_Opoly'( 'v_pa____', 'tc_Complex_Ocomplex' ), X ),
% 0.90/1.30 'tc_Complex_Ocomplex' ), 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 911, [ ~( 'class_HOL_Ozero'( X ) ), ~( =( hAPP( hAPP( hAPP( Y,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ) ), Z ), Z ) ), =( 'c_Polynomial_Opoly__rec'(
% 0.90/1.30 Z, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), T, X ), Z
% 0.90/1.30 ) ] )
% 0.90/1.30 , clause( 912, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( hAPP(
% 0.90/1.30 'c_Polynomial_Opoly'( Y, X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ), =(
% 0.90/1.30 'c_Polynomial_Oorder'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.90/1.30 ) ] )
% 0.90/1.30 , clause( 913, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 0.90/1.30 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 0.90/1.30 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 0.90/1.30 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.90/1.30 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.90/1.30 , clause( 914, [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 0.90/1.30 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 0.90/1.30 ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_nat' ) ) ] )
% 0.90/1.30 , clause( 915, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 0.90/1.30 ), Z ) ) ) ] )
% 0.90/1.30 , clause( 916, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 0.90/1.30 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 0.90/1.30 , clause( 917, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.90/1.30 'class_Int_Onumber__ring'( X ) ), ~( =( hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ), =( T, U ), =( Z,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.30 , clause( 918, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.30 , clause( 919, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.30 , clause( 920, [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_Omonom'(
% 0.90/1.30 Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ),
% 0.90/1.30 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.30 , clause( 921, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ] )
% 0.90/1.30 , clause( 922, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.30 , clause( 923, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.30 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) )
% 0.90/1.30 ) ] )
% 0.90/1.30 , clause( 924, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( hAPP(
% 0.90/1.30 'c_Polynomial_Opoly'( 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'(
% 0.90/1.30 X ) ), X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.30 , clause( 925, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.90/1.30 hAPP( 'c_Polynomial_Opoly'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 0.90/1.30 ] )
% 0.90/1.30 , clause( 926, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.90/1.30 'class_Int_Onumber__ring'( X ) ), ~( =( hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ] )
% 0.90/1.30 , clause( 927, [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) )
% 0.90/1.30 , ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ] )
% 0.90/1.30 , clause( 928, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 0.90/1.30 ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ] )
% 0.90/1.30 , clause( 929, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 0.90/1.30 ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ] )
% 0.90/1.30 , clause( 930, [ ~( 'class_HOL_Ozero'( X ) ), =( 'c_Polynomial_OpCons'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 0.90/1.30 , clause( 931, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 0.90/1.30 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.30 , clause( 932, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =(
% 0.90/1.30 'c_Polynomial_Osmult'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.90/1.30 )
% 0.90/1.30 , clause( 933, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ] )
% 0.90/1.30 , clause( 934, [ =( 'v_n____',
% 0.90/1.30 'c_Fundamental__Theorem__Algebra__Mirabelle_Opsize'( 'v_pa____',
% 0.90/1.30 'tc_Complex_Ocomplex' ) ) ] )
% 0.90/1.30 , clause( 935, [ ~( 'class_HOL_Ozero'( X ) ), =(
% 0.90/1.30 'c_Fundamental__Theorem__Algebra__Mirabelle_Opsize'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ), X ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 0.90/1.30 , clause( 936, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.90/1.30 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.30 , clause( 937, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.90/1.30 hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 0.90/1.30 ), T ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Z
% 0.90/1.30 ), T ) ) ) ] )
% 0.90/1.30 , clause( 938, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ] )
% 0.90/1.30 , clause( 939, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.30 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~( 'c_lessequals'(
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.30 , clause( 940, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.90/1.30 hAPP( 'c_Polynomial_Opoly'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), Y ), Z ), X ), T ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_Polynomial_Opoly'( Y, X ), T )
% 0.90/1.30 ), hAPP( 'c_Polynomial_Opoly'( Z, X ), T ) ) ) ] )
% 0.90/1.30 , clause( 941, [ ~( 'class_HOL_Ozero'( X ) ), ~( =(
% 0.90/1.30 'c_Fundamental__Theorem__Algebra__Mirabelle_Opsize'( Y, X ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 0.90/1.30 , clause( 942, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ] )
% 0.90/1.30 , clause( 943, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 0.90/1.30 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ] )
% 0.90/1.30 , clause( 944, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ] )
% 0.90/1.30 , clause( 945, [ ~( 'class_HOL_Ozero'( X ) ), ~( =( 'c_Polynomial_OpCons'(
% 0.90/1.30 Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ),
% 0.90/1.30 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.30 , clause( 946, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldl'(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ), Z, X, X
% 0.90/1.30 ) ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ) ) ]
% 0.90/1.30 )
% 0.90/1.30 , clause( 947, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( 'c_HOL_Ouminus__class_Ouminus'( Y
% 0.90/1.30 , X ), Z ) ] )
% 0.90/1.30 , clause( 948, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 0.90/1.30 Z, X ) ) ] )
% 0.90/1.30 , clause( 949, [ ~( =( hAPP( 'c_Polynomial_Opoly'( 'v_pa____',
% 0.90/1.30 'tc_Complex_Ocomplex' ), 'v_c____' ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_Complex_Ocomplex' ) ) ), =( hAPP( 'c_Polynomial_Opoly'( 'v_pa____',
% 0.90/1.30 'tc_Complex_Ocomplex' ), 'v_sko__unknown__thm__rrS__1'( 'v_pa____' ) ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_Complex_Ocomplex' ) ) ] )
% 0.90/1.30 , clause( 950, [ ~( 'class_HOL_Ozero'( 't_a' ) ), =(
% 0.90/1.30 'c_Fundamental__Theorem__Algebra__Mirabelle_Opsize'( 'v_p', 't_a' ),
% 0.90/1.30 'c_HOL_OIf'( 'c_fequal'( 'v_p', 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_Polynomial_Opoly'( 't_a' ) ), 'tc_Polynomial_Opoly'( 't_a' ) ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( 'c_Polynomial_Odegree'(
% 0.90/1.30 'v_p', 't_a' ) ), 'tc_nat' ) ) ] )
% 0.90/1.30 , clause( 951, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.90/1.30 hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.90/1.30 Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.30 , clause( 952, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 0.90/1.30 hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 0.90/1.30 , clause( 953, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.90/1.30 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 0.90/1.30 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 0.90/1.30 , clause( 954, [ ~( 'class_Ring__and__Field_Oidom'( 't_a' ) ), =( hAPP(
% 0.90/1.30 'c_Polynomial_Opoly'( X, 't_a' ), Y ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 't_a' ), hAPP( 'c_Polynomial_Opoly'( X, 't_a'
% 0.90/1.30 ), 'c_HOL_Ozero__class_Ozero'( 't_a' ) ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( 't_a' ), hAPP( hAPP(
% 0.90/1.30 'c_Power_Opower__class_Opower'( 't_a' ), Y ),
% 0.90/1.30 'v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1'( X
% 0.90/1.30 ) ) ), hAPP( 'c_Polynomial_Opoly'( 'c_Polynomial_OpCons'(
% 0.90/1.30 'v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__2'( X
% 0.90/1.30 ),
% 0.90/1.30 'v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__3'( X
% 0.90/1.30 ), 't_a' ), 't_a' ), Y ) ) ) ),
% 0.90/1.30 'c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant'(
% 0.90/1.30 'c_Polynomial_Opoly'( X, 't_a' ), 't_a', 't_a' ) ] )
% 0.90/1.30 , clause( 955, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 0.90/1.30 'c_OrderedGroup_Ocomm__monoid__add__axioms'( 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 X ), 'c_HOL_Oplus__class_Oplus'( X ), X ) ] )
% 0.90/1.30 , clause( 956, [ =( hAPP( 'c_Polynomial_Opoly'(
% 0.90/1.30 'v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1'( X, Y
% 0.90/1.30 ), 'tc_Complex_Ocomplex' ), Z ), hAPP( 'c_Polynomial_Opoly'( Y,
% 0.90/1.30 'tc_Complex_Ocomplex' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.30 'tc_Complex_Ocomplex' ), X ), Z ) ) ) ] )
% 0.90/1.30 , clause( 957, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ),
% 0.90/1.30 'c_OrderedGroup_Omonoid__add__axioms'( 'c_HOL_Ozero__class_Ozero'( X ),
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( X ), X ) ] )
% 0.90/1.30 , clause( 958, [ ~( 'class_Ring__and__Field_Oidom'( 't_a' ) ), =( hAPP(
% 0.90/1.30 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 0.90/1.30 'c_Fundamental__Theorem__Algebra__Mirabelle_Opsize'(
% 0.90/1.30 'v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__3'( X
% 0.90/1.30 ), 't_a' ) ),
% 0.90/1.30 'v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1'( X
% 0.90/1.30 ) ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ),
% 0.90/1.30 'c_Fundamental__Theorem__Algebra__Mirabelle_Opsize'( X, 't_a' ) ),
% 0.90/1.30 'c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant'(
% 0.90/1.30 'c_Polynomial_Opoly'( X, 't_a' ), 't_a', 't_a' ) ] )
% 0.90/1.30 , clause( 959, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =(
% 0.90/1.30 'c_Polynomial_Oorder'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 0.90/1.30 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ),
% 0.90/1.30 ~( =( hAPP( 'c_Polynomial_Opoly'( Z, X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 0.90/1.30 X ) ) ) ] )
% 0.90/1.30 , clause( 960, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =(
% 0.90/1.30 'c_Polynomial_Osmult'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 0.90/1.30 , clause( 961, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.90/1.30 'c_Polynomial_Osmult'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'( X ) ) ) ] )
% 0.90/1.30 , clause( 962, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.30 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 0.90/1.30 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.30 , clause( 963, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 0.90/1.30 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.30 , clause( 964, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X )
% 0.90/1.30 ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z )
% 0.90/1.30 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 0.90/1.30 , clause( 965, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) )
% 0.90/1.30 , =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 0.90/1.30 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 0.90/1.30 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 0.90/1.30 )
% 0.90/1.30 , clause( 966, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.90/1.30 'class_Int_Oring__char__0'( X ) ), ~( =( 'c_Polynomial_Opoly'( Y, X ),
% 0.90/1.30 'c_Polynomial_Opoly'( 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'(
% 0.90/1.30 X ) ), X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_Polynomial_Opoly'(
% 0.90/1.30 X ) ) ) ] )
% 0.90/1.30 , clause( 967, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 0.90/1.30 'class_Int_Oring__char__0'( X ) ), ~( =( 'c_Polynomial_Opoly'( Y, X ),
% 0.90/1.30 'c_Polynomial_Opoly'( Z, X ) ) ), =( Y, Z ) ] )
% 0.90/1.30 , clause( 968, [ =( hAPP( X, Y ), hAPP( X, Z ) ), ~(
% 0.90/1.30 'c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant'( X, 't_a', 't_b' )
% 0.90/1.30 ) ] )
% 0.90/1.30 , clause( 969, [ ~( 'class_Ring__and__Field_Oidom'( 't_a' ) ), ~( =(
% 0.90/1.30 'v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1'( X
% 0.90/1.30 ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 0.90/1.30 'c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant'(
% 0.90/1.30 'c_Polynomial_Opoly'( X, 't_a' ), 't_a', 't_a' ) ] )
% 0.90/1.30 , clause( 970, [ ~( 'c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant'(
% 0.90/1.30 'c_Polynomial_Opoly'( 'v_p', 'tc_Complex_Ocomplex' ),
% 0.90/1.30 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ) ) ] )
% 0.90/1.30 , clause( 971, [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), =(
% 0.90/1.30 hAPP( 'c_Polynomial_Opoly'( 'c_Polynomial_Opcompose'( Y, Z, X ), X ), T )
% 0.90/1.30 , hAPP( 'c_Polynomial_Opoly'( Y, X ), hAPP( 'c_Polynomial_Opoly'( Z, X )
% 0.90/1.30 , T ) ) ) ] )
% 0.90/1.30 , clause( 972, [ =( 'c_Fundamental__Theorem__Algebra__Mirabelle_Opsize'(
% 0.90/1.30 'v_q____', 'tc_Complex_Ocomplex' ),
% 0.90/1.30 'c_Fundamental__Theorem__Algebra__Mirabelle_Opsize'( 'v_pa____',
% 0.90/1.30 'tc_Complex_Ocomplex' ) ) ] )
% 0.90/1.30 , clause( 973, [ =( hAPP( 'c_Polynomial_Opoly'( 'v_q____',
% 0.90/1.30 'tc_Complex_Ocomplex' ), X ), hAPP( 'c_Polynomial_Opoly'( 'v_pa____',
% 0.90/1.30 'tc_Complex_Ocomplex' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 0.90/1.30 'tc_Complex_Ocomplex' ), 'v_c____' ), X ) ) ) ] )
% 0.90/1.30 , clause( 974, [ ~( 'c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant'(
% 0.90/1.30 'c_Polynomial_Opoly'( 'v_pa____', 'tc_Complex_Ocomplex' ),
% 0.90/1.30 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ) ) ] )
% 0.90/1.30 , clause( 975, [ ~( 'class_Ring__and__Field_Oidom'( 't_a' ) ), ~( =(
% 0.90/1.30 'v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__2'( X
% 0.90/1.30 ), 'c_HOL_Ozero__class_Ozero'( 't_a' ) ) ),
% 0.90/1.30 'c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant'(
% 0.90/1.30 'c_Polynomial_Opoly'( X, 't_a' ), 't_a', 't_a' ) ] )
% 0.90/1.30 , clause( 976, [ ~( 'c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant'(
% 0.90/1.30 'c_Polynomial_Opoly'( 'v_q____', 'tc_Complex_Ocomplex' ),
% 0.90/1.30 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ) ) ] )
% 0.90/1.30 , clause( 977, [ 'c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant'(
% 0.90/1.30 'c_Polynomial_Opoly'( 'v_q____', 'tc_Complex_Ocomplex' ),
% 0.90/1.30 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ) ] )
% 0.90/1.30 , clause( 978, [ 'class_OrderedGroup_Ocancel__comm__monoid__add'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.90/1.30 'class_OrderedGroup_Ocancel__comm__monoid__add'( X ) ) ] )
% 0.90/1.30 , clause( 979, [ 'class_Ring__and__Field_Ocomm__ring__1'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Ocomm__ring__1'(
% 0.90/1.30 X ) ) ] )
% 0.90/1.30 , clause( 980, [ 'class_Ring__and__Field_Ocomm__ring'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Ocomm__ring'( X
% 0.90/1.30 ) ) ] )
% 0.90/1.30 , clause( 981, [ 'class_OrderedGroup_Ocancel__comm__monoid__add'(
% 0.90/1.30 'tc_Complex_Ocomplex' ) ] )
% 0.90/1.30 , clause( 982, [ 'class_Ring__and__Field_Ocomm__ring__1'(
% 0.90/1.30 'tc_Complex_Ocomplex' ) ] )
% 0.90/1.30 , clause( 983, [ 'class_Ring__and__Field_Ocomm__ring'(
% 0.90/1.30 'tc_Complex_Ocomplex' ) ] )
% 0.90/1.30 , clause( 984, [ 'class_OrderedGroup_Ocancel__comm__monoid__add'(
% 0.90/1.30 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 985, [ 'class_Ring__and__Field_Ocomm__ring__1'(
% 0.90/1.30 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 986, [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_RealDef_Oreal' )
% 0.90/1.30 ] )
% 0.90/1.30 , clause( 987, [ 'class_OrderedGroup_Ocancel__comm__monoid__add'( 'tc_nat'
% 0.90/1.30 ) ] )
% 0.90/1.30 , clause( 988, [ 'class_Lattices_Oboolean__algebra'( 'tc_fun'( X, Y ) ),
% 0.90/1.30 ~( 'class_Lattices_Oboolean__algebra'( Y ) ) ] )
% 0.90/1.30 , clause( 989, [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 0.90/1.30 'class_Orderings_Opreorder'( Y ) ) ] )
% 0.90/1.30 , clause( 990, [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 0.90/1.30 'class_Orderings_Oorder'( Y ) ) ] )
% 0.90/1.30 , clause( 991, [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 0.90/1.30 'tc_nat' ) ] )
% 0.90/1.30 , clause( 992, [
% 0.90/1.30 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat' ) ]
% 0.90/1.30 )
% 0.90/1.30 , clause( 993, [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 0.90/1.30 'tc_nat' ) ] )
% 0.90/1.30 , clause( 994, [ 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 0.90/1.30 'tc_nat' ) ] )
% 0.90/1.30 , clause( 995, [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 0.90/1.30 'tc_nat' ) ] )
% 0.90/1.30 , clause( 996, [ 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 0.90/1.30 'tc_nat' ) ] )
% 0.90/1.30 , clause( 997, [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 0.90/1.30 'tc_nat' ) ] )
% 0.90/1.30 , clause( 998, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat'
% 0.90/1.30 ) ] )
% 0.90/1.30 , clause( 999, [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ]
% 0.90/1.30 )
% 0.90/1.30 , clause( 1000, [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' )
% 0.90/1.30 ] )
% 0.90/1.30 , clause( 1001, [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ]
% 0.90/1.30 )
% 0.90/1.30 , clause( 1002, [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' )
% 0.90/1.30 ] )
% 0.90/1.30 , clause( 1003, [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ]
% 0.90/1.30 )
% 0.90/1.30 , clause( 1004, [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ]
% 0.90/1.30 )
% 0.90/1.30 , clause( 1005, [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_nat' ) ]
% 0.90/1.30 )
% 0.90/1.30 , clause( 1006, [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ]
% 0.90/1.30 )
% 0.90/1.30 , clause( 1007, [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ] )
% 0.90/1.30 , clause( 1008, [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ] )
% 0.90/1.30 , clause( 1009, [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ] )
% 0.90/1.30 , clause( 1010, [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ] )
% 0.90/1.30 , clause( 1011, [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ] )
% 0.90/1.30 , clause( 1012, [ 'class_OrderedGroup_Osemigroup__add'( 'tc_nat' ) ] )
% 0.90/1.30 , clause( 1013, [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ] )
% 0.90/1.30 , clause( 1014, [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ] )
% 0.90/1.30 , clause( 1015, [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ] )
% 0.90/1.30 , clause( 1016, [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ] )
% 0.90/1.30 , clause( 1017, [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ] )
% 0.90/1.30 , clause( 1018, [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ] )
% 0.90/1.30 , clause( 1019, [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ] )
% 0.90/1.30 , clause( 1020, [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ] )
% 0.90/1.30 , clause( 1021, [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ] )
% 0.90/1.30 , clause( 1022, [ 'class_Orderings_Opreorder'( 'tc_nat' ) ] )
% 0.90/1.30 , clause( 1023, [ 'class_Orderings_Olinorder'( 'tc_nat' ) ] )
% 0.90/1.30 , clause( 1024, [ 'class_Orderings_Oorder'( 'tc_nat' ) ] )
% 0.90/1.30 , clause( 1025, [ 'class_Power_Opower'( 'tc_nat' ) ] )
% 0.90/1.30 , clause( 1026, [ 'class_HOL_Ozero'( 'tc_nat' ) ] )
% 0.90/1.30 , clause( 1027, [
% 0.90/1.30 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 0.90/1.30 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 1028, [
% 0.90/1.30 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 0.90/1.30 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 1029, [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 0.90/1.30 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 1030, [ 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 0.90/1.30 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 1031, [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 0.90/1.30 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 1032, [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 0.90/1.30 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 1033, [ 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 0.90/1.30 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 1034, [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 0.90/1.30 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 1035, [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 0.90/1.30 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 1036, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 0.90/1.30 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 1037, [ 'class_Ring__and__Field_Oordered__ring__strict'(
% 0.90/1.30 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 1038, [ 'class_OrderedGroup_Opordered__ab__group__add'(
% 0.90/1.30 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 1039, [ 'class_OrderedGroup_Olordered__ab__group__add'(
% 0.90/1.30 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 1040, [ 'class_OrderedGroup_Oordered__ab__group__add'(
% 0.90/1.30 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 1041, [ 'class_OrderedGroup_Ocancel__semigroup__add'(
% 0.90/1.30 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 1042, [ 'class_Ring__and__Field_Opordered__semiring'(
% 0.90/1.30 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 1043, [ 'class_Ring__and__Field_Oordered__semiring'(
% 0.90/1.30 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 1044, [ 'class_Ring__and__Field_Ono__zero__divisors'(
% 0.90/1.30 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 1045, [ 'class_Ring__and__Field_Oordered__semidom'(
% 0.90/1.30 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 1046, [ 'class_Ring__and__Field_Ocomm__semiring__1'(
% 0.90/1.30 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 1047, [ 'class_Ring__and__Field_Ocomm__semiring__0'(
% 0.90/1.30 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 1048, [ 'class_RealVector_Oreal__normed__algebra'(
% 0.90/1.30 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 1049, [ 'class_OrderedGroup_Oab__semigroup__mult'(
% 0.90/1.30 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 1050, [ 'class_RealVector_Oreal__normed__vector'(
% 0.90/1.30 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 1051, [ 'class_OrderedGroup_Ocomm__monoid__mult'(
% 0.90/1.30 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 1052, [ 'class_OrderedGroup_Oab__semigroup__add'(
% 0.90/1.30 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 1053, [ 'class_Ring__and__Field_Opordered__ring'(
% 0.90/1.30 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 1054, [ 'class_Ring__and__Field_Ocomm__semiring'(
% 0.90/1.30 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 1055, [ 'class_OrderedGroup_Ocomm__monoid__add'(
% 0.90/1.30 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 1056, [ 'class_Ring__and__Field_Ozero__neq__one'(
% 0.90/1.30 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 1057, [ 'class_Ring__and__Field_Oordered__idom'(
% 0.90/1.30 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 1058, [ 'class_OrderedGroup_Osemigroup__add'( 'tc_RealDef_Oreal'
% 0.90/1.30 ) ] )
% 0.90/1.30 , clause( 1059, [ 'class_Ring__and__Field_Osemiring__1'( 'tc_RealDef_Oreal'
% 0.90/1.30 ) ] )
% 0.90/1.30 , clause( 1060, [ 'class_Ring__and__Field_Osemiring__0'( 'tc_RealDef_Oreal'
% 0.90/1.30 ) ] )
% 0.90/1.30 , clause( 1061, [ 'class_Ring__and__Field_Omult__mono1'( 'tc_RealDef_Oreal'
% 0.90/1.30 ) ] )
% 0.90/1.30 , clause( 1062, [ 'class_OrderedGroup_Oab__group__add'( 'tc_RealDef_Oreal'
% 0.90/1.30 ) ] )
% 0.90/1.30 , clause( 1063, [ 'class_Ring__and__Field_Omult__zero'( 'tc_RealDef_Oreal'
% 0.90/1.30 ) ] )
% 0.90/1.30 , clause( 1064, [ 'class_Ring__and__Field_Omult__mono'( 'tc_RealDef_Oreal'
% 0.90/1.30 ) ] )
% 0.90/1.30 , clause( 1065, [ 'class_OrderedGroup_Omonoid__mult'( 'tc_RealDef_Oreal' )
% 0.90/1.30 ] )
% 0.90/1.30 , clause( 1066, [ 'class_Ring__and__Field_Osemiring'( 'tc_RealDef_Oreal' )
% 0.90/1.30 ] )
% 0.90/1.30 , clause( 1067, [ 'class_OrderedGroup_Omonoid__add'( 'tc_RealDef_Oreal' ) ]
% 0.90/1.30 )
% 0.90/1.30 , clause( 1068, [ 'class_OrderedGroup_Ogroup__add'( 'tc_RealDef_Oreal' ) ]
% 0.90/1.30 )
% 0.90/1.30 , clause( 1069, [ 'class_Ring__and__Field_Oring__1'( 'tc_RealDef_Oreal' ) ]
% 0.90/1.30 )
% 0.90/1.30 , clause( 1070, [ 'class_Ring__and__Field_Oring'( 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 1071, [ 'class_Ring__and__Field_Oidom'( 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 1072, [ 'class_Nat_Osemiring__char__0'( 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 1073, [ 'class_Orderings_Opreorder'( 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 1074, [ 'class_Orderings_Olinorder'( 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 1075, [ 'class_Orderings_Oorder'( 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 1076, [ 'class_Int_Oring__char__0'( 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 1077, [ 'class_Int_Onumber__ring'( 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 1078, [ 'class_Power_Opower'( 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 1079, [ 'class_HOL_Ozero'( 'tc_RealDef_Oreal' ) ] )
% 0.90/1.30 , clause( 1080, [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 0.90/1.30 'tc_Complex_Ocomplex' ) ] )
% 0.90/1.30 , clause( 1081, [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 0.90/1.30 'tc_Complex_Ocomplex' ) ] )
% 0.90/1.30 , clause( 1082, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 0.90/1.30 'tc_Complex_Ocomplex' ) ] )
% 0.90/1.30 , clause( 1083, [ 'class_OrderedGroup_Ocancel__semigroup__add'(
% 0.90/1.30 'tc_Complex_Ocomplex' ) ] )
% 0.90/1.30 , clause( 1084, [ 'class_Ring__and__Field_Ono__zero__divisors'(
% 0.90/1.30 'tc_Complex_Ocomplex' ) ] )
% 0.90/1.30 , clause( 1085, [ 'class_Ring__and__Field_Ocomm__semiring__1'(
% 0.90/1.30 'tc_Complex_Ocomplex' ) ] )
% 0.90/1.30 , clause( 1086, [ 'class_Ring__and__Field_Ocomm__semiring__0'(
% 0.90/1.30 'tc_Complex_Ocomplex' ) ] )
% 0.90/1.30 , clause( 1087, [ 'class_RealVector_Oreal__normed__algebra'(
% 0.90/1.30 'tc_Complex_Ocomplex' ) ] )
% 0.90/1.30 , clause( 1088, [ 'class_OrderedGroup_Oab__semigroup__mult'(
% 0.90/1.30 'tc_Complex_Ocomplex' ) ] )
% 0.90/1.30 , clause( 1089, [ 'class_RealVector_Oreal__normed__vector'(
% 0.90/1.30 'tc_Complex_Ocomplex' ) ] )
% 0.90/1.30 , clause( 1090, [ 'class_OrderedGroup_Ocomm__monoid__mult'(
% 0.90/1.30 'tc_Complex_Ocomplex' ) ] )
% 0.90/1.30 , clause( 1091, [ 'class_OrderedGroup_Oab__semigroup__add'(
% 0.90/1.30 'tc_Complex_Ocomplex' ) ] )
% 0.90/1.30 , clause( 1092, [ 'class_Ring__and__Field_Ocomm__semiring'(
% 0.90/1.30 'tc_Complex_Ocomplex' ) ] )
% 0.90/1.30 , clause( 1093, [ 'class_OrderedGroup_Ocomm__monoid__add'(
% 0.90/1.30 'tc_Complex_Ocomplex' ) ] )
% 0.90/1.30 , clause( 1094, [ 'class_Ring__and__Field_Ozero__neq__one'(
% 0.90/1.30 'tc_Complex_Ocomplex' ) ] )
% 0.90/1.30 , clause( 1095, [ 'class_OrderedGroup_Osemigroup__add'(
% 0.90/1.30 'tc_Complex_Ocomplex' ) ] )
% 0.90/1.30 , clause( 1096, [ 'class_Ring__and__Field_Osemiring__1'(
% 0.90/1.30 'tc_Complex_Ocomplex' ) ] )
% 0.90/1.30 , clause( 1097, [ 'class_Ring__and__Field_Osemiring__0'(
% 0.90/1.30 'tc_Complex_Ocomplex' ) ] )
% 0.90/1.30 , clause( 1098, [ 'class_OrderedGroup_Oab__group__add'(
% 0.90/1.30 'tc_Complex_Ocomplex' ) ] )
% 0.90/1.30 , clause( 1099, [ 'class_Ring__and__Field_Omult__zero'(
% 0.90/1.30 'tc_Complex_Ocomplex' ) ] )
% 0.90/1.30 , clause( 1100, [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Complex_Ocomplex'
% 0.90/1.30 ) ] )
% 0.90/1.30 , clause( 1101, [ 'class_Ring__and__Field_Osemiring'( 'tc_Complex_Ocomplex'
% 0.90/1.30 ) ] )
% 0.90/1.30 , clause( 1102, [ 'class_OrderedGroup_Omonoid__add'( 'tc_Complex_Ocomplex'
% 0.90/1.30 ) ] )
% 0.90/1.30 , clause( 1103, [ 'class_OrderedGroup_Ogroup__add'( 'tc_Complex_Ocomplex' )
% 0.90/1.30 ] )
% 0.90/1.30 , clause( 1104, [ 'class_Ring__and__Field_Oring__1'( 'tc_Complex_Ocomplex'
% 0.90/1.30 ) ] )
% 0.90/1.30 , clause( 1105, [ 'class_Ring__and__Field_Oring'( 'tc_Complex_Ocomplex' ) ]
% 0.90/1.30 )
% 0.90/1.30 , clause( 1106, [ 'class_Ring__and__Field_Oidom'( 'tc_Complex_Ocomplex' ) ]
% 0.90/1.30 )
% 0.90/1.30 , clause( 1107, [ 'class_Nat_Osemiring__char__0'( 'tc_Complex_Ocomplex' ) ]
% 0.90/1.30 )
% 0.90/1.30 , clause( 1108, [ 'class_Int_Oring__char__0'( 'tc_Complex_Ocomplex' ) ] )
% 0.90/1.30 , clause( 1109, [ 'class_Int_Onumber__ring'( 'tc_Complex_Ocomplex' ) ] )
% 0.90/1.30 , clause( 1110, [ 'class_Power_Opower'( 'tc_Complex_Ocomplex' ) ] )
% 0.90/1.30 , clause( 1111, [ 'class_HOL_Ozero'( 'tc_Complex_Ocomplex' ) ] )
% 0.90/1.30 , clause( 1112, [
% 0.90/1.30 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 0.90/1.30 X ) ) ] )
% 0.90/1.30 , clause( 1113, [
% 0.90/1.30 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 0.90/1.30 X ) ) ] )
% 0.90/1.30 , clause( 1114, [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 0.90/1.30 X ) ) ] )
% 0.90/1.30 , clause( 1115, [ 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 0.90/1.30 X ) ) ] )
% 0.90/1.30 , clause( 1116, [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oidom'( X ) ) ]
% 0.90/1.30 )
% 0.90/1.30 , clause( 1117, [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 0.90/1.30 X ) ) ] )
% 0.90/1.30 , clause( 1118, [ 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 0.90/1.30 X ) ) ] )
% 0.90/1.30 , clause( 1119, [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 0.90/1.30 X ) ) ] )
% 0.90/1.30 , clause( 1120, [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oidom'( X ) ) ]
% 0.90/1.30 )
% 0.90/1.30 , clause( 1121, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.90/1.30 'class_OrderedGroup_Ocancel__comm__monoid__add'( X ) ) ] )
% 0.90/1.30 , clause( 1122, [ 'class_Ring__and__Field_Oordered__ring__strict'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 0.90/1.30 X ) ) ] )
% 0.90/1.30 , clause( 1123, [ 'class_OrderedGroup_Opordered__ab__group__add'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 0.90/1.30 X ) ) ] )
% 0.90/1.30 , clause( 1124, [ 'class_OrderedGroup_Oordered__ab__group__add'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 0.90/1.30 X ) ) ] )
% 0.90/1.30 , clause( 1125, [ 'class_OrderedGroup_Ocancel__semigroup__add'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.90/1.30 'class_OrderedGroup_Ocancel__comm__monoid__add'( X ) ) ] )
% 0.90/1.30 , clause( 1126, [ 'class_Ring__and__Field_Opordered__semiring'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 0.90/1.30 X ) ) ] )
% 0.90/1.30 , clause( 1127, [ 'class_Ring__and__Field_Oordered__semiring'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 0.90/1.30 X ) ) ] )
% 0.90/1.30 , clause( 1128, [ 'class_Ring__and__Field_Ono__zero__divisors'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oidom'( X ) ) ]
% 0.90/1.30 )
% 0.90/1.30 , clause( 1129, [ 'class_Ring__and__Field_Oordered__semidom'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 0.90/1.30 X ) ) ] )
% 0.90/1.30 , clause( 1130, [ 'class_Ring__and__Field_Ocomm__semiring__1'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.90/1.30 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ) ] )
% 0.90/1.30 , clause( 1131, [ 'class_Ring__and__Field_Ocomm__semiring__0'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.90/1.30 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ] )
% 0.90/1.30 , clause( 1132, [ 'class_OrderedGroup_Oab__semigroup__mult'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.90/1.30 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ] )
% 0.90/1.30 , clause( 1133, [ 'class_OrderedGroup_Ocomm__monoid__mult'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.90/1.30 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ) ] )
% 0.90/1.30 , clause( 1134, [ 'class_OrderedGroup_Oab__semigroup__add'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), ~( 'class_OrderedGroup_Ocomm__monoid__add'(
% 0.90/1.30 X ) ) ] )
% 0.90/1.30 , clause( 1135, [ 'class_Ring__and__Field_Opordered__ring'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 0.90/1.30 X ) ) ] )
% 0.90/1.30 , clause( 1136, [ 'class_Ring__and__Field_Ocomm__semiring'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.90/1.30 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ] )
% 0.90/1.30 , clause( 1137, [ 'class_OrderedGroup_Ocomm__monoid__add'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), ~( 'class_OrderedGroup_Ocomm__monoid__add'(
% 0.90/1.30 X ) ) ] )
% 0.90/1.30 , clause( 1138, [ 'class_Ring__and__Field_Ozero__neq__one'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.90/1.30 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ) ] )
% 0.90/1.30 , clause( 1139, [ 'class_Ring__and__Field_Oordered__idom'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 0.90/1.30 X ) ) ] )
% 0.90/1.30 , clause( 1140, [ 'class_OrderedGroup_Osemigroup__add'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), ~( 'class_OrderedGroup_Ocomm__monoid__add'(
% 0.90/1.30 X ) ) ] )
% 0.90/1.30 , clause( 1141, [ 'class_Ring__and__Field_Osemiring__1'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.90/1.30 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ) ] )
% 0.90/1.30 , clause( 1142, [ 'class_Ring__and__Field_Osemiring__0'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.90/1.30 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ] )
% 0.90/1.30 , clause( 1143, [ 'class_Ring__and__Field_Omult__mono1'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 0.90/1.30 X ) ) ] )
% 0.90/1.30 , clause( 1144, [ 'class_OrderedGroup_Oab__group__add'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), ~( 'class_OrderedGroup_Oab__group__add'( X
% 0.90/1.30 ) ) ] )
% 0.90/1.30 , clause( 1145, [ 'class_Ring__and__Field_Omult__zero'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.90/1.30 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ] )
% 0.90/1.30 , clause( 1146, [ 'class_Ring__and__Field_Omult__mono'(
% 0.90/1.30 'tc_Polynomial_Opoly'( X ) ), ~( 'class_Ring__and__Field_Oordered__idom'(
% 0.90/1.30 X ) ) ] )
% 0.90/1.30 , clause( 1147, [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Polynomial_Opoly'(
% 0.90/1.30 X ) ), ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ) ] )
% 0.90/1.30 , clause( 1148, [ 'class_Ring__and__Field_Osemiring'( 'tc_Polynomial_Opoly'(
% 0.94/1.31 X ) ), ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ) ] )
% 0.94/1.31 , clause( 1149, [ 'class_OrderedGroup_Omonoid__add'( 'tc_Polynomial_Opoly'(
% 0.94/1.31 X ) ), ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ) ] )
% 0.94/1.31 , clause( 1150, [ 'class_OrderedGroup_Ogroup__add'( 'tc_Polynomial_Opoly'(
% 0.94/1.31 X ) ), ~( 'class_OrderedGroup_Oab__group__add'( X ) ) ] )
% 0.94/1.31 , clause( 1151, [ 'class_Ring__and__Field_Oring__1'( 'tc_Polynomial_Opoly'(
% 0.94/1.31 X ) ), ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ) ] )
% 0.94/1.31 , clause( 1152, [ 'class_Ring__and__Field_Oring'( 'tc_Polynomial_Opoly'( X
% 0.94/1.31 ) ), ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ) ] )
% 0.94/1.31 , clause( 1153, [ 'class_Ring__and__Field_Oidom'( 'tc_Polynomial_Opoly'( X
% 0.94/1.31 ) ), ~( 'class_Ring__and__Field_Oidom'( X ) ) ] )
% 0.94/1.31 , clause( 1154, [ 'class_Nat_Osemiring__char__0'( 'tc_Polynomial_Opoly'( X
% 0.94/1.31 ) ), ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ] )
% 0.94/1.31 , clause( 1155, [ 'class_Orderings_Opreorder'( 'tc_Polynomial_Opoly'( X ) )
% 0.94/1.31 , ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ] )
% 0.94/1.31 , clause( 1156, [ 'class_Orderings_Olinorder'( 'tc_Polynomial_Opoly'( X ) )
% 0.94/1.31 , ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ] )
% 0.94/1.31 , clause( 1157, [ 'class_Orderings_Oorder'( 'tc_Polynomial_Opoly'( X ) ),
% 0.94/1.31 ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ] )
% 0.94/1.31 , clause( 1158, [ 'class_Int_Oring__char__0'( 'tc_Polynomial_Opoly'( X ) )
% 0.94/1.31 , ~( 'class_Ring__and__Field_Oordered__idom'( X ) ) ] )
% 0.94/1.31 , clause( 1159, [ 'class_Int_Onumber__ring'( 'tc_Polynomial_Opoly'( X ) ),
% 0.94/1.31 ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ) ] )
% 0.94/1.31 , clause( 1160, [ 'class_Power_Opower'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.94/1.31 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ) ] )
% 0.94/1.31 , clause( 1161, [ 'class_HOL_Ozero'( 'tc_Polynomial_Opoly'( X ) ), ~(
% 0.94/1.31 'class_HOL_Ozero'( X ) ) ] )
% 0.94/1.31 , clause( 1162, [ hBOOL( 'c_fequal'( X, X, Y ) ) ] )
% 0.94/1.31 , clause( 1163, [ =( X, Y ), ~( hBOOL( 'c_fequal'( X, Y, Z ) ) ) ] )
% 0.94/1.31 ] ).
% 0.94/1.31
% 0.94/1.31
% 0.94/1.31
% 0.94/1.31 subsumption(
% 0.94/1.31 clause( 448, [ ~( 'c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant'(
% 0.94/1.31 'c_Polynomial_Opoly'( 'v_q____', 'tc_Complex_Ocomplex' ),
% 0.94/1.31 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ) ) ] )
% 0.94/1.31 , clause( 976, [ ~( 'c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant'(
% 0.94/1.31 'c_Polynomial_Opoly'( 'v_q____', 'tc_Complex_Ocomplex' ),
% 0.94/1.31 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ) ) ] )
% 0.94/1.31 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 0.94/1.31
% 0.94/1.31
% 0.94/1.31 resolution(
% 0.94/1.31 clause( 2441, [] )
% 0.94/1.31 , clause( 448, [ ~( 'c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant'(
% 0.94/1.31 'c_Polynomial_Opoly'( 'v_q____', 'tc_Complex_Ocomplex' ),
% 0.94/1.31 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ) ) ] )
% 0.94/1.31 , 0, clause( 977, [ 'c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant'(
% 0.94/1.31 'c_Polynomial_Opoly'( 'v_q____', 'tc_Complex_Ocomplex' ),
% 0.94/1.31 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ) ] )
% 0.94/1.31 , 0, substitution( 0, [] ), substitution( 1, [] )).
% 0.94/1.31
% 0.94/1.31
% 0.94/1.31 subsumption(
% 0.94/1.31 clause( 449, [] )
% 0.94/1.31 , clause( 2441, [] )
% 0.94/1.31 , substitution( 0, [] ), permutation( 0, [] ) ).
% 0.94/1.31
% 0.94/1.31
% 0.94/1.31 end.
% 0.94/1.31
% 0.94/1.31 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 0.94/1.31
% 0.94/1.31 Memory use:
% 0.94/1.31
% 0.94/1.31 space for terms: 35975
% 0.94/1.31 space for clauses: 40094
% 0.94/1.31
% 0.94/1.31
% 0.94/1.31 clauses generated: 527
% 0.94/1.31 clauses kept: 450
% 0.94/1.31 clauses selected: 0
% 0.94/1.31 clauses deleted: 0
% 0.94/1.31 clauses inuse deleted: 0
% 0.94/1.31
% 0.94/1.31 subsentry: 10047
% 0.94/1.31 literals s-matched: 3901
% 0.94/1.31 literals matched: 3845
% 0.94/1.31 full subsumption: 753
% 0.94/1.31
% 0.94/1.31 checksum: -1791510324
% 0.94/1.31
% 0.94/1.31
% 0.94/1.31 Bliksem ended
%------------------------------------------------------------------------------