TSTP Solution File: SWV628-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV628-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 16:27:15 EDT 2022
% Result : Timeout 300.07s 300.52s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.07 % Problem : SWV628-1 : TPTP v8.1.0. Released v4.1.0.
% 0.04/0.07 % Command : bliksem %s
% 0.07/0.26 % Computer : n020.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % DateTime : Wed Jun 15 23:31:34 EDT 2022
% 0.07/0.26 % CPUTime :
% 1.10/1.48 *** allocated 10000 integers for termspace/termends
% 1.10/1.48 *** allocated 10000 integers for clauses
% 1.10/1.48 *** allocated 10000 integers for justifications
% 1.10/1.48 *** allocated 15000 integers for termspace/termends
% 1.10/1.48 *** allocated 22500 integers for termspace/termends
% 1.10/1.48 *** allocated 33750 integers for termspace/termends
% 1.10/1.48 *** allocated 50625 integers for termspace/termends
% 1.10/1.48 Bliksem 1.12
% 1.10/1.48
% 1.10/1.48
% 1.10/1.48 Automatic Strategy Selection
% 1.10/1.48
% 1.10/1.48 Clauses:
% 1.10/1.48 [
% 1.10/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Olcm'( X, Y
% 1.10/1.48 , 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y
% 1.10/1.48 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z,
% 1.10/1.48 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Olcm'( X
% 1.10/1.48 , Y, 'tc_nat' ), 'tc_nat' ) ],
% 1.10/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Olcm'( Y
% 1.10/1.48 , X, 'tc_nat' ), 'tc_nat' ) ],
% 1.10/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Olcm'( X, Y
% 1.10/1.48 , 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y
% 1.10/1.48 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z,
% 1.10/1.48 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.10/1.48 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.48 , X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.48 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.10/1.48 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.48 , X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.48 , X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.48 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.48 , X ) ) ],
% 1.10/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.48 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 1.10/1.48 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.48 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Y, X
% 1.10/1.48 ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 1.10/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.48 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.48 X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.48 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.10/1.48 ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.10/1.48 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.10/1.48 ), X ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.48 X ), X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.48 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.10/1.48 ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.48 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.10/1.48 , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.48 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.10/1.48 ), X ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48 ), Y, X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.48 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.10/1.48 ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), =( Y, 'c_HOL_Oinverse__class_Odivide'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.10/1.48 ), X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), =(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48 ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.10/1.48 ), X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y ), =(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48 ) ) ],
% 1.10/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 1.10/1.48 'c_Divides_Odiv__class_Odiv'( T, U, X ), X ),
% 1.10/1.48 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( U, T, X ) ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.10/1.48 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.10/1.48 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.48 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.10/1.48 ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.10/1.48 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ), ~(
% 1.10/1.48 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.10/1.48 [ =( 'c_Fact_Ofact__class_Ofact'( 'c_Suc'( X ), 'tc_nat' ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), 'c_Fact_Ofact__class_Ofact'(
% 1.10/1.48 X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.10/1.48 , X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Y,
% 1.10/1.48 'c_HOL_Oone__class_Oone'( X ), X ), X ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.10/1.48 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 1.10/1.48 Z ), T, 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T,
% 1.10/1.48 'tc_nat' ), X ), Y, X ) ), ~( 'c_lessequals'( T, Z, 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 1.10/1.48 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' )
% 1.10/1.48 , 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.10/1.48 , 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, T, X )
% 1.10/1.48 , 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.10/1.48 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.10/1.48 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'( Z,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.10/1.48 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.10/1.48 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.10/1.48 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.10/1.48 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'( Z,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.10/1.48 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.10/1.48 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.10/1.48 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.10/1.48 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 1.10/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Olcm'( Y
% 1.10/1.48 , X, 'tc_nat' ), 'tc_nat' ) ],
% 1.10/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Olcm'( X
% 1.10/1.48 , Y, 'tc_nat' ), 'tc_nat' ) ],
% 1.10/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Olcm'( X, Y
% 1.10/1.48 , 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y
% 1.10/1.48 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z,
% 1.10/1.48 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Olcm'( X
% 1.10/1.48 , Y, 'tc_nat' ), 'tc_nat' ) ],
% 1.10/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Olcm'( Y
% 1.10/1.48 , X, 'tc_nat' ), 'tc_nat' ) ],
% 1.10/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Olcm'( X, Y
% 1.10/1.48 , 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y
% 1.10/1.48 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z,
% 1.10/1.48 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Olcm'( X, Y
% 1.10/1.48 , 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y
% 1.10/1.48 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z,
% 1.10/1.48 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Olcm'( X
% 1.10/1.48 , Y, 'tc_nat' ), Z, 'tc_nat' ) ), 'c_Ring__and__Field_Odvd__class_Odvd'(
% 1.10/1.48 X, Z, 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X,
% 1.10/1.48 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Olcm'( X
% 1.10/1.48 , Y, 'tc_nat' ), Z, 'tc_nat' ) ), 'c_Ring__and__Field_Odvd__class_Odvd'(
% 1.10/1.48 Y, Z, 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y,
% 1.10/1.48 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 1.10/1.48 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 1.10/1.48 ,
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 1.10/1.48 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ]
% 1.10/1.48 ,
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 1.10/1.48 , X ), Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 1.10/1.48 , X ), Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.10/1.48 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), =( Y
% 1.10/1.48 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.48 , X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.10/1.48 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.10/1.48 , Y, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.48 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 1.10/1.48 X ), X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.10/1.48 , T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.10/1.48 ), ~( 'c_lessequals'( Z, T, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.10/1.48 , T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.10/1.48 ), ~( 'c_lessequals'( Z, T, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.10/1.48 , Z, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.10/1.48 ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.10/1.48 , T, X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.10/1.48 ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.10/1.48 , Z, X ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.10/1.48 ), ~( 'c_lessequals'( T, Y, X ) ) ],
% 1.10/1.48 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.10/1.48 Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), 'tc_nat' ) ) ), =( Z, T )
% 1.10/1.48 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.10/1.48 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 Z, T, X ), X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ), =( T, U ), =( Z,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.48 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.48 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.48 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ), 'tc_nat' ) ],
% 1.10/1.48 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 1.10/1.48 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.10/1.48 ), =( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Z ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48 ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.10/1.48 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.10/1.48 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X
% 1.10/1.48 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.10/1.48 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, T,
% 1.10/1.48 X ), Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.10/1.48 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.10/1.48 X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.10/1.48 Z, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.10/1.48 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.10/1.48 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.10/1.48 Z, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.10/1.48 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.10/1.48 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.10/1.48 X ), Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.10/1.48 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.10/1.48 Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.48 X ), Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.10/1.48 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.10/1.48 X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.48 X ), T, X ) ) ],
% 1.10/1.48 [ ~( 'class_Int_Onumber'( X ) ), ~( 'class_HOL_Oord'( X ) ), =(
% 1.10/1.48 'c_Orderings_Oord__class_Omax'( 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.10/1.48 ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), 'c_lessequals'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.10/1.48 [ =( 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.10/1.48 , 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 1.10/1.48 , 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omin'( X, Z,
% 1.10/1.48 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.48 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.48 ,
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.10/1.48 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.10/1.48 ,
% 1.10/1.48 [ ~( 'class_Int_Onumber'( X ) ), ~( 'class_HOL_Oord'( X ) ), =(
% 1.10/1.48 'c_Orderings_Oord__class_Omin'( 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.10/1.48 ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), 'c_lessequals'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.10/1.48 Z, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, Z
% 1.10/1.48 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.10/1.48 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.10/1.48 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.10/1.48 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.10/1.48 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.10/1.48 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.10/1.48 T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X ) ),
% 1.10/1.48 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.10/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.48 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.48 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.10/1.48 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.10/1.48 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.10/1.48 , Z, X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ],
% 1.10/1.48 [ ~( =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ) ) ), =( Y, Z )
% 1.10/1.48 ],
% 1.10/1.48 [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.10/1.48 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.10/1.48 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ), T, X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.10/1.48 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.48 , X ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48 ), X ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.10/1.48 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.10/1.48 'tc_nat' ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.48 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.10/1.48 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Z,
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), X ), X ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.10/1.48 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.10/1.48 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( T, U, X ) ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.10/1.48 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.10/1.48 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( T, U, X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.10/1.48 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.10/1.48 , U, X ) ) ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( U, T, X ) ) ]
% 1.10/1.48 ,
% 1.10/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.10/1.48 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.10/1.48 , U, X ) ) ), 'c_lessequals'( U, T, X ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 1.10/1.48 ,
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.10/1.48 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.48 T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y,
% 1.10/1.48 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.10/1.48 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.48 T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y,
% 1.10/1.48 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.48 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.10/1.48 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ),
% 1.10/1.48 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.10/1.48 ) ) ],
% 1.10/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.48 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.48 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 1.10/1.48 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 1.10/1.48 ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.48 'c_HOL_Ominus__class_Ominus'( Z, 'c_HOL_Otimes__class_Otimes'( T, U, X )
% 1.10/1.48 , X ), W, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( Z, W, X ), X ) ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, U, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 1.10/1.48 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Z,
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( U, W, X ), X ), T, X ), X ) ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, W, X ) ) ],
% 1.10/1.48 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.10/1.48 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 1.10/1.48 X ), X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 1.10/1.48 Y, Z, X ), 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.10/1.48 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 1.10/1.48 , T, X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 1.10/1.48 Y, T, X ), 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( Y,
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z, X ),
% 1.10/1.48 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z, X ),
% 1.10/1.48 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ), Y ) ],
% 1.10/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.10/1.48 'c_Divides_Odiv__class_Odiv'( Z, Y, X ), X ),
% 1.10/1.48 'c_Divides_Odiv__class_Omod'( Z, Y, X ), X ), Z ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.10/1.48 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.10/1.48 ,
% 1.10/1.48 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 1.10/1.48 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.10/1.48 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.10/1.48 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 1.10/1.48 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.10/1.48 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.10/1.48 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 1.10/1.48 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.10/1.48 ,
% 1.10/1.48 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.10/1.48 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.10/1.48 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 1.10/1.48 ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.10/1.48 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 1.10/1.48 X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.10/1.48 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 1.10/1.48 ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.10/1.48 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 1.10/1.48 X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.10/1.48 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 1.10/1.48 ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.10/1.48 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 1.10/1.48 ) ],
% 1.10/1.48 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.10/1.48 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.48 Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.10/1.48 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.10/1.48 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.10/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Otimes__class_Otimes'( Z,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), X ) ],
% 1.10/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.10/1.48 'tc_nat' ), 'tc_nat' ) ],
% 1.10/1.48 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 1.10/1.48 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), 'tc_nat' ),
% 1.10/1.48 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 1.10/1.48 ), 'c_Suc'( Y ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 1.10/1.48 ,
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.10/1.48 T, Z, X ), X ), ~( 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.10/1.48 'c_HOL_Oabs__class_Oabs'( T, X ), X ) ), ~(
% 1.10/1.48 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Y, X ) ],
% 1.10/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, X, 'tc_nat' ) ],
% 1.10/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.10/1.48 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) )
% 1.10/1.48 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 1.10/1.48 , 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ),
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Z, Y
% 1.10/1.48 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y, Z
% 1.10/1.48 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 1.10/1.48 , 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y
% 1.10/1.48 , Z, 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 1.10/1.48 , 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.10/1.48 , Z, 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Z, Y
% 1.10/1.48 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y, Z
% 1.10/1.48 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y, Z
% 1.10/1.48 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Z, Y
% 1.10/1.48 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.10/1.48 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.10/1.48 'c_Orderings_Oord__class_Omax'( Y, Y, X ), Y ) ],
% 1.10/1.48 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_GCD_Ogcd__class_Olcm'( X, Y,
% 1.10/1.48 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.10/1.48 ), =( Z, Y ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.10/1.48 ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.10/1.48 ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.10/1.48 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.10/1.48 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.10/1.48 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 1.10/1.48 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.10/1.48 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 1.10/1.48 , Y, 'tc_nat' ) ) ],
% 1.10/1.48 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 1.10/1.48 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), =( Y, X
% 1.10/1.48 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 1.10/1.48 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' )
% 1.10/1.48 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.10/1.48 [ =( X, Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 1.10/1.48 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), =( Y, X
% 1.10/1.48 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ), =( Y, X ) ]
% 1.10/1.48 ,
% 1.10/1.48 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.10/1.48 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.10/1.48 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.10/1.48 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.10/1.48 [ =( 'c_GCD_Ogcd__class_Olcm'( X, 'c_GCD_Ogcd__class_Ogcd'( X, Y,
% 1.10/1.48 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.10/1.48 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.10/1.48 , Y, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.48 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.10/1.48 ), T, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.10/1.48 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 1.10/1.48 Z, T, X ), X ) ) ],
% 1.10/1.48 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.10/1.48 'tc_nat' ), Y, 'tc_nat' ), 'c_Orderings_Oord__class_Omax'( X, Y, 'tc_nat'
% 1.10/1.48 ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Oinverse__class_Odivide'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), Y, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), Y, X ), Z ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ),
% 1.10/1.48 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 1.10/1.48 'c_HOL_Oabs__class_Oabs'( T, X ), X ), X ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.10/1.48 , Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.10/1.48 , Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.10/1.48 'c_Orderings_Oord__class_Omin'( Y, Y, X ), Y ) ],
% 1.10/1.48 [ =( 'c_Nat_Osize__class_Osize'( 'c_Suc'( X ), 'tc_nat' ),
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( 'c_Nat_Osize__class_Osize'( X, 'tc_nat' ),
% 1.10/1.48 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.48 Z, X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.10/1.48 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.10/1.48 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( Y,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.10/1.48 ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.10/1.48 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'( Y,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ],
% 1.10/1.48 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.10/1.48 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 1.10/1.48 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.10/1.48 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.10/1.48 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.10/1.48 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.48 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.10/1.48 'c_lessequals'( Z, X, 'tc_nat' ) ) ],
% 1.10/1.48 [ =( 'c_Fact_Ofact__class_Ofact'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.48 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.10/1.48 ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.48 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48 ), X ) ],
% 1.10/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.48 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 1.10/1.48 , X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.48 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 1.10/1.48 , X ), Z ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48 [ =( 'c_Nat_Osize__class_Osize'( X, 'tc_nat' ), X ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.10/1.48 , 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.10/1.48 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X
% 1.10/1.48 ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.48 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ), ~(
% 1.10/1.48 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.48 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ), ~(
% 1.10/1.48 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.10/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Suc'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.10/1.48 , Z, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.48 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.10/1.48 ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.10/1.48 ), X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.10/1.48 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.10/1.48 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.48 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.10/1.48 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 1.10/1.48 Z, T, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.48 ,
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.10/1.48 ,
% 1.10/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.10/1.48 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.48 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.10/1.48 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ), U, 'tc_nat' ) ) ), ~(
% 1.10/1.48 'c_lessequals'( X, T, 'tc_nat' ) ), =( Z, 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( T, X,
% 1.10/1.48 'tc_nat' ), Y, 'tc_nat' ), U, 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.10/1.48 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ), U, 'tc_nat' ) ) ), ~(
% 1.10/1.48 'c_lessequals'( T, X, 'tc_nat' ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, T,
% 1.10/1.48 'tc_nat' ), Y, 'tc_nat' ), Z, 'tc_nat' ), U ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.10/1.48 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.10/1.48 ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'( Z,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.10/1.48 ,
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.48 'c_HOL_Oinverse__class_Oinverse'( 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.10/1.48 ), X ), 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Oinverse'(
% 1.10/1.48 Y, X ), Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.10/1.48 , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.10/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.10/1.48 , X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.48 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.10/1.48 , X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.48 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.10/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Fact_Ofact__class_Ofact'( Y,
% 1.10/1.48 'tc_nat' ), X ), X ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.10/1.48 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.10/1.48 , 'tc_nat' ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_Power_Opower__class_Opower'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 1.10/1.48 , 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.10/1.48 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oabs__class_Oabs'( Y
% 1.10/1.48 , X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), 'c_HOL_Oabs__class_Oabs'(
% 1.10/1.48 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), X ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), X ) ), ~(
% 1.10/1.48 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.48 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.10/1.48 , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.48 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( T, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.10/1.48 ), X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.48 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.10/1.48 ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.10/1.48 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.10/1.48 ), X ), Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.10/1.48 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 1.10/1.48 T, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.10/1.48 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.10/1.48 X ), Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.10/1.48 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 1.10/1.48 T, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.10/1.48 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.10/1.48 X ), T, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.10/1.48 , X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.10/1.48 T, X ), X ) ) ],
% 1.10/1.48 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.10/1.48 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.10/1.48 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.10/1.48 X ), T, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.10/1.48 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.10/1.48 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.10/1.48 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.10/1.48 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.10/1.48 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.10/1.48 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.10/1.48 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.48 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.10/1.48 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.10/1.48 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.10/1.48 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.10/1.48 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.10/1.48 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.10/1.48 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.10/1.48 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.10/1.48 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ),
% 1.10/1.48 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Z, Y, X ), X ) )
% 1.10/1.48 ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.10/1.48 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( T, Y
% 1.10/1.48 , X ), 'c_Power_Opower__class_Opower'( T, Z, X ), X ) ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.10/1.48 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( T, Y
% 1.10/1.48 , X ), 'c_Power_Opower__class_Opower'( T, Z, X ), X ) ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.10/1.48 Y, T, X ), X ), ~( 'c_lessequals'( Z, T, 'tc_nat' ) ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.10/1.48 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Z, X )
% 1.10/1.48 , T, X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.48 X ), T, X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, T,
% 1.10/1.48 X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.10/1.48 X ), ~( 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.48 ,
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.48 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.10/1.48 , X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.48 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 1.10/1.48 , X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.48 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.10/1.48 , X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.48 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 1.10/1.48 , X ) ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.10/1.48 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omax'( Y, Z,
% 1.10/1.48 X ), X ), 'c_Orderings_Oord__class_Omax'( Y, Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.10/1.48 X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ), =(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.10/1.48 , T, X ), Z ), =( T, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.10/1.48 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 1.10/1.48 ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.10/1.48 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.10/1.48 , 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.10/1.48 , Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ), =( U,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.48 ) ],
% 1.10/1.48 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 1.10/1.48 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) )
% 1.10/1.48 ],
% 1.10/1.48 [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X,
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( X, X, 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ]
% 1.10/1.48 ,
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.10/1.48 , U, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.10/1.48 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.10/1.48 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.10/1.48 , U, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.10/1.48 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.10/1.48 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.10/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.48 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.10/1.48 'c_Divides_Odiv__class_Odiv'( Z, T, X ) ), =( Y,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.48 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 1.10/1.48 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), =( Z,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 1.10/1.48 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 1.10/1.48 'c_Power_Opower__class_Opower'( T, 'c_Suc'( Z ), X ) ) ), =( Y, T ), ~(
% 1.10/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.10/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.10/1.48 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Osgn__class_Osgn'( Y, X ), X ),
% 1.10/1.48 'c_HOL_Osgn__class_Osgn'( Y, X ) ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.10/1.48 , =( 'c_HOL_Oplus__class_Oplus'( 'c_Orderings_Oord__class_Omax'( Y, Z, X
% 1.10/1.48 ), T, X ), 'c_Orderings_Oord__class_Omax'( 'c_HOL_Oplus__class_Oplus'( Y
% 1.10/1.48 , T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.10/1.48 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ), Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y
% 1.10/1.48 , X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.10/1.48 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.10/1.48 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.10/1.48 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ]
% 1.10/1.48 ,
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.10/1.48 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.10/1.48 X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.10/1.48 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.10/1.48 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.10/1.48 X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.10/1.48 , X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.10/1.48 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.10/1.48 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ]
% 1.10/1.48 ,
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.10/1.48 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.10/1.48 T, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 Y, T, X ), Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.10/1.48 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.10/1.48 T, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 Y, T, X ), Z, X ) ) ],
% 1.10/1.48 [ 'c_lessequals'( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), Y,
% 1.10/1.48 'tc_nat' ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_lessequals'( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), X,
% 1.10/1.48 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.10/1.48 'tc_nat' ), 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' )
% 1.10/1.48 , 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.10/1.48 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.10/1.48 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 1.10/1.48 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ]
% 1.10/1.48 ,
% 1.10/1.48 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.10/1.48 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.10/1.48 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.10/1.48 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.10/1.48 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.10/1.48 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( Y, X,
% 1.10/1.48 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.10/1.48 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 1.10/1.48 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ]
% 1.10/1.48 ,
% 1.10/1.48 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.10/1.48 'tc_nat' ), 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' )
% 1.10/1.48 , 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.10/1.48 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.10/1.48 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.10/1.48 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.10/1.48 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.10/1.48 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.10/1.48 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( Y, X,
% 1.10/1.48 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.10/1.48 Y, 'tc_nat' ), 'tc_nat' ) ), 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 1.10/1.48 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.10/1.48 Y, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 1.10/1.48 'tc_nat' ) ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.10/1.48 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.10/1.48 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.10/1.48 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.10/1.48 'tc_nat' ), 'tc_nat' ) ],
% 1.10/1.48 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.10/1.48 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.10/1.48 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oplus__class_Oplus'( Y, X,
% 1.10/1.48 'tc_nat' ), 'tc_nat' ) ],
% 1.10/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Olcm'( X,
% 1.10/1.48 'c_GCD_Ogcd__class_Ogcd'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 1.10/1.48 'c_GCD_Ogcd__class_Ogcd'( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ),
% 1.10/1.48 'c_GCD_Ogcd__class_Olcm'( X, Z, 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ],
% 1.10/1.48 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.10/1.48 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.10/1.48 [ =( X, 'c_Suc'( Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 1.10/1.48 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.10/1.48 'c_Power_Opower__class_Opower'( Y, Z, X ), X ),
% 1.10/1.48 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.48 ,
% 1.10/1.48 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.10/1.48 , 'tc_nat' ), 'tc_nat' ), Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 1.10/1.48 ,
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.10/1.48 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z, X )
% 1.10/1.48 , 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.10/1.48 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.10/1.48 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.10/1.48 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Y, Z,
% 1.10/1.48 X ), X ), Y ) ],
% 1.10/1.48 [ ~( 'class_Int_Onumber'( X ) ), ~( 'class_HOL_Oord'( X ) ), =(
% 1.10/1.48 'c_Orderings_Oord__class_Omin'( 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.10/1.48 ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), ~( 'c_lessequals'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.10/1.48 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X, 'tc_nat'
% 1.10/1.48 ), 'tc_nat' ) ],
% 1.10/1.48 [ ~( 'c_Ring__and__Field_Ozero__neq__one'( X, X, Y ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.10/1.48 , T, X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.10/1.48 Y, T, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.10/1.48 , T, X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.10/1.48 Y, T, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.10/1.48 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.10/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.10/1.48 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.10/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.10/1.48 X ), 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.48 , X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.10/1.48 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.10/1.48 ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.10/1.48 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.48 X ), 'c_HOL_Oinverse__class_Odivide'( Z,
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_HOL_Osgn__class_Osgn'( Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_HOL_Osgn__class_Osgn'( Y, X ), X ) ) ],
% 1.10/1.48 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), T, 'tc_nat' ),
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 1.10/1.48 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), T,
% 1.10/1.48 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.10/1.48 'c_Power_Opower__class_Opower'( Y, T, X ), X ),
% 1.10/1.48 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T,
% 1.10/1.48 'tc_nat' ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ominus__class_Ominus'( Z
% 1.10/1.48 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.10/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Ominus__class_Ominus'(
% 1.10/1.48 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.10/1.48 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 1.10/1.48 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.10/1.48 , T, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.10/1.48 , Z, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.10/1.48 , T, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.10/1.48 , Z, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.10/1.48 , 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.10/1.48 ,
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y
% 1.10/1.48 , 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.10/1.48 ,
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.10/1.48 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.10/1.48 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ]
% 1.10/1.48 ,
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.10/1.48 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.10/1.48 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), Z, X ) ) ]
% 1.10/1.48 ,
% 1.10/1.48 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 1.10/1.48 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.10/1.48 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ),
% 1.10/1.48 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.10/1.48 ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.48 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ), ~(
% 1.10/1.48 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Osgn__class_Osgn'( Y, X ),
% 1.10/1.48 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), Y ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y,
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ), X ), ~(
% 1.10/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.10/1.48 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.48 , 'tc_nat' ), 'tc_nat' ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.10/1.48 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.48 , 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.48 X ), 'c_Power_Opower__class_Opower'( Y,
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ), X ) ) ],
% 1.10/1.48 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.48 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ) ],
% 1.10/1.48 [ =( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ), X ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( =( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ), Y ) ),
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ],
% 1.10/1.48 [ ~( =( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ), X ) ),
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ],
% 1.10/1.48 [ =( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ), X ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( =( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ), Y ) ),
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ],
% 1.10/1.48 [ =( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ), Y ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.10/1.48 [ =( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ), X ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 1.10/1.48 [ =( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ), Y ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.10/1.48 ), =( 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.48 Y, X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ), X ),
% 1.10/1.48 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.10/1.48 , T, X ), X ) ) ],
% 1.10/1.48 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 1.10/1.48 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 1.10/1.48 , X, 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.10/1.48 , T, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.10/1.48 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.10/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.10/1.48 , T, X ), X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 1.10/1.48 ,
% 1.10/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.10/1.48 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.10/1.48 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.10/1.48 W, X ), X ), ~( 'c_lessequals'( T, 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.10/1.48 , X ), W, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( Y
% 1.10/1.48 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U, X ), W, X ), X ), ~(
% 1.10/1.48 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 T, U, X ), Y, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Z, U, X ), W, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.10/1.48 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.10/1.48 W, X ), X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 1.10/1.48 , X ), T, X ), W, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ), U, X ), W, X ), ~(
% 1.10/1.48 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 Y, T, X ), U, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Z, T, X ), W, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.10/1.48 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.10/1.48 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.48 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.10/1.48 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 1.10/1.48 ],
% 1.10/1.48 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.10/1.48 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.10/1.48 ],
% 1.10/1.48 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 1.10/1.48 Y, 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.10/1.48 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 1.10/1.48 ],
% 1.10/1.48 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.10/1.48 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.10/1.48 ],
% 1.10/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Olcm'( Z, X,
% 1.10/1.48 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Olcm'( X, Z,
% 1.10/1.48 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Olcm'( Y
% 1.10/1.48 , Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.10/1.48 , Z, 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Olcm'( Y
% 1.10/1.48 , Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.10/1.48 , Y, 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Olcm'( Z, X,
% 1.10/1.48 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Olcm'( X, Z,
% 1.10/1.48 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Olcm'( Y
% 1.10/1.48 , Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.10/1.48 , Y, 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Olcm'( Y
% 1.10/1.48 , Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.10/1.48 , Z, 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.10/1.48 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.10/1.48 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.10/1.48 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z, X )
% 1.10/1.48 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.10/1.48 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 1.10/1.48 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.10/1.48 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'( Y, Z, X )
% 1.10/1.48 , T, X ), 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'(
% 1.10/1.48 Y, T, X ), 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.10/1.48 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 1.10/1.48 X ), X ), 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'(
% 1.10/1.48 Y, Z, X ), 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Obot'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_Orderings_Obot__class_Obot'( X ), Y, X ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 1.10/1.48 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 1.10/1.48 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 1.10/1.48 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.10/1.48 'c_Orderings_Oord__class_Omax'( Y, Z, X ), X ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.10/1.48 'c_Orderings_Oord__class_Omax'( Z, Y, X ), X ) ],
% 1.10/1.48 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z,
% 1.10/1.48 'tc_nat' ), ~( 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Z, Y,
% 1.10/1.48 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ),
% 1.10/1.48 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 1.10/1.48 ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.10/1.48 Y, 'tc_nat' ) ), 'tc_nat' ) ],
% 1.10/1.48 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.10/1.48 X, 'tc_nat' ) ), 'tc_nat' ) ],
% 1.10/1.48 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.10/1.48 Y, 'tc_nat' ) ), 'tc_nat' ) ],
% 1.10/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 1.10/1.48 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 1.10/1.48 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.10/1.48 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), X, 'tc_nat' ),
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat'
% 1.10/1.48 ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 1.10/1.48 ,
% 1.10/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 1.10/1.48 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 1.10/1.48 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.10/1.48 'tc_nat' ), Z, 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), T, 'tc_nat' ),
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat'
% 1.10/1.48 ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 1.10/1.48 ,
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.10/1.48 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Z, Y, X ),
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_HOL_Ominus__class_Ominus'( T, Y, X ), Z, X ), U, X ), X ),
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 1.10/1.48 ) ) ],
% 1.10/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.48 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.10/1.48 ), 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Odiv'( Y, T, X ),
% 1.10/1.48 'c_Divides_Odiv__class_Odiv'( Z, T, X ), X ) ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( T, Y, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Olordered__ring'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.10/1.48 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.10/1.48 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_Suc'( Y ), X ),
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48 [ =( 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ), 'tc_nat' ),
% 1.10/1.48 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.10/1.48 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y
% 1.10/1.48 , X ), Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.10/1.48 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.10/1.48 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.10/1.48 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y
% 1.10/1.48 , X ) ) ],
% 1.10/1.48 [ =( 'c_nat_Onat__size'( 'c_Suc'( X ) ), 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.48 'c_nat_Onat__size'( X ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.10/1.48 ), 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.10/1.48 ,
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.48 ,
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.48 ,
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.10/1.48 ,
% 1.10/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 1.10/1.48 , 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ),
% 1.10/1.48 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 1.10/1.48 X ), X ), X ) ],
% 1.10/1.48 [ =( 'c_List_Odrop'( X, 'c_List_Oreplicate'( Y, Z, T ), T ),
% 1.10/1.48 'c_List_Oreplicate'( 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, T
% 1.10/1.48 ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.10/1.48 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 1.10/1.48 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.10/1.48 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oinverse__class_Oinverse'(
% 1.10/1.48 Y, X ), X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ), =( Z,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.48 ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.10/1.48 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.10/1.48 Z, X ), X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ), =( Z,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.48 ) ],
% 1.10/1.48 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_GCD_Ogcd__class_Ogcd'( Y, Z,
% 1.10/1.48 'tc_nat' ), 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.10/1.48 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Otimes__class_Otimes'( Y,
% 1.10/1.48 'c_HOL_Osgn__class_Osgn'( Y, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Int_Onumber'( X ) ), ~( 'class_HOL_Oord'( X ) ), =(
% 1.10/1.48 'c_Orderings_Oord__class_Omax'( 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.10/1.48 ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), ~( 'c_lessequals'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.10/1.48 'c_Orderings_Oord__class_Omax'( Y, Z, X ), 'c_Orderings_Oord__class_Omax'(
% 1.10/1.48 Z, Y, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.48 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oone__class_Oone'( X ), X ), X ), Z
% 1.10/1.48 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'(
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.48 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oone__class_Oone'( X ), X ), X ), X
% 1.10/1.48 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.10/1.48 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), Z, X ) ), =( Z,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.10/1.48 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Z,
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), T, X ) ), =( T,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, U,
% 1.10/1.48 X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'(
% 1.10/1.48 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Fact_Ofact__class_Ofact'( Y,
% 1.10/1.48 'tc_nat' ), X ), X ), X ) ],
% 1.10/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Divides_Odiv__class_Odiv'( Y, T
% 1.10/1.48 , X ), 'c_Divides_Odiv__class_Odiv'( Z, T, X ), X ) ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( T, Y, X ) ) ],
% 1.10/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Divides_Odiv__class_Odiv'( Y, Z
% 1.10/1.48 , X ), 'c_Divides_Odiv__class_Odiv'( T, Z, X ), X ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.10/1.48 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 1.10/1.48 X ), Y, 'tc_nat' ), 'c_Suc'( Z ), 'tc_nat' ),
% 1.10/1.48 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.10/1.48 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Osgn__class_Osgn'( Y, X ),
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Osgn__class_Osgn'( Y, X ),
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.10/1.48 'c_HOL_Oabs__class_Oabs'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X
% 1.10/1.48 ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ],
% 1.10/1.48 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.10/1.48 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.10/1.48 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.10/1.48 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.10/1.48 , T, X ), X ), T, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.10/1.48 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.10/1.48 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.48 ,
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.10/1.48 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.48 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.10/1.48 ,
% 1.10/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.10/1.48 , =( 'c_HOL_Oplus__class_Oplus'( 'c_Orderings_Oord__class_Omin'( Y, Z, X
% 1.10/1.48 ), T, X ), 'c_Orderings_Oord__class_Omin'( 'c_HOL_Oplus__class_Oplus'( Y
% 1.10/1.48 , T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ],
% 1.10/1.48 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ) ) ), =( X, Z ) ],
% 1.10/1.48 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ],
% 1.10/1.48 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.10/1.48 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =(
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 1.10/1.48 X ) ) ), =( Z, T ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 1.10/1.48 X ) ) ), =( Z, T ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 1.10/1.48 X ) ) ), =( Y, T ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Olcm'( Y
% 1.10/1.48 , Z, 'tc_nat' ), 'tc_nat' ), 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X
% 1.10/1.48 , 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' )
% 1.10/1.48 ) ],
% 1.10/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Olcm'( Y
% 1.10/1.48 , Z, 'tc_nat' ), 'tc_nat' ), 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X
% 1.10/1.48 , 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' )
% 1.10/1.48 ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.48 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.48 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.10/1.48 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.10/1.48 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.10/1.48 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.10/1.48 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.10/1.48 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.48 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.10/1.48 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.10/1.48 , X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.10/1.48 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.10/1.48 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Z
% 1.10/1.48 , X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ), =( Z,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.48 ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.10/1.48 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.48 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.10/1.48 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.48 , 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.48 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.48 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.10/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.10/1.48 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.48 ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.10/1.48 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ), Z, X ),
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.10/1.48 [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.10/1.48 'tc_nat' ), X, 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( Y, X, 'tc_nat' ) ),
% 1.10/1.48 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.10/1.48 [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.10/1.48 'tc_nat' ), Y, 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ) ),
% 1.10/1.48 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), =( Y,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.10/1.48 Z, 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Z, X )
% 1.10/1.48 , T, X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.48 X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Y, T, X ),
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.10/1.48 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.10/1.48 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.10/1.48 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ) ],
% 1.10/1.48 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.10/1.48 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.10/1.48 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.48 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T,
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ), ~(
% 1.10/1.48 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.48 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48 ), X ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.10/1.48 ), X ), Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z,
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ],
% 1.10/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.48 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' )
% 1.10/1.48 , ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.48 'tc_nat' ) ), X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.10/1.48 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.10/1.48 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Suc'( Y ), X ),
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 1.10/1.48 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ],
% 1.10/1.48 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.10/1.48 Y, T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X )
% 1.10/1.48 ), ~( 'c_lessequals'( Z, T, 'tc_nat' ) ) ],
% 1.10/1.48 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.48 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.10/1.48 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 1.10/1.48 , T, X ), 'c_Orderings_Oord__class_Omin'( Y,
% 1.10/1.48 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.10/1.48 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 1.10/1.48 X ), X ), 'c_Orderings_Oord__class_Omin'( Z,
% 1.10/1.48 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ) ) ],
% 1.10/1.48 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ),
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.10/1.48 ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.48 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T
% 1.10/1.48 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Z, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.10/1.48 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.48 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 Y, 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), =(
% 1.10/1.48 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omax'( Y, Z, X ),
% 1.10/1.48 T, X ), 'c_Orderings_Oord__class_Omax'( 'c_HOL_Ominus__class_Ominus'( Y,
% 1.10/1.48 T, X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.10/1.48 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ), ~( 'c_lessequals'( Y, Z,
% 1.10/1.48 X ) ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 1.10/1.48 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ) ), 'c_lessequals'( Y, Z, X
% 1.10/1.48 ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.10/1.48 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z ), ~( 'c_lessequals'( Z, Y,
% 1.10/1.48 X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 1.10/1.48 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 1.10/1.48 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) )
% 1.10/1.48 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 1.10/1.48 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 1.10/1.48 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.10/1.48 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.48 X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), =( Y
% 1.10/1.48 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.10/1.48 , X ) ) ],
% 1.10/1.48 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.10/1.48 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.10/1.48 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.10/1.48 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 1.10/1.48 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.10/1.48 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.10/1.48 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 1.10/1.48 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.48 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.48 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y,
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ), X ), ~(
% 1.10/1.48 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.48 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.48 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 1.10/1.48 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z
% 1.10/1.48 , X ) ) ],
% 1.10/1.48 [ 'c_lessequals'( 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ),
% 1.10/1.48 'c_Fact_Ofact__class_Ofact'( Y, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 1.10/1.48 X, Y, 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.10/1.48 , Z, X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.48 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.10/1.48 ), X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.10/1.48 ), X ), Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.48 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( T, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.10/1.48 ), X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( T, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.10/1.48 ), X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~( 'c_lessequals'( Y,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, T, X ) ) ]
% 1.10/1.48 ,
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z, X ) )
% 1.10/1.48 ],
% 1.10/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.10/1.48 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 1.10/1.48 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.10/1.48 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 1.10/1.48 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.10/1.48 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 1.10/1.48 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z, X ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y, X ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.10/1.48 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.10/1.48 ), X ) ) ],
% 1.10/1.48 [ ~( 'class_SEQ_Obanach'( X ) ), ~(
% 1.10/1.48 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.10/1.48 'c_Transcendental_Oexp'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ),
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( 'c_Transcendental_Oexp'( Y, X ),
% 1.10/1.48 'c_Transcendental_Oexp'( Z, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.48 T, X ) ) ],
% 1.10/1.48 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'(
% 1.10/1.48 X, Y, 'tc_nat' ) ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 1.10/1.48 X ), 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.10/1.48 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( =( 'c_List_Oreplicate'( X, Y, Z ), 'c_List_Oreplicate'( T, U, Z ) )
% 1.10/1.48 ), =( X, T ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 1.10/1.48 , Y, X ), X ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 1.10/1.48 , Z, X ), X ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Odvd'( X ) ),
% 1.10/1.48 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 1.10/1.48 , Z, X ), X ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( U, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.10/1.48 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.10/1.48 ],
% 1.10/1.48 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.48 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ),
% 1.10/1.48 'c_Power_Opower__class_Opower'( Y, Z, X ), X ),
% 1.10/1.48 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'(
% 1.10/1.48 'c_HOL_Oone__class_Oone'( X ), Y, X ), Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.10/1.48 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~( 'c_lessequals'( Y,
% 1.10/1.48 Z, 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.10/1.48 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.10/1.48 Y, X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.48 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.48 Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.10/1.48 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.10/1.48 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.10/1.48 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.10/1.48 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 1.10/1.48 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.10/1.48 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 1.10/1.48 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.48 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.10/1.48 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 1.10/1.48 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.48 [ =( 'c_Orderings_Oord__class_Omax'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 1.10/1.48 'tc_nat' ), 'c_Suc'( 'c_Orderings_Oord__class_Omax'( X, Y, 'tc_nat' ) ) )
% 1.10/1.48 ],
% 1.10/1.48 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.48 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( 'c_lessequals'(
% 1.10/1.48 'c_Power_Opower__class_Opower'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 1.10/1.48 , 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.10/1.48 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'(
% 1.10/1.48 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 1.10/1.48 X ), 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X
% 1.10/1.48 ), X ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.10/1.48 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Y, Z,
% 1.10/1.48 X ), X ), 'c_Orderings_Oord__class_Omin'( Y, Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Z, X ), U, X ) ),
% 1.10/1.48 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), T, X ) )
% 1.10/1.48 ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.48 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.48 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48 ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T
% 1.10/1.48 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), Z, X
% 1.10/1.48 ), Y ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.48 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.10/1.48 ), X ), Y ) ],
% 1.10/1.48 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.10/1.48 'tc_nat' ) ],
% 1.10/1.48 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.10/1.48 'tc_nat' ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.48 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 Y, 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.48 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.48 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T
% 1.10/1.48 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.10/1.48 'c_Power_Opower__class_Opower'( 'c_Power_Opower__class_Opower'( Y, Z, X )
% 1.10/1.48 , T, X ), 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 Z, T, 'tc_nat' ), X ) ) ],
% 1.10/1.48 [ =( 'c_Complex_Ocnj'( 'c_HOL_Ozero__class_Ozero'( 'tc_Complex_Ocomplex'
% 1.10/1.48 ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_Complex_Ocomplex' ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.10/1.48 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.10/1.48 ), X ) ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.10/1.48 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.10/1.48 Y, X ) ) ],
% 1.10/1.48 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( Y,
% 1.10/1.48 'c_Suc'( Z ), X ), 'c_HOL_Otimes__class_Otimes'( Y,
% 1.10/1.48 'c_Power_Opower__class_Opower'( Y, Z, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.10/1.48 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.10/1.48 ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_HOL_Oinverse__class_Oinverse'( 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.10/1.48 'c_Fact_Ofact__class_Ofact'( Y, 'tc_nat' ), X ), X ), X ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 1.10/1.48 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.10/1.48 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.10/1.48 ,
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.10/1.48 , Y, X ) ) ],
% 1.10/1.48 [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.10/1.48 , Y, X ) ) ],
% 1.10/1.48 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.48 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.10/1.48 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.48 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.10/1.48 , T, X ), X ), T, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ), T, X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.10/1.48 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.48 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.48 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.48 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.48 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.10/1.48 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.10/1.48 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y,
% 1.10/1.48 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ),
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.10/1.48 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.48 , 'tc_nat' ), 'tc_nat' ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.10/1.48 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 1.10/1.48 ) ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.10/1.48 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.10/1.48 ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.10/1.48 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.10/1.48 ) ) ],
% 1.10/1.48 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.10/1.48 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.48 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.10/1.48 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.10/1.48 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 1.10/1.48 ) ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.10/1.48 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.10/1.48 ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.10/1.48 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.10/1.48 ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.10/1.48 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 1.10/1.48 ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.10/1.48 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 1.10/1.48 ) ) ],
% 1.10/1.48 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.10/1.48 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.10/1.48 ) ) ],
% 1.10/1.48 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.10/1.48 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.48 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y, X
% 1.10/1.48 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.10/1.48 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T,
% 1.10/1.48 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.48 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.10/1.48 Y, T, X ), X ) ) ],
% 1.10/1.48 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Suc'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ],
% 1.10/1.48 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.10/1.48 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.10/1.48 Z, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X )
% 1.10/1.48 , 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ) ],
% 1.10/1.48 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 1.10/1.48 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 1.10/1.48 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.10/1.48 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 1.10/1.48 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.10/1.48 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 1.10/1.48 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.10/1.48 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'(
% 1.10/1.48 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_Suc'(
% 1.10/1.48 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X, 'tc_nat' ) ), 'tc_nat' ) )
% 1.10/1.48 ],
% 1.10/1.48 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.10/1.48 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.10/1.48 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 1.10/1.48 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 1.10/1.48 , X ), 'c_lessequals'( Y, Y, X ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.10/1.48 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.10/1.48 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.10/1.48 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.10/1.48 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.10/1.49 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.10/1.49 [ =( 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 1.10/1.49 X ), Y, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.49 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.10/1.49 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat'
% 1.10/1.49 ), 'tc_nat' ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X
% 1.10/1.49 ), 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.49 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.10/1.49 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.10/1.49 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 1.10/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.49 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.10/1.49 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.49 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 1.10/1.49 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Olcm'(
% 1.10/1.49 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X,
% 1.10/1.49 Z, 'tc_nat' ), 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X,
% 1.10/1.49 'c_GCD_Ogcd__class_Olcm'( Y, Z, 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.10/1.49 ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.10/1.49 ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.10/1.49 ), X ) ) ],
% 1.10/1.49 [ ~( 'class_SEQ_Obanach'( X ) ), ~(
% 1.10/1.49 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_Transcendental_Oexp'( Y, X ),
% 1.10/1.49 'c_Transcendental_Oexp'( Z, X ), X ), 'c_Transcendental_Oexp'(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.10/1.49 , 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ), =(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( Y, T, X ), U ) ],
% 1.10/1.49 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X,
% 1.10/1.49 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.49 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' )
% 1.10/1.49 ) ],
% 1.10/1.49 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X,
% 1.10/1.49 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.49 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' )
% 1.10/1.49 ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.10/1.49 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Z ), ~( 'c_lessequals'( Y, Z,
% 1.10/1.49 X ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 1.10/1.49 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Z ) ), 'c_lessequals'( Y, Z, X
% 1.10/1.49 ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.10/1.49 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Y ), ~( 'c_lessequals'( Z, Y,
% 1.10/1.49 X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z
% 1.10/1.49 ), X ), 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.10/1.49 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.10/1.49 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.10/1.49 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.10/1.49 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'(
% 1.10/1.49 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), X ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.10/1.49 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.10/1.49 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ],
% 1.10/1.49 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.10/1.49 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.10/1.49 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'c_lessequals'( X, X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X,
% 1.10/1.49 'c_Suc'( X ), 'tc_nat' ) ],
% 1.10/1.49 [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' )
% 1.10/1.49 , 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 1.10/1.49 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) )
% 1.10/1.49 ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.10/1.49 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 1.10/1.49 ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.10/1.49 , X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.10/1.49 , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.49 ,
% 1.10/1.49 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 1.10/1.49 ), U, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.49 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 1.10/1.49 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.10/1.49 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 1.10/1.49 ), U, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z,
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.49 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 1.10/1.49 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.10/1.49 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.10/1.49 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.10/1.49 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.10/1.49 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y,
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_RealVector_Oreal__field'( X ) ), =(
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.10/1.49 , U, X ), X ), W, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oinverse__class_Odivide'(
% 1.10/1.49 'c_HOL_Ominus__class_Ominus'( Z, U, X ), W, X ), X ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'(
% 1.10/1.49 'c_HOL_Ominus__class_Ominus'( Y, T, X ), W, X ), U, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.49 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.10/1.49 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.10/1.49 ), =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.10/1.49 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ),
% 1.10/1.49 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), X ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Z, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.10/1.49 ), X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.10/1.49 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( T, U,
% 1.10/1.49 X ), X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'(
% 1.10/1.49 'c_HOL_Ominus__class_Ominus'( Y, T, X ), X ), 'c_HOL_Oabs__class_Oabs'(
% 1.10/1.49 'c_HOL_Ominus__class_Ominus'( Z, U, X ), X ), X ), X ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.10/1.49 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.10/1.49 , ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.10/1.49 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 1.10/1.49 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 1.10/1.49 ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), =(
% 1.10/1.49 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ),
% 1.10/1.49 T, X ), 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ominus__class_Ominus'( Y,
% 1.10/1.49 T, X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ), X ) ) ],
% 1.10/1.49 [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 1.10/1.49 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X, Y,
% 1.10/1.49 'tc_nat' ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.10/1.49 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.49 ,
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.10/1.49 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.49 ,
% 1.10/1.49 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.10/1.49 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~(
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Ominus__class_Ominus'( Z
% 1.10/1.49 , Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.10/1.49 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~(
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ), ~(
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Ominus__class_Ominus'( Y
% 1.10/1.49 , Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.10/1.49 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.49 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), X ) ) ],
% 1.10/1.49 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, X, 'tc_nat' ), X ) ],
% 1.10/1.49 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.49 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 1.10/1.49 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.10/1.49 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.10/1.49 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.49 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ), ~(
% 1.10/1.49 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Oone__class_Oone'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X )
% 1.10/1.49 , X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.10/1.49 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ),
% 1.10/1.49 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 1.10/1.49 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ],
% 1.10/1.49 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ), 'c_Suc'(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.10/1.49 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.10/1.49 W, X ) ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.49 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.10/1.49 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.10/1.49 W, X ) ) ), =( T, 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.10/1.49 , X ), W, X ) ) ],
% 1.10/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z
% 1.10/1.49 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ), T, X ),
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ],
% 1.10/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Odiv'( Z, Y, X )
% 1.10/1.49 , X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ), X ), T, X ),
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( Z, T, X ) ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.49 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.49 X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.49 Y, 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), T, X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.10/1.49 ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.49 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T,
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Z, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.10/1.49 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'( Z,
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.49 , X ), X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.49 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49 ), X ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.10/1.49 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'( X, Y
% 1.10/1.49 , 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 1.10/1.49 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'( X, Y
% 1.10/1.49 , 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X,
% 1.10/1.49 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.10/1.49 , Z, X ), 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 1.10/1.49 'c_lessequals'( Z, T, 'tc_nat' ) ) ],
% 1.10/1.49 [ =( 'c_Complex_Ocnj'( 'c_Complex_Ocnj'( X ) ), X ) ],
% 1.10/1.49 [ =( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ),
% 1.10/1.49 'c_GCD_Ogcd__class_Olcm'( Y, X, 'tc_nat' ) ) ],
% 1.10/1.49 [ =( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ),
% 1.10/1.49 'c_GCD_Ogcd__class_Olcm'( Y, X, 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.10/1.49 Y, T, X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X )
% 1.10/1.49 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.10/1.49 'c_lessequals'( T, Z, 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.49 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( T, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.10/1.49 ), X ), Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.49 X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.49 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.10/1.49 ), X ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49 ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.10/1.49 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.10/1.49 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.10/1.49 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.10/1.49 , 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 1.10/1.49 X ) ) ],
% 1.10/1.49 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ) ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 X, T, 'tc_nat' ) ],
% 1.10/1.49 [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 1.10/1.49 X ) ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 1.10/1.49 X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49 ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49 ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( Z,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49 ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49 ), X ) ) ],
% 1.10/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.10/1.49 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.10/1.49 ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.10/1.49 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.49 Z, X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.10/1.49 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.10/1.49 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.10/1.49 'c_lessequals'( Z, Y, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.10/1.49 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.10/1.49 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.10/1.49 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.49 'c_lessequals'( Z, Y, X ) ) ],
% 1.10/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.49 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.10/1.49 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.49 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.10/1.49 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.49 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.10/1.49 , T, X ), X ), T, X ) ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.10/1.49 Y, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'(
% 1.10/1.49 Y, Z, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.10/1.49 'c_lessequals'( Y, T, X ), ~( 'c_lessequals'( Y,
% 1.10/1.49 'c_Orderings_Oord__class_Omax'( T, Z, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.10/1.49 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ]
% 1.10/1.49 ,
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.10/1.49 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X ), X ) ) ]
% 1.10/1.49 ,
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 1.10/1.49 T, X ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 1.10/1.49 T, X ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 1.10/1.49 T, X ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 1.10/1.49 T, X ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.10/1.49 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ]
% 1.10/1.49 ,
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.10/1.49 ), X ) ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.10/1.49 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.10/1.49 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.10/1.49 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 1.10/1.49 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.10/1.49 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 1.10/1.49 ],
% 1.10/1.49 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.10/1.49 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.10/1.49 'c_lessequals'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) )
% 1.10/1.49 , ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.10/1.49 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.10/1.49 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.10/1.49 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.10/1.49 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.10/1.49 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), 'c_Nitpick_Onat__gcd'(
% 1.10/1.49 X, Y ) ) ],
% 1.10/1.49 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.10/1.49 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.49 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.10/1.49 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X,
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.10/1.49 T, Z, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 1.10/1.49 ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.10/1.49 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.10/1.49 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 1.10/1.49 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), =( X, Z ) ]
% 1.10/1.49 ,
% 1.10/1.49 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.10/1.49 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.10/1.49 , T, X ) ) ), =( Z, T ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.10/1.49 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.10/1.49 , T, X ) ) ), =( Y, Z ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.10/1.49 X ) ), =( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Oplus__class_Oplus'( Z
% 1.10/1.49 , T, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.10/1.49 , T, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.10/1.49 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Y, Z,
% 1.10/1.49 X ), X ), Y ) ],
% 1.10/1.49 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.10/1.49 'tc_nat' ) ), =( Y, Z ) ],
% 1.10/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.10/1.49 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.49 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 1.10/1.49 ) ) ],
% 1.10/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.10/1.49 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y
% 1.10/1.49 , X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat'
% 1.10/1.49 ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.10/1.49 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), =( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'(
% 1.10/1.49 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.10/1.49 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49 ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.10/1.49 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.10/1.49 , T, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.10/1.49 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.10/1.49 , Z, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.49 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X
% 1.10/1.49 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 1.10/1.49 ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.49 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.10/1.49 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.49 X ), T, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.49 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( T, Z, X
% 1.10/1.49 ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.10/1.49 ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.49 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.10/1.49 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.10/1.49 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.10/1.49 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.10/1.49 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.10/1.49 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.49 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.10/1.49 , 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat'
% 1.10/1.49 ) ) ],
% 1.10/1.49 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.10/1.49 ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =( Y, Z ) ],
% 1.10/1.49 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.10/1.49 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.49 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.10/1.49 , U, X ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'(
% 1.10/1.49 Y, T, X ), U, X ), X ), 'c_HOL_Otimes__class_Otimes'( T,
% 1.10/1.49 'c_HOL_Ominus__class_Ominus'( Z, U, X ), X ), X ) ) ],
% 1.10/1.49 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.10/1.49 , 'tc_nat' ), 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat'
% 1.10/1.49 ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.10/1.49 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.10/1.49 , 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 1.10/1.49 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ]
% 1.10/1.49 ,
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.10/1.49 ), X ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.10/1.49 ), X ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.10/1.49 'class_OrderedGroup_Omonoid__mult'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.10/1.49 ), X ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.49 'c_Suc'( X ), 'tc_nat' ) ],
% 1.10/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.49 'c_Suc'( X ), 'tc_nat' ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.10/1.49 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ),
% 1.10/1.49 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.10/1.49 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omax'( T, Y
% 1.10/1.49 , X ), Z, X ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.10/1.49 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omax'( Y, T
% 1.10/1.49 , X ), Z, X ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.49 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.49 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.49 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.49 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.10/1.49 'c_Orderings_Oord__class_Omin'( Y, Z, X ), 'c_Orderings_Oord__class_Omin'(
% 1.10/1.49 Z, Y, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.10/1.49 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.10/1.49 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.10/1.49 , Y, X ) ) ],
% 1.10/1.49 [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.10/1.49 'tc_nat' ), Y, 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ) ) ]
% 1.10/1.49 ,
% 1.10/1.49 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.10/1.49 'tc_nat' ), 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ) ) ]
% 1.10/1.49 ,
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 1.10/1.49 ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ), U, X ) ) ],
% 1.10/1.49 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.10/1.49 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z,
% 1.10/1.49 Y, 'tc_nat' ), T, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 1.10/1.49 ), Y, 'tc_nat' ), T, 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), X,
% 1.10/1.49 'tc_nat' ) ],
% 1.10/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.10/1.49 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.49 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) )
% 1.10/1.49 ],
% 1.10/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.10/1.49 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.49 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' ) )
% 1.10/1.49 ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.10/1.49 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.10/1.49 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.10/1.49 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, Z, X ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.49 X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.49 X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 1.10/1.49 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.10/1.49 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 1.10/1.49 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.10/1.49 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.10/1.49 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.10/1.49 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.49 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 1.10/1.49 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.10/1.49 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.10/1.49 X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.10/1.49 , X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.10/1.49 X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.10/1.49 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T,
% 1.10/1.49 'tc_nat' ), X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.10/1.49 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.10/1.49 Y, T, X ), X ) ), ~( 'c_lessequals'( T, Z, 'tc_nat' ) ), =( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ =( 'c_GCD_Ogcd__class_Olcm'( X, X, 'tc_nat' ), X ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.10/1.49 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.49 'c_HOL_Ominus__class_Ominus'( Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.10/1.49 , U, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.10/1.49 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omin'( T
% 1.10/1.49 , Z, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.10/1.49 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omin'( Z
% 1.10/1.49 , T, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.10/1.49 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.10/1.49 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.10/1.49 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.10/1.49 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.10/1.49 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.10/1.49 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 1.10/1.49 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.49 , 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.10/1.49 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.10/1.49 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.49 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.10/1.49 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.49 , X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.10/1.49 ,
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.49 , X ) ) ],
% 1.10/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), T
% 1.10/1.49 , X ), 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.10/1.49 X ), Z, X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ]
% 1.10/1.49 ,
% 1.10/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.10/1.49 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.10/1.49 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z
% 1.10/1.49 , 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X
% 1.10/1.49 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ),
% 1.10/1.49 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X )
% 1.10/1.49 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat'
% 1.10/1.49 ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), =( 'c_Suc'( X
% 1.10/1.49 ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_lessequals'( Y, X,
% 1.10/1.49 'tc_nat' ) ],
% 1.10/1.49 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( Y )
% 1.10/1.49 , X, 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.10/1.49 'c_Power_Opower__class_Opower'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.10/1.49 , 'c_Power_Opower__class_Opower'( Y, Z, X ) ), ~(
% 1.10/1.49 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.10/1.49 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.49 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.10/1.49 , 'tc_nat' ), 'tc_nat' ), 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.49 X ), X ), ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( Z,
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y,
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.10/1.49 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.10/1.49 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.10/1.49 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat' ),
% 1.10/1.49 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.10/1.49 'c_HOL_Oabs__class_Oabs'( 'c_Power_Opower__class_Opower'( Y, Z, X ), X )
% 1.10/1.49 , 'c_Power_Opower__class_Opower'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X
% 1.10/1.49 ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.49 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.49 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.10/1.49 ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.49 X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.49 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.10/1.49 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.49 T, 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Z, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.10/1.49 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49 ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.10/1.49 , Z, X ), 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~(
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.10/1.49 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X ), X ) ) ]
% 1.10/1.49 ,
% 1.10/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.49 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), T, X ),
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( Z, 'c_Divides_Odiv__class_Odiv'( Y, T, X ), X
% 1.10/1.49 ) ), =( T, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.49 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), Z, X ),
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( T, 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), X
% 1.10/1.49 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.10/1.49 ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.10/1.49 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.10/1.49 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.10/1.49 , Y, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.10/1.49 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.49 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.10/1.49 X ), Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.49 , Z, X ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.10/1.49 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.10/1.49 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.10/1.49 X ), Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.49 , Z, X ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.10/1.49 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.10/1.49 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.10/1.49 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T, Z, X
% 1.10/1.49 ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X
% 1.10/1.49 ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.10/1.49 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ),
% 1.10/1.49 ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oinverse__class_Odivide'( Y, T, X
% 1.10/1.49 ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.10/1.49 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.49 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.10/1.49 T, X ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.49 , T, X ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.10/1.49 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.49 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.10/1.49 T, X ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.49 , T, X ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.10/1.49 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.49 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.10/1.49 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.10/1.49 Z, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.10/1.49 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), Z, X ), Z, X ) ), =( Z,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.10/1.49 X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 1.10/1.49 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ],
% 1.10/1.49 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.10/1.49 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.10/1.49 , T, X ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49 ), T, X ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.10/1.49 , T, X ), Z, X ) ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.10/1.49 'c_lessequals'( Y, 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.10/1.49 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.10/1.49 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.10/1.49 , 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.10/1.49 , T, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.10/1.49 , T, X ), Z, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.10/1.49 , X ), U, X ), W, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), U, X
% 1.10/1.49 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, X ),
% 1.10/1.49 W, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 1.10/1.49 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 1.10/1.49 , X ), T, X ), W, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 1.10/1.49 , X ), W, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X
% 1.10/1.49 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ),
% 1.10/1.49 W, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 1.10/1.49 ), X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.10/1.49 , X ), W, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.10/1.49 'c_lessequals'( T, Z, X ), ~( 'c_lessequals'(
% 1.10/1.49 'c_Orderings_Oord__class_Omin'( T, Y, X ), Z, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), =( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.49 , X ), X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), =(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49 ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), =( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.49 , X ), X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y ), =(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49 ) ) ],
% 1.10/1.49 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.49 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), T,
% 1.10/1.49 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), T, 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 1.10/1.49 , X ) ) ],
% 1.10/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.10/1.49 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.10/1.49 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.10/1.49 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.10/1.49 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( U, Y, X ), Z, X
% 1.10/1.49 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( W, T, X ),
% 1.10/1.49 Z, X ) ) ],
% 1.10/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.49 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 1.10/1.49 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.10/1.49 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z, X ) ) ]
% 1.10/1.49 ,
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.10/1.49 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z, X ) ) ]
% 1.10/1.49 ,
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.10/1.49 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z,
% 1.10/1.49 X ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.10/1.49 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 1.10/1.49 X ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.10/1.49 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z,
% 1.10/1.49 X ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.10/1.49 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 1.10/1.49 X ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.10/1.49 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z, X ) ) ]
% 1.10/1.49 ,
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.10/1.49 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z, X ) ) ]
% 1.10/1.49 ,
% 1.10/1.49 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z,
% 1.10/1.49 'tc_nat' ), ~( 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 1.10/1.49 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 1.10/1.49 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Z,
% 1.10/1.49 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.49 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.49 ,
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.10/1.49 , X ), 'c_HOL_Oord__class_Oless'( Y, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 Y, 'c_Orderings_Oord__class_Omax'( T, Z, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.49 'c_Power_Opower__class_Opower'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 1.10/1.49 T, X ), 'c_Divides_Odiv__class_Odiv'( 'c_Power_Opower__class_Opower'( Y,
% 1.10/1.49 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ), ~(
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ],
% 1.10/1.49 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.10/1.49 'tc_nat' ), Z, 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), ~(
% 1.10/1.49 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.49 X, Z, 'tc_nat' ), T, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 1.10/1.49 ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 1.10/1.49 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.49 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 1.10/1.49 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.10/1.49 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat'
% 1.10/1.49 ), X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 1.10/1.49 ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 1.10/1.49 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( Z,
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.49 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 1.10/1.49 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.10/1.49 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.10/1.49 , 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.49 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.10/1.49 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.10/1.49 , X ), 'c_HOL_Oord__class_Oless'( T, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_Orderings_Oord__class_Omin'( T, Y, X ), Z, X ) ) ],
% 1.10/1.49 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.10/1.49 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 1.10/1.49 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 1.10/1.49 , T ), =( X, Z ) ],
% 1.10/1.49 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.10/1.49 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 1.10/1.49 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 1.10/1.49 , T ), =( X, Z ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.10/1.49 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 1.10/1.49 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 1.10/1.49 ,
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.10/1.49 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 1.10/1.49 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 1.10/1.49 ,
% 1.10/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.49 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), 'tc_nat' ), =( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.49 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), 'tc_nat' ), =( X,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.10/1.49 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), 'c_HOL_Otimes__class_Otimes'( Y, Y
% 1.10/1.49 , X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.10/1.49 'c_HOL_Oinverse__class_Oinverse'( 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.10/1.49 ), X ), 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Oinverse'(
% 1.10/1.49 Y, X ), Z, X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat'
% 1.10/1.49 ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Z, X )
% 1.10/1.49 , T, X ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.10/1.49 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y, Z,
% 1.10/1.49 'tc_nat' ), 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( Y,
% 1.10/1.49 'c_GCD_Ogcd__class_Ogcd'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.49 [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat'
% 1.10/1.49 ), Z, 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 1.10/1.49 Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.49 [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat'
% 1.10/1.49 ), Z, 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 1.10/1.49 Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.49 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 1.10/1.49 , 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 1.10/1.49 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) )
% 1.10/1.49 , 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.10/1.49 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.10/1.49 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.10/1.49 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.10/1.49 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.10/1.49 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( U, Y, X ), Z
% 1.10/1.49 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( W, T,
% 1.10/1.49 X ), Z, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.10/1.49 , Z, X ), Z, X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), =( Z,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.49 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( Z, X )
% 1.10/1.49 , T, X ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_lessequals'(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.10/1.49 , Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ), =( U,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.49 ) ],
% 1.10/1.49 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.49 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat'
% 1.10/1.49 ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.10/1.49 'tc_nat' ), X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ]
% 1.10/1.49 ,
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.10/1.49 , Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.10/1.49 , Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z, X
% 1.10/1.49 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.10/1.49 'c_HOL_Oone__class_Oone'( X ), X ), Z, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X
% 1.10/1.49 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Z,
% 1.10/1.49 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ],
% 1.10/1.49 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 1.10/1.49 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.10/1.49 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.10/1.49 X ) ), =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z
% 1.10/1.49 , X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ),
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), X ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Z, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.10/1.49 ), X ), X ) ) ],
% 1.10/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.10/1.49 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 1.10/1.49 ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ),
% 1.10/1.49 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) )
% 1.10/1.49 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.10/1.49 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.49 Y, X, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.10/1.49 , Y, 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Oplus__class_Oplus'( Y,
% 1.10/1.49 X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.49 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.10/1.49 X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.10/1.49 Z, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.10/1.49 Z, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 1.10/1.49 ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 1.10/1.49 ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.10/1.49 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.10/1.49 ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.10/1.49 , Y, X ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 1.10/1.49 , X ) ) ],
% 1.10/1.49 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X
% 1.10/1.49 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 1.10/1.49 'c_HOL_Ominus__class_Ominus'( T, Y, X ), X ), Z, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.49 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 1.10/1.49 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) )
% 1.10/1.49 ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.49 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 1.10/1.49 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.10/1.49 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.10/1.49 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.49 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.49 ,
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.49 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.49 ,
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.49 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.49 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.10/1.49 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.10/1.49 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 1.10/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.49 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.10/1.49 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.49 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 1.10/1.49 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.49 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.10/1.49 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ), 'tc_nat' ) ],
% 1.10/1.49 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X, 'tc_nat' ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ), 'tc_nat' ) ) ]
% 1.10/1.49 ,
% 1.10/1.49 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y,
% 1.10/1.49 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ),
% 1.10/1.49 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Z,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 1.10/1.49 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.10/1.49 T, Z, X ) ) ), =( Y, T ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.10/1.49 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.10/1.49 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.10/1.49 , 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ), =( Z,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.10/1.49 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ), =( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( X ), 'tc_nat' ) ],
% 1.10/1.49 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.10/1.49 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( X ), 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( X ), 'tc_nat' ),
% 1.10/1.49 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.10/1.49 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~(
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_Suc'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.49 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.49 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.10/1.49 ), X ), Z, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.49 Y, 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), T, X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'( Y,
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( T, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.49 , X ), X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.49 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.10/1.49 ), X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Z, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.10/1.49 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49 ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.49 , X ), X ), Z, X ) ) ],
% 1.10/1.49 [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X, X, 'tc_nat' ),
% 1.10/1.49 'tc_nat' ) ],
% 1.10/1.49 [ ~( 'class_SEQ_Obanach'( X ) ), ~(
% 1.10/1.49 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.10/1.49 'c_Transcendental_Oexp'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_Transcendental_Oexp'( Y, X ),
% 1.10/1.49 'c_Transcendental_Oexp'( Z, X ), X ) ) ],
% 1.10/1.49 [ =( 'c_Fact_Ofact__class_Ofact'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.10/1.49 , 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.10/1.49 , T, X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.49 Y, T, X ), Z, X ) ) ],
% 1.10/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Odiv'( Z, Y, X )
% 1.10/1.49 , X ), Z ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.10/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z
% 1.10/1.49 , X ), Y ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.10/1.49 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.10/1.49 , 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 1.10/1.49 ) ],
% 1.10/1.49 [ =( 'c_Orderings_Oord__class_Omin'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 1.10/1.49 'tc_nat' ), 'c_Suc'( 'c_Orderings_Oord__class_Omin'( X, Y, 'tc_nat' ) ) )
% 1.10/1.49 ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.10/1.49 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.49 X ), T, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.10/1.49 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.10/1.49 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.10/1.49 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.10/1.49 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 1.10/1.49 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.10/1.49 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.10/1.49 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.10/1.49 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.10/1.49 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.10/1.49 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.10/1.49 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.10/1.49 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.10/1.49 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.10/1.49 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.10/1.49 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.10/1.49 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.10/1.49 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.10/1.49 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 1.10/1.49 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Fact_Ofact__class_Ofact'( Y,
% 1.10/1.49 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.10/1.49 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 1.10/1.49 X ), X ), 'c_Orderings_Oord__class_Omax'( Z,
% 1.10/1.49 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.10/1.49 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omax'( Y, Z, X )
% 1.10/1.49 , T, X ), 'c_Orderings_Oord__class_Omax'( Y,
% 1.10/1.49 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.49 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), Z, X ),
% 1.10/1.49 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.10/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.49 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), T, X ),
% 1.10/1.49 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.10/1.49 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.10/1.49 , 'tc_nat' ), 'tc_nat' ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.10/1.49 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'(
% 1.10/1.49 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 1.10/1.49 , X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 1.10/1.49 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.10/1.49 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), =( Z,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Z, X
% 1.10/1.49 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 1.10/1.49 ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.10/1.49 , X ), X ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.10/1.49 , X ), X ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z,
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( Y,
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ), ~( 'c_lessequals'( Y,
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.10/1.49 'c_Fact_Ofact__class_Ofact'( Y, 'tc_nat' ), X ), X ) ],
% 1.10/1.49 [ =( 'c_Complex_Ocnj'( 'c_Power_Opower__class_Opower'( X, Y,
% 1.10/1.49 'tc_Complex_Ocomplex' ) ), 'c_Power_Opower__class_Opower'(
% 1.10/1.49 'c_Complex_Ocnj'( X ), Y, 'tc_Complex_Ocomplex' ) ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.10/1.49 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 1.10/1.49 ), Y ) ],
% 1.10/1.49 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.10/1.49 'tc_nat' ), X, 'tc_nat' ), Y ) ],
% 1.10/1.49 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.10/1.49 'tc_nat' ), Y, 'tc_nat' ), X ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.10/1.49 ), ~( =( 'c_Power_Opower__class_Opower'( Y,
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49 ) ) ],
% 1.10/1.49 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y
% 1.10/1.49 , Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.10/1.49 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 1.10/1.49 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 1.10/1.49 Y, Z, 'tc_nat' ), 'tc_nat' ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.10/1.49 , Z, 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat'
% 1.10/1.49 ) ) ],
% 1.10/1.49 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'(
% 1.10/1.49 Y, Z, 'tc_nat' ), 'tc_nat' ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.10/1.49 , Y, 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat'
% 1.10/1.49 ) ) ],
% 1.10/1.49 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y
% 1.10/1.49 , Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.10/1.49 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 1.10/1.49 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y
% 1.10/1.49 , Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.10/1.49 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 1.10/1.49 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 1.10/1.49 , 'tc_nat' ), Y, 'tc_nat' ) ],
% 1.10/1.49 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 1.10/1.49 , 'tc_nat' ), X, 'tc_nat' ) ],
% 1.10/1.49 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 1.10/1.49 , 'tc_nat' ), X, 'tc_nat' ) ],
% 1.10/1.49 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 1.10/1.49 , 'tc_nat' ), Y, 'tc_nat' ) ],
% 1.10/1.49 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 1.10/1.49 , 'tc_nat' ), X, 'tc_nat' ) ],
% 1.10/1.49 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 1.10/1.49 , 'tc_nat' ), Y, 'tc_nat' ) ],
% 1.10/1.49 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y
% 1.10/1.49 , Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.10/1.49 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 1.10/1.49 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y
% 1.10/1.49 , Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.10/1.49 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 1.10/1.49 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_GCD_Ogcd__class_Ogcd'( Y
% 1.10/1.49 , Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X
% 1.10/1.49 , Z, 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y,
% 1.10/1.49 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 1.10/1.49 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, T
% 1.10/1.49 , X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 1.10/1.49 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, T
% 1.10/1.49 , X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 1.10/1.49 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), T, X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.10/1.49 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Z, T, X )
% 1.10/1.49 , Y, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.10/1.49 , Y, X ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.10/1.49 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.10/1.49 [ ~( 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ),
% 1.10/1.49 'tc_nat' ) ), =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.49 Y, X, 'tc_nat' ), X, 'tc_nat' ), Y ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oabs__class_Oabs'(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49 ), X ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.49 [ =( 'c_GCD_Ogcd__class_Olcm'( X, 'c_GCD_Ogcd__class_Olcm'( X, Y,
% 1.10/1.49 'tc_nat' ), 'tc_nat' ), 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ) ) ]
% 1.10/1.49 ,
% 1.10/1.49 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.10/1.49 'tc_nat' ) ],
% 1.10/1.49 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.10/1.49 'tc_nat' ) ],
% 1.10/1.49 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ),
% 1.10/1.49 'tc_nat' ) ],
% 1.10/1.49 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.10/1.49 'tc_nat' ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.10/1.49 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.10/1.49 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.10/1.49 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.10/1.49 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.10/1.49 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 1.10/1.49 X ), Z, X ) ) ],
% 1.10/1.49 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.10/1.49 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.10/1.49 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.10/1.49 ,
% 1.10/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.10/1.49 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.49 , X ) ) ],
% 1.10/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 1.10/1.49 ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.10/1.49 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.10/1.49 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.10/1.49 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.10/1.49 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.10/1.49 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.10/1.49 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.10/1.49 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.10/1.49 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.10/1.49 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.10/1.49 , X ) ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.10/1.49 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.10/1.49 , X ) ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.49 , X ) ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.10/1.49 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.10/1.49 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.49 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'( Z,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.10/1.49 'c_Power_Opower__class_Opower'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49 ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.10/1.49 'tc_nat' ), Y, 'tc_nat' ), X ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 1.10/1.49 ,
% 1.10/1.49 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, X,
% 1.10/1.49 'tc_nat' ), 'tc_nat' ), Y ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( Y,
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat'
% 1.10/1.49 ), X, 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.10/1.49 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.10/1.49 'tc_nat' ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Z, X
% 1.10/1.49 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 1.10/1.49 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.10/1.49 , Z, 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( X
% 1.10/1.49 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 1.10/1.49 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.10/1.49 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.10/1.49 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.49 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.10/1.49 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.49 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.49 , 'tc_nat' ), X ), X ) ) ],
% 1.10/1.49 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.10/1.49 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.10/1.49 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.10/1.49 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.10/1.49 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.10/1.49 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.10/1.49 [ =( 'c_List_Odrop'( X, 'c_List_Odrop'( Y, Z, T ), T ), 'c_List_Odrop'(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, T ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.10/1.49 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.10/1.49 ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( T ), X ),
% 1.10/1.49 'c_Power_Opower__class_Opower'( Z, 'c_Suc'( T ), X ), X ) ) ],
% 1.10/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.49 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.10/1.49 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.49 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.10/1.49 [ =( 'c_GCD_Ogcd__class_Olcm'( X, 'c_GCD_Ogcd__class_Olcm'( Y, Z,
% 1.10/1.49 'tc_nat' ), 'tc_nat' ), 'c_GCD_Ogcd__class_Olcm'( Y,
% 1.10/1.49 'c_GCD_Ogcd__class_Olcm'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.49 [ =( 'c_GCD_Ogcd__class_Olcm'( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat'
% 1.10/1.49 ), Z, 'tc_nat' ), 'c_GCD_Ogcd__class_Olcm'( X, 'c_GCD_Ogcd__class_Olcm'(
% 1.10/1.49 Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.49 [ =( 'c_GCD_Ogcd__class_Olcm'( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat'
% 1.10/1.49 ), Z, 'tc_nat' ), 'c_GCD_Ogcd__class_Olcm'( X, 'c_GCD_Ogcd__class_Olcm'(
% 1.10/1.49 Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.10/1.49 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.49 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.49 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.10/1.49 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.10/1.49 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.10/1.49 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.10/1.49 ,
% 1.10/1.49 [ ~( =( 'c_Complex_Ocnj'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.49 'tc_Complex_Ocomplex' ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.49 'tc_Complex_Ocomplex' ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 1.10/1.49 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.10/1.49 Y, T, X ) ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X
% 1.10/1.49 ), Y, X ) ), =( Z, T ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.10/1.49 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.10/1.49 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.10/1.49 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ],
% 1.10/1.49 [ ~( 'class_Int_Onumber'( X ) ), ~( 'class_Divides_Osemiring__div'( X )
% 1.10/1.49 ), =( 'c_Divides_Odiv__class_Omod'( 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.49 Y, X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.49 Z, X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Int_Onumber'( X ) ), ~( 'class_Divides_Osemiring__div'( X )
% 1.10/1.49 ), ~( =( 'c_Divides_Odiv__class_Omod'(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.49 Z, X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.49 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.49 , 'tc_nat' ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.10/1.49 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.49 , 'tc_nat' ), 'tc_nat' ) ],
% 1.10/1.49 [ ~( =( 'c_Complex_Ocnj'( X ), 'c_Complex_Ocnj'( Y ) ) ), =( X, Y ) ]
% 1.10/1.49 ,
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.10/1.49 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 1.10/1.49 , X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.10/1.49 ), X ), 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.10/1.49 Y, X ), 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ) ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.10/1.49 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y
% 1.10/1.49 , Z, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X
% 1.10/1.49 ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.10/1.49 , Z, X ), 'c_Power_Opower__class_Opower'( T, U, X ), X ), ~(
% 1.10/1.49 'c_lessequals'( Z, U, 'tc_nat' ) ), ~(
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 1.10/1.49 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), =( Y,
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_Int_Onumber__class_Onumber__of'( T, X )
% 1.10/1.49 , Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ), ~( 'c_lessequals'( X, Y,
% 1.10/1.49 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( X ), Y,
% 1.10/1.49 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.10/1.49 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.10/1.49 ) ), X, 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( Y, X,
% 1.10/1.49 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.10/1.49 ) ), X, 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.49 Y, 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.10/1.49 Z, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oinverse__class_Oinverse'(
% 1.10/1.49 Z, X ), X ) ) ],
% 1.10/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' )
% 1.10/1.49 , 'c_Fact_Ofact__class_Ofact'( Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.10/1.49 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'c_lessequals'( 'c_Suc'( X ), X, 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.49 'c_GCD_Ogcd__class_Ogcd'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.10/1.49 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.10/1.49 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 1.10/1.49 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' )
% 1.10/1.49 , 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.10/1.49 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 1.10/1.49 ],
% 1.10/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.49 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T
% 1.10/1.49 , X ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), ~(
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ) ],
% 1.10/1.49 [ ~( =( 'c_Complex_Oii', 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.49 'tc_Complex_Ocomplex' ) ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.10/1.49 ), =( 'c_HOL_Oinverse__class_Oinverse'(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ),
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.10/1.49 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.10/1.49 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.10/1.49 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.10/1.49 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 1.10/1.49 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 1.10/1.49 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 1.10/1.49 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.10/1.49 X ), T, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.10/1.49 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 1.10/1.49 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.10/1.49 X ), T, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.10/1.49 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49 ), X ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), X ) ), ~(
% 1.10/1.49 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), T, X ), Z, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.49 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.10/1.49 ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.10/1.49 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.10/1.49 ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.10/1.49 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.10/1.49 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.10/1.49 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.10/1.49 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.10/1.49 ), T, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.10/1.49 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 1.10/1.49 Z, T, X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =(
% 1.10/1.49 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ominus__class_Ominus'( Y, Z
% 1.10/1.49 , 'tc_nat' ), X ), 'c_HOL_Ominus__class_Ominus'(
% 1.10/1.49 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.10/1.49 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ), ~( 'c_lessequals'( Z
% 1.10/1.49 , Y, 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.10/1.49 , X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Z, U, X ) ), ~(
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.10/1.49 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.49 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 1.10/1.49 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.10/1.49 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 1.10/1.49 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.10/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ]
% 1.10/1.49 ,
% 1.10/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ),
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ), ~(
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ), ~(
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ), ~(
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ) ),
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ), ~(
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ) ) ],
% 1.10/1.49 [ =( 'c_Power_Opower__class_Opower'( 'c_FFT__Mirabelle_Oroot'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_Complex_Ocomplex' ),
% 1.10/1.49 'c_Power_Opower__class_Opower'( 'c_FFT__Mirabelle_Oroot'( Y ), Z,
% 1.10/1.49 'tc_Complex_Ocomplex' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~( =(
% 1.10/1.49 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.10/1.49 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.10/1.49 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.49 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.10/1.49 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.49 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.10/1.49 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Osgn__if'( X ) ), =(
% 1.10/1.49 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 1.10/1.49 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.49 , X ) ],
% 1.10/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.49 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.49 ) ],
% 1.10/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.49 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.10/1.49 ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.10/1.49 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.10/1.49 ), X ), Y ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.10/1.49 , X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.10/1.49 ,
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.49 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.49 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.10/1.49 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.10/1.49 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ), =( Z,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.49 ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 1.10/1.49 =( 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.49 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.10/1.49 ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49 ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.49 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.49 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.49 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.49 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.49 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.10/1.49 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.10/1.49 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.49 ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.10/1.49 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.49 ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.10/1.49 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.10/1.49 ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.10/1.49 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.49 ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.10/1.49 X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y, X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.10/1.49 X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ), =( Z,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.49 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.10/1.49 ,
% 1.10/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.10/1.49 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.10/1.49 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.49 ) ), =( Y, Z ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.10/1.49 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.49 ) ), =( Y, Z ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.10/1.49 X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.10/1.49 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.10/1.49 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.10/1.49 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.10/1.49 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.10/1.49 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.10/1.49 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~( =(
% 1.10/1.49 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.10/1.49 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_SEQ_Obanach'( X ) ), ~(
% 1.10/1.49 'class_RealVector_Oreal__normed__field'( X ) ), ~( =(
% 1.10/1.49 'c_Transcendental_Oexp'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ]
% 1.10/1.49 ,
% 1.10/1.49 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 1.10/1.49 ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.10/1.49 ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 1.10/1.49 ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.10/1.49 X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49 ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.10/1.49 ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.10/1.49 ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 1.10/1.49 ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.10/1.49 ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.10/1.49 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.10/1.49 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.49 ,
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.10/1.49 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.10/1.49 ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.10/1.49 ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.10/1.49 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.10/1.49 ,
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.10/1.49 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.10/1.49 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.10/1.49 ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.10/1.49 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.10/1.49 ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y, X ), ~( 'c_lessequals'( Z,
% 1.10/1.49 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z, X ), ~( 'c_lessequals'( Y,
% 1.10/1.49 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.10/1.49 , X ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.49 X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Y
% 1.10/1.49 , X ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.49 X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Y
% 1.10/1.49 , X ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.49 X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 1.10/1.49 'c_HOL_Oone__class_Oone'( X ), X ), X ) ],
% 1.10/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.49 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 1.10/1.49 ), 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Oone__class_Oone'( X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49 ) ) ],
% 1.10/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.49 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Y, X
% 1.10/1.49 ), 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Odiv'( Z, Y, X ),
% 1.10/1.49 'c_HOL_Oone__class_Oone'( X ), X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.49 ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.10/1.49 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.10/1.49 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.49 X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.10/1.49 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Osgn__if'( X ) ), =(
% 1.10/1.49 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =(
% 1.10/1.49 Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.10/1.49 X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.10/1.49 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.10/1.49 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_lessequals'( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.10/1.49 X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 'c_lessequals'(
% 1.10/1.49 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.10/1.49 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.10/1.49 ), =( 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'(
% 1.10/1.49 Y, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.10/1.49 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.10/1.49 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ), =(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.49 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.10/1.49 , X ), X ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.10/1.49 ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 1.10/1.49 'c_Power_Opower__class_Opower'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 1.10/1.49 , 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ]
% 1.10/1.49 ,
% 1.10/1.49 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.10/1.49 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 1.10/1.49 ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.10/1.49 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.10/1.49 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ]
% 1.10/1.49 ,
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.49 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~(
% 1.10/1.49 'c_lessequals'( Z, 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ]
% 1.10/1.49 ,
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.10/1.49 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.10/1.49 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), Y ), ~(
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Y, X, 'tc_nat' ) ) ],
% 1.10/1.49 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), X ), ~(
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ), X ) ),
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.49 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.10/1.49 , X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T,
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.49 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.10/1.49 ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.49 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ) ]
% 1.10/1.49 ,
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Power_Opower__class_Opower'(
% 1.10/1.49 Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.49 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 1.10/1.49 ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ),
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 1.10/1.49 ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.10/1.49 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.10/1.49 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 1.10/1.49 X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.10/1.49 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 Z, T, X ) ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 Z, T, X ) ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.10/1.49 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 1.10/1.49 X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.10/1.49 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 Y, T, X ) ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 Y, T, X ) ) ],
% 1.10/1.49 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.10/1.49 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.10/1.49 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y,
% 1.10/1.49 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.49 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 1.10/1.49 ,
% 1.10/1.49 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 1.10/1.49 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 1.10/1.49 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z, Y, 'tc_nat' )
% 1.10/1.49 ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.10/1.49 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.10/1.49 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 1.10/1.49 , X ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.10/1.49 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.10/1.49 , X ) ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.10/1.49 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 1.10/1.49 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y,
% 1.10/1.49 'c_HOL_Oplus__class_Oplus'( Z, U, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.10/1.49 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.10/1.49 , Z, X ), T, X ), ~( 'c_lessequals'( Z, U, 'tc_nat' ) ), ~(
% 1.10/1.49 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.10/1.49 , U, X ), T, X ) ) ],
% 1.10/1.49 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.10/1.49 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.10/1.49 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 1.10/1.49 ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.10/1.49 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 1.10/1.49 ) ) ],
% 1.10/1.49 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.10/1.49 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.10/1.49 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.49 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.10/1.49 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.10/1.49 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.10/1.49 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Otimes__class_Otimes'( Y, X,
% 1.10/1.49 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.49 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.10/1.49 , 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.10/1.49 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.49 , X ), ~( 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), X ) ) ],
% 1.10/1.49 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.49 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.49 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.49 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.10/1.49 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.10/1.49 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.49 'c_Int_Onumber__class_Onumber__of'( T, X ), Z, X ), Y, X ) ),
% 1.10/1.49 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.10/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.49 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 1.10/1.49 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.49 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 1.10/1.49 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.49 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 1.10/1.49 'c_GCD_Ogcd__class_Ogcd'( Y, X, 'tc_nat' ) ) ],
% 1.10/1.50 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 1.10/1.50 'c_GCD_Ogcd__class_Ogcd'( Y, X, 'tc_nat' ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.50 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.50 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.10/1.50 , X ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T,
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ), ~(
% 1.10/1.50 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.10/1.50 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.10/1.50 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.10/1.50 ) ), ~( 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ), ~( 'c_lessequals'(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( Y, 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.10/1.50 ), X ), Z, X ) ) ],
% 1.10/1.50 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 1.10/1.50 , ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.10/1.50 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.10/1.50 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ),
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.50 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.10/1.50 , Y, X ), X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ), =( Z,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.50 ) ],
% 1.10/1.50 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.10/1.50 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), ~(
% 1.10/1.50 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( Y, X,
% 1.10/1.50 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.50 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.10/1.50 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.10/1.50 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.10/1.50 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.50 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ),
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Odiv'( Y, Z, X ), Z
% 1.10/1.50 , X ), X ), Y ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =(
% 1.10/1.50 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.10/1.50 ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.10/1.50 , Y, X ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.10/1.50 , T, X ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.10/1.50 , T, X ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.10/1.50 , Y, X ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.10/1.50 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'(
% 1.10/1.50 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), T, X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.50 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.50 , 'tc_nat' ), X ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.10/1.50 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.50 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.10/1.50 'tc_nat' ), X ), X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.50 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.10/1.50 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.10/1.50 'tc_nat' ) ) ],
% 1.10/1.50 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.10/1.50 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 1.10/1.50 X ), X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 1.10/1.50 Y, Z, X ), 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ), X ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.10/1.50 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Z, Y, X
% 1.10/1.50 ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.10/1.50 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.10/1.50 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.10/1.50 ), X ) ), 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.10/1.50 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.10/1.50 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.10/1.50 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), ~( 'c_lessequals'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.10/1.50 ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.10/1.50 'c_Power_Opower__class_Opower'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), X ),
% 1.10/1.50 'c_Power_Opower__class_Opower'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.10/1.50 , 'tc_nat' ), X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.50 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, X,
% 1.10/1.50 'tc_nat' ), 'tc_nat' ), Y ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' )
% 1.10/1.50 ],
% 1.10/1.50 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'( Y
% 1.10/1.50 ), 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.10/1.50 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_GCD_Ogcd__class_Ogcd'( X, Y,
% 1.10/1.50 'tc_nat' ), 'tc_nat' ), 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ) ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ) ), =( U,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.50 ), =( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( T, Z, X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.10/1.50 , U, X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( U,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 1.10/1.50 , U, X ), 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ],
% 1.10/1.50 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.10/1.50 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T,
% 1.10/1.50 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'(
% 1.10/1.50 'c_Power_Opower__class_Opower'( Y, Z, X ), T, X ) ) ],
% 1.10/1.50 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_HOL_Oplus__class_Oplus'(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat' )
% 1.10/1.50 , 'c_GCD_Ogcd__class_Ogcd'( X, Z, 'tc_nat' ) ) ],
% 1.10/1.50 [ ~( 'class_RealVector_Oreal__normed__div__algebra'( X ) ), =(
% 1.10/1.50 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Osgn__class_Osgn'( Y, X ),
% 1.10/1.50 'c_HOL_Osgn__class_Osgn'( Z, X ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.10/1.50 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Osgn__class_Osgn'( Y, X ),
% 1.10/1.50 'c_HOL_Osgn__class_Osgn'( Z, X ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.50 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Omod'( Z, T, X )
% 1.10/1.50 , X ) ) ],
% 1.10/1.50 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.50 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z
% 1.10/1.50 , X ) ) ],
% 1.10/1.50 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.10/1.50 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ) ) ],
% 1.10/1.50 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.10/1.50 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oabs__class_Oabs'(
% 1.10/1.50 Y, X ), X ) ],
% 1.10/1.50 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 1.10/1.50 , 'tc_nat' ), Z, 'tc_nat' ), 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X
% 1.10/1.50 , 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' )
% 1.10/1.50 ) ],
% 1.10/1.50 [ 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_GCD_Ogcd__class_Ogcd'( X, Y
% 1.10/1.50 , 'tc_nat' ), Z, 'tc_nat' ), 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y
% 1.10/1.50 , 'tc_nat' ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' )
% 1.10/1.50 ) ],
% 1.10/1.50 [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.10/1.50 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.10/1.50 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( X ),
% 1.10/1.50 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y, X ),
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.10/1.50 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) ),
% 1.10/1.50 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ],
% 1.10/1.50 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.10/1.50 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.10/1.50 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.10/1.50 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.10/1.50 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.10/1.50 'c_lessequals'( Z, Y, X ) ],
% 1.10/1.50 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ), ~(
% 1.10/1.50 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ),
% 1.10/1.50 'c_Ring__and__Field_Odvd__class_Odvd'( Z, X, 'tc_nat' ), ~(
% 1.10/1.50 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 1.10/1.50 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, Y, 'tc_nat' ),
% 1.10/1.50 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, 'tc_nat' ), ~(
% 1.10/1.50 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, 'tc_nat' ) ), ~(
% 1.10/1.50 'c_Ring__and__Field_Odvd__class_Odvd'( X, Z, 'tc_nat' ) ) ],
% 1.10/1.50 [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X, 'tc_nat' ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.10/1.50 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.10/1.50 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.10/1.50 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.10/1.50 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.10/1.50 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.50 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.10/1.50 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.10/1.50 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.10/1.50 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.10/1.50 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y
% 1.10/1.50 ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.10/1.50 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.10/1.50 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.10/1.50 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 1.10/1.50 X ) ],
% 1.10/1.50 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.10/1.50 ],
% 1.10/1.50 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 1.10/1.50 ],
% 1.10/1.50 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 1.10/1.50 ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 1.10/1.50 ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.10/1.50 ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 1.10/1.50 ],
% 1.10/1.50 [ ~( 'class_RealVector_Oreal__normed__algebra__1'( X ) ), =(
% 1.10/1.50 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.10/1.50 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.10/1.50 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.10/1.50 ), =( Y, 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.10/1.50 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.50 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.10/1.50 ],
% 1.10/1.50 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.50 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.50 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.50 [ ~( =( 'c_GCD_Ogcd__class_Ogcd'( X, Y, 'tc_nat' ),
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.50 [ =( 'c_Nat_Osize__class_Osize'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.10/1.50 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.50 [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.50 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ],
% 1.10/1.50 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.50 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.10/1.50 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.50 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.50 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.50 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.10/1.50 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.50 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.50 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.50 [ 'c_Ring__and__Field_Odvd__class_Odvd'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.50 'tc_nat' ), 'tc_nat' ) ],
% 1.10/1.50 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.50 'tc_nat' ), 'tc_nat' ) ],
% 1.10/1.50 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( Y, Z ), =( X,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.50 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( X,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 1.10/1.50 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.10/1.50 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ), =( Y,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 1.10/1.50 [ =( 'c_Nitpick_Onat__gcd'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.10/1.50 , X ) ],
% 1.10/1.50 [ =( 'c_GCD_Ogcd__class_Ogcd'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.10/1.50 , 'tc_nat' ), X ) ],
% 1.10/1.50 [ =( 'c_GCD_Ogcd__class_Ogcd'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 1.10/1.50 , 'tc_nat' ), X ) ],
% 1.10/1.50 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.10/1.50 ), 'tc_nat' ) ) ],
% 1.10/1.50 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.10/1.50 ), 'tc_nat' ) ) ],
% 1.10/1.50 [ ~( =( 'c_Fact_Ofact__class_Ofact'( X, 'tc_nat' ),
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.10/1.50 [ =( 'c_List_Oreplicate'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, Y )
% 1.10/1.50 , 'c_List_Oreplicate'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, Y ) ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ =( 'c_Orderings_Oord__class_Omax'( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.50 'tc_nat' ), X, 'tc_nat' ), X ) ],
% 1.10/1.50 [ =( 'c_Orderings_Oord__class_Omax'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.50 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.10/1.50 [ ~( =( 'c_List_Oreplicate'( X, Y, Z ), 'c_List_Oreplicate'( T, U, Z ) )
% 1.10/1.50 ), =( Y, U ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.50 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.10/1.50 ), X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.10/1.50 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.50 'tc_nat' ), 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.50 [ =( 'c_GCD_Ogcd__class_Olcm'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.10/1.50 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.50 [ =( 'c_GCD_Ogcd__class_Olcm'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 1.10/1.50 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.50 [ =( 'c_GCD_Ogcd__class_Olcm'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.10/1.50 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.50 [ =( 'c_GCD_Ogcd__class_Olcm'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 1.10/1.50 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.50 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 1.10/1.50 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ],
% 1.10/1.50 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.50 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.50 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.50 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.50 [ =( 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.50 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ =( 'c_Orderings_Oord__class_Omin'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.50 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.50 [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.50 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.50 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.10/1.50 [ ~( =( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.50 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X ) ), =( Y,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.50 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.10/1.50 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.10/1.50 [ ~( =( 'c_GCD_Ogcd__class_Olcm'( X, Y, 'tc_nat' ),
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.50 [ =( 'c_nat_Onat__size'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.50 [ =( 'c_String_Ochar_Ochar__size'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.50 'tc_nat' ) ) ],
% 1.10/1.50 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.10/1.50 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.50 [ =( 'c_Orderings_Obot__class_Obot'( 'tc_nat' ),
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.50 [ =( 'c_List_Odrop'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, Y ), X )
% 1.10/1.50 ],
% 1.10/1.50 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.10/1.50 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.50 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' )
% 1.10/1.50 ],
% 1.10/1.50 [ =( 'c_Nat_Osize__class_Osize'( X, 'tc_String_Ochar' ),
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.50 [ =( X, 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.50 'tc_nat' ), 'tc_nat' ) ) ],
% 1.10/1.50 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.10/1.50 ), 'tc_nat' ), X ) ],
% 1.10/1.50 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.10/1.50 , X, 'tc_nat' ), X ) ],
% 1.10/1.50 [ =( 'c_Complex_Ocnj'( 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' )
% 1.10/1.50 ), 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ) ],
% 1.10/1.50 [ ~( =( 'c_Complex_Oii', 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex'
% 1.10/1.50 ) ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.10/1.50 'class_Power_Opower'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.10/1.50 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =(
% 1.10/1.50 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), X ),
% 1.10/1.50 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.10/1.50 [ ~( =( 'c_FFT__Mirabelle_Oroot'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.50 'tc_Complex_Ocomplex' ) ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.10/1.50 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.10/1.50 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.50 X ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.50 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.10/1.50 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.10/1.50 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.10/1.50 'c_Divides_Odiv__class_Odiv'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.10/1.50 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ),
% 1.10/1.50 'c_Ring__and__Field_Ozero__neq__one'( 'c_HOL_Oone__class_Oone'( X ),
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.10/1.50 [ ~( 'class_SEQ_Obanach'( X ) ), ~(
% 1.10/1.50 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.10/1.50 'c_Transcendental_Oexp'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.10/1.50 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.10/1.50 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 1.10/1.50 , Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.10/1.50 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.10/1.50 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.10/1.50 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.50 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.10/1.50 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.10/1.50 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.10/1.50 ), =( 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.10/1.50 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.10/1.50 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.10/1.50 ), ~( =( 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.10/1.50 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.10/1.50 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.10/1.50 , X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.10/1.50 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( Y,
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( X
% 1.10/1.50 ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.10/1.50 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.10/1.50 X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.10/1.50 [ =( 'c_Power_Opower__class_Opower'( 'c_FFT__Mirabelle_Oroot'( X ), X,
% 1.10/1.50 'tc_Complex_Ocomplex' ), 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex'
% 1.10/1.50 ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.10/1.50 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.10/1.50 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.10/1.50 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.10/1.50 [ ~( =( 'c_FFT__Mirabelle_Oroot'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.10/1.50 ), 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ) ) ],
% 1.10/1.50 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.10/1.50 ],
% 1.10/1.50 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.10/1.50 ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.10/1.50 ],
% 1.10/1.50 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.10/1.50 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 1.10/1.50 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.10/1.50 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.10/1.50 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.10/1.50 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.10/1.50 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.10/1.50 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.10/1.50 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.10/1.50 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.10/1.50 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.10/1.50 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 1.10/1.50 [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Odvd'( 'tc_nat' ) ],
% 1.10/1.50 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.10/1.50 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.10/1.50 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.10/1.50 [ 'class_Orderings_Obot'( 'tc_nat' ) ],
% 1.10/1.50 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 1.10/1.50 [ 'class_Int_Onumber'( 'tc_nat' ) ],
% 1.10/1.50 [ 'class_HOL_Oord'( 'tc_nat' ) ],
% 1.10/1.50 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.10/1.50 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.10/1.50 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.10/1.50 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_Int_Oint' )
% 1.10/1.50 ],
% 1.10/1.50 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'( 'tc_Int_Oint' )
% 1.10/1.50 ],
% 1.10/1.50 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_Int_Oint' ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ 'class_OrderedGroup_Opordered__ab__group__add__abs'( 'tc_Int_Oint' ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ 'class_OrderedGroup_Olordered__ab__group__add__abs'( 'tc_Int_Oint' ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_Int_Oint' ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_Int_Oint' ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_Int_Oint' ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Opordered__ring__abs'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Olordered__ring'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Omult__mono'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Osemiring'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Osgn__if'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Oring__1'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Oabs__if'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_Divides_Osemiring__div'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Oring'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Oidom'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_Nat_Osemiring__char__0'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Odvd'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_Orderings_Opreorder'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_Orderings_Olinorder'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_Divides_Oring__div'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_Orderings_Oorder'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_Int_Oring__char__0'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_Int_Onumber__ring'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_Power_Opower'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_Int_Onumber'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_HOL_Oord'( 'tc_Int_Oint' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 1.10/1.50 'tc_Complex_Ocomplex' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 1.10/1.50 'tc_Complex_Ocomplex' ) ],
% 1.10/1.50 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 1.10/1.50 'tc_Complex_Ocomplex' ) ],
% 1.10/1.50 [ 'class_RealVector_Oreal__normed__div__algebra'( 'tc_Complex_Ocomplex'
% 1.10/1.50 ) ],
% 1.10/1.50 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Complex_Ocomplex' )
% 1.10/1.50 ],
% 1.10/1.50 [ 'class_RealVector_Oreal__normed__algebra__1'( 'tc_Complex_Ocomplex' )
% 1.10/1.50 ],
% 1.10/1.50 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Complex_Ocomplex' )
% 1.10/1.50 ],
% 1.10/1.50 [ 'class_Ring__and__Field_Odivision__by__zero'( 'tc_Complex_Ocomplex' )
% 1.10/1.50 ],
% 1.10/1.50 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ 'class_RealVector_Oreal__normed__algebra'( 'tc_Complex_Ocomplex' ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ 'class_RealVector_Oreal__normed__vector'( 'tc_Complex_Ocomplex' ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Complex_Ocomplex' ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ 'class_Ring__and__Field_Odivision__ring'( 'tc_Complex_Ocomplex' ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Complex_Ocomplex' ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ 'class_RealVector_Oreal__normed__field'( 'tc_Complex_Ocomplex' ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Complex_Ocomplex' ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Complex_Ocomplex' ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.10/1.50 ,
% 1.10/1.50 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Complex_Ocomplex' ) ],
% 1.10/1.50 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Complex_Ocomplex' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Complex_Ocomplex' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_Complex_Ocomplex' ) ],
% 1.10/1.50 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Complex_Ocomplex' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Osemiring'( 'tc_Complex_Ocomplex' ) ],
% 1.10/1.50 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Complex_Ocomplex' ) ],
% 1.10/1.50 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Complex_Ocomplex' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Oring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.10/1.50 [ 'class_RealVector_Oreal__field'( 'tc_Complex_Ocomplex' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Ofield'( 'tc_Complex_Ocomplex' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Oring'( 'tc_Complex_Ocomplex' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Oidom'( 'tc_Complex_Ocomplex' ) ],
% 1.10/1.50 [ 'class_Nat_Osemiring__char__0'( 'tc_Complex_Ocomplex' ) ],
% 1.10/1.50 [ 'class_Ring__and__Field_Odvd'( 'tc_Complex_Ocomplex' ) ],
% 1.10/1.50 [ 'class_Int_Oring__char__0'( 'tc_Complex_Ocomplex' ) ],
% 1.10/1.50 [ 'class_Int_Onumber__ring'( 'tc_Complex_Ocomplex' ) ],
% 1.10/1.50 [ 'class_Power_Opower'( 'tc_Complex_Ocomplex' ) ],
% 1.10/1.50 [ 'class_SEQ_Obanach'( 'tc_Complex_Ocomplex' ) ],
% 1.10/1.50 [ 'class_Int_Onumber'( 'tc_Complex_Ocomplex' ) ]
% 1.10/1.50 ] .
% 1.10/1.50
% 1.10/1.50
% 1.10/1.50 percentage equality = 0.198323, percentage horn = 0.830030
% 1.10/1.50 This is a problem with some equality
% 1.10/1.50
% 1.10/1.50
% 1.10/1.50
% 1.10/1.50 Options Used:
% 1.10/1.50
% 1.10/1.50 useres = 1
% 1.10/1.50 useparamod = 1
% 1.10/1.50 useeqrefl = 1
% 1.10/1.50 useeqfact = 1
% 1.10/1.50 usefactor = 1
% 1.10/1.50 usesimpsplitting = 0
% 1.10/1.50 usesimpdemod = 5
% 1.10/1.50 usesimpres = 3
% 1.10/1.50
% 1.10/1.50 resimpinuse = 1000
% 1.10/1.50 resimpclauses = 20000
% 1.10/1.50 substype = eqrewr
% 1.10/1.50 backwardsubs = 1
% 1.10/1.50 selectoldest = 5
% 1.10/1.50
% 1.10/1.50 litorderings [0] = split
% 1.10/1.50 litorderings [1] = extend the termordering, first sorting on arguments
% 1.10/1.50
% 1.10/1.50 termordering = kbo
% 1.10/1.50
% 1.10/1.50 litapriori = 0
% 1.10/1.50 termapriori = 1
% 1.10/1.50 litaposteriori = 0
% 1.10/1.50 termaposteriori = 0
% 1.10/1.50 demodaposteriori = 0
% 1.10/1.50 ordereqreflfact = 0
% 1.10/1.50
% 1.10/1.50 litselect = negord
% 1.10/1.50
% 1.10/1.50 maxweight = 15
% 1.10/1.50 maxdepth = 30000
% 1.10/1.50 maxlength = 115
% 1.10/1.50 maxnrvars = 195
% 1.10/1.50 excuselevel = 1
% 1.10/1.50 increasemaxweight = 1
% 1.10/1.50
% 1.10/1.50 maxselected = 10000000
% 1.10/1.50 maxnrclauses = 10000000
% 1.10/1.50
% 1.10/1.50 showgenerated = 0
% 1.10/1.50 showkept = 0
% 1.10/1.50 showselected = 0
% 1.10/1.50 showdeleted = 0
% 1.10/1.50 showresimp = 1
% 1.10/1.50 showstatus = 2000
% 1.10/1.50
% 1.10/1.50 prologoutput = 1
% 1.10/1.50 nrgoals = 5000000
% 1.10/1.50 totalproof = 1
% 1.10/1.50
% 1.10/1.50 Symbols occurring in the translation:
% 1.10/1.50
% 1.10/1.50 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.10/1.50 . [1, 2] (w:1, o:140, a:1, s:1, b:0),
% 1.10/1.50 ! [4, 1] (w:0, o:54, a:1, s:1, b:0),
% 1.10/1.50 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.10/1.50 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.10/1.50 'tc_nat' [41, 0] (w:1, o:14, a:1, s:1, b:0),
% 1.10/1.50 'c_GCD_Ogcd__class_Olcm' [42, 3] (w:1, o:175, a:1, s:1, b:0),
% 1.10/1.50 'c_Ring__and__Field_Odvd__class_Odvd' [44, 3] (w:1, o:176, a:1, s:1
% 1.10/1.50 , b:0),
% 1.10/1.50 'class_Ring__and__Field_Oordered__ring__strict' [49, 1] (w:1, o:61
% 1.10/1.50 , a:1, s:1, b:0),
% 1.10/1.50 'c_HOL_Ozero__class_Ozero' [50, 1] (w:1, o:62, a:1, s:1, b:0),
% 1.10/1.50 'c_lessequals' [51, 3] (w:1, o:177, a:1, s:1, b:0),
% 1.10/1.50 'c_HOL_Otimes__class_Otimes' [52, 3] (w:1, o:179, a:1, s:1, b:0),
% 1.10/1.50 'class_Divides_Osemiring__div' [53, 1] (w:1, o:64, a:1, s:1, b:0),
% 1.10/1.50 'c_HOL_Oplus__class_Oplus' [54, 3] (w:1, o:181, a:1, s:1, b:0),
% 1.10/1.50 'c_Divides_Odiv__class_Omod' [55, 3] (w:1, o:182, a:1, s:1, b:0),
% 1.10/1.50 'c_Divides_Odiv__class_Odiv' [56, 3] (w:1, o:183, a:1, s:1, b:0),
% 1.10/1.50 'class_Ring__and__Field_Oordered__field' [57, 1] (w:1, o:65, a:1, s:1
% 1.10/1.50 , b:0),
% 1.10/1.50 'class_Ring__and__Field_Odivision__by__zero' [58, 1] (w:1, o:70, a:1
% 1.10/1.50 , s:1, b:0),
% 1.10/1.50 'class_Int_Onumber' [59, 1] (w:1, o:72, a:1, s:1, b:0),
% 1.10/1.50 'c_Int_Onumber__class_Onumber__of' [61, 2] (w:1, o:168, a:1, s:1, b:0
% 1.10/1.50 ),
% 1.10/1.50 'c_HOL_Oinverse__class_Odivide' [62, 3] (w:1, o:184, a:1, s:1, b:0),
% 1.10/1.50
% 1.10/1.50 'c_HOL_Oord__class_Oless' [63, 3] (w:1, o:180, a:1, s:1, b:0),
% 1.10/1.50 'class_Ring__and__Field_Ofield' [64, 1] (w:1, o:73, a:1, s:1, b:0),
% 1.46/1.84 'c_Suc' [69, 1] (w:1, o:75, a:1, s:1, b:0),
% 1.46/1.84 'c_Fact_Ofact__class_Ofact' [70, 2] (w:1, o:169, a:1, s:1, b:0),
% 1.46/1.84 'class_OrderedGroup_Oab__semigroup__idem__mult' [71, 1] (w:1, o:77
% 1.46/1.84 , a:1, s:1, b:0),
% 1.46/1.84 'class_Ring__and__Field_Oordered__semidom' [72, 1] (w:1, o:78, a:1
% 1.46/1.84 , s:1, b:0),
% 1.46/1.84 'c_HOL_Oone__class_Oone' [73, 1] (w:1, o:79, a:1, s:1, b:0),
% 1.46/1.84 'class_OrderedGroup_Omonoid__mult' [74, 1] (w:1, o:82, a:1, s:1, b:0)
% 1.46/1.84 ,
% 1.46/1.84 'c_HOL_Ominus__class_Ominus' [76, 3] (w:1, o:185, a:1, s:1, b:0),
% 1.46/1.84 'c_Power_Opower__class_Opower' [77, 3] (w:1, o:188, a:1, s:1, b:0),
% 1.46/1.84 'class_Ring__and__Field_Opordered__ring__abs' [78, 1] (w:1, o:87, a:1
% 1.46/1.84 , s:1, b:0),
% 1.46/1.84 'c_HOL_Oabs__class_Oabs' [79, 2] (w:1, o:165, a:1, s:1, b:0),
% 1.46/1.84 'class_Ring__and__Field_Oordered__idom' [80, 1] (w:1, o:83, a:1, s:1
% 1.46/1.84 , b:0),
% 1.46/1.84 'class_Ring__and__Field_Oordered__semiring__strict' [81, 1] (w:1, o:
% 1.46/1.84 84, a:1, s:1, b:0),
% 1.46/1.84 'class_Ring__and__Field_Ocomm__semiring__1' [82, 1] (w:1, o:68, a:1
% 1.46/1.84 , s:1, b:0),
% 1.46/1.84 'c_HOL_Oinverse__class_Oinverse' [83, 2] (w:1, o:166, a:1, s:1, b:0)
% 1.46/1.84 ,
% 1.46/1.84 'class_Ring__and__Field_Omult__mono1' [84, 1] (w:1, o:89, a:1, s:1
% 1.46/1.84 , b:0),
% 1.46/1.84 'class_Ring__and__Field_Omult__mono' [85, 1] (w:1, o:90, a:1, s:1, b:
% 1.46/1.84 0),
% 1.46/1.84 'class_Ring__and__Field_Opordered__ring' [86, 1] (w:1, o:91, a:1, s:1
% 1.46/1.84 , b:0),
% 1.46/1.84 'class_Ring__and__Field_Oidom' [89, 1] (w:1, o:92, a:1, s:1, b:0),
% 1.46/1.84 'class_Int_Onumber__ring' [90, 1] (w:1, o:93, a:1, s:1, b:0),
% 1.46/1.84 'class_Ring__and__Field_Odivision__ring' [91, 1] (w:1, o:94, a:1, s:1
% 1.46/1.84 , b:0),
% 1.46/1.84 'c_Parity_Oeven__odd__class_Oeven' [92, 2] (w:1, o:170, a:1, s:1, b:0
% 1.46/1.84 ),
% 1.46/1.84 'class_HOL_Oord' [93, 1] (w:1, o:71, a:1, s:1, b:0),
% 1.46/1.84 'c_Orderings_Oord__class_Omax' [96, 3] (w:1, o:186, a:1, s:1, b:0),
% 1.46/1.84 'c_Orderings_Oord__class_Omin' [98, 3] (w:1, o:187, a:1, s:1, b:0),
% 1.46/1.84 'class_Ring__and__Field_Osemiring__1' [100, 1] (w:1, o:100, a:1, s:1
% 1.46/1.84 , b:0),
% 1.46/1.84 'c_Nat_Osemiring__1__class_Oof__nat' [101, 2] (w:1, o:171, a:1, s:1
% 1.46/1.84 , b:0),
% 1.46/1.84 'class_OrderedGroup_Opordered__ab__group__add' [102, 1] (w:1, o:101
% 1.46/1.84 , a:1, s:1, b:0),
% 1.46/1.84 'class_OrderedGroup_Ocomm__monoid__mult' [106, 1] (w:1, o:102, a:1
% 1.46/1.84 , s:1, b:0),
% 1.46/1.84 'class_Ring__and__Field_Odvd' [107, 1] (w:1, o:103, a:1, s:1, b:0),
% 1.46/1.84 'class_Ring__and__Field_Ocomm__ring' [108, 1] (w:1, o:66, a:1, s:1
% 1.46/1.84 , b:0),
% 1.46/1.84 'class_Orderings_Olinorder' [111, 1] (w:1, o:104, a:1, s:1, b:0),
% 1.46/1.84 'class_Orderings_Oorder' [112, 1] (w:1, o:105, a:1, s:1, b:0),
% 1.46/1.84 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [113, 1]
% 1.46/1.84 (w:1, o:106, a:1, s:1, b:0),
% 1.46/1.84 'class_OrderedGroup_Opordered__ab__semigroup__add' [114, 1] (w:1, o:
% 1.46/1.84 107, a:1, s:1, b:0),
% 1.46/1.84 'c_GCD_Ogcd__class_Ogcd' [115, 3] (w:1, o:178, a:1, s:1, b:0),
% 1.46/1.84 'class_OrderedGroup_Opordered__ab__group__add__abs' [116, 1] (w:1, o:
% 1.46/1.84 108, a:1, s:1, b:0),
% 1.46/1.84 'class_OrderedGroup_Olordered__ab__group__add__abs' [117, 1] (w:1, o:
% 1.46/1.84 80, a:1, s:1, b:0),
% 1.46/1.84 'c_Nat_Osize__class_Osize' [119, 2] (w:1, o:172, a:1, s:1, b:0),
% 1.46/1.84 'class_OrderedGroup_Opordered__comm__monoid__add' [124, 1] (w:1, o:
% 1.46/1.84 109, a:1, s:1, b:0),
% 1.46/1.84 'class_OrderedGroup_Olordered__ab__group__add' [125, 1] (w:1, o:81
% 1.46/1.84 , a:1, s:1, b:0),
% 1.46/1.84 'class_Ring__and__Field_Opordered__cancel__semiring' [126, 1] (w:1
% 1.46/1.84 , o:110, a:1, s:1, b:0),
% 1.46/1.84 'class_OrderedGroup_Oab__semigroup__mult' [127, 1] (w:1, o:111, a:1
% 1.46/1.84 , s:1, b:0),
% 1.46/1.84 'class_RealVector_Oreal__normed__algebra' [128, 1] (w:1, o:112, a:1
% 1.46/1.84 , s:1, b:0),
% 1.46/1.84 'class_Ring__and__Field_Ocomm__semiring' [133, 1] (w:1, o:69, a:1, s:
% 1.46/1.84 1, b:0),
% 1.46/1.84 'class_Ring__and__Field_Opordered__semiring' [135, 1] (w:1, o:113, a:
% 1.46/1.84 1, s:1, b:0),
% 1.46/1.84 'c_HOL_Osgn__class_Osgn' [136, 2] (w:1, o:167, a:1, s:1, b:0),
% 1.46/1.84 'c_Ring__and__Field_Ozero__neq__one' [137, 3] (w:1, o:189, a:1, s:1
% 1.46/1.84 , b:0),
% 1.46/1.84 'class_RealVector_Oreal__normed__field' [138, 1] (w:1, o:114, a:1, s:
% 1.46/1.84 1, b:0),
% 1.46/1.84 'class_Ring__and__Field_Ocomm__ring__1' [139, 1] (w:1, o:67, a:1, s:1
% 9.99/10.41 , b:0),
% 9.99/10.41 'class_Ring__and__Field_Oordered__semiring' [140, 1] (w:1, o:85, a:1
% 9.99/10.41 , s:1, b:0),
% 9.99/10.41 'class_Nat_Osemiring__char__0' [141, 1] (w:1, o:76, a:1, s:1, b:0),
% 9.99/10.41 'class_Ring__and__Field_Oring' [142, 1] (w:1, o:95, a:1, s:1, b:0),
% 9.99/10.41 'class_OrderedGroup_Ocomm__monoid__add' [143, 1] (w:1, o:115, a:1, s:
% 9.99/10.41 1, b:0),
% 9.99/10.41 'class_Orderings_Obot' [144, 1] (w:1, o:116, a:1, s:1, b:0),
% 9.99/10.41 'c_Orderings_Obot__class_Obot' [145, 1] (w:1, o:117, a:1, s:1, b:0),
% 9.99/10.41
% 9.99/10.41 'class_Ring__and__Field_Olordered__ring' [146, 1] (w:1, o:88, a:1, s:
% 9.99/10.41 1, b:0),
% 9.99/10.41 'class_Ring__and__Field_Osemiring__0' [147, 1] (w:1, o:99, a:1, s:1
% 9.99/10.41 , b:0),
% 9.99/10.41 'class_Power_Opower' [148, 1] (w:1, o:126, a:1, s:1, b:0),
% 9.99/10.41 'c_nat_Onat__size' [149, 1] (w:1, o:127, a:1, s:1, b:0),
% 9.99/10.41 'c_List_Oreplicate' [150, 3] (w:1, o:190, a:1, s:1, b:0),
% 9.99/10.41 'c_List_Odrop' [151, 3] (w:1, o:191, a:1, s:1, b:0),
% 9.99/10.41 'class_Divides_Oring__div' [152, 1] (w:1, o:63, a:1, s:1, b:0),
% 9.99/10.41 'class_OrderedGroup_Ocancel__ab__semigroup__add' [153, 1] (w:1, o:118
% 9.99/10.41 , a:1, s:1, b:0),
% 9.99/10.41 'class_OrderedGroup_Ocancel__semigroup__add' [154, 1] (w:1, o:119, a:
% 9.99/10.41 1, s:1, b:0),
% 9.99/10.41 'class_SEQ_Obanach' [156, 1] (w:1, o:136, a:1, s:1, b:0),
% 9.99/10.41 'c_Transcendental_Oexp' [157, 2] (w:1, o:173, a:1, s:1, b:0),
% 9.99/10.41 'class_OrderedGroup_Ogroup__add' [158, 1] (w:1, o:120, a:1, s:1, b:0)
% 9.99/10.41 ,
% 9.99/10.41 'tc_Complex_Ocomplex' [159, 0] (w:1, o:47, a:1, s:1, b:0),
% 9.99/10.41 'c_Complex_Ocnj' [160, 1] (w:1, o:137, a:1, s:1, b:0),
% 9.99/10.41 'class_Orderings_Opreorder' [161, 1] (w:1, o:121, a:1, s:1, b:0),
% 9.99/10.41 'class_OrderedGroup_Oab__group__add' [162, 1] (w:1, o:122, a:1, s:1
% 9.99/10.41 , b:0),
% 9.99/10.41 'class_OrderedGroup_Oab__semigroup__add' [163, 1] (w:1, o:123, a:1
% 9.99/10.41 , s:1, b:0),
% 9.99/10.41 'class_RealVector_Oreal__field' [164, 1] (w:1, o:128, a:1, s:1, b:0)
% 9.99/10.41 ,
% 9.99/10.41 'c_Nitpick_Onat__gcd' [166, 2] (w:1, o:174, a:1, s:1, b:0),
% 9.99/10.41 'class_Ring__and__Field_Osemiring' [167, 1] (w:1, o:129, a:1, s:1, b:
% 9.99/10.41 0),
% 9.99/10.41 'class_Int_Oring__char__0' [168, 1] (w:1, o:138, a:1, s:1, b:0),
% 9.99/10.41 'class_Ring__and__Field_Oordered__comm__semiring__strict' [170, 1]
% 9.99/10.41 (w:1, o:86, a:1, s:1, b:0),
% 9.99/10.41 'class_Ring__and__Field_Ozero__neq__one' [171, 1] (w:1, o:130, a:1
% 9.99/10.41 , s:1, b:0),
% 9.99/10.41 'class_Ring__and__Field_Ono__zero__divisors' [172, 1] (w:1, o:60, a:1
% 9.99/10.41 , s:1, b:0),
% 9.99/10.41 'class_Ring__and__Field_Omult__zero' [173, 1] (w:1, o:59, a:1, s:1
% 9.99/10.41 , b:0),
% 9.99/10.41 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [174, 1]
% 9.99/10.41 (w:1, o:124, a:1, s:1, b:0),
% 9.99/10.41 'c_Complex_Oii' [176, 0] (w:1, o:49, a:1, s:1, b:0),
% 9.99/10.41 'class_Ring__and__Field_Oabs__if' [177, 1] (w:1, o:131, a:1, s:1, b:0
% 9.99/10.41 ),
% 9.99/10.41 'class_Ring__and__Field_Oring__1' [178, 1] (w:1, o:96, a:1, s:1, b:0)
% 9.99/10.41 ,
% 9.99/10.41 'c_FFT__Mirabelle_Oroot' [179, 1] (w:1, o:139, a:1, s:1, b:0),
% 9.99/10.41 'class_Ring__and__Field_Osgn__if' [180, 1] (w:1, o:132, a:1, s:1, b:0
% 9.99/10.41 ),
% 9.99/10.41 'class_RealVector_Oreal__normed__vector' [181, 1] (w:1, o:133, a:1
% 9.99/10.41 , s:1, b:0),
% 9.99/10.41 'class_Ring__and__Field_Oring__no__zero__divisors' [182, 1] (w:1, o:
% 9.99/10.41 97, a:1, s:1, b:0),
% 9.99/10.41 'class_Ring__and__Field_Oring__1__no__zero__divisors' [183, 1] (w:1
% 9.99/10.41 , o:98, a:1, s:1, b:0),
% 9.99/10.41 'class_OrderedGroup_Omonoid__add' [184, 1] (w:1, o:125, a:1, s:1, b:0
% 9.99/10.41 ),
% 9.99/10.41 'class_RealVector_Oreal__normed__div__algebra' [185, 1] (w:1, o:134
% 9.99/10.41 , a:1, s:1, b:0),
% 9.99/10.41 'class_RealVector_Oreal__normed__algebra__1' [186, 1] (w:1, o:135, a:
% 9.99/10.41 1, s:1, b:0),
% 9.99/10.41 'c_String_Ochar_Ochar__size' [189, 1] (w:1, o:74, a:1, s:1, b:0),
% 9.99/10.41 'tc_String_Ochar' [190, 0] (w:1, o:52, a:1, s:1, b:0),
% 9.99/10.41 'tc_Int_Oint' [191, 0] (w:1, o:53, a:1, s:1, b:0).
% 9.99/10.41
% 9.99/10.41
% 9.99/10.41 Starting Search:
% 9.99/10.41
% 9.99/10.41 Resimplifying inuse:
% 9.99/10.41 Done
% 9.99/10.41
% 9.99/10.41
% 9.99/10.41 Intermediate Status:
% 9.99/10.41 Generated: 3418
% 9.99/10.41 Kept: 2061
% 9.99/10.41 Inuse: 194
% 9.99/10.41 Deleted: 12
% 9.99/10.41 Deletedinuse: 0
% 9.99/10.41
% 9.99/10.41 Resimplifying inuse:
% 9.99/10.41 Done
% 9.99/10.41
% 9.99/10.41
% 9.99/10.41 Intermediate Status:
% 9.99/10.41 Generated: 12436
% 9.99/10.41 Kept: 4250
% 9.99/10.41 Inuse: 249
% 9.99/10.41 Deleted: 12
% 9.99/10.41 Deletedinuse: 0
% 9.99/10.41
% 9.99/10.41 Resimplifying inuse:
% 9.99/10.41 Done
% 9.99/10.41
% 9.99/10.41 Resimplifying inuse:
% 9.99/10.41 Done
% 9.99/10.41
% 9.99/10.41
% 9.99/10.41 Intermediate Status:
% 9.99/10.41 Generated: 19740
% 9.99/10.41 Kept: 6261
% 9.99/10.41 Inuse: 385
% 34.33/34.70 Deleted: 16
% 34.33/34.70 Deletedinuse: 0
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70
% 34.33/34.70 Intermediate Status:
% 34.33/34.70 Generated: 30012
% 34.33/34.70 Kept: 8321
% 34.33/34.70 Inuse: 464
% 34.33/34.70 Deleted: 22
% 34.33/34.70 Deletedinuse: 0
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70
% 34.33/34.70 Intermediate Status:
% 34.33/34.70 Generated: 39953
% 34.33/34.70 Kept: 10354
% 34.33/34.70 Inuse: 486
% 34.33/34.70 Deleted: 23
% 34.33/34.70 Deletedinuse: 1
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70
% 34.33/34.70 Intermediate Status:
% 34.33/34.70 Generated: 48826
% 34.33/34.70 Kept: 13526
% 34.33/34.70 Inuse: 509
% 34.33/34.70 Deleted: 23
% 34.33/34.70 Deletedinuse: 1
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70
% 34.33/34.70 Intermediate Status:
% 34.33/34.70 Generated: 56003
% 34.33/34.70 Kept: 15583
% 34.33/34.70 Inuse: 544
% 34.33/34.70 Deleted: 23
% 34.33/34.70 Deletedinuse: 1
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70
% 34.33/34.70 Intermediate Status:
% 34.33/34.70 Generated: 70517
% 34.33/34.70 Kept: 18092
% 34.33/34.70 Inuse: 642
% 34.33/34.70 Deleted: 30
% 34.33/34.70 Deletedinuse: 1
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70
% 34.33/34.70 Intermediate Status:
% 34.33/34.70 Generated: 84473
% 34.33/34.70 Kept: 20815
% 34.33/34.70 Inuse: 657
% 34.33/34.70 Deleted: 30
% 34.33/34.70 Deletedinuse: 1
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70 Resimplifying clauses:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70
% 34.33/34.70 Intermediate Status:
% 34.33/34.70 Generated: 96532
% 34.33/34.70 Kept: 22859
% 34.33/34.70 Inuse: 677
% 34.33/34.70 Deleted: 482
% 34.33/34.70 Deletedinuse: 2
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70
% 34.33/34.70 Intermediate Status:
% 34.33/34.70 Generated: 104719
% 34.33/34.70 Kept: 24864
% 34.33/34.70 Inuse: 702
% 34.33/34.70 Deleted: 482
% 34.33/34.70 Deletedinuse: 2
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70
% 34.33/34.70 Intermediate Status:
% 34.33/34.70 Generated: 114892
% 34.33/34.70 Kept: 27268
% 34.33/34.70 Inuse: 732
% 34.33/34.70 Deleted: 482
% 34.33/34.70 Deletedinuse: 2
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70
% 34.33/34.70 Intermediate Status:
% 34.33/34.70 Generated: 124203
% 34.33/34.70 Kept: 29373
% 34.33/34.70 Inuse: 782
% 34.33/34.70 Deleted: 482
% 34.33/34.70 Deletedinuse: 2
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70
% 34.33/34.70 Intermediate Status:
% 34.33/34.70 Generated: 136917
% 34.33/34.70 Kept: 31908
% 34.33/34.70 Inuse: 827
% 34.33/34.70 Deleted: 482
% 34.33/34.70 Deletedinuse: 2
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70
% 34.33/34.70 Intermediate Status:
% 34.33/34.70 Generated: 147046
% 34.33/34.70 Kept: 34046
% 34.33/34.70 Inuse: 877
% 34.33/34.70 Deleted: 482
% 34.33/34.70 Deletedinuse: 2
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70
% 34.33/34.70 Intermediate Status:
% 34.33/34.70 Generated: 157492
% 34.33/34.70 Kept: 36108
% 34.33/34.70 Inuse: 917
% 34.33/34.70 Deleted: 483
% 34.33/34.70 Deletedinuse: 3
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70
% 34.33/34.70 Intermediate Status:
% 34.33/34.70 Generated: 167609
% 34.33/34.70 Kept: 38165
% 34.33/34.70 Inuse: 967
% 34.33/34.70 Deleted: 483
% 34.33/34.70 Deletedinuse: 3
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70
% 34.33/34.70 Intermediate Status:
% 34.33/34.70 Generated: 187008
% 34.33/34.70 Kept: 41464
% 34.33/34.70 Inuse: 1004
% 34.33/34.70 Deleted: 491
% 34.33/34.70 Deletedinuse: 8
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70 Resimplifying clauses:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70
% 34.33/34.70 Intermediate Status:
% 34.33/34.70 Generated: 201861
% 34.33/34.70 Kept: 43536
% 34.33/34.70 Inuse: 1014
% 34.33/34.70 Deleted: 1113
% 34.33/34.70 Deletedinuse: 8
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70
% 34.33/34.70 Intermediate Status:
% 34.33/34.70 Generated: 215279
% 34.33/34.70 Kept: 45549
% 34.33/34.70 Inuse: 1039
% 34.33/34.70 Deleted: 1113
% 34.33/34.70 Deletedinuse: 8
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70
% 34.33/34.70 Intermediate Status:
% 34.33/34.70 Generated: 230417
% 34.33/34.70 Kept: 47551
% 34.33/34.70 Inuse: 1054
% 34.33/34.70 Deleted: 1113
% 34.33/34.70 Deletedinuse: 8
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70
% 34.33/34.70 Intermediate Status:
% 34.33/34.70 Generated: 241994
% 34.33/34.70 Kept: 49574
% 34.33/34.70 Inuse: 1093
% 34.33/34.70 Deleted: 1113
% 34.33/34.70 Deletedinuse: 8
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70
% 34.33/34.70 Intermediate Status:
% 34.33/34.70 Generated: 256225
% 34.33/34.70 Kept: 52448
% 34.33/34.70 Inuse: 1134
% 34.33/34.70 Deleted: 1113
% 34.33/34.70 Deletedinuse: 8
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70
% 34.33/34.70 Intermediate Status:
% 34.33/34.70 Generated: 266236
% 34.33/34.70 Kept: 54449
% 34.33/34.70 Inuse: 1172
% 34.33/34.70 Deleted: 1115
% 34.33/34.70 Deletedinuse: 10
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70
% 34.33/34.70 Intermediate Status:
% 34.33/34.70 Generated: 282235
% 34.33/34.70 Kept: 57164
% 34.33/34.70 Inuse: 1193
% 34.33/34.70 Deleted: 1117
% 34.33/34.70 Deletedinuse: 11
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70
% 34.33/34.70 Intermediate Status:
% 34.33/34.70 Generated: 291642
% 34.33/34.70 Kept: 59311
% 34.33/34.70 Inuse: 1233
% 34.33/34.70 Deleted: 1117
% 34.33/34.70 Deletedinuse: 11
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70 Resimplifying inuse:
% 34.33/34.70 Done
% 34.33/34.70
% 34.33/34.70
% 34.33/34.70 Intermediate Status:
% 34.33/34.70 Generated: 307355
% 34.33/34.70 Kept: 62524
% 34.33/34.70 Inuse: 1263
% 78.20/78.58 Deleted: 1117
% 78.20/78.58 Deletedinuse: 11
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58 Resimplifying clauses:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58
% 78.20/78.58 Intermediate Status:
% 78.20/78.58 Generated: 318229
% 78.20/78.58 Kept: 64533
% 78.20/78.58 Inuse: 1292
% 78.20/78.58 Deleted: 4807
% 78.20/78.58 Deletedinuse: 32
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58
% 78.20/78.58 Intermediate Status:
% 78.20/78.58 Generated: 326428
% 78.20/78.58 Kept: 66533
% 78.20/78.58 Inuse: 1321
% 78.20/78.58 Deleted: 4807
% 78.20/78.58 Deletedinuse: 32
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58
% 78.20/78.58 Intermediate Status:
% 78.20/78.58 Generated: 339180
% 78.20/78.58 Kept: 68682
% 78.20/78.58 Inuse: 1347
% 78.20/78.58 Deleted: 4807
% 78.20/78.58 Deletedinuse: 32
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58
% 78.20/78.58 Intermediate Status:
% 78.20/78.58 Generated: 355131
% 78.20/78.58 Kept: 70930
% 78.20/78.58 Inuse: 1402
% 78.20/78.58 Deleted: 4809
% 78.20/78.58 Deletedinuse: 34
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58
% 78.20/78.58 Intermediate Status:
% 78.20/78.58 Generated: 368624
% 78.20/78.58 Kept: 73220
% 78.20/78.58 Inuse: 1442
% 78.20/78.58 Deleted: 4809
% 78.20/78.58 Deletedinuse: 34
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58
% 78.20/78.58 Intermediate Status:
% 78.20/78.58 Generated: 379512
% 78.20/78.58 Kept: 75285
% 78.20/78.58 Inuse: 1472
% 78.20/78.58 Deleted: 4809
% 78.20/78.58 Deletedinuse: 34
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58
% 78.20/78.58 Intermediate Status:
% 78.20/78.58 Generated: 393162
% 78.20/78.58 Kept: 77292
% 78.20/78.58 Inuse: 1512
% 78.20/78.58 Deleted: 4809
% 78.20/78.58 Deletedinuse: 34
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58
% 78.20/78.58 Intermediate Status:
% 78.20/78.58 Generated: 414669
% 78.20/78.58 Kept: 80010
% 78.20/78.58 Inuse: 1522
% 78.20/78.58 Deleted: 4809
% 78.20/78.58 Deletedinuse: 34
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58
% 78.20/78.58 Intermediate Status:
% 78.20/78.58 Generated: 429777
% 78.20/78.58 Kept: 82750
% 78.20/78.58 Inuse: 1552
% 78.20/78.58 Deleted: 4809
% 78.20/78.58 Deletedinuse: 34
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58 Resimplifying clauses:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58
% 78.20/78.58 Intermediate Status:
% 78.20/78.58 Generated: 449231
% 78.20/78.58 Kept: 84810
% 78.20/78.58 Inuse: 1592
% 78.20/78.58 Deleted: 6087
% 78.20/78.58 Deletedinuse: 34
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58
% 78.20/78.58 Intermediate Status:
% 78.20/78.58 Generated: 470641
% 78.20/78.58 Kept: 88866
% 78.20/78.58 Inuse: 1622
% 78.20/78.58 Deleted: 6087
% 78.20/78.58 Deletedinuse: 34
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58
% 78.20/78.58 Intermediate Status:
% 78.20/78.58 Generated: 483416
% 78.20/78.58 Kept: 91674
% 78.20/78.58 Inuse: 1627
% 78.20/78.58 Deleted: 6087
% 78.20/78.58 Deletedinuse: 34
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58
% 78.20/78.58 Intermediate Status:
% 78.20/78.58 Generated: 507094
% 78.20/78.58 Kept: 93878
% 78.20/78.58 Inuse: 1637
% 78.20/78.58 Deleted: 6087
% 78.20/78.58 Deletedinuse: 34
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58
% 78.20/78.58 Intermediate Status:
% 78.20/78.58 Generated: 531437
% 78.20/78.58 Kept: 96150
% 78.20/78.58 Inuse: 1647
% 78.20/78.58 Deleted: 6087
% 78.20/78.58 Deletedinuse: 34
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58
% 78.20/78.58 Intermediate Status:
% 78.20/78.58 Generated: 563991
% 78.20/78.58 Kept: 100207
% 78.20/78.58 Inuse: 1677
% 78.20/78.58 Deleted: 6087
% 78.20/78.58 Deletedinuse: 34
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58
% 78.20/78.58 Intermediate Status:
% 78.20/78.58 Generated: 579323
% 78.20/78.58 Kept: 102557
% 78.20/78.58 Inuse: 1702
% 78.20/78.58 Deleted: 6087
% 78.20/78.58 Deletedinuse: 34
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58 Resimplifying clauses:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58
% 78.20/78.58 Intermediate Status:
% 78.20/78.58 Generated: 590741
% 78.20/78.58 Kept: 104574
% 78.20/78.58 Inuse: 1726
% 78.20/78.58 Deleted: 6450
% 78.20/78.58 Deletedinuse: 35
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58
% 78.20/78.58 Intermediate Status:
% 78.20/78.58 Generated: 612339
% 78.20/78.58 Kept: 107675
% 78.20/78.58 Inuse: 1767
% 78.20/78.58 Deleted: 6450
% 78.20/78.58 Deletedinuse: 35
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58
% 78.20/78.58 Intermediate Status:
% 78.20/78.58 Generated: 629750
% 78.20/78.58 Kept: 110533
% 78.20/78.58 Inuse: 1777
% 78.20/78.58 Deleted: 6452
% 78.20/78.58 Deletedinuse: 37
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58
% 78.20/78.58 Intermediate Status:
% 78.20/78.58 Generated: 642973
% 78.20/78.58 Kept: 112557
% 78.20/78.58 Inuse: 1807
% 78.20/78.58 Deleted: 6452
% 78.20/78.58 Deletedinuse: 37
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58
% 78.20/78.58 Intermediate Status:
% 78.20/78.58 Generated: 667375
% 78.20/78.58 Kept: 115727
% 78.20/78.58 Inuse: 1837
% 78.20/78.58 Deleted: 6453
% 78.20/78.58 Deletedinuse: 38
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58
% 78.20/78.58 Intermediate Status:
% 78.20/78.58 Generated: 681617
% 78.20/78.58 Kept: 117727
% 78.20/78.58 Inuse: 1872
% 78.20/78.58 Deleted: 6453
% 78.20/78.58 Deletedinuse: 38
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58
% 78.20/78.58 Intermediate Status:
% 78.20/78.58 Generated: 699275
% 78.20/78.58 Kept: 119799
% 78.20/78.58 Inuse: 1912
% 78.20/78.58 Deleted: 6453
% 78.20/78.58 Deletedinuse: 38
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 78.20/78.58 Done
% 78.20/78.58
% 78.20/78.58 Resimplifying inuse:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63
% 162.21/162.63 Intermediate Status:
% 162.21/162.63 Generated: 710401
% 162.21/162.63 Kept: 121815
% 162.21/162.63 Inuse: 1938
% 162.21/162.63 Deleted: 6459
% 162.21/162.63 Deletedinuse: 39
% 162.21/162.63
% 162.21/162.63 Resimplifying inuse:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63
% 162.21/162.63 Intermediate Status:
% 162.21/162.63 Generated: 724006
% 162.21/162.63 Kept: 123931
% 162.21/162.63 Inuse: 1967
% 162.21/162.63 Deleted: 6459
% 162.21/162.63 Deletedinuse: 39
% 162.21/162.63
% 162.21/162.63 Resimplifying clauses:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63 Resimplifying inuse:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63 Resimplifying inuse:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63
% 162.21/162.63 Intermediate Status:
% 162.21/162.63 Generated: 753523
% 162.21/162.63 Kept: 130013
% 162.21/162.63 Inuse: 2008
% 162.21/162.63 Deleted: 7010
% 162.21/162.63 Deletedinuse: 41
% 162.21/162.63
% 162.21/162.63 Resimplifying inuse:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63 Resimplifying inuse:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63
% 162.21/162.63 Intermediate Status:
% 162.21/162.63 Generated: 764726
% 162.21/162.63 Kept: 132098
% 162.21/162.63 Inuse: 2037
% 162.21/162.63 Deleted: 7010
% 162.21/162.63 Deletedinuse: 41
% 162.21/162.63
% 162.21/162.63 Resimplifying inuse:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63 Resimplifying inuse:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63
% 162.21/162.63 Intermediate Status:
% 162.21/162.63 Generated: 775650
% 162.21/162.63 Kept: 134127
% 162.21/162.63 Inuse: 2065
% 162.21/162.63 Deleted: 7011
% 162.21/162.63 Deletedinuse: 42
% 162.21/162.63
% 162.21/162.63 Resimplifying inuse:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63 Resimplifying inuse:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63
% 162.21/162.63 Intermediate Status:
% 162.21/162.63 Generated: 793691
% 162.21/162.63 Kept: 137502
% 162.21/162.63 Inuse: 2087
% 162.21/162.63 Deleted: 7011
% 162.21/162.63 Deletedinuse: 42
% 162.21/162.63
% 162.21/162.63 Resimplifying inuse:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63 Resimplifying inuse:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63
% 162.21/162.63 Intermediate Status:
% 162.21/162.63 Generated: 803618
% 162.21/162.63 Kept: 139519
% 162.21/162.63 Inuse: 2112
% 162.21/162.63 Deleted: 7011
% 162.21/162.63 Deletedinuse: 42
% 162.21/162.63
% 162.21/162.63 Resimplifying inuse:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63 Resimplifying inuse:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63
% 162.21/162.63 Intermediate Status:
% 162.21/162.63 Generated: 814890
% 162.21/162.63 Kept: 141539
% 162.21/162.63 Inuse: 2138
% 162.21/162.63 Deleted: 7011
% 162.21/162.63 Deletedinuse: 42
% 162.21/162.63
% 162.21/162.63 Resimplifying inuse:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63 Resimplifying inuse:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63
% 162.21/162.63 Intermediate Status:
% 162.21/162.63 Generated: 825710
% 162.21/162.63 Kept: 143590
% 162.21/162.63 Inuse: 2162
% 162.21/162.63 Deleted: 7012
% 162.21/162.63 Deletedinuse: 43
% 162.21/162.63
% 162.21/162.63 Resimplifying inuse:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63 Resimplifying clauses:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63 Resimplifying inuse:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63
% 162.21/162.63 Intermediate Status:
% 162.21/162.63 Generated: 836570
% 162.21/162.63 Kept: 145841
% 162.21/162.63 Inuse: 2187
% 162.21/162.63 Deleted: 7919
% 162.21/162.63 Deletedinuse: 43
% 162.21/162.63
% 162.21/162.63 Resimplifying inuse:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63 Resimplifying inuse:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63
% 162.21/162.63 Intermediate Status:
% 162.21/162.63 Generated: 848043
% 162.21/162.63 Kept: 148007
% 162.21/162.63 Inuse: 2217
% 162.21/162.63 Deleted: 7920
% 162.21/162.63 Deletedinuse: 44
% 162.21/162.63
% 162.21/162.63 Resimplifying inuse:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63 Resimplifying inuse:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63
% 162.21/162.63 Intermediate Status:
% 162.21/162.63 Generated: 859972
% 162.21/162.63 Kept: 150114
% 162.21/162.63 Inuse: 2247
% 162.21/162.63 Deleted: 7920
% 162.21/162.63 Deletedinuse: 44
% 162.21/162.63
% 162.21/162.63 Resimplifying inuse:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63
% 162.21/162.63 Intermediate Status:
% 162.21/162.63 Generated: 875781
% 162.21/162.63 Kept: 152550
% 162.21/162.63 Inuse: 2262
% 162.21/162.63 Deleted: 7920
% 162.21/162.63 Deletedinuse: 44
% 162.21/162.63
% 162.21/162.63 Resimplifying inuse:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63
% 162.21/162.63 Intermediate Status:
% 162.21/162.63 Generated: 885994
% 162.21/162.63 Kept: 154584
% 162.21/162.63 Inuse: 2267
% 162.21/162.63 Deleted: 7920
% 162.21/162.63 Deletedinuse: 44
% 162.21/162.63
% 162.21/162.63 Resimplifying inuse:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63 Resimplifying inuse:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63
% 162.21/162.63 Intermediate Status:
% 162.21/162.63 Generated: 897184
% 162.21/162.63 Kept: 156593
% 162.21/162.63 Inuse: 2293
% 162.21/162.63 Deleted: 7920
% 162.21/162.63 Deletedinuse: 44
% 162.21/162.63
% 162.21/162.63 Resimplifying inuse:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63 Resimplifying inuse:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63
% 162.21/162.63 Intermediate Status:
% 162.21/162.63 Generated: 907134
% 162.21/162.63 Kept: 158608
% 162.21/162.63 Inuse: 2311
% 162.21/162.63 Deleted: 7920
% 162.21/162.63 Deletedinuse: 44
% 162.21/162.63
% 162.21/162.63 Resimplifying inuse:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63 Resimplifying inuse:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63
% 162.21/162.63 Intermediate Status:
% 162.21/162.63 Generated: 918144
% 162.21/162.63 Kept: 160869
% 162.21/162.63 Inuse: 2332
% 162.21/162.63 Deleted: 7920
% 162.21/162.63 Deletedinuse: 44
% 162.21/162.63
% 162.21/162.63 Resimplifying inuse:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63 Resimplifying inuse:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63
% 162.21/162.63 Intermediate Status:
% 162.21/162.63 Generated: 928067
% 162.21/162.63 Kept: 163278
% 162.21/162.63 Inuse: 2352
% 162.21/162.63 Deleted: 7920
% 162.21/162.63 Deletedinuse: 44
% 162.21/162.63
% 162.21/162.63 Resimplifying inuse:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63 Resimplifying clauses:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63 Resimplifying inuse:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63
% 162.21/162.63 Intermediate Status:
% 162.21/162.63 Generated: 940484
% 162.21/162.63 Kept: 165369
% 162.21/162.63 Inuse: 2382
% 162.21/162.63 Deleted: 8434
% 162.21/162.63 Deletedinuse: 44
% 162.21/162.63
% 162.21/162.63 Resimplifying inuse:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63 Resimplifying inuse:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63
% 162.21/162.63 Intermediate Status:
% 162.21/162.63 Generated: 950418
% 162.21/162.63 Kept: 167641
% 162.21/162.63 Inuse: 2397
% 162.21/162.63 Deleted: 8434
% 162.21/162.63 Deletedinuse: 44
% 162.21/162.63
% 162.21/162.63 Resimplifying inuse:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63 Resimplifying inuse:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63
% 162.21/162.63 Intermediate Status:
% 162.21/162.63 Generated: 970576
% 162.21/162.63 Kept: 169969
% 162.21/162.63 Inuse: 2419
% 162.21/162.63 Deleted: 8438
% 162.21/162.63 Deletedinuse: 45
% 162.21/162.63
% 162.21/162.63 Resimplifying inuse:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63
% 162.21/162.63 Intermediate Status:
% 162.21/162.63 Generated: 992972
% 162.21/162.63 Kept: 173830
% 162.21/162.63 Inuse: 2425
% 162.21/162.63 Deleted: 8438
% 162.21/162.63 Deletedinuse: 45
% 162.21/162.63
% 162.21/162.63 Resimplifying inuse:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63 Resimplifying inuse:
% 162.21/162.63 Done
% 162.21/162.63
% 162.21/162.63
% 162.21/162.63 Intermediate Status:
% 162.21/162.63 Generated: 1001726
% 162.21/162.63 Kept: 175972
% 162.21/162.63 Inuse: 2434
% 162.21/162.63 Deleted: 8438
% 162.21/162.63 Deletedinuse: 45
% 162.21/162.63
% 162.21/162.63
% 162.21/162.63 Intermediate Status:
% 162.21/162.63 Generated: 1024364
% 162.21/162.63 Kept: 180555
% 162.21/162.63 Inuse: 2438
% 162.21/162.63 Deleted: 8438
% 162.21/162.63 Deletedinuse: 45
% 162.21/162.63
% 162.21/162.63 Resimplifying inuse:
% 162.21/162.63 DCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------