TSTP Solution File: SWV717-1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV717-1 : 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 16:28:02 EDT 2022
% Result : Timeout 300.11s 300.51s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV717-1 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Tue Jun 14 17:06:49 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.17/1.58 *** allocated 10000 integers for termspace/termends
% 1.17/1.58 *** allocated 10000 integers for clauses
% 1.17/1.58 *** allocated 10000 integers for justifications
% 1.17/1.58 *** allocated 15000 integers for termspace/termends
% 1.17/1.58 *** allocated 22500 integers for termspace/termends
% 1.17/1.58 *** allocated 33750 integers for termspace/termends
% 1.17/1.58 Bliksem 1.12
% 1.17/1.58
% 1.17/1.58
% 1.17/1.58 Automatic Strategy Selection
% 1.17/1.58
% 1.17/1.58 Clauses:
% 1.17/1.58 [
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( U, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.17/1.58 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.17/1.58 ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), hAPP(
% 1.17/1.58 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.17/1.58 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.17/1.58 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), Z ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.17/1.58 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.58 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.17/1.58 ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.17/1.58 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.58 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.17/1.58 ) ) ],
% 1.17/1.58 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.17/1.58 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.58 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.17/1.58 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.58 ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.58 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.17/1.58 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.58 ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.17/1.58 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.17/1.58 ), Z ), Y ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.17/1.58 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.17/1.58 ), X ), Y ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.58 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.17/1.58 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.58 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.58 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.58 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.17/1.58 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.58 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.58 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.58 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.17/1.58 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.17/1.58 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.58 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.17/1.58 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.17/1.58 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.17/1.58 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.58 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ) ) ],
% 1.17/1.58 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.17/1.58 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.17/1.58 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.58 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.17/1.58 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.17/1.58 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 1.17/1.58 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.17/1.58 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.17/1.58 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.17/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.17/1.58 [ =( 'c_List_Odrop'( X, 'c_List_Otake'( Y, Z, T ), T ), 'c_List_Otake'(
% 1.17/1.58 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'c_List_Odrop'( X, Z, T )
% 1.17/1.58 , T ) ) ],
% 1.17/1.58 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.58 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.58 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.17/1.58 ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.58 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.17/1.58 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.58 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.17/1.58 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.17/1.58 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.17/1.58 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.17/1.58 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.17/1.58 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.17/1.58 [ =( 'c_List_Onth'( 'c_List_Otake'( X, Y, Z ), T, Z ), 'c_List_Onth'( Y
% 1.17/1.58 , T, Z ) ), ~( 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.17/1.58 ), Y ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.17/1.58 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.17/1.58 , 'tc_nat' ), 'tc_nat' ) ],
% 1.17/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.17/1.58 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.58 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.17/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.58 X ), Y ), Z ) ), T ) ) ],
% 1.17/1.58 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.17/1.58 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.17/1.58 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.17/1.58 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.58 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.17/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.58 X ), Y ), Z ) ), T ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.58 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.17/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.58 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.17/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.17/1.58 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.17/1.58 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.58 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.17/1.58 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.17/1.58 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.58 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.17/1.58 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ) ],
% 1.17/1.58 [ =( 'c_List_Otake'( X, 'c_List_Odrop'( Y, Z, T ), T ), 'c_List_Odrop'(
% 1.17/1.58 Y, 'c_List_Otake'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.17/1.58 ), Y ), Z, T ), T ) ) ],
% 1.17/1.58 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.17/1.58 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.17/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.17/1.58 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.17/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 1.17/1.58 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 1.17/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 1.17/1.58 , X ), 'c_lessequals'( Y, Y, X ) ],
% 1.17/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.17/1.58 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.17/1.58 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.58 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 'c_lessequals'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z, X ) )
% 1.17/1.58 ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 'c_lessequals'( Y
% 1.17/1.58 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.17/1.58 ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.58 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.58 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.58 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.58 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.17/1.58 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.58 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.58 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.17/1.58 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.17/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.58 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.58 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.17/1.58 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.58 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.58 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.17/1.58 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.58 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.58 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.17/1.58 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.58 ), Y ), T ), Z, X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.58 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.17/1.58 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y
% 1.17/1.58 , X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.17/1.58 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.17/1.58 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.58 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.17/1.58 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.17/1.58 T, X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.58 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( T, Y, X
% 1.17/1.58 ) ), Z ) ), U ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.17/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.17/1.58 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.17/1.58 ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.58 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'(
% 1.17/1.58 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ),
% 1.17/1.58 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'( 'c_Suc'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ), X ), ~(
% 1.17/1.58 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.17/1.58 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.17/1.58 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), 'tc_nat' ) ],
% 1.17/1.58 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.17/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.17/1.58 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.17/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.17/1.58 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.17/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.17/1.58 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.17/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.17/1.58 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 1.17/1.58 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.58 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.17/1.58 'tc_nat' ) ) ],
% 1.17/1.58 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.58 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.17/1.58 'tc_nat' ) ) ],
% 1.17/1.58 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.58 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.17/1.58 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.58 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.17/1.58 'tc_nat' ) ) ],
% 1.17/1.58 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.58 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.17/1.58 'tc_nat' ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.58 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.17/1.58 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.58 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.17/1.58 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.17/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 1.17/1.58 ) ), T ) ), U ), W, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.58 X ), Y ), T ) ), U ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.17/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), W ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.17/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.58 X ), U ), Z ) ), W ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.58 X ), 'c_HOL_Ominus__class_Ominus'( Y, U, X ) ), Z ) ), T ), W, X ) ) ]
% 1.17/1.58 ,
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( Y
% 1.17/1.58 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X
% 1.17/1.58 ) ), U ) ), W ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.58 X ), T ), U ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.17/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ), W ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.17/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.58 X ), U ), Z ) ), W ), X ), ~( 'c_lessequals'( T, hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.58 X ), 'c_HOL_Ominus__class_Ominus'( U, Y, X ) ), Z ) ), W ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.17/1.58 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.17/1.58 'c_HOL_Ominus__class_Ominus'( Z, T, X ) ), 'c_HOL_Ominus__class_Ominus'(
% 1.17/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.17/1.58 , X ) ), T ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.17/1.58 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.58 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.17/1.58 ), X ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.17/1.58 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.17/1.58 , 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.58 X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.58 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.17/1.58 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.17/1.58 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.17/1.58 , 'tc_nat' ), 'tc_nat' ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.58 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.17/1.58 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.17/1.58 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.17/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.17/1.58 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), Z, X ) ) ]
% 1.17/1.58 ,
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.17/1.58 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.17/1.58 ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.17/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.17/1.58 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ]
% 1.17/1.58 ,
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.17/1.58 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ),
% 1.17/1.58 Z, X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y
% 1.17/1.58 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.17/1.58 ,
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.17/1.58 , 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.17/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.17/1.58 ,
% 1.17/1.58 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.17/1.58 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.58 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.17/1.58 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.17/1.58 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.17/1.58 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.17/1.58 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.17/1.58 'tc_nat' ), Y, 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat'
% 1.17/1.58 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.17/1.58 , Y, 'tc_nat' ) ) ],
% 1.17/1.58 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.17/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.58 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.17/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.58 [ =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_Int_Oint' ), X ) ],
% 1.17/1.58 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.17/1.58 , T, X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.17/1.58 Y, T, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.17/1.58 , T, X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.17/1.58 Y, T, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.17/1.58 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.17/1.58 ,
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.17/1.58 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.58 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.17/1.58 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.58 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.17/1.58 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.17/1.58 ,
% 1.17/1.58 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat'
% 1.17/1.58 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.17/1.58 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.17/1.58 ,
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.17/1.58 ,
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.17/1.58 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ) ],
% 1.17/1.58 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( X )
% 1.17/1.58 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP(
% 1.17/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.17/1.58 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), 'c_Suc'(
% 1.17/1.58 Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.17/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.17/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.58 X ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.17/1.58 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.17/1.58 Y, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.58 X ), T ), Z ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.17/1.58 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.17/1.58 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.58 ), Y ), T ), Z, X ) ) ],
% 1.17/1.58 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.17/1.58 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.58 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.17/1.58 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.17/1.58 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.58 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.58 ), Y ), Z ), Y, X ), Z ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.58 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.58 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.58 ), Y ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.17/1.58 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.17/1.58 ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), U ) ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.17/1.58 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'( Y,
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.17/1.58 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'(
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~( 'c_lessequals'( Y, Z
% 1.17/1.58 , 'tc_Int_Oint' ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.17/1.58 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( Y, Z, 'tc_Int_Oint' ),
% 1.17/1.58 ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.17/1.58 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( X, 'tc_Int_Oint' ),
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_Int_Oint' ), 'tc_Int_Oint' ) )
% 1.17/1.58 ],
% 1.17/1.58 [ 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_Int_Oint' )
% 1.17/1.58 , 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_Int_Oint' ), 'tc_Int_Oint' )
% 1.17/1.58 , ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.17/1.58 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.58 X ), Y ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.17/1.58 ,
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.58 X ), Y ), Z ), Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.17/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), Y, X ), Z ) ]
% 1.17/1.58 ,
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Oinverse__class_Odivide'(
% 1.17/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), Y, X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.17/1.58 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.17/1.58 Z, X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.17/1.58 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.17/1.58 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.17/1.58 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.17/1.58 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.17/1.58 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.17/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.17/1.58 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 1.17/1.58 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.17/1.58 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.17/1.58 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.17/1.58 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 1.17/1.58 'tc_nat' ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ],
% 1.17/1.58 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.17/1.58 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_Int_Oint' ) ), ~(
% 1.17/1.58 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.17/1.58 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.17/1.58 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.17/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.17/1.58 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.17/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.17/1.58 ) ],
% 1.17/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.17/1.58 ) ],
% 1.17/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.17/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.17/1.58 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.17/1.58 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.17/1.58 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.17/1.58 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.58 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.58 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T
% 1.17/1.58 , X ) ), T, X ) ) ],
% 1.17/1.58 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.58 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.58 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.17/1.58 ), Z ), T, X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.17/1.58 ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.17/1.58 ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.17/1.58 ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.17/1.58 ), X ) ) ],
% 1.17/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.17/1.58 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.58 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.17/1.58 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.17/1.58 [ =( 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.58 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.17/1.58 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.17/1.58 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.58 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.17/1.58 ],
% 1.17/1.58 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.17/1.58 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.17/1.58 , T, X ) ) ), =( Z, T ) ],
% 1.17/1.58 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.17/1.58 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.17/1.58 , T, X ) ) ), =( Y, Z ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.17/1.58 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.58 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.17/1.58 , X ) ), T ) ) ) ],
% 1.17/1.58 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.17/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.17/1.58 'tc_nat' ) ), =( Y, Z ) ],
% 1.17/1.58 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.17/1.58 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ) ) ],
% 1.17/1.58 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.17/1.58 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), 'tc_nat' ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.17/1.58 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), =( Y,
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'( hAPP( hAPP(
% 1.17/1.58 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.17/1.58 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.17/1.58 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.17/1.58 'c_Power_Opower__class_Opower'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.58 X ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.17/1.58 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.17/1.58 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.17/1.58 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.17/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.17/1.58 'c_lessequals'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.17/1.58 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.17/1.58 ,
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.17/1.58 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.17/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.17/1.58 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.17/1.58 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.17/1.58 ,
% 1.17/1.58 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =(
% 1.17/1.58 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.58 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X
% 1.17/1.58 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.58 X ), 'c_HOL_Ominus__class_Ominus'( Y, T, X ) ),
% 1.17/1.58 'c_HOL_Ominus__class_Ominus'( Z, U, X ) ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, T, X
% 1.17/1.58 ) ), U ) ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.17/1.58 'c_HOL_Ominus__class_Ominus'( Z, U, X ) ) ) ) ],
% 1.17/1.58 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.17/1.58 , 'tc_nat' ), 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat'
% 1.17/1.58 ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.17/1.58 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.17/1.58 , 'tc_nat' ), 'tc_nat' ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y,
% 1.17/1.58 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ]
% 1.17/1.58 ,
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.58 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.17/1.58 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.58 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.17/1.58 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.17/1.58 'class_OrderedGroup_Omonoid__mult'( X ) ), 'c_lessequals'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.58 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.17/1.58 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.17/1.58 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ),
% 1.17/1.58 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.17/1.58 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.17/1.58 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.17/1.58 , Y, X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.58 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.58 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), U )
% 1.17/1.58 ) ],
% 1.17/1.58 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ), T ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), T ) ) ],
% 1.17/1.58 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.17/1.58 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.58 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.17/1.58 ), 'tc_nat' ) ) ],
% 1.17/1.58 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.17/1.58 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.58 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X
% 1.17/1.58 ), 'tc_nat' ) ) ],
% 1.17/1.58 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.17/1.58 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.17/1.58 ,
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.17/1.58 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Z ),
% 1.17/1.58 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.17/1.58 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.17/1.58 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.58 X ), Z ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y )
% 1.17/1.58 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.58 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.17/1.58 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.17/1.58 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.17/1.58 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), U ), Z ) ), X ), hAPP( hAPP(
% 1.17/1.58 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.17/1.58 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.17/1.58 'c_Power_Opower__class_Opower'( X ), Y ), U ), X ) ), Z ) ), =( Y,
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.58 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z,
% 1.17/1.58 T, X ) ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.17/1.58 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ominus__class_Ominus'( Z,
% 1.17/1.58 T, X ) ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.17/1.58 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.17/1.58 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z ),
% 1.17/1.58 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.58 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.17/1.58 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.17/1.58 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.17/1.58 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ),
% 1.17/1.58 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.58 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.17/1.58 ), X ), Z ), 'tc_nat' ) ) ],
% 1.17/1.58 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 1.17/1.58 ) ), T ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.17/1.58 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 1.17/1.58 ) ), T ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.17/1.58 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.17/1.58 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.58 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ),
% 1.17/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ominus__class_Ominus'(
% 1.17/1.58 Y, T, X ) ), 'c_HOL_Ominus__class_Ominus'( Z, U, X ) ) ) ],
% 1.17/1.58 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.17/1.58 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.17/1.58 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.17/1.58 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.58 , X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.17/1.58 ,
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.17/1.58 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.58 , X ) ) ],
% 1.17/1.58 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X
% 1.17/1.58 , 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.17/1.58 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.17/1.58 'tc_nat' ) ) ],
% 1.17/1.58 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.17/1.58 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.17/1.58 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.17/1.58 'tc_nat' ) ) ],
% 1.17/1.58 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.58 'tc_nat' ), 'c_Suc'( Z ) ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.58 'tc_nat' ), 'c_Suc'( Z ) ), Y ), 'tc_nat' ) ) ],
% 1.17/1.58 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.58 'tc_nat' ), 'c_Suc'( X ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.58 'tc_nat' ), 'c_Suc'( X ) ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 Y, Z, 'tc_nat' ) ) ],
% 1.17/1.58 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.17/1.58 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.17/1.58 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.17/1.58 , 'tc_nat' ), 'tc_nat' ), 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.58 X ), X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.17/1.58 X ), Z ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.17/1.58 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.17/1.58 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.58 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.17/1.58 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.58 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.58 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.58 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.58 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.17/1.58 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.17/1.58 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.58 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), Z, X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.58 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.17/1.58 ,
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.58 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.17/1.58 ,
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.58 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.58 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.58 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z,
% 1.17/1.58 T, X ) ), T, X ) ) ],
% 1.17/1.58 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.58 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.58 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.17/1.58 ) ), Z ), T, X ) ) ],
% 1.17/1.58 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.17/1.58 , Y, 'tc_nat' ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.58 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.17/1.58 ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.58 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.17/1.58 ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.17/1.58 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.58 'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ), =( Y, T ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.17/1.58 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.17/1.58 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.58 X ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.17/1.58 ), 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ), =( Z,
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.58 X ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.17/1.58 ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ), =( Y,
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.58 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.17/1.58 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.58 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.17/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.58 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'( Y,
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( T, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.17/1.58 , X ), X ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.58 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.17/1.58 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.17/1.58 ), X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.58 X ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.58 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( T
% 1.17/1.58 , X ), X ), Z, X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.17/1.58 , X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.17/1.58 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.17/1.58 , 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 1.17/1.58 ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.17/1.58 'c_Groebner__Basis_Ogb__semiring'( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( X ),
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.17/1.58 ,
% 1.17/1.58 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.17/1.58 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Z ),
% 1.17/1.58 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.58 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.17/1.58 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.17/1.58 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.17/1.58 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ),
% 1.17/1.58 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.58 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.17/1.58 ), X ), Z ), 'tc_nat' ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.58 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.17/1.58 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.17/1.58 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.58 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.17/1.58 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.58 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.17/1.58 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.58 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.17/1.58 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.17/1.58 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.58 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.17/1.58 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.17/1.58 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.58 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.17/1.58 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.58 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.17/1.58 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.58 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.17/1.58 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.17/1.58 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.58 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.17/1.58 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.17/1.58 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.58 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.17/1.58 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.17/1.58 ), =( Z, Y ) ],
% 1.17/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.17/1.58 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.17/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.17/1.58 'c_lessequals'( Z, T, X ) ) ],
% 1.17/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.17/1.58 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.17/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.17/1.58 'c_lessequals'( Y, T, X ) ) ],
% 1.17/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.17/1.58 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.17/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.17/1.58 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.17/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.17/1.58 'c_lessequals'( Z, T, X ) ) ],
% 1.17/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.17/1.58 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.17/1.58 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.17/1.58 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.17/1.58 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.17/1.58 'c_lessequals'( Y, T, X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.17/1.58 , X ) ), 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ),
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.58 X ), Y ), T ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ), X
% 1.17/1.58 ) ) ],
% 1.17/1.58 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.17/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.17/1.58 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.17/1.58 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.58 'tc_nat' ), X ), 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z,
% 1.17/1.58 'tc_nat' ) ) ) ],
% 1.17/1.58 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.58 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.17/1.58 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.17/1.58 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.58 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.17/1.58 ), Z ), Y ), 'tc_nat' ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.58 , Y ), 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.17/1.58 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.17/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.58 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.17/1.58 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.58 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.17/1.58 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.58 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.17/1.58 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.58 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.17/1.58 ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.58 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.58 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.17/1.58 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ),
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.17/1.58 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.17/1.58 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.17/1.58 'tc_nat' ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.58 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.58 ), Y, X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.17/1.58 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.17/1.58 ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.58 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.17/1.58 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.17/1.58 , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.17/1.58 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.17/1.58 ), X ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.58 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.58 X ), X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.17/1.58 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.17/1.58 ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.58 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.17/1.58 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.17/1.58 ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.17/1.58 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.17/1.58 ), X ) ],
% 1.17/1.58 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.58 'tc_nat' ) ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y ), 'tc_nat' ),
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.58 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.58 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.58 ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z )
% 1.17/1.58 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.58 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.58 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.58 , Y ), Z ), Y, X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 1.17/1.58 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.58 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.58 , Y ), Z ), Z, X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.17/1.58 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.58 X ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.17/1.58 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.58 X ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.17/1.58 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.17/1.58 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.58 X ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.17/1.58 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.17/1.58 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.58 X ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.58 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.17/1.58 ,
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.58 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.17/1.58 ,
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.58 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.17/1.58 ,
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.58 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.17/1.58 ,
% 1.17/1.58 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), hAPP(
% 1.17/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ),
% 1.17/1.58 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.17/1.58 'tc_nat' ), Z, 'tc_nat' ) ) ), 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.17/1.58 'tc_nat' ) ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), =( Y
% 1.17/1.58 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.58 , X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.17/1.58 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.17/1.58 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.17/1.58 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 1.17/1.58 X ), X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ) ) ],
% 1.17/1.58 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.58 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.17/1.58 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ) ), T ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' ) ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.17/1.58 'tc_nat' ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'( hAPP(
% 1.17/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.17/1.58 ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.17/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.17/1.58 ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.17/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.17/1.58 ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.17/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'( Y,
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 1.17/1.58 ,
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.17/1.58 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.17/1.58 ,
% 1.17/1.58 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.17/1.58 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.17/1.58 'tc_nat' ), Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' )
% 1.17/1.58 ],
% 1.17/1.58 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.17/1.58 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ) ) ), =( Z, T ), =( Y
% 1.17/1.58 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.17/1.58 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ), =( T, U ), =( Z,
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.17/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.58 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.17/1.58 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.58 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Oone__class_Oone'( X
% 1.17/1.58 ) ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Z ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.17/1.58 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.17/1.58 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.17/1.58 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.17/1.58 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.58 ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), Z, X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.17/1.58 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.17/1.58 X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.58 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.58 Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.17/1.58 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.17/1.58 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.17/1.58 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.17/1.58 ,
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.17/1.58 , X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.58 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.17/1.58 ,
% 1.17/1.58 [ =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'c_Int_Onat'(
% 1.17/1.58 'c_Int_Onumber__class_Onumber__of'( X, 'tc_Int_Oint' ) ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.58 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.17/1.58 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.58 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.17/1.58 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.59 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.59 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.59 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.17/1.59 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.17/1.59 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), Y ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.17/1.59 Z, 'tc_nat' ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.59 X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.59 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.17/1.59 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.17/1.59 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.17/1.59 T, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.17/1.59 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'( Y
% 1.17/1.59 , T, X ) ), 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.17/1.59 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.59 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ],
% 1.17/1.59 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.59 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.17/1.59 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.17/1.59 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.59 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.17/1.59 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.17/1.59 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.59 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.59 , X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.59 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.17/1.59 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.17/1.59 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( T, U, X ) ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.17/1.59 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.17/1.59 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( T, U, X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.17/1.59 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.17/1.59 , U, X ) ) ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( U, T, X ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.17/1.59 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.17/1.59 , U, X ) ) ), 'c_lessequals'( U, T, X ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.17/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.59 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.59 , Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ),
% 1.17/1.59 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.59 , Y ), Z ), T, X ) ) ],
% 1.17/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.59 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.59 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.17/1.59 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.59 , Y ), T ), Z, X ) ) ],
% 1.17/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( Y, hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.17/1.59 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ) ],
% 1.17/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.17/1.59 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), Y ) ],
% 1.17/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 X ), Y ), 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ),
% 1.17/1.59 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ), Z ) ],
% 1.17/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.17/1.59 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.17/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.17/1.59 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.17/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.17/1.59 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 1.17/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 1.17/1.59 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.17/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.17/1.59 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 1.17/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.17/1.59 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.17/1.59 ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'( Z,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.17/1.59 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.17/1.59 , X ) ), Z ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.17/1.59 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.17/1.59 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.59 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.17/1.59 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.17/1.59 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.17/1.59 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.17/1.59 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.17/1.59 , X, 'tc_nat' ) ) ],
% 1.17/1.59 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.17/1.59 ), Z ), Y ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.17/1.59 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.17/1.59 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.17/1.59 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.17/1.59 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.17/1.59 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.17/1.59 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.17/1.59 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.17/1.59 , X, 'tc_nat' ) ) ],
% 1.17/1.59 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.17/1.59 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 1.17/1.59 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.17/1.59 , Y, 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.59 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.59 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.17/1.59 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.17/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.59 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.59 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.17/1.59 , 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 1.17/1.59 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), Y, 'tc_nat' )
% 1.17/1.59 , 'c_Divides_Odiv__class_Omod'( Z, Y, 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~( 'c_lessequals'(
% 1.17/1.59 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( Y,
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~( 'c_lessequals'(
% 1.17/1.59 Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.17/1.59 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.59 , Y ), Z ), Z, X ), Y ) ],
% 1.17/1.59 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ), Y ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ), X ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.59 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ) ],
% 1.17/1.59 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.59 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.17/1.59 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.17/1.59 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.17/1.59 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), 'c_Int_Oiszero'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.17/1.59 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.59 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.17/1.59 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.59 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Int_Oiszero'( Y, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.17/1.59 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.59 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.17/1.59 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.59 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.17/1.59 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.17/1.59 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.17/1.59 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.17/1.59 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.17/1.59 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.17/1.59 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.17/1.59 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.17/1.59 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.17/1.59 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.59 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.59 ) ],
% 1.17/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.59 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.17/1.59 ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.17/1.59 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.17/1.59 ), X ), Y ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.17/1.59 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.17/1.59 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.17/1.59 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ), =( Z,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.59 ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 1.17/1.59 =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.59 ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.17/1.59 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.59 ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.17/1.59 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.59 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.17/1.59 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.59 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.17/1.59 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.59 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.59 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.59 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.17/1.59 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.59 ) ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.17/1.59 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.59 ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.17/1.59 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.59 ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.17/1.59 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.17/1.59 ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.17/1.59 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.59 ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.17/1.59 X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y, X ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.17/1.59 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 1.17/1.59 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.59 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.17/1.59 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.17/1.59 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.17/1.59 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.59 ) ), =( Y, Z ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.17/1.59 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.59 ) ), =( Y, Z ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.17/1.59 X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.17/1.59 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.17/1.59 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.17/1.59 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.17/1.59 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.17/1.59 Y ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.17/1.59 Y ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.17/1.59 Y ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.17/1.59 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.17/1.59 Y ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.17/1.59 Y ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.17/1.59 Y ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.17/1.59 Y ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 1.17/1.59 X ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), =( Y, hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( T
% 1.17/1.59 , X ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.17/1.59 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.59 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.17/1.59 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), =( Z,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y ), =(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.59 ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), =( Y, hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.59 ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.59 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.17/1.59 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.17/1.59 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.17/1.59 , 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.17/1.59 , 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.17/1.59 , X ) ), Z ), Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.17/1.59 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.17/1.59 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.17/1.59 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.17/1.59 , 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.17/1.59 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.59 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.59 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.17/1.59 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.59 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.59 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.17/1.59 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.17/1.59 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ), Z, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.17/1.59 X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.17/1.59 , X ) ), T ), Z ), =( T, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), =( Y, 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.17/1.59 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ) ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), =(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.59 ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.17/1.59 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ) ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y ), =(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.59 ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.59 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.59 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.17/1.59 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), X ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.17/1.59 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.17/1.59 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.17/1.59 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.17/1.59 , 'tc_nat' ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.17/1.59 ), X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.17/1.59 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.17/1.59 , X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.17/1.59 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, hAPP(
% 1.17/1.59 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.17/1.59 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.17/1.59 ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.17/1.59 ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.59 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.17/1.59 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.17/1.59 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.17/1.59 ) ) ],
% 1.17/1.59 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.17/1.59 ) ) ],
% 1.17/1.59 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.59 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.17/1.59 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.17/1.59 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.59 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.17/1.59 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.17/1.59 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.17/1.59 ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.59 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.17/1.59 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.17/1.59 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.17/1.59 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.17/1.59 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.59 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.17/1.59 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 1.17/1.59 , 'tc_nat' ) ) ],
% 1.17/1.59 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.59 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.17/1.59 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 1.17/1.59 , 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.17/1.59 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.59 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.17/1.59 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.17/1.59 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.17/1.59 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, T, X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.17/1.59 X ), ~( 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.17/1.59 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 X ), Y ), Z ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.17/1.59 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 X ), Z ), Y ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.17/1.59 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 X ), Y ), Z ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.17/1.59 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 X ), Z ), Y ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.17/1.59 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), X
% 1.17/1.59 ) ) ],
% 1.17/1.59 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.59 X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), 'c_Suc'(
% 1.17/1.59 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ) ), 'tc_nat' ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.17/1.59 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.17/1.59 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.17/1.59 , 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ), X ) ), =( U,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.59 ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.17/1.59 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.17/1.59 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.17/1.59 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.17/1.59 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.17/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.59 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.59 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.17/1.59 ), 'c_Divides_Odiv__class_Odiv'( Z, T, X ) ), =( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.59 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.59 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.17/1.59 ), 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), =( Z,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.17/1.59 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), =( X,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.59 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.17/1.59 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 1.17/1.59 Z, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.17/1.59 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.59 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Z, 'tc_nat' ) ),
% 1.17/1.59 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z, 'tc_nat' ) ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y
% 1.17/1.59 , X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.17/1.59 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.17/1.59 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.17/1.59 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.17/1.59 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.59 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.59 ), T ), Z ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.17/1.59 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.17/1.59 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.59 ), T ), Z ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.17/1.59 , X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.17/1.59 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.59 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.17/1.59 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.17/1.59 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.59 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.59 , Y ), T ), Z, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.17/1.59 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.59 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.59 , Y ), T ), Z, X ) ) ],
% 1.17/1.59 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.17/1.59 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.17/1.59 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.17/1.59 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.17/1.59 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.17/1.59 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ),
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ), ~(
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.17/1.59 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ],
% 1.17/1.59 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.59 , Y ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP(
% 1.17/1.59 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.59 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.17/1.59 ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.17/1.59 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.59 , Z ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X )
% 1.17/1.59 ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.17/1.59 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.17/1.59 ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.59 X ), Y ), Z ) ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ),
% 1.17/1.59 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Z,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.59 ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.17/1.59 ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.17/1.59 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ),
% 1.17/1.59 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Z,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.59 ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.17/1.59 'c_HOL_Oone__class_Oone'( X ) ), X ), Z, X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.17/1.59 'c_HOL_Oone__class_Oone'( X ) ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 Y, Z, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.17/1.59 ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), Z, X ) ), =( Z,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oinverse__class_Odivide'( Z
% 1.17/1.59 , T, X ) ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), T, X ) ), =( T,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.59 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.17/1.59 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), T ) )
% 1.17/1.59 , hAPP( hAPP( Y, hAPP( hAPP( X, Z ), U ) ), T ) ), ~(
% 1.17/1.59 'c_Groebner__Basis_Ogb__semiring'( X, Y, W, V0, V1, V2 ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ), hAPP( hAPP( Y, hAPP(
% 1.17/1.59 hAPP( X, Z ), U ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Y, W
% 1.17/1.59 , V0, U, V1 ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ), hAPP( hAPP( Z, hAPP(
% 1.17/1.59 hAPP( X, T ), U ) ), Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, W
% 1.17/1.59 , V0, U, V1 ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, hAPP( hAPP( X, T ), T ) ),
% 1.17/1.59 Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, U, W, T, V0 ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.17/1.59 X, T, U, Y, W, V0 ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.17/1.59 X, T, U, Z, W, V0 ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.17/1.59 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.17/1.59 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.17/1.59 'c_Groebner__Basis_Ogb__semiring'( Y, X, W, V0, V1, V2 ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.17/1.59 T, X, U, Y, W, V0 ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.17/1.59 T, X, U, Z, W, V0 ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.17/1.59 T, X, U, W, Y, V0 ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.17/1.59 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.17/1.59 ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.17/1.59 ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.17/1.59 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.17/1.59 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.17/1.59 ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.17/1.59 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.17/1.59 ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.17/1.59 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Y, X ), ~(
% 1.17/1.59 'c_lessequals'( Z, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.17/1.59 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.17/1.59 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.17/1.59 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Z, X ), ~(
% 1.17/1.59 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.17/1.59 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.17/1.59 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oinverse__class_Oinverse'(
% 1.17/1.59 Y, X ) ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.17/1.59 ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.17/1.59 ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.17/1.59 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.17/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.59 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.59 , Y ), Z ), Z, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.17/1.59 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.17/1.59 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.59 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.59 , Y ), Z ), Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.17/1.59 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.17/1.59 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.17/1.59 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.17/1.59 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.59 X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.17/1.59 X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.17/1.59 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.17/1.59 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_lessequals'( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.17/1.59 X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 'c_lessequals'(
% 1.17/1.59 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.59 , X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.59 'tc_nat' ) ), X ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.17/1.59 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.17/1.59 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.17/1.59 ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.17/1.59 'c_Suc'( T ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.17/1.59 'c_Suc'( T ) ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), T ), 'c_Suc'( Z ) ) ) ), =( Y, T ),
% 1.17/1.59 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.17/1.59 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.17/1.59 ), =( 'c_HOL_Oinverse__class_Oinverse'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.17/1.59 ), Y ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ), ~(
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.17/1.59 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.17/1.59 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.17/1.59 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.17/1.59 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.17/1.59 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.17/1.59 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.17/1.59 , 'tc_nat' ), 'tc_nat' ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.17/1.59 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'(
% 1.17/1.59 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.17/1.59 , 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), ~( 'c_Int_Oiszero'(
% 1.17/1.59 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.17/1.59 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.17/1.59 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.17/1.59 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.17/1.59 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y )
% 1.17/1.59 , 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y
% 1.17/1.59 ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.17/1.59 Y ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.17/1.59 Y ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.17/1.59 Y ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.17/1.59 Y ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.17/1.59 Y ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.17/1.59 Y ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.17/1.59 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.17/1.59 ), =( Y, 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.59 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.17/1.59 ],
% 1.17/1.59 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Omod'( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.17/1.59 , Y ) ) ],
% 1.17/1.59 [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 1.17/1.59 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.59 'tc_nat' ) ) ) ],
% 1.17/1.59 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.17/1.59 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.17/1.59 [ ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), hBOOL(
% 1.17/1.59 hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.59 'tc_nat' ), 'tc_nat' ) ) ) ],
% 1.17/1.59 [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ), ~( hBOOL( hAPP( X
% 1.17/1.59 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.17/1.59 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.17/1.59 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.59 'tc_nat' ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.59 'tc_nat' ) ) ],
% 1.17/1.59 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.59 'tc_nat' ), 'tc_nat' ) ],
% 1.17/1.59 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.17/1.59 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( Y
% 1.17/1.59 , Z ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.17/1.59 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( X
% 1.17/1.59 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 1.17/1.59 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.17/1.59 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), =( Y
% 1.17/1.59 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 1.17/1.59 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.17/1.59 ), 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.17/1.59 ), 'tc_nat' ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ),
% 1.17/1.59 ~( 'c_Groebner__Basis_Ogb__semiring'( T, U, X, W, Z, V0 ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.59 'tc_nat' ) ), Y ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.59 'tc_nat' ) ) ) ],
% 1.17/1.59 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 1.17/1.59 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ],
% 1.17/1.59 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.59 [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.59 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.59 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.17/1.59 [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 1.17/1.59 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 1.17/1.59 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.59 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.59 [ =( 'c_List_Odrop'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, Y ), X )
% 1.17/1.59 ],
% 1.17/1.59 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.17/1.59 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.59 [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.17/1.59 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.17/1.59 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'( Y
% 1.17/1.59 ), 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.17/1.59 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( X ), 'c_Suc'( 'c_Suc'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.17/1.59 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'( 'c_Suc'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ), ~(
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.17/1.59 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 'tc_nat' ), Y ), X ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.17/1.59 ) ), X, 'tc_nat' ) ) ],
% 1.17/1.59 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 'tc_nat' ), X ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.17/1.59 ) ), X, 'tc_nat' ) ) ],
% 1.17/1.59 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.59 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.17/1.59 Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.17/1.59 ) ), Y, 'tc_nat' ) ) ],
% 1.17/1.59 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 'c_Suc'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.17/1.59 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 'c_Suc'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), ~(
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.17/1.59 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( X ), 'c_Suc'( 'c_Suc'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), 'c_Suc'(
% 1.17/1.59 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'( 'c_Suc'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ),
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.17/1.59 [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.17/1.59 'tc_nat' ) ) ],
% 1.17/1.59 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.17/1.59 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( 'c_Suc'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ), 'tc_nat' ) ],
% 1.17/1.59 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( 'c_Suc'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ) ), 'tc_nat' ) ) ],
% 1.17/1.59 [ 'c_lessequals'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint'
% 1.17/1.59 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.17/1.59 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.17/1.59 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.17/1.59 [ 'c_lessequals'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint'
% 1.17/1.59 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.17/1.59 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.17/1.59 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.17/1.59 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.17/1.59 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y
% 1.17/1.59 , 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.17/1.59 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.17/1.59 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) )
% 1.17/1.59 , 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.17/1.59 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 1.17/1.59 , 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.17/1.59 T, X, U, W, Z, V0 ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.17/1.59 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.17/1.59 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.17/1.59 , hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), hAPP( hAPP( X, T ), U ) ) ) ),
% 1.17/1.59 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.17/1.59 , hAPP( hAPP( X, T ), hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), U ) ) ),
% 1.17/1.59 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.17/1.59 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.17/1.59 , V0, V1, V2 ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.17/1.59 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.17/1.59 W, V0, V1, V2 ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.17/1.59 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.17/1.59 , V0, V1, V2 ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.17/1.59 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.17/1.59 W, V0, V1, V2 ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.17/1.59 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.17/1.59 ~( 'c_Groebner__Basis_Ogb__semiring'( X, W, V0, V1, V2, V3 ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.17/1.59 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.17/1.59 W, V0, V1, V2 ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.17/1.59 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.17/1.59 W, V0, V1, V2 ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.17/1.59 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.17/1.59 , V0, V1, V2 ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.17/1.59 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.17/1.59 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.17/1.59 , V0, V1, V2 ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.17/1.59 X, T, U, Y, W, V0 ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.17/1.59 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.17/1.59 , V0, V1, V2 ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.17/1.59 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.17/1.59 T, X, U, Y, W, V0 ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.17/1.59 T, X, U, W, Y, V0 ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.17/1.59 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.17/1.59 , V0, V1, V2 ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.17/1.59 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 1.17/1.59 hAPP( X, Y ), T ) ), hAPP( hAPP( X, Y ), U ) ) ), ~(
% 1.17/1.59 'c_Groebner__Basis_Ogb__semiring'( Z, X, W, V0, V1, V2 ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.17/1.59 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.17/1.59 'c_Groebner__Basis_Ogb__semiring'( W, Y, X, V0, V1, V2 ) ) ],
% 1.17/1.59 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.17/1.59 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.17/1.59 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.17/1.59 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.17/1.59 , T, X ), X ), T, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.17/1.59 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.17/1.59 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.17/1.59 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.59 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.17/1.59 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 1.17/1.59 ) ],
% 1.17/1.59 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.17/1.59 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.17/1.59 ) ],
% 1.17/1.59 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.17/1.59 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.17/1.59 ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.17/1.59 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 1.17/1.59 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 1.17/1.59 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.17/1.59 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.17/1.59 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.59 , Y ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.17/1.59 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.17/1.59 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.17/1.59 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.17/1.59 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.17/1.59 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.17/1.59 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.17/1.59 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.17/1.59 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.17/1.59 ) ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.17/1.59 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X
% 1.17/1.59 ) ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ) ) ), =( Z,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.59 ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.17/1.59 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), =( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.17/1.59 Z, 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.17/1.59 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, T, X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.59 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.17/1.59 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ),
% 1.17/1.59 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ) ],
% 1.17/1.59 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.17/1.59 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.17/1.59 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.59 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.59 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.17/1.59 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.17/1.59 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.59 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.17/1.59 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.17/1.59 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.17/1.59 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.17/1.59 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T
% 1.17/1.59 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.17/1.59 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.59 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.17/1.59 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oinverse__class_Odivide'(
% 1.17/1.59 Y, 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.17/1.59 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.59 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), =( Y
% 1.17/1.59 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.17/1.59 , X ) ) ],
% 1.17/1.59 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.17/1.59 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.17/1.59 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.17/1.59 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 1.17/1.59 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.17/1.59 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.17/1.59 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 1.17/1.59 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.17/1.59 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 1.17/1.59 [ =( 'c_Suc'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.17/1.59 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ),
% 1.17/1.59 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'( 'c_Suc'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ), X ),
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.17/1.59 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.17/1.59 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X
% 1.17/1.59 , 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ), Y ) ) ), =( X,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.17/1.59 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.17/1.59 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.17/1.59 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.17/1.59 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.17/1.59 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.17/1.59 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.17/1.59 , X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.17/1.59 , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( hBOOL( hAPP( X, 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), Y, 'tc_nat' ) ) ) ),
% 1.17/1.59 hBOOL( hAPP( X, Z ) ) ],
% 1.17/1.59 [ ~( hBOOL( hAPP( X, 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), Y, 'tc_nat' ) ) ) ),
% 1.17/1.59 hBOOL( hAPP( X, Z ) ) ],
% 1.17/1.59 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( X ), Y, 'tc_nat' ), hAPP(
% 1.17/1.59 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 1.17/1.59 Y, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( 'c_Suc'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ),
% 1.17/1.59 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.59 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ),
% 1.17/1.59 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.59 'tc_nat' ) ), Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.17/1.59 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.17/1.59 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.17/1.59 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.17/1.59 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_RealVector_Oreal__field'( X ) ), =(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), W, X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 X ), Y ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'(
% 1.17/1.59 Z, U, X ), W, X ) ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, T, X )
% 1.17/1.59 , W, X ) ), U ) ) ) ],
% 1.17/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.59 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.17/1.59 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.17/1.59 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.17/1.59 'c_HOL_Ominus__class_Ominus'( Y, Z, X ) ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ) ),
% 1.17/1.59 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.59 ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.17/1.59 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.59 , Z ), T ), X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ), X ),
% 1.17/1.59 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.17/1.59 'tc_nat' ) ) ],
% 1.17/1.59 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ), Y ),
% 1.17/1.59 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.17/1.59 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.17/1.59 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 X ), 'c_HOL_Ominus__class_Ominus'( Y, U, X ) ), Z ) ), T ) ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.17/1.59 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.17/1.59 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.17/1.59 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 1.17/1.59 X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.17/1.59 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( hAPP(
% 1.17/1.59 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( Y, U, X
% 1.17/1.59 ) ), Z ) ), T ), W ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.17/1.59 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( T, hAPP(
% 1.17/1.59 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ominus__class_Ominus'( U, Y, X
% 1.17/1.59 ) ), Z ) ), W ) ) ],
% 1.17/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.59 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.17/1.59 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.17/1.59 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ), T ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ],
% 1.17/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.59 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.17/1.59 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ), 'c_Divides_Odiv__class_Omod'(
% 1.17/1.59 Z, Y, X ) ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.17/1.59 ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.17/1.59 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.17/1.59 'c_Groebner__Basis_Ogb__semiring'( U, W, X, V0, V1, V2 ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.17/1.59 ), X ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T,
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), Y, X ) ) ],
% 1.17/1.59 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat'
% 1.17/1.59 ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'( Y
% 1.17/1.59 ) ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y
% 1.17/1.59 ) ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 1.17/1.59 , Y ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.17/1.59 Y ) ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 1.17/1.59 , Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'(
% 1.17/1.59 Y ) ) ) ],
% 1.17/1.59 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 1.17/1.59 X ), Y, 'tc_nat' ), 'c_Suc'( Z ), 'tc_nat' ),
% 1.17/1.59 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.17/1.59 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.17/1.59 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.17/1.59 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ],
% 1.17/1.59 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.17/1.59 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( X
% 1.17/1.59 ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'(
% 1.17/1.59 X ) ), Z ) ) ), =( Y, Z ) ],
% 1.17/1.59 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 1.17/1.59 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, Y ), 'c_Suc'( Z ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.17/1.59 X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1
% 1.17/1.59 ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, Y ), 'c_Suc'( Z ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.17/1.59 X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1
% 1.17/1.59 ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ), hAPP( hAPP( Y, Z ),
% 1.17/1.59 'c_Suc'( T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Y, W, V0,
% 1.17/1.59 V1 ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ), hAPP( hAPP( Z, Y ),
% 1.17/1.59 'c_Suc'( T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Z, W, V0,
% 1.17/1.59 V1 ) ) ],
% 1.17/1.59 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.17/1.59 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.17/1.59 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.17/1.59 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 1.17/1.59 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =( 'c_Suc'(
% 1.17/1.59 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ],
% 1.17/1.59 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), =( 'c_Suc'( X
% 1.17/1.59 ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( X ), 'tc_nat' ) ) ],
% 1.17/1.59 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( X ), 'tc_nat' ),
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.17/1.59 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.17/1.59 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.17/1.59 [ 'c_lessequals'( 'c_Int_OPls', 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.17/1.59 [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint'
% 1.17/1.59 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.17/1.59 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.17/1.59 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint' ) ) ],
% 1.17/1.59 [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint'
% 1.17/1.59 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.17/1.59 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.17/1.59 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint' ) ) ],
% 1.17/1.59 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.17/1.59 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), Y,
% 1.17/1.59 'tc_nat' ) ) ],
% 1.17/1.59 [ =( 'c_List_Otake'( X, 'c_List_Olist_ONil'( Y ), Y ),
% 1.17/1.59 'c_List_Olist_ONil'( Y ) ) ],
% 1.17/1.59 [ =( 'c_List_Odrop'( X, 'c_List_Olist_ONil'( Y ), Y ),
% 1.17/1.59 'c_List_Olist_ONil'( Y ) ) ],
% 1.17/1.59 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.17/1.59 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( Y,
% 1.17/1.59 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), Y ),
% 1.17/1.59 ~( 'c_Groebner__Basis_Ogb__semiring'( Z, T, X, U, W, V0 ) ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.17/1.59 'tc_nat' ) ), Y ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.17/1.59 'tc_nat' ) ), Y ) ],
% 1.17/1.59 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oone__class_Oone'(
% 1.17/1.59 'tc_nat' ), 'tc_nat' ) ) ],
% 1.17/1.59 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.17/1.59 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.17/1.59 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ), X ) ],
% 1.17/1.59 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.17/1.59 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ],
% 1.17/1.59 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.17/1.59 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 1.17/1.59 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.17/1.59 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 1.17/1.59 'tc_nat' ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.17/1.59 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.17/1.59 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.17/1.59 [ =( 'c_List_Odrop'( X, 'c_List_Omap'( Y, Z, T, U ), U ), 'c_List_Omap'(
% 1.17/1.59 Y, 'c_List_Odrop'( X, Z, T ), T, U ) ) ],
% 1.17/1.59 [ =( 'c_List_Otake'( X, 'c_List_Omap'( Y, Z, T, U ), U ), 'c_List_Omap'(
% 1.17/1.59 Y, 'c_List_Otake'( X, Z, T ), T, U ) ) ],
% 1.17/1.59 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.17/1.59 X ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.17/1.59 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ) ), Z ), X ) )
% 1.17/1.59 ],
% 1.17/1.59 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.17/1.59 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.17/1.59 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.17/1.59 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.17/1.59 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ),
% 1.17/1.59 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ),
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Odiv'(
% 1.17/1.59 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.17/1.59 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.17/1.59 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.59 ), X ), ~( 'c_lessequals'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( Y, 'c_Int_OPls',
% 1.17/1.59 'tc_Int_Oint' ), ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.17/1.59 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.17/1.59 ), X ), ~( 'c_lessequals'( 'c_Int_OPls', Y, 'tc_Int_Oint' ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( 'c_Int_OPls', Y,
% 1.17/1.59 'tc_Int_Oint' ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.17/1.59 ), Y ), 'c_Suc'( Z ) ), 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.59 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ) ) ],
% 1.17/1.59 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ), 'c_Int_Onat'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_Int_Oint' ) ) ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), Y ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oone__class_Oone'(
% 1.17/1.59 'tc_nat' ), 'tc_nat' ) ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.17/1.59 [ =( X, 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.17/1.59 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.17/1.59 'tc_nat' ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.17/1.59 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.17/1.59 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.17/1.59 'tc_nat' ) ), Y ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ =( 'c_List_Otake'( X, 'c_List_Olist_OCons'( Y, Z, T ), T ),
% 1.17/1.59 'c_List_Olist_OCons'( Y, 'c_List_Otake'( 'c_HOL_Ominus__class_Ominus'( X
% 1.17/1.59 , 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Z, T ), T ) ), =( X,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.59 [ =( 'c_List_Onth'( 'c_List_Olist_OCons'( X, Y, Z ), T, Z ),
% 1.17/1.59 'c_List_Onth'( Y, 'c_HOL_Ominus__class_Ominus'( T,
% 1.17/1.59 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Z ) ), =( T,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.59 [ =( 'c_List_Odrop'( X, 'c_List_Olist_OCons'( Y, Z, T ), T ),
% 1.17/1.59 'c_List_Odrop'( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oone__class_Oone'(
% 1.17/1.59 'tc_nat' ), 'tc_nat' ), Z, T ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.59 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.17/1.59 ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.17/1.59 ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), X ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.17/1.59 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.17/1.59 ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.59 X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.59 X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.59 X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.17/1.59 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.17/1.59 ],
% 1.17/1.59 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.17/1.59 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.17/1.59 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ) ), Z ) ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.17/1.59 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.17/1.59 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.17/1.59 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.17/1.59 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.17/1.59 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.17/1.59 , ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.17/1.59 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( Y
% 1.17/1.59 , X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), ~( =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.17/1.59 Z, X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.17/1.59 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.17/1.59 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.17/1.59 X ), 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.59 , X ) ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.17/1.59 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.17/1.59 ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.17/1.59 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.59 X ), 'c_HOL_Oinverse__class_Odivide'( Z,
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.59 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.17/1.59 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.59 X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.59 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.59 'c_Divides_Odiv__class_Odiv'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.17/1.59 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.17/1.59 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 1.17/1.59 , Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.17/1.59 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.17/1.59 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.17/1.59 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.17/1.59 ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.59 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.17/1.59 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.59 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.59 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.17/1.59 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.17/1.59 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.59 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.17/1.59 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.17/1.59 X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X )
% 1.17/1.59 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.17/1.59 ), ~( 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 1.17/1.59 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.17/1.59 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.17/1.59 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.17/1.59 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ) ), Y ),
% 1.17/1.59 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.59 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.59 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.17/1.59 , X ), X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.17/1.59 , X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.17/1.59 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.17/1.59 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), X, 'tc_nat' ),
% 1.17/1.59 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.59 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.59 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.17/1.59 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.17/1.59 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 X, T, 'tc_nat' ) ],
% 1.17/1.59 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 1.17/1.59 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.59 ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.59 ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( Z,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.59 ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.59 ), X ) ) ],
% 1.17/1.59 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.17/1.59 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.17/1.59 ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.17/1.59 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.59 Z, X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.17/1.59 'c_lessequals'( Z, Y, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.17/1.59 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.59 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.17/1.59 'c_lessequals'( Z, Y, X ) ) ],
% 1.17/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.59 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.17/1.59 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.59 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.59 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.17/1.59 ) ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, Z ), U ) )
% 1.17/1.59 , hAPP( hAPP( Y, Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.17/1.59 , T ), U ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, Y, V0, V1, V2
% 1.17/1.59 ) ) ],
% 1.17/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.59 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.59 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.17/1.59 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ),
% 1.17/1.59 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ) ), =( T,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.59 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.59 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.17/1.59 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ),
% 1.17/1.59 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ) ), =( Z,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.59 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.17/1.59 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.59 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.17/1.59 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.17/1.59 X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.17/1.59 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.17/1.59 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.17/1.59 , ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.59 ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z
% 1.17/1.59 , 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.17/1.59 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.59 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.17/1.59 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.59 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.17/1.59 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.59 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.17/1.59 , ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 X ), Y ), T ), Z, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.17/1.59 X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.59 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.17/1.59 Y ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.17/1.59 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.17/1.59 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.17/1.59 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.59 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.17/1.59 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.17/1.59 'c_HOL_Ominus__class_Ominus'( Y, Z, X ) ), T ) ), U ), W, X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.17/1.59 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), U ), hAPP(
% 1.17/1.59 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), W ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.17/1.59 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP(
% 1.17/1.59 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.17/1.59 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.17/1.59 'c_HOL_Ominus__class_Ominus'( Y, U, X ) ), Z ) ), T ), W, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.59 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.17/1.59 'c_HOL_Ominus__class_Ominus'( Z, T, X ) ), U ) ), W ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.17/1.59 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), Y ), hAPP(
% 1.17/1.59 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ), W ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.17/1.59 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP(
% 1.17/1.59 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.59 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.17/1.59 'c_HOL_Ominus__class_Ominus'( U, Y, X ) ), Z ) ), W ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( hAPP(
% 1.17/1.59 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.59 ), Y ), Y, X ) ) ],
% 1.17/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.17/1.59 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.17/1.59 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.17/1.59 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.17/1.59 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.59 , U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), W ), T ), Z, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.17/1.59 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.59 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.17/1.59 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, T ) ) ],
% 1.17/1.59 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ) ), Y, 'tc_nat'
% 1.17/1.59 ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'( Z ), Y, 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.17/1.59 , Z ) ],
% 1.17/1.59 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.17/1.59 , Z ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.17/1.59 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.17/1.59 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.17/1.59 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.17/1.59 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.17/1.59 'c_HOL_Oinverse__class_Oinverse'( hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.17/1.59 , X ) ), Z ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.17/1.59 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.59 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.17/1.59 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.17/1.59 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.17/1.59 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.17/1.59 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.17/1.59 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.59 ), U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), W ), T ), Z, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.59 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.59 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.17/1.59 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.17/1.59 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_lessequals'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.17/1.59 ) ), 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.59 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ) ), hAPP(
% 1.17/1.59 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ), X ) ), =( U,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.59 ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.17/1.59 , X ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z
% 1.17/1.59 , X ) ), Z ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.17/1.59 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ) ), Y ),
% 1.17/1.59 'c_HOL_Ominus__class_Ominus'( X, 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.17/1.59 'tc_nat' ), 'tc_nat' ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.17/1.59 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ),
% 1.17/1.59 'c_HOL_Ominus__class_Ominus'( Y, 'c_Divides_Odiv__class_Omod'( Y, X,
% 1.17/1.59 'tc_nat' ), 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 X ), Y ), Z ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.17/1.59 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.17/1.59 ) ), Z ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.59 X ), Z ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.17/1.59 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ],
% 1.17/1.59 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.17/1.59 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 1.17/1.59 ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.17/1.59 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.17/1.59 X ) ) ],
% 1.17/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 1.17/1.59 , X ) ) ],
% 1.17/1.59 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.17/1.59 , Y, X ) ) ],
% 1.17/1.59 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.17/1.59 , Y, X ) ) ],
% 1.17/1.59 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.17/1.59 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.17/1.59 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.17/1.59 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.17/1.59 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.17/1.59 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.17/1.59 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 1.17/1.59 X ), Z, X ) ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.17/1.59 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.17/1.59 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.59 , X ) ) ],
% 1.17/1.59 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.59 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.17/1.59 , Z ), T ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) )
% 1.17/1.59 , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.17/1.59 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.17/1.59 T, X ) ) ],
% 1.17/1.59 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.17/1.59 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.17/1.59 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.17/1.59 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.17/1.59 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.17/1.59 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.17/1.59 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.17/1.59 , X ) ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.17/1.59 , X ) ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.59 , X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'( Z,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.59 X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.17/1.59 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.17/1.59 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.17/1.59 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.59 ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.17/1.59 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.17/1.59 'c_Suc'( Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.17/1.59 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.59 ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.59 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.59 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.17/1.59 ) ), ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'(
% 1.17/1.59 'c_Int_OBit1'( Y ), X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Int_Onumber__ring'( X ) ), 'c_Int_Oiszero'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), X ) ],
% 1.17/1.59 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.17/1.59 'c_Int_OPls', X ) ), Y ), Y ) ],
% 1.17/1.59 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Int_Onumber__class_Onumber__of'(
% 1.17/1.59 'c_Int_OPls', X ) ), Y ) ],
% 1.17/1.59 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.17/1.59 ) ), 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.17/1.59 ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y
% 1.17/1.59 ), X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.17/1.59 ) ), 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.17/1.59 Y ), X ), X ), ~( 'c_Int_Oiszero'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.17/1.59 , X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.17/1.59 , X ), ~( 'c_lessequals'( Y, 'c_Int_OBit1'( 'c_Int_OPls' ), 'tc_Int_Oint'
% 1.17/1.59 ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( Y, 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ), 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.17/1.59 , X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.17/1.59 , X ), ~( 'c_lessequals'( 'c_Int_OBit1'( 'c_Int_OPls' ), Y, 'tc_Int_Oint'
% 1.17/1.59 ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ), Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.17/1.59 , X ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.17/1.59 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.59 'tc_nat' ) ) ) ],
% 1.17/1.59 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.17/1.59 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.17/1.59 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.59 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.59 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 1.17/1.59 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.59 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.17/1.59 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.59 [ =( 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ) ],
% 1.17/1.59 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.17/1.59 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.17/1.59 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.17/1.59 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.17/1.59 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.17/1.59 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.17/1.59 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.59 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.17/1.59 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.59 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.17/1.59 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.17/1.59 , 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat'
% 1.17/1.59 ) ) ],
% 1.17/1.59 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.59 'c_Suc'( X ), 'tc_nat' ) ],
% 1.17/1.59 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.59 'c_Suc'( X ), 'tc_nat' ) ],
% 1.17/1.59 [ ~( =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) )
% 1.17/1.59 , =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.17/1.59 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.17/1.59 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.17/1.59 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.17/1.59 ), Y ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.59 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.59 X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.17/1.59 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ],
% 1.17/1.59 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y )
% 1.17/1.59 , Y ) ) ],
% 1.17/1.59 [ =( 'c_List_Odrop'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.59 'c_List_Olist_OCons'( X, Y, Z ), Z ), 'c_List_Olist_OCons'( X, Y, Z ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ =( 'c_List_Onth'( 'c_List_Olist_OCons'( X, Y, Z ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z ), X ) ],
% 1.17/1.59 [ 'c_lessequals'( 'c_Int_OPls', 'c_Int_OBit1'( X ), 'tc_Int_Oint' ), ~(
% 1.17/1.59 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ) ) ],
% 1.17/1.59 [ 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.17/1.59 'c_Int_OPls', 'c_Int_OBit1'( X ), 'tc_Int_Oint' ) ) ],
% 1.17/1.59 [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint'
% 1.17/1.59 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.17/1.59 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.17/1.59 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.17/1.59 [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint'
% 1.17/1.59 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.17/1.59 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.17/1.59 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.17/1.59 [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OPls', 'tc_Int_Oint' ), ~(
% 1.17/1.59 'c_lessequals'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.17/1.59 [ 'c_lessequals'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.17/1.59 'c_Int_OBit0'( X ), 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.17/1.59 [ 'c_lessequals'( 'c_Int_OPls', 'c_Int_OBit0'( X ), 'tc_Int_Oint' ), ~(
% 1.17/1.59 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ) ) ],
% 1.17/1.59 [ 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.17/1.59 'c_Int_OPls', 'c_Int_OBit0'( X ), 'tc_Int_Oint' ) ) ],
% 1.17/1.59 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.17/1.59 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( Y,
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.17/1.59 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ), Y, 'tc_nat'
% 1.17/1.59 ) ) ],
% 1.17/1.59 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ),
% 1.17/1.59 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.59 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.17/1.59 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ),
% 1.17/1.59 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.59 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.17/1.59 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'( 'c_Suc'( 'c_Suc'( Y ) ) )
% 1.17/1.59 , 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 1.17/1.59 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ), Y
% 1.17/1.59 , 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 1.17/1.59 [ =( 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'( 'c_Suc'( 'c_Suc'( Y ) ) )
% 1.17/1.59 , 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 1.17/1.59 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ), Y
% 1.17/1.59 , 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.17/1.59 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP( T, hAPP(
% 1.17/1.59 hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ), ~(
% 1.17/1.59 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.17/1.59 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ), 'c_Int_Onat'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_Int_Oint' ) ) ) ],
% 1.17/1.59 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 X ), Y ), Y ) ) ],
% 1.17/1.59 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'tc_nat' ) ],
% 1.17/1.59 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.17/1.59 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.17/1.59 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ),
% 1.17/1.59 ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.59 'tc_nat' ), X ), X ) ) ],
% 1.17/1.59 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ) ) ],
% 1.17/1.59 [ =( 'c_List_Otake'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, Y ),
% 1.17/1.59 'c_List_Olist_ONil'( Y ) ) ],
% 1.17/1.59 [ ~( =( 'c_List_Otake'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ), =( Y,
% 1.17/1.59 'c_List_Olist_ONil'( Z ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.17/1.59 ) ],
% 1.17/1.59 [ =( 'c_List_Odrop'( 'c_Suc'( X ), 'c_List_Olist_OCons'( Y, Z, T ), T )
% 1.17/1.59 , 'c_List_Odrop'( X, Z, T ) ) ],
% 1.17/1.59 [ =( 'c_List_Onth'( 'c_List_Olist_OCons'( X, Y, Z ), 'c_Suc'( T ), Z ),
% 1.17/1.59 'c_List_Onth'( Y, T, Z ) ) ],
% 1.17/1.59 [ =( 'c_List_Otake'( 'c_Suc'( X ), 'c_List_Olist_OCons'( Y, Z, T ), T )
% 1.17/1.59 , 'c_List_Olist_OCons'( Y, 'c_List_Otake'( X, Z, T ), T ) ) ],
% 1.17/1.59 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.59 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.59 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.17/1.59 'tc_nat' ) ) ],
% 1.17/1.59 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.17/1.59 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.17/1.59 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 1.17/1.59 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.17/1.59 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.17/1.59 ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.17/1.59 [ =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'c_Suc'(
% 1.17/1.59 'c_HOL_Ominus__class_Ominus'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.17/1.59 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.17/1.59 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Int_Onumber__class_Onumber__of'( X
% 1.17/1.59 , 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 1.17/1.59 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.17/1.59 [ =( 'c_List_Otake'( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.17/1.59 'c_List_Olist_OCons'( Y, Z, T ), T ), 'c_List_Olist_OCons'( Y,
% 1.17/1.59 'c_List_Otake'( 'c_HOL_Ominus__class_Ominus'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.17/1.59 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Z, T ), T ) ), =(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.59 [ =( 'c_List_Odrop'( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.17/1.59 'c_List_Olist_OCons'( Y, Z, T ), T ), 'c_List_Odrop'(
% 1.17/1.59 'c_HOL_Ominus__class_Ominus'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.17/1.59 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Z, T ) ),
% 1.17/1.59 =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.59 [ =( 'c_List_Onth'( 'c_List_Olist_OCons'( X, Y, Z ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( T, 'tc_nat' ), Z ), 'c_List_Onth'( Y
% 1.17/1.59 , 'c_HOL_Ominus__class_Ominus'( 'c_Int_Onumber__class_Onumber__of'( T,
% 1.17/1.59 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Z ) ), =(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( T, 'tc_nat' ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( =( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.17/1.59 ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.17/1.59 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.17/1.59 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 1.17/1.59 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.17/1.59 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.17/1.59 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ),
% 1.17/1.59 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.17/1.59 [ =( 'c_Suc'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.17/1.59 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ) ],
% 1.17/1.59 [ =( 'c_Suc'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.17/1.59 ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.17/1.59 [ =( 'c_List_Odrop'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.17/1.59 'c_List_Olist_OCons'( X, Y, Z ), Z ), Y ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), X ), X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), X ), X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.17/1.59 ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.17/1.59 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.17/1.59 ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.17/1.59 =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.17/1.59 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.59 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.17/1.59 [ =( 'c_Int_Onat'( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_Int_Oint'
% 1.17/1.59 ) ), 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ) ],
% 1.17/1.59 [ =( 'c_List_Odrop'( X, 'c_List_Odrop'( Y, Z, T ), T ), 'c_List_Odrop'(
% 1.17/1.59 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, T ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.17/1.59 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), U ) ) ) ), =(
% 1.17/1.59 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.17/1.59 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.59 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.17/1.59 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.59 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.17/1.59 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.17/1.59 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.17/1.59 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.17/1.59 ,
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Z
% 1.17/1.59 , T ) ],
% 1.17/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.17/1.59 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.17/1.59 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.17/1.59 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.17/1.59 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.17/1.59 , 'tc_nat' ), 'tc_nat' ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ), 'c_Suc'( Z ) ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oinverse__class_Oinverse'(
% 1.17/1.59 Z, X ) ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.17/1.59 Z, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.17/1.59 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.17/1.59 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.17/1.59 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.17/1.59 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.17/1.59 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.17/1.59 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X )
% 1.17/1.59 ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.59 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.17/1.59 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.17/1.59 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.17/1.59 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~(
% 1.17/1.59 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.59 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.59 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.17/1.59 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.59 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.59 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.17/1.59 ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.59 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.59 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.17/1.59 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.59 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.17/1.59 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.17/1.59 ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.17/1.59 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.17/1.59 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.59 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.59 'tc_nat' ), X ), Y ), X, 'tc_nat' ) ) ],
% 1.17/1.59 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.17/1.59 Z, X ) ), T ), 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.17/1.59 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ), =( Z,
% 1.17/1.59 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.59 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP(
% 1.17/1.59 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ),
% 1.17/1.59 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.17/1.59 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.17/1.59 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.17/1.59 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.17/1.59 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.17/1.59 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.60 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.17/1.60 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.17/1.60 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~(
% 1.17/1.60 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.17/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.17/1.60 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ]
% 1.17/1.60 ,
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.17/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.17/1.60 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.17/1.60 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.17/1.60 Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.17/1.60 X ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.17/1.60 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.17/1.60 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.17/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~(
% 1.17/1.60 'c_lessequals'( Z, 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ]
% 1.17/1.60 ,
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.17/1.60 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.17/1.60 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.17/1.60 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.17/1.60 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.17/1.60 , X ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.17/1.60 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.17/1.60 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.17/1.60 , X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.60 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.17/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.17/1.60 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.17/1.60 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.17/1.60 ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.60 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.17/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.17/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.60 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.17/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.60 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.60 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.60 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.17/1.60 , Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.17/1.60 ],
% 1.17/1.60 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.17/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.60 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.17/1.60 , Z ), Y ), 'tc_nat' ) ) ],
% 1.17/1.60 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.60 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.17/1.60 , X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) )
% 1.17/1.60 ],
% 1.17/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.17/1.60 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.60 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.17/1.60 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.17/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.17/1.60 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.60 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ),
% 1.17/1.60 ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.17/1.60 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.17/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.17/1.60 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.17/1.60 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.17/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.17/1.60 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.60 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.17/1.60 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.17/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.17/1.60 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.17/1.60 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ),
% 1.17/1.60 ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.17/1.60 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.17/1.60 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.17/1.60 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.17/1.60 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.17/1.60 [ ~( =( 'c_List_Odrop'( X, Y, Z ), 'c_List_Olist_OCons'( T, U, Z ) ) ),
% 1.17/1.60 =( 'c_List_Onth'( Y, X, Z ), T ) ],
% 1.17/1.60 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 1.17/1.60 ,
% 1.17/1.60 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 1.17/1.60 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'( Z, Y,
% 1.17/1.60 'tc_Int_Oint' ) ), ~( 'c_lessequals'( X, Z, 'tc_Int_Oint' ) ) ],
% 1.17/1.60 [ 'c_lessequals'( X, X, 'tc_Int_Oint' ) ],
% 1.17/1.60 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.17/1.60 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 1.17/1.60 , X ) ) ],
% 1.17/1.60 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.17/1.60 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.17/1.60 , X ) ) ],
% 1.17/1.60 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.17/1.60 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.17/1.60 , X ), ~( 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.17/1.60 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ), X ) ) ],
% 1.17/1.60 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.17/1.60 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.17/1.60 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.17/1.60 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.17/1.60 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.17/1.60 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 1.17/1.60 ) ) ],
% 1.17/1.60 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.17/1.60 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 1.17/1.60 ) ) ],
% 1.17/1.60 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.17/1.60 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.17/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.17/1.60 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.60 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.17/1.60 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.17/1.60 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.17/1.60 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.17/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.17/1.60 [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~(
% 1.17/1.60 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~( hBOOL( hAPP( X,
% 1.17/1.60 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ) ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.17/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.17/1.60 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.60 , X ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.60 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.17/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.17/1.60 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.60 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.17/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.17/1.60 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.17/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ),
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.60 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.60 ), Y ), Z ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.60 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.60 ), Y ), Z ), Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.17/1.60 'c_HOL_Oinverse__class_Odivide'( Y, 'c_Int_Onumber__class_Onumber__of'( Z
% 1.17/1.60 , X ), X ), T, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.17/1.60 , X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.60 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.17/1.60 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.60 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y,
% 1.17/1.60 'c_HOL_Oinverse__class_Odivide'( Z, 'c_Int_Onumber__class_Onumber__of'( T
% 1.17/1.60 , X ), X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.17/1.60 ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.17/1.60 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.17/1.60 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.17/1.60 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.17/1.60 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), hAPP( hAPP(
% 1.17/1.60 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.17/1.60 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.17/1.60 ) ), 'c_HOL_Ominus__class_Ominus'( Z, Y, X ) ) ),
% 1.17/1.60 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Z,
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.60 ) ],
% 1.17/1.60 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.17/1.60 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.17/1.60 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), ~(
% 1.17/1.60 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( Y, X,
% 1.17/1.60 'tc_nat' ), 'tc_nat' ) ) ],
% 1.17/1.60 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.17/1.60 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.17/1.60 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.17/1.60 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.17/1.60 'tc_nat' ), 'tc_nat' ) ) ],
% 1.17/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.17/1.60 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X )
% 1.17/1.60 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.17/1.60 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ), Y ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( hAPP(
% 1.17/1.60 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.17/1.60 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.17/1.60 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.17/1.60 ,
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.17/1.60 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.60 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.17/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.17/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.17/1.60 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.17/1.60 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.17/1.60 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.60 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.17/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.17/1.60 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.17/1.60 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.17/1.60 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), hAPP( hAPP(
% 1.17/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.17/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.60 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), =( Y,
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.17/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.17/1.60 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.17/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.17/1.60 'tc_nat' ) ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.17/1.60 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'(
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.60 'c_Power_Opower__class_Opower'( X ), Z ), Y ), X ) ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.60 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.17/1.60 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.60 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ),
% 1.17/1.60 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.60 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.17/1.60 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.17/1.60 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), ~( 'c_lessequals'(
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.60 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ) ],
% 1.17/1.60 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.17/1.60 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ) ), Y ),
% 1.17/1.60 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.17/1.60 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.17/1.60 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ) ), =( U,
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.60 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ), hAPP(
% 1.17/1.60 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.17/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.17/1.60 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), =( Z,
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ) ), =( U, 'c_HOL_Ozero__class_Ozero'( X )
% 1.17/1.60 ), =( 'c_HOL_Oinverse__class_Odivide'( Y, U, X ),
% 1.17/1.60 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ],
% 1.17/1.60 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.17/1.60 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.17/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.17/1.60 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.17/1.60 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ) ) ],
% 1.17/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.60 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.60 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.17/1.60 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.17/1.60 'c_Divides_Odiv__class_Omod'( Z, T, X ) ) ) ],
% 1.17/1.60 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.17/1.60 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.17/1.60 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.17/1.60 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.17/1.60 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), Z ) ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.17/1.60 'c_HOL_Oinverse__class_Odivide'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.60 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), Y, X ),
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.60 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.17/1.60 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.17/1.60 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.17/1.60 'c_lessequals'( Z, Y, X ) ],
% 1.17/1.60 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), 'c_lessequals'( Y, X,
% 1.17/1.60 'tc_Int_Oint' ) ],
% 1.17/1.60 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.17/1.60 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.17/1.60 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.17/1.60 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.17/1.60 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.17/1.60 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.17/1.60 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.60 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.17/1.60 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.60 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), =( Y, Z ), ~( 'c_lessequals'(
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.17/1.60 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.17/1.60 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.60 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.60 ) ) ],
% 1.17/1.60 [ =( 'c_Int_Onat'( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.17/1.60 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_Int_Oint' ) ), 'c_Suc'( 'c_Suc'(
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.17/1.60 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), ~( 'class_Int_Onumber'(
% 1.17/1.60 X ) ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.60 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.17/1.60 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.17/1.60 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_Suc'( hAPP( hAPP(
% 1.17/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.60 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), 'tc_nat' ) ) ],
% 1.17/1.60 [ =( hAPP( hAPP( X, Y ), 'c_Suc'( hAPP( hAPP(
% 1.17/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.60 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.17/1.60 T, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ) ), ~(
% 1.17/1.60 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.17/1.60 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.17/1.60 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.17/1.60 ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.60 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ), X ),
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.60 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ), hAPP( hAPP(
% 1.17/1.60 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.60 X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.17/1.60 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.17/1.60 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.17/1.60 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.17/1.60 , 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ), =(
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.17/1.60 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.17/1.60 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'(
% 1.17/1.60 Y, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.17/1.60 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.17/1.60 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.17/1.60 ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =( hAPP( hAPP(
% 1.17/1.60 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.17/1.60 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.17/1.60 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.17/1.60 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.17/1.60 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ), X ), X ) ],
% 1.17/1.60 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( Y ), X ), hAPP( hAPP(
% 1.17/1.60 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.17/1.60 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.17/1.60 Y, X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.60 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Oinverse'(
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.17/1.60 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X
% 1.17/1.60 ) ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.60 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.17/1.60 ), Y ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.17/1.60 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.17/1.60 ), Y ) ],
% 1.17/1.60 [ ~( 'class_Int_Onumber__ring'( X ) ), ~( 'c_Int_Oiszero'(
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ), X
% 1.17/1.60 ) ) ],
% 1.17/1.60 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.17/1.60 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.17/1.60 'c_Int_OBit1'( 'c_Int_OPls' ), X ) ), Y ), Y ) ],
% 1.17/1.60 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.17/1.60 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ) )
% 1.17/1.60 , Y ) ],
% 1.17/1.60 [ ~( =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X,
% 1.17/1.60 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.17/1.60 [ =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 1.17/1.60 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.17/1.60 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ) ), 'c_lessequals'( X
% 1.17/1.60 , 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.17/1.60 [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 1.17/1.60 , 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.17/1.60 [ =( 'c_Suc'( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.17/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.60 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.17/1.60 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.17/1.60 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.60 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.60 'tc_nat' ) ) ],
% 1.17/1.60 [ =( 'c_Suc'( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.17/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.17/1.60 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ) ), X ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.60 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.17/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.17/1.60 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ) ), X ) ), =( X,
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.60 [ ~( =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( 'c_List_Onth'(
% 1.17/1.60 'c_List_Olist_OCons'( Y, Z, T ), 'c_Int_Onumber__class_Onumber__of'( X,
% 1.17/1.60 'tc_nat' ), T ), Y ) ],
% 1.17/1.60 [ ~( =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( 'c_List_Odrop'(
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'c_List_Olist_OCons'(
% 1.17/1.60 Y, Z, T ), T ), 'c_List_Olist_OCons'( Y, Z, T ) ) ],
% 1.17/1.60 [ =( 'c_List_Otake'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.60 'c_List_Olist_OCons'( X, Y, Z ), Z ), 'c_List_Olist_ONil'( Z ) ) ],
% 1.17/1.60 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.17/1.60 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.17/1.60 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.60 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.17/1.60 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.60 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.17/1.60 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.60 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.60 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ],
% 1.17/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.60 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.17/1.60 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.17/1.60 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.17/1.60 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.17/1.60 [ =( 'c_List_Otake'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.17/1.60 'c_List_Olist_OCons'( X, Y, Z ), Z ), 'c_List_Olist_OCons'( X,
% 1.17/1.60 'c_List_Olist_ONil'( Z ), Z ) ) ],
% 1.17/1.60 [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.17/1.60 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.60 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' )
% 1.17/1.60 , 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.60 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 1.17/1.60 'tc_nat' ) ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.17/1.60 'class_Power_Opower'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.17/1.60 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( hAPP( hAPP(
% 1.17/1.60 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.17/1.60 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.17/1.60 [ =( 'c_Suc'( 'c_Suc'( 'c_Suc'( X ) ) ), hAPP( hAPP(
% 1.17/1.60 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.17/1.60 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.17/1.60 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, Y ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.60 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( T
% 1.17/1.60 , X, Z, U, W, V0 ) ) ],
% 1.17/1.60 [ ~( =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( 'c_List_Otake'(
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'c_List_Olist_OCons'(
% 1.17/1.60 Y, Z, T ), T ), 'c_List_Olist_ONil'( T ) ) ],
% 1.17/1.60 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.17/1.60 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.17/1.60 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.17/1.60 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.17/1.60 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.60 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.60 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.60 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.17/1.60 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.60 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y
% 1.17/1.60 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.17/1.60 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.60 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.17/1.60 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.60 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ],
% 1.17/1.60 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_Suc'( 'c_Suc'( X ) ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.60 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 1.17/1.60 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.17/1.60 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.17/1.60 ) ],
% 1.17/1.60 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.60 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Suc'( 'c_Suc'( X ) ) ) ],
% 1.17/1.60 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.60 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_Suc'( 'c_Suc'( X ) ) ) ],
% 1.17/1.60 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Suc'( X ) ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.60 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X
% 1.17/1.60 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.60 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.17/1.60 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.17/1.60 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.17/1.60 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.17/1.60 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.17/1.60 [ =( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.17/1.60 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.60 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.17/1.60 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.17/1.60 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.17/1.60 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'(
% 1.17/1.60 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.17/1.60 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.17/1.60 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.17/1.60 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.17/1.60 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.17/1.60 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.17/1.60 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.17/1.60 ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), =(
% 1.17/1.60 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.17/1.60 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.17/1.60 ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.60 [ ~( =( 'c_List_Omap'( X, Y, Z, T ), 'c_List_Olist_ONil'( T ) ) ), =( Y
% 1.17/1.60 , 'c_List_Olist_ONil'( Z ) ) ],
% 1.17/1.60 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X
% 1.17/1.60 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ) ) ],
% 1.17/1.60 [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ) ) ],
% 1.17/1.60 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.60 'c_Int_OPls' ) ), 'tc_nat' ), 'c_Suc'( 'c_Suc'(
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.17/1.60 [ =( 'c_Int_OBit0'( 'c_Int_OPls' ), 'c_Int_OPls' ) ],
% 1.17/1.60 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.17/1.60 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.17/1.60 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.17/1.60 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.17/1.60 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ),
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.17/1.60 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ),
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.17/1.60 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_Suc'(
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.17/1.60 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.17/1.60 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.17/1.60 [ ~( =( 'c_Int_OPls', 'c_Int_OBit1'( X ) ) ) ],
% 1.17/1.60 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OPls' ) ) ],
% 1.17/1.60 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OPls' ) ), =( X, 'c_Int_OPls' ) ]
% 1.17/1.60 ,
% 1.17/1.60 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ) ) ), =( X, Y ) ],
% 1.17/1.60 [ =( 'c_List_Omap'( X, 'c_List_Olist_ONil'( Y ), Y, Z ),
% 1.17/1.60 'c_List_Olist_ONil'( Z ) ) ],
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.17/1.60 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ) ]
% 1.17/1.60 ,
% 1.17/1.60 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ) ]
% 1.17/1.60 ,
% 1.17/1.60 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.17/1.60 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.17/1.60 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ),
% 1.17/1.60 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.17/1.60 [ ~( =( X, 'c_List_Olist_OCons'( Y, X, Z ) ) ) ],
% 1.17/1.60 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), Y ) ) ],
% 1.17/1.60 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ) ) ) ],
% 1.17/1.60 [ =( 'c_Int_OPls', 'c_Int_OBit0'( 'c_Int_OPls' ) ) ],
% 1.17/1.60 [ =( 'c_List_Olist_ONil'( X ), 'c_List_Omap'( Y, 'c_List_Olist_ONil'( Z
% 1.17/1.60 ), Z, X ) ) ],
% 1.17/1.60 [ =( 'c_FFT__Mirabelle_OFFT'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 1.17/1.60 ), X ) ],
% 1.17/1.60 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oone__class_Oone'( X )
% 1.17/1.60 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X )
% 1.17/1.60 ) ],
% 1.17/1.60 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.17/1.60 'tc_nat' ) ) ],
% 1.17/1.60 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.17/1.60 'c_Int_OPls' ) ), 'tc_nat' ), 'c_Suc'( 'c_Suc'( 'c_Suc'(
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ],
% 1.17/1.60 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_OCons'( T, U, Z )
% 1.17/1.60 ) ), =( X, T ) ],
% 1.17/1.60 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_OCons'( T, U, Z )
% 1.17/1.60 ) ), =( Y, U ) ],
% 1.17/1.60 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 1.17/1.60 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 1.17/1.60 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Olist_OCons'( Y, Z, X ) ) ) ]
% 1.17/1.60 ,
% 1.17/1.60 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.17/1.60 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.17/1.60 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Omap'( Y, Z, T, X ) ) ), =( Z
% 1.17/1.60 , 'c_List_Olist_ONil'( T ) ) ],
% 1.17/1.60 [ ~( =( 'c_Int_OPls', 'c_Int_OBit0'( X ) ) ), =( 'c_Int_OPls', X ) ]
% 1.17/1.60 ,
% 1.17/1.60 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.17/1.60 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.17/1.60 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ) ) ), =( X, Y ) ],
% 1.17/1.60 [ =( 'c_Suc'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.60 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.17/1.60 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.17/1.60 ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =( Y, Z ) ],
% 1.17/1.60 [ =( 'c_List_Omap'( X, 'c_List_Olist_OCons'( Y, Z, T ), T, U ),
% 1.17/1.60 'c_List_Olist_OCons'( hAPP( X, Y ), 'c_List_Omap'( X, Z, T, U ), U ) ) ]
% 1.17/1.60 ,
% 1.17/1.60 [ =( 'c_List_Olist_OCons'( hAPP( X, Y ), 'c_List_Omap'( X, Z, T, U ), U
% 1.17/1.60 ), 'c_List_Omap'( X, 'c_List_Olist_OCons'( Y, Z, T ), T, U ) ) ],
% 1.17/1.60 [ =( 'c_List_Omap'( X, 'c_List_Olist_OCons'( Y, Z, T ), T, U ),
% 1.17/1.60 'c_List_Olist_OCons'( hAPP( X, Y ), 'c_List_Omap'( X, Z, T, U ), U ) ) ]
% 1.17/1.60 ,
% 1.17/1.60 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ) ) ) ],
% 1.17/1.60 [ ~( =( 'c_List_Omap'( 'c_FFT__Mirabelle_OFFT'( 'c_Suc'( 'c_Suc'(
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'v_a' ), 'c_List_Olist_OCons'(
% 1.17/1.60 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_List_Olist_OCons'(
% 1.17/1.60 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_List_Olist_OCons'(
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.17/1.60 'c_Int_OPls' ) ), 'tc_nat' ), 'c_List_Olist_OCons'(
% 1.17/1.60 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.17/1.60 'c_Int_OPls' ) ), 'tc_nat' ), 'c_List_Olist_ONil'( 'tc_nat' ), 'tc_nat' )
% 1.17/1.60 , 'tc_nat' ), 'tc_nat' ), 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex' ),
% 1.17/1.60 'v_x' ) ) ],
% 1.17/1.60 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 1.17/1.60 'class_Orderings_Opreorder'( Y ) ) ],
% 1.17/1.60 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 1.17/1.60 'class_Orderings_Oorder'( Y ) ) ],
% 1.17/1.60 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.21/1.60 ],
% 1.21/1.60 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.21/1.60 ) ],
% 1.21/1.60 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.21/1.60 ],
% 1.21/1.60 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 1.21/1.60 ,
% 1.21/1.60 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.21/1.60 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 1.21/1.60 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.21/1.60 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.21/1.60 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.21/1.60 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 1.21/1.60 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 1.21/1.60 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.21/1.60 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.21/1.60 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.21/1.60 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.21/1.60 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.21/1.60 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.21/1.60 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.21/1.60 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.21/1.60 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.21/1.60 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.21/1.60 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.21/1.60 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.21/1.60 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.21/1.60 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.21/1.60 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.21/1.60 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.21/1.60 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.21/1.60 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 1.21/1.60 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.21/1.60 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.21/1.60 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.21/1.60 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 1.21/1.60 [ 'class_Int_Onumber'( 'tc_nat' ) ],
% 1.21/1.60 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.21/1.60 'tc_Int_Oint' ) ],
% 1.21/1.60 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.21/1.60 'tc_Int_Oint' ) ],
% 1.21/1.60 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.21/1.60 'tc_Int_Oint' ) ],
% 1.21/1.60 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_Int_Oint' )
% 1.21/1.60 ],
% 1.21/1.60 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'( 'tc_Int_Oint' )
% 1.21/1.60 ],
% 1.21/1.60 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_Int_Oint' ) ]
% 1.21/1.60 ,
% 1.21/1.60 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.21/1.60 ,
% 1.21/1.60 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_Int_Oint' ) ]
% 1.21/1.60 ,
% 1.21/1.60 [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_Int_Oint' ) ]
% 1.21/1.60 ,
% 1.21/1.60 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.21/1.60 ,
% 1.21/1.60 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_Int_Oint' ) ]
% 1.21/1.60 ,
% 1.21/1.60 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.21/1.60 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.21/1.60 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.21/1.60 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_Int_Oint' ) ],
% 1.21/1.60 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_Int_Oint' ) ],
% 1.21/1.60 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Int_Oint' ) ],
% 1.21/1.60 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_Int_Oint' ) ],
% 1.21/1.60 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Int_Oint' ) ],
% 1.21/1.60 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Int_Oint' ) ],
% 1.21/1.60 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Int_Oint' ) ],
% 1.21/1.60 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.21/1.60 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_Int_Oint' ) ],
% 1.21/1.60 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Int_Oint' ) ],
% 1.21/1.60 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Int_Oint' ) ],
% 1.21/1.60 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Int_Oint' ) ],
% 1.21/1.60 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Int_Oint' ) ],
% 1.21/1.60 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Int_Oint' ) ],
% 1.21/1.60 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Int_Oint' ) ],
% 1.21/1.60 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_Int_Oint' ) ],
% 1.21/1.60 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Int_Oint' ) ],
% 1.21/1.60 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Int_Oint' ) ],
% 1.21/1.60 [ 'class_Ring__and__Field_Omult__mono'( 'tc_Int_Oint' ) ],
% 1.21/1.60 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Int_Oint' ) ],
% 1.21/1.60 [ 'class_Ring__and__Field_Osemiring'( 'tc_Int_Oint' ) ],
% 1.21/1.60 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Int_Oint' ) ],
% 1.21/1.60 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Int_Oint' ) ],
% 1.21/1.60 [ 'class_Divides_Osemiring__div'( 'tc_Int_Oint' ) ],
% 1.21/1.60 [ 'class_Ring__and__Field_Oring'( 'tc_Int_Oint' ) ],
% 1.21/1.60 [ 'class_Ring__and__Field_Oidom'( 'tc_Int_Oint' ) ],
% 1.21/1.60 [ 'class_Orderings_Opreorder'( 'tc_Int_Oint' ) ],
% 1.21/1.60 [ 'class_Orderings_Olinorder'( 'tc_Int_Oint' ) ],
% 1.21/1.60 [ 'class_Divides_Oring__div'( 'tc_Int_Oint' ) ],
% 1.21/1.60 [ 'class_Orderings_Oorder'( 'tc_Int_Oint' ) ],
% 1.21/1.60 [ 'class_Int_Oring__char__0'( 'tc_Int_Oint' ) ],
% 1.21/1.60 [ 'class_Int_Onumber__ring'( 'tc_Int_Oint' ) ],
% 1.21/1.60 [ 'class_Power_Opower'( 'tc_Int_Oint' ) ],
% 1.21/1.60 [ 'class_Int_Onumber'( 'tc_Int_Oint' ) ],
% 1.21/1.60 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 1.21/1.60 'tc_Complex_Ocomplex' ) ],
% 1.21/1.60 [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 1.21/1.60 'tc_Complex_Ocomplex' ) ],
% 1.21/1.60 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 1.21/1.60 'tc_Complex_Ocomplex' ) ],
% 1.21/1.60 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Complex_Ocomplex' )
% 1.21/1.60 ],
% 1.21/1.60 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Complex_Ocomplex' )
% 1.21/1.60 ],
% 1.21/1.60 [ 'class_Ring__and__Field_Odivision__by__zero'( 'tc_Complex_Ocomplex' )
% 1.21/1.60 ],
% 1.21/1.60 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.21/1.60 ,
% 1.21/1.60 [ 'class_RealVector_Oreal__normed__algebra'( 'tc_Complex_Ocomplex' ) ]
% 1.21/1.60 ,
% 1.21/1.60 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.21/1.60 ,
% 1.21/1.60 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.21/1.60 ,
% 1.21/1.60 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Complex_Ocomplex' ) ]
% 1.21/1.60 ,
% 1.21/1.60 [ 'class_Ring__and__Field_Odivision__ring'( 'tc_Complex_Ocomplex' ) ]
% 1.21/1.60 ,
% 1.21/1.60 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Complex_Ocomplex' ) ]
% 1.21/1.60 ,
% 1.21/1.60 [ 'class_RealVector_Oreal__normed__field'( 'tc_Complex_Ocomplex' ) ]
% 1.21/1.60 ,
% 1.21/1.60 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Complex_Ocomplex' ) ]
% 1.21/1.60 ,
% 1.21/1.60 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Complex_Ocomplex' ) ]
% 1.21/1.60 ,
% 1.21/1.60 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.21/1.60 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Complex_Ocomplex' ) ],
% 1.21/1.60 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Complex_Ocomplex' ) ],
% 1.21/1.60 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Complex_Ocomplex' ) ],
% 1.21/1.60 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Complex_Ocomplex' ) ],
% 1.21/1.60 [ 'class_Ring__and__Field_Osemiring'( 'tc_Complex_Ocomplex' ) ],
% 1.21/1.60 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Complex_Ocomplex' ) ],
% 1.21/1.60 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Complex_Ocomplex' ) ],
% 1.21/1.60 [ 'class_RealVector_Oreal__field'( 'tc_Complex_Ocomplex' ) ],
% 1.21/1.60 [ 'class_Ring__and__Field_Ofield'( 'tc_Complex_Ocomplex' ) ],
% 1.21/1.60 [ 'class_Ring__and__Field_Oring'( 'tc_Complex_Ocomplex' ) ],
% 1.21/1.60 [ 'class_Ring__and__Field_Oidom'( 'tc_Complex_Ocomplex' ) ],
% 1.21/1.60 [ 'class_Int_Oring__char__0'( 'tc_Complex_Ocomplex' ) ],
% 1.21/1.60 [ 'class_Int_Onumber__ring'( 'tc_Complex_Ocomplex' ) ],
% 1.21/1.60 [ 'class_Power_Opower'( 'tc_Complex_Ocomplex' ) ],
% 1.21/1.60 [ 'class_Int_Onumber'( 'tc_Complex_Ocomplex' ) ],
% 1.21/1.60 [ 'c_fequal'( X, X, Y ) ],
% 1.21/1.60 [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ]
% 1.21/1.60 ] .
% 1.21/1.60
% 1.21/1.60
% 1.21/1.60 percentage equality = 0.228368, percentage horn = 0.809283
% 1.21/1.60 This is a problem with some equality
% 1.21/1.60
% 1.21/1.60
% 1.21/1.60
% 1.21/1.60 Options Used:
% 1.21/1.60
% 1.21/1.60 useres = 1
% 1.21/1.60 useparamod = 1
% 1.21/1.60 useeqrefl = 1
% 1.21/1.60 useeqfact = 1
% 1.21/1.60 usefactor = 1
% 1.21/1.60 usesimpsplitting = 0
% 1.21/1.60 usesimpdemod = 5
% 1.21/1.60 usesimpres = 3
% 1.21/1.60
% 1.21/1.60 resimpinuse = 1000
% 1.21/1.60 resimpclauses = 20000
% 1.21/1.60 substype = eqrewr
% 1.21/1.60 backwardsubs = 1
% 1.21/1.60 selectoldest = 5
% 1.21/1.60
% 1.21/1.60 litorderings [0] = split
% 1.21/1.60 litorderings [1] = extend the termordering, first sorting on arguments
% 1.21/1.60
% 1.21/1.60 termordering = kbo
% 1.21/1.60
% 1.21/1.60 litapriori = 0
% 1.21/1.60 termapriori = 1
% 1.21/1.60 litaposteriori = 0
% 1.33/1.71 termaposteriori = 0
% 1.33/1.71 demodaposteriori = 0
% 1.33/1.71 ordereqreflfact = 0
% 1.33/1.71
% 1.33/1.71 litselect = negord
% 1.33/1.71
% 1.33/1.71 maxweight = 15
% 1.33/1.71 maxdepth = 30000
% 1.33/1.71 maxlength = 115
% 1.33/1.71 maxnrvars = 195
% 1.33/1.71 excuselevel = 1
% 1.33/1.71 increasemaxweight = 1
% 1.33/1.71
% 1.33/1.71 maxselected = 10000000
% 1.33/1.71 maxnrclauses = 10000000
% 1.33/1.71
% 1.33/1.71 showgenerated = 0
% 1.33/1.71 showkept = 0
% 1.33/1.71 showselected = 0
% 1.33/1.71 showdeleted = 0
% 1.33/1.71 showresimp = 1
% 1.33/1.71 showstatus = 2000
% 1.33/1.71
% 1.33/1.71 prologoutput = 1
% 1.33/1.71 nrgoals = 5000000
% 1.33/1.71 totalproof = 1
% 1.33/1.71
% 1.33/1.71 Symbols occurring in the translation:
% 1.33/1.71
% 1.33/1.71 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.33/1.71 . [1, 2] (w:1, o:142, a:1, s:1, b:0),
% 1.33/1.71 ! [4, 1] (w:0, o:70, a:1, s:1, b:0),
% 1.33/1.71 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.33/1.71 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.33/1.71 'class_Ring__and__Field_Oordered__field' [40, 1] (w:1, o:76, a:1, s:1
% 1.33/1.71 , b:0),
% 1.33/1.71 'c_HOL_Oinverse__class_Odivide' [43, 3] (w:1, o:174, a:1, s:1, b:0),
% 1.33/1.71
% 1.33/1.71 'c_HOL_Oord__class_Oless' [46, 3] (w:1, o:175, a:1, s:1, b:0),
% 1.33/1.71 'c_HOL_Ozero__class_Ozero' [47, 1] (w:1, o:77, a:1, s:1, b:0),
% 1.33/1.71 'c_lessequals' [48, 3] (w:1, o:176, a:1, s:1, b:0),
% 1.33/1.71 'class_Ring__and__Field_Ofield' [49, 1] (w:1, o:78, a:1, s:1, b:0),
% 1.33/1.71 'class_Ring__and__Field_Odivision__by__zero' [50, 1] (w:1, o:81, a:1
% 1.33/1.71 , s:1, b:0),
% 1.33/1.71 'c_HOL_Oone__class_Oone' [51, 1] (w:1, o:82, a:1, s:1, b:0),
% 1.33/1.71 'c_Power_Opower__class_Opower' [52, 1] (w:1, o:83, a:1, s:1, b:0),
% 1.33/1.71 hAPP [54, 2] (w:1, o:167, a:1, s:1, b:0),
% 1.33/1.71 'class_Ring__and__Field_Oidom' [56, 1] (w:1, o:84, a:1, s:1, b:0),
% 1.33/1.71 'class_Int_Onumber__ring' [57, 1] (w:1, o:85, a:1, s:1, b:0),
% 1.33/1.71 'c_HOL_Oplus__class_Oplus' [58, 1] (w:1, o:86, a:1, s:1, b:0),
% 1.33/1.71 'c_HOL_Otimes__class_Otimes' [59, 1] (w:1, o:87, a:1, s:1, b:0),
% 1.33/1.71 'tc_nat' [62, 0] (w:1, o:41, a:1, s:1, b:0),
% 1.33/1.71 'class_Int_Onumber' [63, 1] (w:1, o:88, a:1, s:1, b:0),
% 1.33/1.71 'c_Int_Onumber__class_Onumber__of' [65, 2] (w:1, o:169, a:1, s:1, b:0
% 1.33/1.71 ),
% 1.33/1.71 'class_OrderedGroup_Ogroup__add' [66, 1] (w:1, o:89, a:1, s:1, b:0),
% 1.33/1.71
% 1.33/1.71 'c_HOL_Ominus__class_Ominus' [67, 3] (w:1, o:177, a:1, s:1, b:0),
% 1.33/1.71 'class_Ring__and__Field_Odivision__ring' [68, 1] (w:1, o:90, a:1, s:1
% 1.33/1.71 , b:0),
% 1.33/1.71 'c_HOL_Oinverse__class_Oinverse' [69, 2] (w:1, o:168, a:1, s:1, b:0)
% 1.33/1.71 ,
% 1.33/1.71 'class_Ring__and__Field_Ocomm__semiring__1' [70, 1] (w:1, o:79, a:1
% 1.33/1.71 , s:1, b:0),
% 1.33/1.71 'c_Suc' [73, 1] (w:1, o:91, a:1, s:1, b:0),
% 1.33/1.71 'class_OrderedGroup_Omonoid__mult' [74, 1] (w:1, o:93, a:1, s:1, b:0)
% 1.33/1.71 ,
% 1.33/1.71 'class_Power_Opower' [75, 1] (w:1, o:111, a:1, s:1, b:0),
% 1.33/1.71 'class_OrderedGroup_Opordered__comm__monoid__add' [76, 1] (w:1, o:94
% 1.33/1.71 , a:1, s:1, b:0),
% 1.33/1.71 'c_List_Otake' [79, 3] (w:1, o:178, a:1, s:1, b:0),
% 1.33/1.71 'c_List_Odrop' [80, 3] (w:1, o:179, a:1, s:1, b:0),
% 1.33/1.71 'class_Divides_Osemiring__div' [81, 1] (w:1, o:113, a:1, s:1, b:0),
% 1.33/1.71 'c_Divides_Odiv__class_Omod' [82, 3] (w:1, o:180, a:1, s:1, b:0),
% 1.33/1.71 'class_Orderings_Oorder' [83, 1] (w:1, o:95, a:1, s:1, b:0),
% 1.33/1.71 'class_Orderings_Opreorder' [84, 1] (w:1, o:96, a:1, s:1, b:0),
% 1.33/1.71 'c_List_Onth' [86, 3] (w:1, o:181, a:1, s:1, b:0),
% 1.33/1.71 'class_Ring__and__Field_Oordered__idom' [87, 1] (w:1, o:114, a:1, s:1
% 1.33/1.71 , b:0),
% 1.33/1.71 'c_Parity_Oeven__odd__class_Oeven' [88, 2] (w:1, o:170, a:1, s:1, b:0
% 1.33/1.71 ),
% 1.33/1.71 'class_OrderedGroup_Ocomm__monoid__add' [89, 1] (w:1, o:97, a:1, s:1
% 1.33/1.71 , b:0),
% 1.33/1.71 'class_OrderedGroup_Oab__group__add' [90, 1] (w:1, o:98, a:1, s:1, b:
% 1.33/1.71 0),
% 1.33/1.71 'class_OrderedGroup_Oab__semigroup__add' [92, 1] (w:1, o:99, a:1, s:1
% 1.33/1.71 , b:0),
% 1.33/1.71 'class_Orderings_Olinorder' [93, 1] (w:1, o:100, a:1, s:1, b:0),
% 1.33/1.71 'class_Ring__and__Field_Oordered__semiring__strict' [94, 1] (w:1, o:
% 1.33/1.71 116, a:1, s:1, b:0),
% 1.33/1.71 'class_Ring__and__Field_Oring' [95, 1] (w:1, o:117, a:1, s:1, b:0),
% 1.33/1.71 'c_Divides_Odiv__class_Odiv' [97, 3] (w:1, o:182, a:1, s:1, b:0),
% 1.33/1.71 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [98, 1]
% 1.33/1.71 (w:1, o:101, a:1, s:1, b:0),
% 1.33/1.71 'class_Ring__and__Field_Opordered__ring' [100, 1] (w:1, o:121, a:1
% 1.33/1.71 , s:1, b:0),
% 1.33/1.71 'class_Ring__and__Field_Oordered__ring__strict' [102, 1] (w:1, o:115
% 7.44/7.80 , a:1, s:1, b:0),
% 7.44/7.80 'class_Ring__and__Field_Oordered__semiring' [103, 1] (w:1, o:118, a:1
% 7.44/7.80 , s:1, b:0),
% 7.44/7.80 'tc_Int_Oint' [104, 0] (w:1, o:50, a:1, s:1, b:0),
% 7.44/7.80 'class_RealVector_Oreal__normed__field' [105, 1] (w:1, o:122, a:1, s:
% 7.44/7.80 1, b:0),
% 7.44/7.80 'class_OrderedGroup_Olordered__ab__group__add' [107, 1] (w:1, o:92
% 7.44/7.80 , a:1, s:1, b:0),
% 7.44/7.80 'class_Ring__and__Field_Oordered__semidom' [108, 1] (w:1, o:119, a:1
% 7.44/7.80 , s:1, b:0),
% 7.44/7.80 hBOOL [115, 1] (w:1, o:123, a:1, s:1, b:0),
% 7.44/7.80 'class_Ring__and__Field_Osemiring' [119, 1] (w:1, o:126, a:1, s:1, b:
% 7.44/7.80 0),
% 7.44/7.80 'class_RealVector_Oreal__normed__algebra' [120, 1] (w:1, o:127, a:1
% 7.44/7.80 , s:1, b:0),
% 7.44/7.80 'c_Groebner__Basis_Ogb__semiring' [124, 6] (w:1, o:186, a:1, s:1, b:0
% 7.44/7.80 ),
% 7.44/7.80 'class_Ring__and__Field_Oordered__comm__semiring__strict' [125, 1]
% 7.44/7.80 (w:1, o:120, a:1, s:1, b:0),
% 7.44/7.80 'class_OrderedGroup_Opordered__ab__semigroup__add' [126, 1] (w:1, o:
% 7.44/7.80 102, a:1, s:1, b:0),
% 7.44/7.80 'class_OrderedGroup_Oab__semigroup__idem__mult' [127, 1] (w:1, o:103
% 7.44/7.80 , a:1, s:1, b:0),
% 7.44/7.80 'class_Ring__and__Field_Omult__mono1' [129, 1] (w:1, o:128, a:1, s:1
% 7.44/7.80 , b:0),
% 7.44/7.80 'class_Ring__and__Field_Omult__mono' [130, 1] (w:1, o:129, a:1, s:1
% 7.44/7.80 , b:0),
% 7.44/7.80 'c_Int_Onat' [131, 1] (w:1, o:130, a:1, s:1, b:0),
% 7.44/7.80 'class_OrderedGroup_Opordered__ab__group__add' [132, 1] (w:1, o:104
% 7.44/7.80 , a:1, s:1, b:0),
% 7.44/7.80 'class_OrderedGroup_Ocomm__monoid__mult' [133, 1] (w:1, o:105, a:1
% 7.44/7.80 , s:1, b:0),
% 7.44/7.80 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [134, 1]
% 7.44/7.80 (w:1, o:106, a:1, s:1, b:0),
% 7.44/7.80 'class_Ring__and__Field_Osemiring__1' [135, 1] (w:1, o:132, a:1, s:1
% 7.44/7.80 , b:0),
% 7.44/7.80 'c_Int_Oiszero' [136, 2] (w:1, o:171, a:1, s:1, b:0),
% 7.44/7.80 'class_Ring__and__Field_Oring__no__zero__divisors' [137, 1] (w:1, o:
% 7.44/7.80 124, a:1, s:1, b:0),
% 7.44/7.80 'class_Ring__and__Field_Omult__zero' [138, 1] (w:1, o:133, a:1, s:1
% 7.44/7.80 , b:0),
% 7.44/7.80 'class_Ring__and__Field_Oring__1__no__zero__divisors' [139, 1] (w:1
% 7.44/7.80 , o:125, a:1, s:1, b:0),
% 7.44/7.80 'class_Ring__and__Field_Ozero__neq__one' [140, 1] (w:1, o:134, a:1
% 7.44/7.80 , s:1, b:0),
% 7.44/7.80 'class_Ring__and__Field_Ono__zero__divisors' [141, 1] (w:1, o:75, a:1
% 7.44/7.80 , s:1, b:0),
% 7.44/7.80 'class_OrderedGroup_Omonoid__add' [142, 1] (w:1, o:107, a:1, s:1, b:0
% 7.44/7.80 ),
% 7.44/7.80 'class_Ring__and__Field_Opordered__cancel__semiring' [143, 1] (w:1
% 7.44/7.80 , o:135, a:1, s:1, b:0),
% 7.44/7.80 'class_OrderedGroup_Oab__semigroup__mult' [144, 1] (w:1, o:108, a:1
% 7.44/7.80 , s:1, b:0),
% 7.44/7.80 'class_Ring__and__Field_Ocomm__semiring' [145, 1] (w:1, o:80, a:1, s:
% 7.44/7.80 1, b:0),
% 7.44/7.80 'class_Ring__and__Field_Opordered__semiring' [146, 1] (w:1, o:136, a:
% 7.44/7.80 1, s:1, b:0),
% 7.44/7.80 'c_Int_OBit1' [153, 1] (w:1, o:138, a:1, s:1, b:0),
% 7.44/7.80 'class_Divides_Oring__div' [155, 1] (w:1, o:112, a:1, s:1, b:0),
% 7.44/7.80 'class_OrderedGroup_Ocancel__ab__semigroup__add' [156, 1] (w:1, o:109
% 7.44/7.80 , a:1, s:1, b:0),
% 7.44/7.80 'class_OrderedGroup_Ocancel__semigroup__add' [157, 1] (w:1, o:110, a:
% 7.44/7.80 1, s:1, b:0),
% 7.44/7.80 'class_RealVector_Oreal__field' [158, 1] (w:1, o:139, a:1, s:1, b:0)
% 7.44/7.80 ,
% 7.44/7.80 'c_Int_OPls' [160, 0] (w:1, o:57, a:1, s:1, b:0),
% 7.44/7.80 'c_Int_OBit0' [161, 1] (w:1, o:137, a:1, s:1, b:0),
% 7.44/7.80 'c_List_Olist_ONil' [162, 1] (w:1, o:140, a:1, s:1, b:0),
% 7.44/7.80 'c_List_Omap' [165, 4] (w:1, o:185, a:1, s:1, b:0),
% 7.44/7.80 'c_List_Olist_OCons' [166, 3] (w:1, o:183, a:1, s:1, b:0),
% 7.44/7.80 'class_Ring__and__Field_Osemiring__0' [167, 1] (w:1, o:131, a:1, s:1
% 7.44/7.80 , b:0),
% 7.44/7.80 'class_Int_Oring__char__0' [169, 1] (w:1, o:141, a:1, s:1, b:0),
% 7.44/7.80 'c_FFT__Mirabelle_OFFT' [176, 2] (w:1, o:172, a:1, s:1, b:0),
% 7.44/7.80 'v_a' [178, 0] (w:1, o:63, a:1, s:1, b:0),
% 7.44/7.80 'tc_Complex_Ocomplex' [179, 0] (w:1, o:64, a:1, s:1, b:0),
% 7.44/7.80 'v_x' [180, 0] (w:1, o:65, a:1, s:1, b:0),
% 7.44/7.80 'tc_fun' [183, 2] (w:1, o:173, a:1, s:1, b:0),
% 7.44/7.80 'c_fequal' [184, 3] (w:1, o:184, a:1, s:1, b:0).
% 7.44/7.80
% 7.44/7.80
% 7.44/7.80 Starting Search:
% 7.44/7.80
% 7.44/7.80 Resimplifying inuse:
% 7.44/7.80 Done
% 7.44/7.80
% 7.44/7.80
% 7.44/7.80 Intermediate Status:
% 7.44/7.80 Generated: 5679
% 7.44/7.80 Kept: 2000
% 7.44/7.80 Inuse: 298
% 7.44/7.80 Deleted: 21
% 7.44/7.80 Deletedinuse: 0
% 7.44/7.80
% 7.44/7.80 Resimplifying inuse:
% 7.44/7.80 Done
% 7.44/7.80
% 7.44/7.80 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56
% 36.13/36.56 Intermediate Status:
% 36.13/36.56 Generated: 9857
% 36.13/36.56 Kept: 4012
% 36.13/36.56 Inuse: 393
% 36.13/36.56 Deleted: 29
% 36.13/36.56 Deletedinuse: 1
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56
% 36.13/36.56 Intermediate Status:
% 36.13/36.56 Generated: 16434
% 36.13/36.56 Kept: 6022
% 36.13/36.56 Inuse: 483
% 36.13/36.56 Deleted: 31
% 36.13/36.56 Deletedinuse: 3
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56
% 36.13/36.56 Intermediate Status:
% 36.13/36.56 Generated: 23203
% 36.13/36.56 Kept: 8645
% 36.13/36.56 Inuse: 568
% 36.13/36.56 Deleted: 36
% 36.13/36.56 Deletedinuse: 3
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56
% 36.13/36.56 Intermediate Status:
% 36.13/36.56 Generated: 34693
% 36.13/36.56 Kept: 11258
% 36.13/36.56 Inuse: 593
% 36.13/36.56 Deleted: 36
% 36.13/36.56 Deletedinuse: 3
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56
% 36.13/36.56 Intermediate Status:
% 36.13/36.56 Generated: 42702
% 36.13/36.56 Kept: 13295
% 36.13/36.56 Inuse: 647
% 36.13/36.56 Deleted: 37
% 36.13/36.56 Deletedinuse: 3
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56
% 36.13/36.56 Intermediate Status:
% 36.13/36.56 Generated: 51622
% 36.13/36.56 Kept: 15394
% 36.13/36.56 Inuse: 681
% 36.13/36.56 Deleted: 40
% 36.13/36.56 Deletedinuse: 5
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56
% 36.13/36.56 Intermediate Status:
% 36.13/36.56 Generated: 57252
% 36.13/36.56 Kept: 17821
% 36.13/36.56 Inuse: 700
% 36.13/36.56 Deleted: 40
% 36.13/36.56 Deletedinuse: 5
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56
% 36.13/36.56 Intermediate Status:
% 36.13/36.56 Generated: 63387
% 36.13/36.56 Kept: 19938
% 36.13/36.56 Inuse: 750
% 36.13/36.56 Deleted: 41
% 36.13/36.56 Deletedinuse: 5
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56 Resimplifying clauses:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56
% 36.13/36.56 Intermediate Status:
% 36.13/36.56 Generated: 70237
% 36.13/36.56 Kept: 22100
% 36.13/36.56 Inuse: 780
% 36.13/36.56 Deleted: 412
% 36.13/36.56 Deletedinuse: 11
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56
% 36.13/36.56 Intermediate Status:
% 36.13/36.56 Generated: 76964
% 36.13/36.56 Kept: 24305
% 36.13/36.56 Inuse: 790
% 36.13/36.56 Deleted: 412
% 36.13/36.56 Deletedinuse: 11
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56
% 36.13/36.56 Intermediate Status:
% 36.13/36.56 Generated: 83937
% 36.13/36.56 Kept: 26373
% 36.13/36.56 Inuse: 845
% 36.13/36.56 Deleted: 412
% 36.13/36.56 Deletedinuse: 11
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56
% 36.13/36.56 Intermediate Status:
% 36.13/36.56 Generated: 93776
% 36.13/36.56 Kept: 29358
% 36.13/36.56 Inuse: 880
% 36.13/36.56 Deleted: 413
% 36.13/36.56 Deletedinuse: 12
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56
% 36.13/36.56 Intermediate Status:
% 36.13/36.56 Generated: 106665
% 36.13/36.56 Kept: 31368
% 36.13/36.56 Inuse: 914
% 36.13/36.56 Deleted: 414
% 36.13/36.56 Deletedinuse: 13
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56
% 36.13/36.56 Intermediate Status:
% 36.13/36.56 Generated: 114704
% 36.13/36.56 Kept: 33379
% 36.13/36.56 Inuse: 957
% 36.13/36.56 Deleted: 414
% 36.13/36.56 Deletedinuse: 13
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56
% 36.13/36.56 Intermediate Status:
% 36.13/36.56 Generated: 125571
% 36.13/36.56 Kept: 35449
% 36.13/36.56 Inuse: 980
% 36.13/36.56 Deleted: 414
% 36.13/36.56 Deletedinuse: 13
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56
% 36.13/36.56 Intermediate Status:
% 36.13/36.56 Generated: 134348
% 36.13/36.56 Kept: 37573
% 36.13/36.56 Inuse: 1030
% 36.13/36.56 Deleted: 414
% 36.13/36.56 Deletedinuse: 13
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56
% 36.13/36.56 Intermediate Status:
% 36.13/36.56 Generated: 144005
% 36.13/36.56 Kept: 39765
% 36.13/36.56 Inuse: 1080
% 36.13/36.56 Deleted: 414
% 36.13/36.56 Deletedinuse: 13
% 36.13/36.56
% 36.13/36.56 Resimplifying clauses:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56
% 36.13/36.56 Intermediate Status:
% 36.13/36.56 Generated: 152854
% 36.13/36.56 Kept: 41912
% 36.13/36.56 Inuse: 1105
% 36.13/36.56 Deleted: 788
% 36.13/36.56 Deletedinuse: 13
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56
% 36.13/36.56 Intermediate Status:
% 36.13/36.56 Generated: 180632
% 36.13/36.56 Kept: 45923
% 36.13/36.56 Inuse: 1140
% 36.13/36.56 Deleted: 789
% 36.13/36.56 Deletedinuse: 14
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56
% 36.13/36.56 Intermediate Status:
% 36.13/36.56 Generated: 202510
% 36.13/36.56 Kept: 48292
% 36.13/36.56 Inuse: 1145
% 36.13/36.56 Deleted: 789
% 36.13/36.56 Deletedinuse: 14
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56
% 36.13/36.56 Intermediate Status:
% 36.13/36.56 Generated: 213951
% 36.13/36.56 Kept: 51290
% 36.13/36.56 Inuse: 1155
% 36.13/36.56 Deleted: 789
% 36.13/36.56 Deletedinuse: 14
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56
% 36.13/36.56 Intermediate Status:
% 36.13/36.56 Generated: 221204
% 36.13/36.56 Kept: 53296
% 36.13/36.56 Inuse: 1170
% 36.13/36.56 Deleted: 789
% 36.13/36.56 Deletedinuse: 14
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56
% 36.13/36.56 Intermediate Status:
% 36.13/36.56 Generated: 229069
% 36.13/36.56 Kept: 55519
% 36.13/36.56 Inuse: 1200
% 36.13/36.56 Deleted: 789
% 36.13/36.56 Deletedinuse: 14
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56
% 36.13/36.56 Intermediate Status:
% 36.13/36.56 Generated: 239583
% 36.13/36.56 Kept: 58164
% 36.13/36.56 Inuse: 1225
% 36.13/36.56 Deleted: 789
% 36.13/36.56 Deletedinuse: 14
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56 Resimplifying inuse:
% 36.13/36.56 Done
% 36.13/36.56
% 36.13/36.56
% 36.13/36.56 Intermediate Status:
% 36.13/36.56 Generated: 255870
% 36.13/36.56 Kept: 60802
% 36.13/36.56 Inuse: 1250
% 36.13/36.56 Deleted: 789
% 87.33/87.76 Deletedinuse: 14
% 87.33/87.76
% 87.33/87.76 Resimplifying inuse:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76 Resimplifying clauses:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76 Resimplifying inuse:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76
% 87.33/87.76 Intermediate Status:
% 87.33/87.76 Generated: 263779
% 87.33/87.76 Kept: 63041
% 87.33/87.76 Inuse: 1279
% 87.33/87.76 Deleted: 986
% 87.33/87.76 Deletedinuse: 15
% 87.33/87.76
% 87.33/87.76 Resimplifying inuse:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76
% 87.33/87.76 Intermediate Status:
% 87.33/87.76 Generated: 274355
% 87.33/87.76 Kept: 65902
% 87.33/87.76 Inuse: 1284
% 87.33/87.76 Deleted: 986
% 87.33/87.76 Deletedinuse: 15
% 87.33/87.76
% 87.33/87.76 Resimplifying inuse:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76
% 87.33/87.76 Intermediate Status:
% 87.33/87.76 Generated: 284983
% 87.33/87.76 Kept: 68729
% 87.33/87.76 Inuse: 1289
% 87.33/87.76 Deleted: 986
% 87.33/87.76 Deletedinuse: 15
% 87.33/87.76
% 87.33/87.76 Resimplifying inuse:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76 Resimplifying inuse:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76
% 87.33/87.76 Intermediate Status:
% 87.33/87.76 Generated: 294130
% 87.33/87.76 Kept: 70968
% 87.33/87.76 Inuse: 1319
% 87.33/87.76 Deleted: 986
% 87.33/87.76 Deletedinuse: 15
% 87.33/87.76
% 87.33/87.76 Resimplifying inuse:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76 Resimplifying inuse:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76
% 87.33/87.76 Intermediate Status:
% 87.33/87.76 Generated: 305185
% 87.33/87.76 Kept: 73260
% 87.33/87.76 Inuse: 1354
% 87.33/87.76 Deleted: 986
% 87.33/87.76 Deletedinuse: 15
% 87.33/87.76
% 87.33/87.76 Resimplifying inuse:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76 Resimplifying inuse:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76
% 87.33/87.76 Intermediate Status:
% 87.33/87.76 Generated: 318258
% 87.33/87.76 Kept: 75418
% 87.33/87.76 Inuse: 1394
% 87.33/87.76 Deleted: 986
% 87.33/87.76 Deletedinuse: 15
% 87.33/87.76
% 87.33/87.76 Resimplifying inuse:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76 Resimplifying inuse:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76
% 87.33/87.76 Intermediate Status:
% 87.33/87.76 Generated: 327956
% 87.33/87.76 Kept: 78776
% 87.33/87.76 Inuse: 1414
% 87.33/87.76 Deleted: 986
% 87.33/87.76 Deletedinuse: 15
% 87.33/87.76
% 87.33/87.76 Resimplifying inuse:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76
% 87.33/87.76 Intermediate Status:
% 87.33/87.76 Generated: 334187
% 87.33/87.76 Kept: 82538
% 87.33/87.76 Inuse: 1419
% 87.33/87.76 Deleted: 986
% 87.33/87.76 Deletedinuse: 15
% 87.33/87.76
% 87.33/87.76 Resimplifying inuse:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76 Resimplifying clauses:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76 Resimplifying inuse:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76
% 87.33/87.76 Intermediate Status:
% 87.33/87.76 Generated: 345189
% 87.33/87.76 Kept: 86081
% 87.33/87.76 Inuse: 1442
% 87.33/87.76 Deleted: 1086
% 87.33/87.76 Deletedinuse: 15
% 87.33/87.76
% 87.33/87.76 Resimplifying inuse:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76 Resimplifying inuse:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76
% 87.33/87.76 Intermediate Status:
% 87.33/87.76 Generated: 359499
% 87.33/87.76 Kept: 88921
% 87.33/87.76 Inuse: 1474
% 87.33/87.76 Deleted: 1086
% 87.33/87.76 Deletedinuse: 15
% 87.33/87.76
% 87.33/87.76 Resimplifying inuse:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76
% 87.33/87.76 Intermediate Status:
% 87.33/87.76 Generated: 414251
% 87.33/87.76 Kept: 91839
% 87.33/87.76 Inuse: 1484
% 87.33/87.76 Deleted: 1086
% 87.33/87.76 Deletedinuse: 15
% 87.33/87.76
% 87.33/87.76 Resimplifying inuse:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76 Resimplifying inuse:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76
% 87.33/87.76 Intermediate Status:
% 87.33/87.76 Generated: 429082
% 87.33/87.76 Kept: 95203
% 87.33/87.76 Inuse: 1494
% 87.33/87.76 Deleted: 1086
% 87.33/87.76 Deletedinuse: 15
% 87.33/87.76
% 87.33/87.76 Resimplifying inuse:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76
% 87.33/87.76 Intermediate Status:
% 87.33/87.76 Generated: 450681
% 87.33/87.76 Kept: 98326
% 87.33/87.76 Inuse: 1499
% 87.33/87.76 Deleted: 1086
% 87.33/87.76 Deletedinuse: 15
% 87.33/87.76
% 87.33/87.76 Resimplifying inuse:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76
% 87.33/87.76 Intermediate Status:
% 87.33/87.76 Generated: 472810
% 87.33/87.76 Kept: 101454
% 87.33/87.76 Inuse: 1504
% 87.33/87.76 Deleted: 1086
% 87.33/87.76 Deletedinuse: 15
% 87.33/87.76
% 87.33/87.76 Resimplifying inuse:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76
% 87.33/87.76 Intermediate Status:
% 87.33/87.76 Generated: 483494
% 87.33/87.76 Kept: 103568
% 87.33/87.76 Inuse: 1519
% 87.33/87.76 Deleted: 1086
% 87.33/87.76 Deletedinuse: 15
% 87.33/87.76
% 87.33/87.76 Resimplifying inuse:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76 Resimplifying clauses:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76
% 87.33/87.76 Intermediate Status:
% 87.33/87.76 Generated: 497007
% 87.33/87.76 Kept: 105877
% 87.33/87.76 Inuse: 1544
% 87.33/87.76 Deleted: 1423
% 87.33/87.76 Deletedinuse: 16
% 87.33/87.76
% 87.33/87.76 Resimplifying inuse:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76
% 87.33/87.76 Intermediate Status:
% 87.33/87.76 Generated: 513648
% 87.33/87.76 Kept: 111822
% 87.33/87.76 Inuse: 1559
% 87.33/87.76 Deleted: 1423
% 87.33/87.76 Deletedinuse: 16
% 87.33/87.76
% 87.33/87.76 Resimplifying inuse:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76
% 87.33/87.76 Intermediate Status:
% 87.33/87.76 Generated: 527155
% 87.33/87.76 Kept: 117341
% 87.33/87.76 Inuse: 1564
% 87.33/87.76 Deleted: 1423
% 87.33/87.76 Deletedinuse: 16
% 87.33/87.76
% 87.33/87.76 Resimplifying inuse:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76
% 87.33/87.76 Intermediate Status:
% 87.33/87.76 Generated: 540027
% 87.33/87.76 Kept: 120210
% 87.33/87.76 Inuse: 1569
% 87.33/87.76 Deleted: 1423
% 87.33/87.76 Deletedinuse: 16
% 87.33/87.76
% 87.33/87.76 Resimplifying inuse:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76 Resimplifying inuse:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76
% 87.33/87.76 Intermediate Status:
% 87.33/87.76 Generated: 553035
% 87.33/87.76 Kept: 124308
% 87.33/87.76 Inuse: 1593
% 87.33/87.76 Deleted: 1423
% 87.33/87.76 Deletedinuse: 16
% 87.33/87.76
% 87.33/87.76 Resimplifying inuse:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76 Resimplifying clauses:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76 Resimplifying inuse:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76
% 87.33/87.76 Intermediate Status:
% 87.33/87.76 Generated: 581856
% 87.33/87.76 Kept: 129086
% 87.33/87.76 Inuse: 1614
% 87.33/87.76 Deleted: 1489
% 87.33/87.76 Deletedinuse: 16
% 87.33/87.76
% 87.33/87.76 Resimplifying inuse:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76 Resimplifying inuse:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76
% 87.33/87.76 Intermediate Status:
% 87.33/87.76 Generated: 591746
% 87.33/87.76 Kept: 131224
% 87.33/87.76 Inuse: 1634
% 87.33/87.76 Deleted: 1489
% 87.33/87.76 Deletedinuse: 16
% 87.33/87.76
% 87.33/87.76 Resimplifying inuse:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76
% 87.33/87.76 Intermediate Status:
% 87.33/87.76 Generated: 603989
% 87.33/87.76 Kept: 133621
% 87.33/87.76 Inuse: 1644
% 87.33/87.76 Deleted: 1489
% 87.33/87.76 Deletedinuse: 16
% 87.33/87.76
% 87.33/87.76 Resimplifying inuse:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76 Resimplifying inuse:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76
% 87.33/87.76 Intermediate Status:
% 87.33/87.76 Generated: 616854
% 87.33/87.76 Kept: 135643
% 87.33/87.76 Inuse: 1670
% 87.33/87.76 Deleted: 1491
% 87.33/87.76 Deletedinuse: 18
% 87.33/87.76
% 87.33/87.76 Resimplifying inuse:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76 Resimplifying inuse:
% 87.33/87.76 Done
% 87.33/87.76
% 87.33/87.76
% 87.33/87.76 Intermediate Status:
% 87.33/87.76 Generated: 626916
% 87.33/87.76 Kept: 137834
% 87.33/87.76 Inuse: 1689
% 210.20/210.58 Deleted: 1491
% 210.20/210.58 Deletedinuse: 18
% 210.20/210.58
% 210.20/210.58 Resimplifying inuse:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58 Resimplifying inuse:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58
% 210.20/210.58 Intermediate Status:
% 210.20/210.58 Generated: 638221
% 210.20/210.58 Kept: 140140
% 210.20/210.58 Inuse: 1709
% 210.20/210.58 Deleted: 1491
% 210.20/210.58 Deletedinuse: 18
% 210.20/210.58
% 210.20/210.58 Resimplifying inuse:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58 Resimplifying inuse:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58
% 210.20/210.58 Intermediate Status:
% 210.20/210.58 Generated: 647791
% 210.20/210.58 Kept: 142156
% 210.20/210.58 Inuse: 1733
% 210.20/210.58 Deleted: 1491
% 210.20/210.58 Deletedinuse: 18
% 210.20/210.58
% 210.20/210.58 Resimplifying inuse:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58
% 210.20/210.58 Intermediate Status:
% 210.20/210.58 Generated: 659421
% 210.20/210.58 Kept: 146507
% 210.20/210.58 Inuse: 1744
% 210.20/210.58 Deleted: 1495
% 210.20/210.58 Deletedinuse: 21
% 210.20/210.58
% 210.20/210.58 Resimplifying inuse:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58 Resimplifying clauses:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58 Resimplifying inuse:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58
% 210.20/210.58 Intermediate Status:
% 210.20/210.58 Generated: 698078
% 210.20/210.58 Kept: 151681
% 210.20/210.58 Inuse: 1758
% 210.20/210.58 Deleted: 2400
% 210.20/210.58 Deletedinuse: 22
% 210.20/210.58
% 210.20/210.58 Resimplifying inuse:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58 Resimplifying inuse:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58
% 210.20/210.58 Intermediate Status:
% 210.20/210.58 Generated: 723286
% 210.20/210.58 Kept: 155441
% 210.20/210.58 Inuse: 1773
% 210.20/210.58 Deleted: 2400
% 210.20/210.58 Deletedinuse: 22
% 210.20/210.58
% 210.20/210.58 Resimplifying inuse:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58
% 210.20/210.58 Intermediate Status:
% 210.20/210.58 Generated: 735254
% 210.20/210.58 Kept: 157606
% 210.20/210.58 Inuse: 1778
% 210.20/210.58 Deleted: 2400
% 210.20/210.58 Deletedinuse: 22
% 210.20/210.58
% 210.20/210.58 Resimplifying inuse:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58 Resimplifying inuse:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58
% 210.20/210.58 Intermediate Status:
% 210.20/210.58 Generated: 745570
% 210.20/210.58 Kept: 159616
% 210.20/210.58 Inuse: 1794
% 210.20/210.58 Deleted: 2400
% 210.20/210.58 Deletedinuse: 22
% 210.20/210.58
% 210.20/210.58 Resimplifying inuse:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58 Resimplifying inuse:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58
% 210.20/210.58 Intermediate Status:
% 210.20/210.58 Generated: 758214
% 210.20/210.58 Kept: 161917
% 210.20/210.58 Inuse: 1813
% 210.20/210.58 Deleted: 2400
% 210.20/210.58 Deletedinuse: 22
% 210.20/210.58
% 210.20/210.58 Resimplifying inuse:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58 Resimplifying inuse:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58
% 210.20/210.58 Intermediate Status:
% 210.20/210.58 Generated: 770000
% 210.20/210.58 Kept: 164191
% 210.20/210.58 Inuse: 1833
% 210.20/210.58 Deleted: 2400
% 210.20/210.58 Deletedinuse: 22
% 210.20/210.58
% 210.20/210.58 Resimplifying inuse:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58 Resimplifying inuse:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58
% 210.20/210.58 Intermediate Status:
% 210.20/210.58 Generated: 780343
% 210.20/210.58 Kept: 166506
% 210.20/210.58 Inuse: 1853
% 210.20/210.58 Deleted: 2400
% 210.20/210.58 Deletedinuse: 22
% 210.20/210.58
% 210.20/210.58 Resimplifying inuse:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58 Resimplifying clauses:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58
% 210.20/210.58 Intermediate Status:
% 210.20/210.58 Generated: 789531
% 210.20/210.58 Kept: 168553
% 210.20/210.58 Inuse: 1868
% 210.20/210.58 Deleted: 2618
% 210.20/210.58 Deletedinuse: 22
% 210.20/210.58
% 210.20/210.58 Resimplifying inuse:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58 Resimplifying inuse:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58
% 210.20/210.58 Intermediate Status:
% 210.20/210.58 Generated: 836637
% 210.20/210.58 Kept: 174208
% 210.20/210.58 Inuse: 1888
% 210.20/210.58 Deleted: 2618
% 210.20/210.58 Deletedinuse: 22
% 210.20/210.58
% 210.20/210.58 Resimplifying inuse:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58 Resimplifying inuse:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58
% 210.20/210.58 Intermediate Status:
% 210.20/210.58 Generated: 857215
% 210.20/210.58 Kept: 176496
% 210.20/210.58 Inuse: 1913
% 210.20/210.58 Deleted: 2618
% 210.20/210.58 Deletedinuse: 22
% 210.20/210.58
% 210.20/210.58 Resimplifying inuse:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58 Resimplifying inuse:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58
% 210.20/210.58 Intermediate Status:
% 210.20/210.58 Generated: 867140
% 210.20/210.58 Kept: 179644
% 210.20/210.58 Inuse: 1928
% 210.20/210.58 Deleted: 2618
% 210.20/210.58 Deletedinuse: 22
% 210.20/210.58
% 210.20/210.58 Resimplifying inuse:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58 Resimplifying inuse:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58
% 210.20/210.58 Intermediate Status:
% 210.20/210.58 Generated: 875112
% 210.20/210.58 Kept: 182646
% 210.20/210.58 Inuse: 1938
% 210.20/210.58 Deleted: 2618
% 210.20/210.58 Deletedinuse: 22
% 210.20/210.58
% 210.20/210.58 Resimplifying inuse:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58 Resimplifying inuse:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58
% 210.20/210.58 Intermediate Status:
% 210.20/210.58 Generated: 884776
% 210.20/210.58 Kept: 185132
% 210.20/210.58 Inuse: 1958
% 210.20/210.58 Deleted: 2618
% 210.20/210.58 Deletedinuse: 22
% 210.20/210.58
% 210.20/210.58 Resimplifying inuse:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58 Resimplifying inuse:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58
% 210.20/210.58 Intermediate Status:
% 210.20/210.58 Generated: 892436
% 210.20/210.58 Kept: 187337
% 210.20/210.58 Inuse: 1978
% 210.20/210.58 Deleted: 2618
% 210.20/210.58 Deletedinuse: 22
% 210.20/210.58
% 210.20/210.58 Resimplifying clauses:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58 Resimplifying inuse:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58 Resimplifying inuse:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58
% 210.20/210.58 Intermediate Status:
% 210.20/210.58 Generated: 900687
% 210.20/210.58 Kept: 189387
% 210.20/210.58 Inuse: 1998
% 210.20/210.58 Deleted: 2728
% 210.20/210.58 Deletedinuse: 22
% 210.20/210.58
% 210.20/210.58 Resimplifying inuse:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58
% 210.20/210.58 Intermediate Status:
% 210.20/210.58 Generated: 915889
% 210.20/210.58 Kept: 192416
% 210.20/210.58 Inuse: 2008
% 210.20/210.58 Deleted: 2728
% 210.20/210.58 Deletedinuse: 22
% 210.20/210.58
% 210.20/210.58 Resimplifying inuse:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58
% 210.20/210.58 Intermediate Status:
% 210.20/210.58 Generated: 928125
% 210.20/210.58 Kept: 194800
% 210.20/210.58 Inuse: 2013
% 210.20/210.58 Deleted: 2728
% 210.20/210.58 Deletedinuse: 22
% 210.20/210.58
% 210.20/210.58 Resimplifying inuse:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58
% 210.20/210.58 Intermediate Status:
% 210.20/210.58 Generated: 940366
% 210.20/210.58 Kept: 197207
% 210.20/210.58 Inuse: 2018
% 210.20/210.58 Deleted: 2728
% 210.20/210.58 Deletedinuse: 22
% 210.20/210.58
% 210.20/210.58 Resimplifying inuse:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58
% 210.20/210.58 Intermediate Status:
% 210.20/210.58 Generated: 957413
% 210.20/210.58 Kept: 200403
% 210.20/210.58 Inuse: 2028
% 210.20/210.58 Deleted: 2728
% 210.20/210.58 Deletedinuse: 22
% 210.20/210.58
% 210.20/210.58 Resimplifying inuse:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58
% 210.20/210.58 Intermediate Status:
% 210.20/210.58 Generated: 972910
% 210.20/210.58 Kept: 202939
% 210.20/210.58 Inuse: 2033
% 210.20/210.58 Deleted: 2728
% 210.20/210.58 Deletedinuse: 22
% 210.20/210.58
% 210.20/210.58 Resimplifying inuse:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58 Resimplifying inuse:
% 210.20/210.58 Done
% 210.20/210.58
% 210.20/210.58
% 210.20/210.58 Intermediate Status:
% 210.20/210.58 Generated: 983676
% 210.20/210.58 Kept: 205224
% 210.20/210.58 Inuse: 2063
% 210.20/210.58 Deleted: 2728
% 210.20/210.58 Deletedinuse: 22
% 210.20/210.58
% 210.20/210.58 ResimpCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------