TSTP Solution File: LCL809-1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL809-1 : 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 : Sun Jul 17 07:58:16 EDT 2022
% Result : Unsatisfiable 2.35s 2.75s
% Output : Refutation 2.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : LCL809-1 : TPTP v8.1.0. Released v4.1.0.
% 0.08/0.13 % 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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % DateTime : Sat Jul 2 21:36:45 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.02/1.44 *** allocated 10000 integers for termspace/termends
% 1.02/1.44 *** allocated 10000 integers for clauses
% 1.02/1.44 *** allocated 10000 integers for justifications
% 1.02/1.44 *** allocated 15000 integers for termspace/termends
% 1.02/1.44 *** allocated 22500 integers for termspace/termends
% 1.02/1.44 *** allocated 33750 integers for termspace/termends
% 1.02/1.44 Bliksem 1.12
% 1.02/1.44
% 1.02/1.44
% 1.02/1.44 Automatic Strategy Selection
% 1.02/1.44
% 1.02/1.44 Clauses:
% 1.02/1.44 [
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.02/1.44 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z, X ) )
% 1.02/1.44 ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.02/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.02/1.44 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.02/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.02/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.02/1.44 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.02/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ) ],
% 1.02/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.02/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.44 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 1.02/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z
% 1.02/1.44 , X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.02/1.44 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.02/1.44 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.02/1.44 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.02/1.44 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y
% 1.02/1.44 , X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.02/1.44 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y
% 1.02/1.44 , X ), Z, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_HOL_Oone__class_Oone'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X )
% 1.02/1.44 , X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.02/1.44 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_Suc'( Y ), X ),
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.02/1.44 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ),
% 1.02/1.44 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 1.02/1.44 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ), 'c_Suc'(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ],
% 1.02/1.44 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Olordered__ring'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.02/1.44 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.02/1.44 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.02/1.44 , X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.02/1.44 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.02/1.44 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_lessequals'( Z, Y, X )
% 1.02/1.44 ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( T, Y, X ), Z, X ), U, X ), X ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 1.02/1.44 ) ) ],
% 1.02/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.02/1.44 'tc_nat' ), Z, 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), T, 'tc_nat' ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat'
% 1.02/1.44 ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 1.02/1.44 ,
% 1.02/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 1.02/1.44 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 1.02/1.44 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.02/1.44 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.02/1.44 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), X, 'tc_nat' ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat'
% 1.02/1.44 ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 1.02/1.44 ,
% 1.02/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 1.02/1.44 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 1.02/1.44 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.02/1.44 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.02/1.44 W, X ) ) ), =( T, 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.02/1.44 , X ), W, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.02/1.44 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.02/1.44 W, X ) ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W ) ],
% 1.02/1.44 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.02/1.44 Y, 'tc_nat' ) ), 'tc_nat' ) ],
% 1.02/1.44 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.02/1.44 X, 'tc_nat' ) ), 'tc_nat' ) ],
% 1.02/1.44 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.02/1.44 Y, 'tc_nat' ) ), 'tc_nat' ) ],
% 1.02/1.44 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z,
% 1.02/1.44 'tc_nat' ), ~( 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Z, Y,
% 1.02/1.44 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.02/1.44 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ),
% 1.02/1.44 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 1.02/1.44 ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 1.02/1.44 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 1.02/1.44 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 1.02/1.44 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.02/1.44 'c_Orderings_Oord__class_Omax'( Y, Z, X ), X ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.02/1.44 'c_Orderings_Oord__class_Omax'( Z, Y, X ), X ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.44 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.44 X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Obot'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_Orderings_Obot__class_Obot'( X ), Y, X ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.02/1.44 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oabs__class_Oabs'(
% 1.02/1.44 Y, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.02/1.44 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'( Y, Z, X )
% 1.02/1.44 , T, X ), 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'(
% 1.02/1.44 Y, T, X ), 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.02/1.44 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 1.02/1.44 X ), X ), 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'(
% 1.02/1.44 Y, Z, X ), 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.02/1.44 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.02/1.44 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 1.02/1.44 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.02/1.44 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z, X )
% 1.02/1.44 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.02/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.02/1.44 , Z, X ), 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 1.02/1.44 'c_lessequals'( Z, T, 'tc_nat' ) ) ],
% 1.02/1.44 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.02/1.44 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.02/1.44 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 1.02/1.44 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.02/1.44 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.02/1.44 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =(
% 1.02/1.44 'c_OrderedGroup_Olordered__ab__group__add__class_Opprt'( Y, X ),
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_lessequals'( Y,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 1.02/1.44 'c_OrderedGroup_Olordered__ab__group__add__class_Opprt'( Y, X ),
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( Y,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.44 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.02/1.44 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 1.02/1.44 ],
% 1.02/1.44 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.02/1.44 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.02/1.44 ],
% 1.02/1.44 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 1.02/1.44 Y, 'tc_nat' ) ) ],
% 1.02/1.44 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.02/1.44 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) )
% 1.02/1.44 ],
% 1.02/1.44 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.02/1.44 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.02/1.44 ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.02/1.44 Y, T, X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X )
% 1.02/1.44 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.02/1.44 'c_lessequals'( T, Z, 'tc_nat' ) ) ],
% 1.02/1.44 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ),
% 1.02/1.44 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.02/1.44 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.02/1.44 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.02/1.44 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.02/1.44 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.02/1.44 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.02/1.44 W, X ), X ), ~( 'c_lessequals'( T, 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.02/1.44 , X ), W, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( Y
% 1.02/1.44 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U, X ), W, X ), X ), ~(
% 1.02/1.44 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.44 T, U, X ), Y, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Z, U, X ), W, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.02/1.44 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.02/1.44 W, X ), X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 1.02/1.44 , X ), T, X ), W, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ), U, X ), W, X ), ~(
% 1.02/1.44 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.44 Y, T, X ), U, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Z, T, X ), W, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.02/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.02/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.02/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.02/1.44 , T, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.02/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.02/1.44 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ), ~(
% 1.02/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.02/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.02/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.02/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.02/1.44 , T, X ), X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 1.02/1.44 ,
% 1.02/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 1.02/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 1.02/1.44 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.02/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.02/1.44 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 1.02/1.44 , X, 'tc_nat' ) ) ],
% 1.02/1.44 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.44 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 1.02/1.44 ), 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.02/1.44 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.02/1.44 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ) ) ],
% 1.02/1.44 [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OAbs'( X ), Y, Z ),
% 1.02/1.44 'c_Lambda_OdB_OAbs'( 'c_Lambda_Osubstn'( X, Y, 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.44 Z, 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.02/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.02/1.44 X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 1.02/1.44 X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 1.02/1.44 X ) ) ],
% 1.02/1.44 [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ) ) ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 X, T, 'tc_nat' ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 1.02/1.44 X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.02/1.44 ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.02/1.44 ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( Z,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.02/1.44 ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( Y,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.02/1.44 ), X ) ) ],
% 1.02/1.44 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.02/1.44 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Osgn__class_Osgn'( Y, X ),
% 1.02/1.44 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), Y ) ],
% 1.02/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.02/1.44 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.02/1.44 ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =(
% 1.02/1.44 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z
% 1.02/1.44 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'(
% 1.02/1.44 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oone__class_Oone'( X ), X ), Z, X
% 1.02/1.44 ), 'c_Power_Opower__class_Opower'( Y, Z, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.02/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ),
% 1.02/1.44 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.02/1.44 ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.02/1.44 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.02/1.44 'c_lessequals'( Z, Y, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.02/1.44 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.02/1.44 ), X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.02/1.44 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.02/1.44 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.44 Z, X ) ), ~( 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.02/1.44 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.02/1.44 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.02/1.44 'c_lessequals'( Z, Y, X ) ) ],
% 1.02/1.44 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 1.02/1.44 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.02/1.44 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.02/1.44 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), Z, X ) ) ]
% 1.02/1.44 ,
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.02/1.44 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.02/1.44 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ]
% 1.02/1.44 ,
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.02/1.44 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.02/1.44 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y
% 1.02/1.44 , 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.02/1.44 ,
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.02/1.44 , 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.02/1.44 ,
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.02/1.44 , T, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.02/1.44 , Z, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.02/1.44 , T, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.02/1.44 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~( 'c_lessequals'( Y,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, T, X ) ) ]
% 1.02/1.44 ,
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y, X ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z, X ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.02/1.44 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 1.02/1.44 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.02/1.44 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 1.02/1.44 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.02/1.44 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 1.02/1.44 X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.02/1.44 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.02/1.44 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.02/1.44 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.02/1.44 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 1.02/1.44 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.02/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.02/1.44 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.02/1.44 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 1.02/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.02/1.44 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.02/1.44 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.02/1.44 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 1.02/1.44 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.02/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.02/1.44 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.02/1.44 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 1.02/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.02/1.44 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.02/1.44 ,
% 1.02/1.44 [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 1.02/1.44 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X, Y,
% 1.02/1.44 'tc_nat' ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), =(
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ),
% 1.02/1.44 T, X ), 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ominus__class_Ominus'( Y,
% 1.02/1.44 T, X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.02/1.44 T, X ) ) ],
% 1.02/1.44 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'(
% 1.02/1.44 X, Y, 'tc_nat' ) ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 1.02/1.44 X ), 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.02/1.44 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( =( 'c_List_Oreplicate'( X, Y, Z ), 'c_List_Oreplicate'( T, U, Z ) )
% 1.02/1.44 ), =( X, T ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 1.02/1.44 ],
% 1.02/1.44 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 1.02/1.44 ), 'tc_nat' ), X ) ],
% 1.02/1.44 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( 'tc_nat' )
% 1.02/1.44 , X, 'tc_nat' ), X ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 1.02/1.44 ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 1.02/1.44 ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.02/1.44 ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.02/1.44 ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 1.02/1.44 ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.02/1.44 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.02/1.44 , ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.02/1.44 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.02/1.44 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.02/1.44 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Odvd'( X ) ),
% 1.02/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 1.02/1.44 , Z, X ), X ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.02/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 1.02/1.44 , Z, X ), X ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.02/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 1.02/1.44 , Y, X ), X ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.02/1.44 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( T, U,
% 1.02/1.44 X ), X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'(
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( Y, T, X ), X ), 'c_HOL_Oabs__class_Oabs'(
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( Z, U, X ), X ), X ), X ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.02/1.44 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( U, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.02/1.44 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.02/1.44 ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.02/1.44 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ),
% 1.02/1.44 'c_Power_Opower__class_Opower'( Y, Z, X ), X ),
% 1.02/1.44 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'(
% 1.02/1.44 'c_HOL_Oone__class_Oone'( X ), Y, X ), Z, X ) ) ],
% 1.02/1.44 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.44 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), 'c_Suc'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.02/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.02/1.44 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.02/1.44 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.02/1.44 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.02/1.44 Y, X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.02/1.44 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~( 'c_lessequals'( Y,
% 1.02/1.44 Z, 'tc_nat' ) ) ],
% 1.02/1.44 [ =( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'(
% 1.02/1.44 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.02/1.44 [ =( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'( X,
% 1.02/1.44 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.02/1.44 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.02/1.44 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.02/1.44 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ), =( Z,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.02/1.44 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.02/1.44 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.02/1.44 ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.02/1.44 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.02/1.44 ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.02/1.44 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.02/1.44 Z, X ) ) ],
% 1.02/1.44 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.02/1.44 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 1.02/1.44 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.02/1.44 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.02/1.44 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 1.02/1.44 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.02/1.44 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.02/1.44 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.02/1.44 X ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.02/1.44 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 1.02/1.44 [ =( 'c_Orderings_Oord__class_Omax'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 1.02/1.44 'tc_nat' ), 'c_Suc'( 'c_Orderings_Oord__class_Omax'( X, Y, 'tc_nat' ) ) )
% 1.02/1.44 ],
% 1.02/1.44 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.44 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.02/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.02/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.02/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.02/1.44 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'(
% 1.02/1.44 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 1.02/1.44 X ), 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X
% 1.02/1.44 ), X ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.02/1.44 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Y, Z,
% 1.02/1.44 X ), X ), 'c_Orderings_Oord__class_Omin'( Y, Z, X ) ) ],
% 1.02/1.44 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 1.02/1.44 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'( Z, X,
% 1.02/1.44 'tc_nat' ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.44 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Z, X ), U, X ) ),
% 1.02/1.44 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), T, X ) )
% 1.02/1.44 ],
% 1.02/1.44 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 1.02/1.44 ), U, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z,
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 1.02/1.44 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.02/1.44 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 1.02/1.44 ), U, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 1.02/1.44 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), Z, X
% 1.02/1.44 ), Y ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.02/1.44 , X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.02/1.44 , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.02/1.44 ,
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.02/1.44 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.02/1.44 ), X ), Y ) ],
% 1.02/1.44 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.02/1.44 'tc_nat' ) ],
% 1.02/1.44 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.02/1.44 'tc_nat' ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.44 'c_Power_Opower__class_Opower'( 'c_Power_Opower__class_Opower'( Y, Z, X )
% 1.02/1.44 , T, X ), 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.44 Z, T, 'tc_nat' ), X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.02/1.44 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.02/1.44 Y, X ) ) ],
% 1.02/1.44 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( Y,
% 1.02/1.44 'c_Suc'( Z ), X ), 'c_HOL_Otimes__class_Otimes'( Y,
% 1.02/1.44 'c_Power_Opower__class_Opower'( Y, Z, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.44 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.02/1.44 ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.44 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.02/1.44 ), X ) ) ],
% 1.02/1.44 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 1.02/1.44 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) )
% 1.02/1.44 ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.02/1.44 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 1.02/1.44 ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.02/1.44 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.02/1.44 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.02/1.44 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.02/1.44 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'c_lessequals'( X, X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X,
% 1.02/1.44 'c_Suc'( X ), 'tc_nat' ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.02/1.44 , Y, X ) ) ],
% 1.02/1.44 [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 1.02/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.02/1.44 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.02/1.44 ,
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.02/1.44 , Y, X ) ) ],
% 1.02/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.02/1.44 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ],
% 1.02/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.02/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.02/1.44 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.44 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.02/1.44 , T, X ), X ), T, X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.02/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'(
% 1.02/1.44 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), X ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.02/1.44 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.02/1.44 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 1.02/1.44 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.02/1.44 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 1.02/1.44 'c_OrderedGroup_Olordered__ab__group__add__class_Opprt'( Y, X ), Y ), ~(
% 1.02/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =(
% 1.02/1.44 'c_OrderedGroup_Olordered__ab__group__add__class_Opprt'( Y, X ), Y ) ),
% 1.02/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z
% 1.02/1.44 ), X ), 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.02/1.44 [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.02/1.44 'tc_nat' ), Y, 'tc_nat' ), 'tc_nat' ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.44 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.02/1.44 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.02/1.44 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Osgn__if'( X ) ), =(
% 1.02/1.44 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.02/1.44 'c_HOL_Oone__class_Oone'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.44 X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.02/1.44 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Z ), ~( 'c_lessequals'( Y, Z,
% 1.02/1.44 X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.02/1.44 , Z, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.02/1.44 , Z, X ) ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), =( Y, Z ) ]
% 1.02/1.44 ,
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.02/1.44 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.02/1.44 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.02/1.44 ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.02/1.44 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 1.02/1.44 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.02/1.44 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.02/1.44 ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 1.02/1.44 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.02/1.44 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.02/1.44 ) ],
% 1.02/1.44 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.02/1.44 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.02/1.44 , Z, X ) ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.02/1.44 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 1.02/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'( T, X ), Z,
% 1.02/1.44 X ) ) ],
% 1.02/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.02/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.02/1.44 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.44 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.02/1.44 , T, X ), X ), T, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.02/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ominus__class_Ominus'( Z
% 1.02/1.44 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.02/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.02/1.44 Y, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'(
% 1.02/1.44 Y, Z, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.02/1.44 'c_lessequals'( Y, T, X ), ~( 'c_lessequals'( Y,
% 1.02/1.44 'c_Orderings_Oord__class_Omax'( T, Z, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.02/1.44 'c_Power_Opower__class_Opower'( Y, T, X ), X ),
% 1.02/1.44 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T,
% 1.02/1.44 'tc_nat' ), X ) ) ],
% 1.02/1.44 [ =( 'c_Lambda_Oliftn'( 'c_Suc'( X ), Y, Z ), 'c_Lambda_Olift'(
% 1.02/1.44 'c_Lambda_Oliftn'( X, Y, Z ), Z ) ) ],
% 1.02/1.44 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), T, 'tc_nat' ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 1.02/1.44 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), T,
% 1.02/1.44 'tc_nat' ), 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.02/1.44 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X ), X ) ) ]
% 1.02/1.44 ,
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.02/1.44 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ]
% 1.02/1.44 ,
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 1.02/1.44 T, X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 1.02/1.44 T, X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 1.02/1.44 T, X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 1.02/1.44 T, X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.02/1.44 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X ), X ) ) ]
% 1.02/1.44 ,
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.02/1.44 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ]
% 1.02/1.44 ,
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.44 'c_HOL_Osgn__class_Osgn'( Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.44 'c_HOL_Osgn__class_Osgn'( Y, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.02/1.44 ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.02/1.44 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.02/1.44 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.02/1.44 , Y, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.02/1.44 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.44 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.02/1.44 X ), Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.02/1.44 , Z, X ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.02/1.44 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.02/1.44 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.02/1.44 X ), Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.02/1.44 , Z, X ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.02/1.44 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.02/1.44 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.02/1.44 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T, Z, X
% 1.02/1.44 ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X
% 1.02/1.44 ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.02/1.44 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ),
% 1.02/1.44 ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oinverse__class_Odivide'( Y, T, X
% 1.02/1.44 ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.02/1.44 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.44 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.02/1.44 T, X ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.02/1.44 , T, X ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.02/1.44 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.44 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.02/1.44 T, X ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.02/1.44 , T, X ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.02/1.44 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.44 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.02/1.44 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.02/1.44 Z, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.02/1.44 X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 1.02/1.44 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.02/1.44 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.02/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.02/1.44 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.02/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.44 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.02/1.44 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.02/1.44 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.02/1.44 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ],
% 1.02/1.44 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_Suc'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.02/1.44 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.02/1.44 , T, X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'(
% 1.02/1.44 Y, T, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.02/1.44 'c_lessequals'( Y, 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ],
% 1.02/1.44 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OAbs'( Y ) ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 1.02/1.44 ), X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.02/1.44 , X ), W, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 1.02/1.44 , X ), W, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X
% 1.02/1.44 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ),
% 1.02/1.44 W, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 1.02/1.44 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 1.02/1.44 , X ), T, X ), W, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.02/1.44 , X ), U, X ), W, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), U, X
% 1.02/1.44 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, X ),
% 1.02/1.44 W, X ), X ) ) ],
% 1.02/1.44 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.02/1.44 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ), U, 'tc_nat' ) ) ), ~(
% 1.02/1.44 'c_lessequals'( T, X, 'tc_nat' ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, T,
% 1.02/1.44 'tc_nat' ), Y, 'tc_nat' ), Z, 'tc_nat' ), U ) ],
% 1.02/1.44 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.02/1.44 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ), U, 'tc_nat' ) ) ), ~(
% 1.02/1.44 'c_lessequals'( X, T, 'tc_nat' ) ), =( Z, 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( T, X,
% 1.02/1.44 'tc_nat' ), Y, 'tc_nat' ), U, 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.44 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.02/1.44 X ), Y ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.02/1.44 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.02/1.44 X ), Y ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.02/1.44 'c_lessequals'( T, Z, X ), ~( 'c_lessequals'(
% 1.02/1.44 'c_Orderings_Oord__class_Omin'( T, Y, X ), Z, X ) ) ],
% 1.02/1.44 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), T,
% 1.02/1.44 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), T, 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 1.02/1.44 , X ) ) ],
% 1.02/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.02/1.44 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.02/1.44 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.02/1.44 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.02/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( U, Y, X ), Z, X
% 1.02/1.44 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( W, T, X ),
% 1.02/1.44 Z, X ) ) ],
% 1.02/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.02/1.44 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.44 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.02/1.44 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.02/1.44 ,
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.02/1.44 ,
% 1.02/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.02/1.44 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.44 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 1.02/1.44 Z, T, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.02/1.44 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z, X ) ) ]
% 1.02/1.44 ,
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.02/1.44 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z, X ) ) ]
% 1.02/1.44 ,
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.02/1.44 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 1.02/1.44 X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.02/1.44 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z,
% 1.02/1.44 X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.02/1.44 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 1.02/1.44 X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.02/1.44 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z,
% 1.02/1.44 X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.02/1.44 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z, X ) ) ]
% 1.02/1.44 ,
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.02/1.44 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z, X ) ) ]
% 1.02/1.44 ,
% 1.02/1.44 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 1.02/1.44 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Z,
% 1.02/1.44 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.02/1.44 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z,
% 1.02/1.44 'tc_nat' ), ~( 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 1.02/1.44 'tc_nat' ), 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.44 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.02/1.44 ,
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.02/1.44 , X ), 'c_HOL_Oord__class_Oless'( Y, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 Y, 'c_Orderings_Oord__class_Omax'( T, Z, X ), X ) ) ],
% 1.02/1.44 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.02/1.44 'tc_nat' ), 'tc_nat' ) ) ],
% 1.02/1.44 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.02/1.44 'tc_nat' ), 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.02/1.44 ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.02/1.44 ), =( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.02/1.44 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.02/1.44 ) ],
% 1.02/1.44 [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 1.02/1.44 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'( Z, X,
% 1.02/1.44 'tc_nat' ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Osgn__if'( X ) ), =(
% 1.02/1.44 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =(
% 1.02/1.44 Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.44 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y ) ) ), =( X, Y
% 1.02/1.44 ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.02/1.44 , Z, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.44 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.02/1.44 'tc_nat' ), Z, 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), ~(
% 1.02/1.44 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.44 X, Z, 'tc_nat' ), T, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 1.02/1.44 ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.02/1.44 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 1.02/1.44 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 1.02/1.44 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.02/1.44 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.02/1.44 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat'
% 1.02/1.44 ), X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 1.02/1.44 ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.02/1.44 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 1.02/1.44 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( Z,
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 1.02/1.44 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.02/1.44 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ), ~(
% 1.02/1.44 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.02/1.44 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.02/1.44 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ), ~(
% 1.02/1.44 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.02/1.44 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.02/1.44 , 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.44 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.02/1.44 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.02/1.44 , X ), 'c_HOL_Oord__class_Oless'( T, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_Orderings_Oord__class_Omin'( T, Y, X ), Z, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.02/1.44 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 1.02/1.44 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 1.02/1.44 ,
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.02/1.44 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y
% 1.02/1.44 , Z, X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ), =( Y, T ) ]
% 1.02/1.44 ,
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 1.02/1.44 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Z ) ), 'c_lessequals'( Y, Z, X
% 1.02/1.44 ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.02/1.44 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Y ), ~( 'c_lessequals'( Z, Y,
% 1.02/1.44 X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.02/1.44 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.02/1.44 ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.02/1.44 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 1.02/1.44 ) ) ],
% 1.02/1.44 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.02/1.44 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.02/1.44 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.02/1.44 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.02/1.44 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.02/1.44 ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.02/1.44 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 1.02/1.44 ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.02/1.44 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.02/1.44 ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.02/1.44 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.02/1.44 ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.02/1.44 , 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 1.02/1.44 ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.02/1.44 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 1.02/1.44 ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 1.02/1.44 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.02/1.44 ) ) ],
% 1.02/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.02/1.44 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.44 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y, X
% 1.02/1.44 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.02/1.44 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T,
% 1.02/1.44 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.44 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.02/1.44 Y, T, X ), X ) ) ],
% 1.02/1.44 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X,
% 1.02/1.44 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.44 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' )
% 1.02/1.44 ) ],
% 1.02/1.44 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X,
% 1.02/1.44 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.44 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' )
% 1.02/1.44 ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.02/1.44 , 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ), =(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Y, T, X ), U ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.02/1.44 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.02/1.44 Z, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X )
% 1.02/1.44 , 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ) ],
% 1.02/1.44 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 1.02/1.44 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.02/1.44 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 1.02/1.44 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.02/1.44 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.02/1.44 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.02/1.44 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 1.02/1.44 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.02/1.44 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ),
% 1.02/1.44 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.02/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.02/1.44 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 1.02/1.44 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.02/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 1.02/1.44 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), =( Y
% 1.02/1.44 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.02/1.44 , X ) ) ],
% 1.02/1.44 [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OVar'( X ), Y ),
% 1.02/1.44 'c_Lambda_OdB_OVar'( 'c_HOL_Oplus__class_Oplus'( X,
% 1.02/1.44 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 1.02/1.44 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 1.02/1.44 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.02/1.44 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.44 X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.02/1.44 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.02/1.44 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 1.02/1.44 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 1.02/1.44 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) )
% 1.02/1.44 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.02/1.44 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ), ~( 'c_lessequals'( Y, Z,
% 1.02/1.44 X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 1.02/1.44 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ) ), 'c_lessequals'( Y, Z, X
% 1.02/1.44 ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.02/1.44 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z ), ~( 'c_lessequals'( Z, Y,
% 1.02/1.44 X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), =(
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omax'( Y, Z, X ),
% 1.02/1.44 T, X ), 'c_Orderings_Oord__class_Omax'( 'c_HOL_Ominus__class_Ominus'( Y,
% 1.02/1.44 T, X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.02/1.44 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 1.02/1.44 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 1.02/1.44 , X ), 'c_lessequals'( Y, Y, X ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.02/1.44 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.02/1.44 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.02/1.44 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.02/1.44 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.02/1.44 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =( 'c_Lambda_Osubst'(
% 1.02/1.44 'c_Lambda_OdB_OVar'( X ), Y, X ), Y ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.02/1.44 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.02/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.44 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.02/1.44 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.44 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_lessequals'( Y,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.02/1.44 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.02/1.44 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.02/1.44 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.02/1.44 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 1.02/1.44 , Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.02/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.02/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.02/1.44 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.44 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 1.02/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.02/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.02/1.44 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.02/1.44 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.02/1.44 ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.02/1.44 ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 1.02/1.44 ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.02/1.44 ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.02/1.44 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 1.02/1.44 , T, X ), 'c_Orderings_Oord__class_Omin'( Y,
% 1.02/1.44 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.02/1.44 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 1.02/1.44 X ), X ), 'c_Orderings_Oord__class_Omin'( Z,
% 1.02/1.44 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ) ) ],
% 1.02/1.44 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.02/1.44 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 1.02/1.44 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.02/1.44 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 1.02/1.44 'tc_nat' ) ) ],
% 1.02/1.44 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.02/1.44 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.02/1.44 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.02/1.44 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.02/1.44 Y, T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X )
% 1.02/1.44 ), ~( 'c_lessequals'( Z, T, 'tc_nat' ) ) ],
% 1.02/1.44 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.02/1.44 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.02/1.44 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.02/1.44 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.02/1.44 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.02/1.44 'c_lessequals'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) )
% 1.02/1.44 , ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.02/1.44 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.02/1.44 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 1.02/1.44 ],
% 1.02/1.44 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.02/1.44 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.02/1.44 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.02/1.44 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X,
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.02/1.44 T, Z, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 1.02/1.44 ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.02/1.44 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 1.02/1.44 ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.02/1.44 , T, X ) ) ), =( Y, Z ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.02/1.44 , T, X ) ) ), =( Z, T ) ],
% 1.02/1.44 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 1.02/1.44 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), =( X, Z ) ]
% 1.02/1.44 ,
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.02/1.44 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Y, Z,
% 1.02/1.44 X ), X ), Y ) ],
% 1.02/1.44 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.02/1.44 'tc_nat' ) ), =( Y, Z ) ],
% 1.02/1.44 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.02/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.02/1.44 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y
% 1.02/1.44 , X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat'
% 1.02/1.44 ) ) ],
% 1.02/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.02/1.44 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X
% 1.02/1.44 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 1.02/1.44 ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.02/1.44 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Suc'( Y ), X ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 1.02/1.44 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_lessequals'( Y,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 1.02/1.44 X ) ) ],
% 1.02/1.44 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.02/1.44 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.02/1.44 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.02/1.44 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.02/1.44 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.02/1.44 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.02/1.44 'tc_nat' ) ) ],
% 1.02/1.44 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.02/1.44 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.02/1.44 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.02/1.44 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.02/1.44 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( T, Z, X
% 1.02/1.44 ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.02/1.44 ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.02/1.44 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.02/1.44 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.44 X ), T, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.02/1.44 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X
% 1.02/1.44 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 1.02/1.44 ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.02/1.44 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.02/1.44 , Z, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.02/1.44 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.02/1.44 , T, X ), X ) ) ],
% 1.02/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.44 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' )
% 1.02/1.44 , ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.44 'tc_nat' ) ), X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.02/1.44 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.02/1.44 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z,
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.02/1.44 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.02/1.44 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.02/1.44 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ],
% 1.02/1.44 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.02/1.44 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.02/1.44 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 1.02/1.44 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 1.02/1.44 , T ), =( X, Z ) ],
% 1.02/1.44 [ ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.02/1.44 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 1.02/1.44 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 1.02/1.44 , T ), =( X, Z ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.02/1.44 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 1.02/1.44 , 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 1.02/1.44 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X
% 1.02/1.44 ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.02/1.44 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), 'c_HOL_Otimes__class_Otimes'( Y, Y
% 1.02/1.44 , X ) ) ],
% 1.02/1.44 [ =( 'c_Nat_Osize__class_Osize'( X, 'tc_nat' ), X ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.02/1.44 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.02/1.44 , X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Oinverse'(
% 1.02/1.44 Y, X ), X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.02/1.44 'c_HOL_Oinverse__class_Oinverse'( 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.02/1.44 ), X ), 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Oinverse'(
% 1.02/1.44 Y, X ), Z, X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.44 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat'
% 1.02/1.44 ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OApp'( Y, Z ) ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.02/1.44 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 Z, Y, X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.02/1.44 , X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.44 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.02/1.44 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) )
% 1.02/1.44 , 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.02/1.44 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 1.02/1.44 , 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 1.02/1.44 [ ~( =( X, 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( X,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 1.02/1.44 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.02/1.44 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.02/1.44 ), X ) ],
% 1.02/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.02/1.44 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.02/1.44 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.02/1.44 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.02/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( U, Y, X ), Z
% 1.02/1.44 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( W, T,
% 1.02/1.44 X ), Z, X ) ) ],
% 1.02/1.44 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.02/1.44 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.02/1.44 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.02/1.44 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.02/1.44 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.02/1.44 'c_lessequals'( Z, X, 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.02/1.44 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 1.02/1.44 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.02/1.44 , Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ), =( U,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.02/1.44 ) ],
% 1.02/1.44 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.44 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat'
% 1.02/1.44 ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.02/1.44 , Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.02/1.44 , Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.02/1.44 ,
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.02/1.44 'c_HOL_Oabs__class_Oabs'( 'c_Power_Opower__class_Opower'(
% 1.02/1.44 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), X ),
% 1.02/1.44 'c_HOL_Oabs__class_Oabs'( 'c_Power_Opower__class_Opower'( Y, Z, X ), X )
% 1.02/1.44 ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z, X
% 1.02/1.44 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.02/1.44 'c_HOL_Oone__class_Oone'( X ), X ), Z, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X
% 1.02/1.44 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Z,
% 1.02/1.44 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ],
% 1.02/1.44 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 1.02/1.44 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.02/1.44 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.02/1.44 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'( Y,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.44 [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.02/1.44 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Y, 'tc_nat' ) ) ), =( X
% 1.02/1.44 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.02/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.02/1.44 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 1.02/1.44 ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( Y,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.02/1.44 ],
% 1.02/1.44 [ =( 'c_Nat_Osize__class_Osize'( 'c_Suc'( X ), 'tc_nat' ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_Nat_Osize__class_Osize'( X, 'tc_nat' ),
% 1.02/1.44 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.02/1.44 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ),
% 1.02/1.44 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) )
% 1.02/1.44 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.02/1.44 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.02/1.44 X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.02/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 1.02/1.44 ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.02/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.02/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 1.02/1.44 ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.02/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.02/1.44 Z, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.02/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.02/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.02/1.44 Z, X ) ) ],
% 1.02/1.44 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.02/1.44 ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.02/1.44 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.02/1.44 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 1.02/1.44 , X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.02/1.44 , Y, X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.02/1.44 , Y, X ) ) ],
% 1.02/1.44 [ ~( 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ),
% 1.02/1.44 'tc_nat' ) ), =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.44 Y, X, 'tc_nat' ), X, 'tc_nat' ), Y ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.02/1.44 'c_Orderings_Oord__class_Omin'( Y, Y, X ), Y ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Oinverse__class_Odivide'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), Y, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), Y, X ), Z ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.02/1.44 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.02/1.44 , Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 1.02/1.44 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.02/1.44 , Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ),
% 1.02/1.44 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 1.02/1.44 'c_HOL_Oabs__class_Oabs'( T, X ), X ), X ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ) ) ],
% 1.02/1.44 [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OVar'( Y ), Z ),
% 1.02/1.44 'c_Lambda_OdB_OVar'( 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ],
% 1.02/1.44 [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OApp'( 'c_Lambda_OdB_OAbs'( X ), Y ),
% 1.02/1.44 'c_Lambda_Osubst'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.02/1.44 ,
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.02/1.44 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.02/1.44 'tc_nat' ) ],
% 1.02/1.44 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ),
% 1.02/1.44 'tc_nat' ) ],
% 1.02/1.44 [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.02/1.44 'tc_nat' ) ],
% 1.02/1.44 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.02/1.44 'tc_nat' ), Y, 'tc_nat' ), 'c_Orderings_Oord__class_Omax'( X, Y, 'tc_nat'
% 1.02/1.44 ) ) ],
% 1.02/1.44 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =(
% 1.02/1.44 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.02/1.44 , X ) ) ), =( Y, Z ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.02/1.44 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 1.02/1.44 , X ) ) ), =( Y, Z ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.02/1.44 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.02/1.44 ), T, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.02/1.44 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 1.02/1.44 Z, T, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.02/1.44 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.44 X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.02/1.44 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.02/1.44 , Y, X ) ) ],
% 1.02/1.44 [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OAbs'( Y ), Z ),
% 1.02/1.44 'c_Lambda_OdB_OAbs'( 'c_Lambda_Oliftn'( X, Y, 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.44 Z, 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.02/1.44 ), =( Z, Y ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.02/1.44 ) ],
% 1.02/1.44 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 1.02/1.44 , Y, 'tc_nat' ) ) ],
% 1.02/1.44 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.02/1.44 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.02/1.44 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.02/1.44 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.02/1.44 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.02/1.44 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.02/1.44 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.02/1.44 ) ],
% 1.02/1.44 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.02/1.44 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.02/1.44 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.02/1.44 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.02/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.02/1.44 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 1.02/1.44 X ), Z, X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.02/1.44 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.02/1.44 , X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.02/1.44 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.02/1.44 ,
% 1.02/1.44 [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oone__class_Oone'(
% 1.02/1.44 'tc_nat' ), 'tc_nat' ) ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.02/1.44 [ =( X, 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.02/1.44 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.02/1.44 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.02/1.44 'c_Orderings_Oord__class_Omax'( Y, Y, X ), Y ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.02/1.44 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.02/1.44 [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OApp'( Z, T ) ) ),
% 1.02/1.44 =( Y, T ) ],
% 1.02/1.44 [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OApp'( Z, T ) ) ),
% 1.02/1.44 =( X, Z ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.02/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 1.02/1.44 ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.02/1.44 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.02/1.44 'tc_nat' ) ) ],
% 1.02/1.44 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.02/1.44 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ],
% 1.02/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.02/1.44 'c_Suc'( X ), 'tc_nat' ) ],
% 1.02/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.02/1.44 'c_Suc'( X ), 'tc_nat' ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.02/1.44 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ),
% 1.02/1.44 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.02/1.44 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.02/1.44 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.02/1.44 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.02/1.44 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.02/1.44 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omax'( Y, T
% 1.02/1.44 , X ), Z, X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.02/1.44 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omax'( T, Y
% 1.02/1.44 , X ), Z, X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.02/1.44 'c_Orderings_Oord__class_Omin'( Y, Z, X ), 'c_Orderings_Oord__class_Omin'(
% 1.02/1.44 Z, Y, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.02/1.44 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.02/1.44 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.02/1.44 , Y, X ) ) ],
% 1.02/1.44 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.02/1.44 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z,
% 1.02/1.44 Y, 'tc_nat' ), T, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 1.02/1.44 ), Y, 'tc_nat' ), T, 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 1.02/1.44 ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ), U, X ) ) ],
% 1.02/1.44 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), X,
% 1.02/1.44 'tc_nat' ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 1.02/1.44 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.02/1.44 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 1.02/1.44 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 1.02/1.44 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.02/1.44 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.44 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' ) )
% 1.02/1.44 ],
% 1.02/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.02/1.44 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.44 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) )
% 1.02/1.44 ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.02/1.44 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.02/1.44 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.02/1.44 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.44 X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, Z, X ),
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.44 X ), X ) ) ],
% 1.02/1.44 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 1.02/1.44 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.02/1.44 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.02/1.44 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.02/1.44 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T,
% 1.02/1.44 'tc_nat' ), X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.02/1.44 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.02/1.44 Y, T, X ), X ) ), ~( 'c_lessequals'( T, Z, 'tc_nat' ) ), =( Y,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.02/1.44 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.02/1.44 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ],
% 1.02/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.02/1.44 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.02/1.44 ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.02/1.44 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omin'( Z
% 1.02/1.44 , T, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.02/1.44 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omin'( T
% 1.02/1.44 , Z, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.02/1.44 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.02/1.44 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.02/1.44 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 1.02/1.44 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.02/1.44 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.02/1.44 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.02/1.44 , X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.02/1.44 , X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.02/1.44 ,
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.02/1.44 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.02/1.44 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.02/1.44 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.02/1.44 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y
% 1.02/1.44 , X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.02/1.44 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.02/1.44 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Z
% 1.02/1.44 , X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ), =( Z,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.02/1.44 ) ],
% 1.02/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.02/1.44 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.02/1.44 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z
% 1.02/1.44 , 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.02/1.44 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.02/1.44 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.02/1.44 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.02/1.44 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.02/1.44 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.02/1.44 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.02/1.44 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X )
% 1.02/1.44 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat'
% 1.02/1.44 ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.02/1.44 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X
% 1.02/1.44 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ),
% 1.02/1.44 'tc_nat' ) ) ],
% 1.02/1.44 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), =( 'c_Suc'( X
% 1.02/1.44 ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( Y )
% 1.02/1.44 , X, 'tc_nat' ) ) ],
% 1.02/1.44 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_lessequals'( Y, X,
% 1.02/1.44 'tc_nat' ) ],
% 1.02/1.44 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ],
% 1.02/1.44 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ) ) ), =( X, Z ) ],
% 1.02/1.44 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.02/1.44 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 1.02/1.44 X ) ) ), =( Z, T ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, T,
% 1.02/1.44 X ) ) ), =( Z, T ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 1.02/1.44 X ) ) ), =( Y, T ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.02/1.44 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ),
% 1.02/1.44 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.02/1.44 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.02/1.44 ), =( Y, 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 1.02/1.44 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.02/1.44 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.02/1.44 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.02/1.44 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ), ~(
% 1.02/1.44 'c_lessequals'( Y, Z, X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.02/1.44 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.02/1.44 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ), ~(
% 1.02/1.44 'c_lessequals'( Y, Z, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.02/1.44 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y
% 1.02/1.44 ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.02/1.44 , =( 'c_HOL_Oplus__class_Oplus'( 'c_Orderings_Oord__class_Omin'( Y, Z, X
% 1.02/1.44 ), T, X ), 'c_Orderings_Oord__class_Omin'( 'c_HOL_Oplus__class_Oplus'( Y
% 1.02/1.44 , T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ],
% 1.02/1.44 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'(
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat' ),
% 1.02/1.44 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z, X ), ~( 'c_lessequals'( Y,
% 1.02/1.44 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.02/1.44 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.02/1.44 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.02/1.44 ,
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.02/1.44 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.02/1.44 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.02/1.44 ,
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.02/1.44 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y, X ), ~( 'c_lessequals'( Z,
% 1.02/1.44 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.02/1.44 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.02/1.44 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ),
% 1.02/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 1.02/1.44 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 1.02/1.44 , T, X ), X ), T, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.02/1.44 'c_HOL_Oabs__class_Oabs'( 'c_Power_Opower__class_Opower'( Y, Z, X ), X )
% 1.02/1.44 , 'c_Power_Opower__class_Opower'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X
% 1.02/1.44 ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.02/1.44 'c_HOL_Oabs__class_Oabs'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X
% 1.02/1.44 ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.02/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.02/1.44 , Z, X ), 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~(
% 1.02/1.44 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.02/1.44 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 1.02/1.44 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) )
% 1.02/1.44 ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.02/1.44 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.02/1.44 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.02/1.44 [ =( 'c_Lambda_Osubst'( 'c_Lambda_Osubst'( X, 'c_Lambda_Olift'( Y, Z ),
% 1.02/1.44 'c_Suc'( T ) ), 'c_Lambda_Osubst'( U, Y, T ), Z ), 'c_Lambda_Osubst'(
% 1.02/1.44 'c_Lambda_Osubst'( X, U, Z ), Y, T ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.02/1.44 'c_HOL_Oplus__class_Oplus'( T, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.02/1.44 'tc_nat' ), 'tc_nat' ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.02/1.44 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 1.02/1.44 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.02/1.44 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.02/1.44 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.44 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.44 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.44 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.44 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.02/1.44 ,
% 1.02/1.44 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.44 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.02/1.44 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.02/1.44 ,
% 1.02/1.44 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.02/1.44 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.02/1.44 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.45 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ],
% 1.02/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.02/1.45 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.02/1.45 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.02/1.45 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ],
% 1.02/1.45 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Osgn__class_Osgn'( Y, X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Osgn__class_Osgn'( Y, X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.45 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 1.02/1.45 X ), Y, 'tc_nat' ), 'c_Suc'( Z ), 'tc_nat' ),
% 1.02/1.45 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.02/1.45 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.02/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.02/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 1.02/1.45 Z, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.02/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 1.02/1.45 Z, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.02/1.45 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.02/1.45 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.02/1.45 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), Z ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( Z, Y, X ), X ), Z ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.02/1.45 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.02/1.45 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.02/1.45 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.02/1.45 ,
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.02/1.45 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.02/1.45 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.02/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.02/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 1.02/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.02/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Y, X ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.02/1.45 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.02/1.45 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.02/1.45 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.02/1.45 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.02/1.45 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.02/1.45 , X ) ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.02/1.45 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ), X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.02/1.45 [ ~( 'c_Lambda_Obeta'( 'c_Lambda_OdB_OVar'( X ), Y ) ) ],
% 1.02/1.45 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 1.02/1.45 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), 'tc_nat' ),
% 1.02/1.45 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 1.02/1.45 ), 'c_Suc'( Y ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 1.02/1.45 ,
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.02/1.45 , X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.02/1.45 , X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.02/1.45 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.02/1.45 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.02/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Otimes__class_Otimes'( Z,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.02/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), X ) ],
% 1.02/1.45 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.02/1.45 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.02/1.45 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.02/1.45 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 1.02/1.45 ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.02/1.45 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 1.02/1.45 X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.02/1.45 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 1.02/1.45 ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.02/1.45 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 1.02/1.45 X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.02/1.45 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 1.02/1.45 ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.02/1.45 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 1.02/1.45 ) ],
% 1.02/1.45 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.02/1.45 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.02/1.45 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.45 Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.02/1.45 [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.02/1.45 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.02/1.45 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.02/1.45 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'( Z,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.02/1.45 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.02/1.45 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.02/1.45 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.02/1.45 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'( Z,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =(
% 1.02/1.45 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.02/1.45 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.02/1.45 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.02/1.45 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.45 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.02/1.45 , 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, T, X )
% 1.02/1.45 , 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.02/1.45 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.02/1.45 X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 1.02/1.45 X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.02/1.45 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.02/1.45 X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.02/1.45 , Z, X ) ) ],
% 1.02/1.45 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( Y,
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat'
% 1.02/1.45 ), X, 'tc_nat' ) ) ],
% 1.02/1.45 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, X,
% 1.02/1.45 'tc_nat' ), 'tc_nat' ), Y ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.02/1.45 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.02/1.45 'tc_nat' ), Y, 'tc_nat' ), X ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 1.02/1.45 ,
% 1.02/1.45 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 1.02/1.45 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.02/1.45 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' )
% 1.02/1.45 , 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.02/1.45 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.02/1.45 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.02/1.45 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.02/1.45 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Y,
% 1.02/1.45 'c_HOL_Oone__class_Oone'( X ), X ), X ) ],
% 1.02/1.45 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.02/1.45 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.02/1.45 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.02/1.45 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.02/1.45 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.02/1.45 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.02/1.45 [ =( 'c_List_Odrop'( X, 'c_List_Odrop'( Y, Z, T ), T ), 'c_List_Odrop'(
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, T ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.02/1.45 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.02/1.45 ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( T ), X ),
% 1.02/1.45 'c_Power_Opower__class_Opower'( Z, 'c_Suc'( T ), X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.02/1.45 , X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.02/1.45 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.02/1.45 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.02/1.45 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.02/1.45 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.45 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.02/1.45 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.02/1.45 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.02/1.45 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.02/1.45 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.02/1.45 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.02/1.45 ,
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.02/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 1.02/1.45 X ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 1.02/1.45 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.02/1.45 Y, T, X ) ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X
% 1.02/1.45 ), Y, X ) ), =( Z, T ) ],
% 1.02/1.45 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( Y,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( X
% 1.02/1.45 ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.45 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.02/1.45 , X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.02/1.45 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 1.02/1.45 'c_Lambda_OdB_OVar'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.02/1.45 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ) ],
% 1.02/1.45 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 1.02/1.45 'c_Lambda_OdB_OVar'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.02/1.45 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.02/1.45 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.02/1.45 'c_HOL_Oone__class_Oone'( X ), X ) ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.02/1.45 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.02/1.45 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.02/1.45 ), X ), 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.02/1.45 Y, X ), 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 1.02/1.45 X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 1.02/1.45 X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.02/1.45 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.02/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.02/1.45 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 1.02/1.45 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.02/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.02/1.45 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Y, X
% 1.02/1.45 ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.02/1.45 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y
% 1.02/1.45 , Z, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X
% 1.02/1.45 ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.02/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.02/1.45 , Z, X ), 'c_Power_Opower__class_Opower'( T, U, X ), X ), ~(
% 1.02/1.45 'c_lessequals'( Z, U, 'tc_nat' ) ), ~(
% 1.02/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.02/1.45 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.02/1.45 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.02/1.45 , X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.02/1.45 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.02/1.45 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.02/1.45 , X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.02/1.45 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.02/1.45 , X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.02/1.45 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.02/1.45 , X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.02/1.45 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.02/1.45 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ],
% 1.02/1.45 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( X ), Y,
% 1.02/1.45 'tc_nat' ) ) ],
% 1.02/1.45 [ 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ), ~( 'c_lessequals'( X, Y,
% 1.02/1.45 'tc_nat' ) ) ],
% 1.02/1.45 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( Y, X,
% 1.02/1.45 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.02/1.45 ) ), X, 'tc_nat' ) ) ],
% 1.02/1.45 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.02/1.45 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.02/1.45 ) ), X, 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.45 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), X ), Z ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.02/1.45 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.02/1.45 Z, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oinverse__class_Oinverse'(
% 1.02/1.45 Z, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.45 Y, 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ) ],
% 1.02/1.45 [ ~( 'c_lessequals'( 'c_Suc'( X ), X, 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.02/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.02/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 1.02/1.45 , X ), Z, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.02/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.02/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 1.02/1.45 , X ), Z, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.02/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 1.02/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.02/1.45 , X ), Z, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 1.02/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ouminus__class_Ouminus'( Y
% 1.02/1.45 , X ), Z, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ]
% 1.02/1.45 ,
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.02/1.45 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ), =( Z,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ominus__class_Ominus'(
% 1.02/1.45 Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 1.02/1.45 Z, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.02/1.45 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.02/1.45 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.02/1.45 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.02/1.45 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.02/1.45 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.02/1.45 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.02/1.45 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 1.02/1.45 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.02/1.45 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.02/1.45 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y,
% 1.02/1.45 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ),
% 1.02/1.45 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.02/1.45 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X, 'tc_nat' ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ), 'tc_nat' ) ) ]
% 1.02/1.45 ,
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Y,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Z,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, U,
% 1.02/1.45 X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.02/1.45 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Z,
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), T, X ) ), =( T,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.02/1.45 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), Z, X ) ), =( Z,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OApp'( X
% 1.02/1.45 , Z ) ), ~( 'c_Lambda_Obeta'( Y, Z ) ) ],
% 1.02/1.45 [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OApp'( Z
% 1.02/1.45 , Y ) ), ~( 'c_Lambda_Obeta'( X, Z ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'(
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.45 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oone__class_Oone'( X ), X ), X ), X
% 1.02/1.45 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.45 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oone__class_Oone'( X ), X ), X ), Z
% 1.02/1.45 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.02/1.45 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.02/1.45 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ) ],
% 1.02/1.45 [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 1.02/1.45 'c_Lambda_OdB_OVar'( 'c_HOL_Ominus__class_Ominus'( X,
% 1.02/1.45 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.02/1.45 'c_Orderings_Oord__class_Omax'( Y, Z, X ), 'c_Orderings_Oord__class_Omax'(
% 1.02/1.45 Z, Y, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 1.02/1.45 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.02/1.45 T, Z, X ) ) ), =( Y, T ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.02/1.45 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.02/1.45 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.02/1.45 , Z ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( T, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.02/1.45 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Otimes__class_Otimes'( Y,
% 1.02/1.45 'c_HOL_Osgn__class_Osgn'( Y, X ), X ) ) ],
% 1.02/1.45 [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OVar'( Y ), Z ),
% 1.02/1.45 'c_Lambda_OdB_OVar'( Y ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat'
% 1.02/1.45 ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.02/1.45 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ), =( Y,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.02/1.45 , 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ), =( Z,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.02/1.45 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.45 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.02/1.45 Z, X ), X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ), =( Z,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.02/1.45 ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.02/1.45 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oinverse__class_Oinverse'(
% 1.02/1.45 Y, X ), X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ), =( Z,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.02/1.45 ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.02/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 1.02/1.45 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 1.02/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ],
% 1.02/1.45 [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( X ), 'tc_nat' ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.02/1.45 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ],
% 1.02/1.45 [ =( 'c_List_Odrop'( X, 'c_List_Oreplicate'( Y, Z, T ), T ),
% 1.02/1.45 'c_List_Oreplicate'( 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, T
% 1.02/1.45 ) ) ],
% 1.02/1.45 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.02/1.45 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 1.02/1.45 , 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ),
% 1.02/1.45 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 1.02/1.45 X ), X ), X ) ],
% 1.02/1.45 [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OApp'( Y, Z ), T ),
% 1.02/1.45 'c_Lambda_OdB_OApp'( 'c_Lambda_Oliftn'( X, Y, T ), 'c_Lambda_Oliftn'( X,
% 1.02/1.45 Z, T ) ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.02/1.45 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.45 'c_OrderedGroup_Olordered__ab__group__add__class_Opprt'( Y, X ), X ) ]
% 1.02/1.45 ,
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.02/1.45 ,
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.02/1.45 ,
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.02/1.45 ,
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.02/1.45 ,
% 1.02/1.45 [ =( 'c_nat_Onat__size'( 'c_Suc'( X ) ), 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.45 'c_nat_Onat__size'( X ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.02/1.45 ), 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.02/1.45 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Y, Z,
% 1.02/1.45 X ), X ), Y ) ],
% 1.02/1.45 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.02/1.45 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 1.02/1.45 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.02/1.45 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ), Z, X ) ) ],
% 1.02/1.45 [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X, X, 'tc_nat' ),
% 1.02/1.45 'tc_nat' ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.02/1.45 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z, X )
% 1.02/1.45 , 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.02/1.45 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.02/1.45 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.02/1.45 , T, X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.45 Y, T, X ), Z, X ) ) ],
% 1.02/1.45 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.02/1.45 , 'tc_nat' ), 'tc_nat' ), Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 1.02/1.45 ,
% 1.02/1.45 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( 'tc_nat' )
% 1.02/1.45 , 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ),
% 1.02/1.45 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.02/1.45 [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OVar'( X ), Y ),
% 1.02/1.45 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat'
% 1.02/1.45 ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y,
% 1.02/1.45 'c_Power_Opower__class_Opower'( Y, Z, X ), X ),
% 1.02/1.45 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.02/1.45 ,
% 1.02/1.45 [ =( 'c_Orderings_Oord__class_Omin'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 1.02/1.45 'tc_nat' ), 'c_Suc'( 'c_Orderings_Oord__class_Omin'( X, Y, 'tc_nat' ) ) )
% 1.02/1.45 ],
% 1.02/1.45 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =( 'c_Lambda_Osubstn'(
% 1.02/1.45 'c_Lambda_OdB_OVar'( X ), Y, X ), 'c_Lambda_Oliftn'( X, Y,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.02/1.45 [ =( X, 'c_Suc'( Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 1.02/1.45 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.02/1.45 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.02/1.45 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ],
% 1.02/1.45 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.02/1.45 [ =( 'c_Lambda_Olift'( 'c_Lambda_Olift'( X, Y ), 'c_Suc'( Z ) ),
% 1.02/1.45 'c_Lambda_Olift'( 'c_Lambda_Olift'( X, Z ), Y ) ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 1.02/1.45 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.02/1.45 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.02/1.45 ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.45 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.02/1.45 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.02/1.45 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.02/1.45 'tc_nat' ) ) ],
% 1.02/1.45 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.02/1.45 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.02/1.45 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.02/1.45 'tc_nat' ) ) ],
% 1.02/1.45 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.02/1.45 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.02/1.45 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.02/1.45 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.02/1.45 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.02/1.45 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.02/1.45 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.02/1.45 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.02/1.45 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 1.02/1.45 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.02/1.45 'tc_nat' ) ) ],
% 1.02/1.45 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.02/1.45 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.02/1.45 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.02/1.45 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.02/1.45 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.02/1.45 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.45 X ), T, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.02/1.45 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.45 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.02/1.45 T, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.45 Y, T, X ), Z, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.02/1.45 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.45 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.02/1.45 T, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.45 Y, T, X ), Z, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.02/1.45 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.45 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.02/1.45 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ]
% 1.02/1.45 ,
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 1.02/1.45 , X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.02/1.45 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.02/1.45 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.02/1.45 X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.02/1.45 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.45 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 1.02/1.45 X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.02/1.45 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.02/1.45 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.02/1.45 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ]
% 1.02/1.45 ,
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y
% 1.02/1.45 , X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.02/1.45 , =( 'c_HOL_Oplus__class_Oplus'( 'c_Orderings_Oord__class_Omax'( Y, Z, X
% 1.02/1.45 ), T, X ), 'c_Orderings_Oord__class_Omax'( 'c_HOL_Oplus__class_Oplus'( Y
% 1.02/1.45 , T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.02/1.45 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Osgn__class_Osgn'( Y, X ), X ),
% 1.02/1.45 'c_HOL_Osgn__class_Osgn'( Y, X ) ) ],
% 1.02/1.45 [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OApp'( X, 'c_Lambda_OdB_OVar'( Y )
% 1.02/1.45 ) ), ~( 'c_InductTermi_OIT'( X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 1.02/1.45 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 1.02/1.45 'c_Power_Opower__class_Opower'( T, 'c_Suc'( Z ), X ) ) ), =( Y, T ), ~(
% 1.02/1.45 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.02/1.45 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.02/1.45 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 1.02/1.45 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) )
% 1.02/1.45 ],
% 1.02/1.45 [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X,
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( X, X, 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ]
% 1.02/1.45 ,
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.02/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 1.02/1.45 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ]
% 1.02/1.45 ,
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.02/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 1.02/1.45 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 1.02/1.45 ,
% 1.02/1.45 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' )
% 1.02/1.45 , 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.02/1.45 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 1.02/1.45 ],
% 1.02/1.45 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.02/1.45 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.02/1.45 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 1.02/1.45 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 1.02/1.45 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.02/1.45 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 1.02/1.45 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat'
% 1.02/1.45 ) ) ],
% 1.02/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.02/1.45 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T
% 1.02/1.45 , X ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), ~(
% 1.02/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.02/1.45 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.02/1.45 ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 1.02/1.45 ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.02/1.45 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.02/1.45 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.02/1.45 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.02/1.45 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 1.02/1.45 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 1.02/1.45 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.02/1.45 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 1.02/1.45 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.02/1.45 X ), T, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.02/1.45 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 1.02/1.45 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.02/1.45 X ), T, X ) ) ],
% 1.02/1.45 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.02/1.45 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.02/1.45 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.02/1.45 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.02/1.45 ), T, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.02/1.45 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 1.02/1.45 Z, T, X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), =( Y
% 1.02/1.45 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.02/1.45 , X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =(
% 1.02/1.45 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ominus__class_Ominus'( Y, Z
% 1.02/1.45 , 'tc_nat' ), X ), 'c_HOL_Ominus__class_Ominus'(
% 1.02/1.45 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.02/1.45 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ), ~( 'c_lessequals'( Z
% 1.02/1.45 , Y, 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.02/1.45 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.02/1.45 , Y, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.02/1.45 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 1.02/1.45 X ), X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.02/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.02/1.45 , X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 1.02/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Z, U, X ) ), ~(
% 1.02/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.02/1.45 , Z, X ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.02/1.45 ), ~( 'c_lessequals'( T, Y, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.02/1.45 , T, X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.02/1.45 ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.02/1.45 , Z, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.02/1.45 ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.02/1.45 , T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.02/1.45 ), ~( 'c_lessequals'( Z, T, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.02/1.45 , T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.02/1.45 ), ~( 'c_lessequals'( Z, T, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.02/1.45 X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.45 Z, T, X ), X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ), =( T, U ), =( Z,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.02/1.45 Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X,
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), 'tc_nat' ) ) ), =( Z, T )
% 1.02/1.45 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.45 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =(
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.45 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.02/1.45 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.45 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 1.02/1.45 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 1.02/1.45 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ],
% 1.02/1.45 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 1.02/1.45 ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.02/1.45 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.02/1.45 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.02/1.45 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.02/1.45 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ]
% 1.02/1.45 ,
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.02/1.45 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~(
% 1.02/1.45 'c_lessequals'( Z, 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ]
% 1.02/1.45 ,
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.02/1.45 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.02/1.45 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 1.02/1.45 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.02/1.45 ), =( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Z ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.45 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ) ]
% 1.02/1.45 ,
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.02/1.45 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.02/1.45 X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.45 X ), T, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.02/1.45 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.02/1.45 Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.45 X ), Z, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X
% 1.02/1.45 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.02/1.45 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, T,
% 1.02/1.45 X ), Z, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 1.02/1.45 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.02/1.45 X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 1.02/1.45 Z, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 1.02/1.45 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.02/1.45 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 1.02/1.45 Z, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 1.02/1.45 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 1.02/1.45 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.02/1.45 X ), Z, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.02/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Power_Opower__class_Opower'(
% 1.02/1.45 Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.45 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 Y, T, X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.02/1.45 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 Y, T, X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.02/1.45 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 1.02/1.45 X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 Z, T, X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.02/1.45 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 Z, T, X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.02/1.45 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 1.02/1.45 X ), X ) ) ],
% 1.02/1.45 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 1.02/1.45 ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.02/1.45 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ),
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.02/1.45 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 1.02/1.45 ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.02/1.45 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.02/1.45 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y,
% 1.02/1.45 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.45 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.02/1.45 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.02/1.45 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.02/1.45 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 1.02/1.45 ) ) ],
% 1.02/1.45 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.02/1.45 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 1.02/1.45 ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.02/1.45 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.02/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.02/1.45 , Z, X ), T, X ), ~( 'c_lessequals'( Z, U, 'tc_nat' ) ), ~(
% 1.02/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 1.02/1.45 , U, X ), T, X ) ) ],
% 1.02/1.45 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.02/1.45 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.02/1.45 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 1.02/1.45 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z, Y, 'tc_nat' )
% 1.02/1.45 ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.02/1.45 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 1.02/1.45 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 1.02/1.45 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 1.02/1.45 ,
% 1.02/1.45 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.02/1.45 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 1.02/1.45 , X ) ) ],
% 1.02/1.45 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.02/1.45 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.02/1.45 , X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.02/1.45 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 1.02/1.45 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y,
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( Z, U, X ), X ) ) ],
% 1.02/1.45 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OApp'( Y, Z ) ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.02/1.45 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.02/1.45 [ =( 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.02/1.45 , 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 1.02/1.45 , 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omin'( X, Z,
% 1.02/1.45 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.02/1.45 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.02/1.45 , 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.02/1.45 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.02/1.45 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.02/1.45 ,
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.02/1.45 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.02/1.45 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.02/1.45 ,
% 1.02/1.45 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ],
% 1.02/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.02/1.45 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 1.02/1.45 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.02/1.45 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 1.02/1.45 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OVar'( Y ) ) ), =( X, Y
% 1.02/1.45 ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.02/1.45 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 1.02/1.45 , ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.02/1.45 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.02/1.45 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.45 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.02/1.45 , Y, X ), X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ), =( Z,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.02/1.45 ) ],
% 1.02/1.45 [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OAbs'( Z ) ) ) ],
% 1.02/1.45 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OVar'( Y ) ) ) ],
% 1.02/1.45 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.02/1.45 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.02/1.45 , U, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.02/1.45 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.02/1.45 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.02/1.45 , U, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.02/1.45 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.02/1.45 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Y
% 1.02/1.45 , X ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.45 X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Y
% 1.02/1.45 , X ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.45 X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 1.02/1.45 , X ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.45 X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.02/1.45 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.45 Y, Y, X ) ) ],
% 1.02/1.45 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.02/1.45 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omax'( Y, Z, X )
% 1.02/1.45 , T, X ), 'c_Orderings_Oord__class_Omax'( Y,
% 1.02/1.45 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.02/1.45 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.45 Y, Z, X ) ) ],
% 1.02/1.45 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.02/1.45 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 1.02/1.45 X ), X ), 'c_Orderings_Oord__class_Omax'( Z,
% 1.02/1.45 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.02/1.45 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 1.02/1.45 X ), 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 1.02/1.45 'c_HOL_Oone__class_Oone'( X ), X ), X ) ],
% 1.02/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.02/1.45 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), T, X ),
% 1.02/1.45 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 1.02/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.02/1.45 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), Z, X ),
% 1.02/1.45 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.02/1.45 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 1.02/1.45 , 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.02/1.45 , Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ), =( U,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.02/1.45 ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 1.02/1.45 ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.02/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.02/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 1.02/1.45 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 1.02/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.02/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 1.02/1.45 , X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.02/1.45 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.02/1.45 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.02/1.45 , X ), X ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.02/1.45 , X ), X ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.02/1.45 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 1.02/1.45 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.45 X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z,
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ), ~( 'c_lessequals'(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( Y,
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ), ~( 'c_lessequals'( Y,
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ],
% 1.02/1.45 [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y ) )
% 1.02/1.45 , ~( 'c_Lambda_Obeta'( X, Y ) ) ],
% 1.02/1.45 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.02/1.45 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omax'( Y, Z,
% 1.02/1.45 X ), X ), 'c_Orderings_Oord__class_Omax'( Y, Z, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.02/1.45 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.02/1.45 , X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.02/1.45 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 1.02/1.45 , X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.02/1.45 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.02/1.45 , X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.02/1.45 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 1.02/1.45 , X ) ) ],
% 1.02/1.45 [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OApp'( X, Y ), Z, T ),
% 1.02/1.45 'c_Lambda_OdB_OApp'( 'c_Lambda_Osubstn'( X, Z, T ), 'c_Lambda_Osubstn'( Y
% 1.02/1.45 , Z, T ) ) ) ],
% 1.02/1.45 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.02/1.45 'tc_nat' ), Y, 'tc_nat' ), X ) ],
% 1.02/1.45 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.02/1.45 'tc_nat' ), X, 'tc_nat' ), Y ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.02/1.45 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 1.02/1.45 ), Y ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.02/1.45 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.02/1.45 X ), ~( 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.02/1.45 ,
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.02/1.45 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( T, Y
% 1.02/1.45 , X ), 'c_Power_Opower__class_Opower'( T, Z, X ), X ) ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.02/1.45 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( T, Y
% 1.02/1.45 , X ), 'c_Power_Opower__class_Opower'( T, Z, X ), X ) ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.02/1.45 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.02/1.45 Y, T, X ), X ), ~( 'c_lessequals'( Z, T, 'tc_nat' ) ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.02/1.45 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.02/1.45 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.02/1.45 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.02/1.45 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 1.02/1.45 ), X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.02/1.45 Y, X ), Z, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 1.02/1.45 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, T
% 1.02/1.45 , X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.02/1.45 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ),
% 1.02/1.45 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Z, Y, X ), X ) )
% 1.02/1.45 ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.02/1.45 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.02/1.45 ), Y ) ],
% 1.02/1.45 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 1.02/1.45 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.02/1.45 ), Y ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 1.02/1.45 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.02/1.45 ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 1.02/1.45 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.02/1.45 ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.02/1.45 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 1.02/1.45 ), Y ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.02/1.45 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.02/1.45 X ), 'c_HOL_Ominus__class_Ominus'( Z, Y, X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 1.02/1.45 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.02/1.45 [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OVar'( Z ) ) ) ],
% 1.02/1.45 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.02/1.45 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ]
% 1.02/1.45 ,
% 1.02/1.45 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.02/1.45 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.02/1.45 'tc_nat' ) ) ],
% 1.02/1.45 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.02/1.45 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.02/1.45 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.02/1.45 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.02/1.45 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 1.02/1.45 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.02/1.45 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.02/1.45 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.02/1.45 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 1.02/1.45 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 1.02/1.45 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.02/1.45 , X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X )
% 1.02/1.45 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.02/1.45 , X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.02/1.45 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 1.02/1.45 , X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 1.02/1.45 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y
% 1.02/1.45 , X ) ) ],
% 1.02/1.45 [ =( 'c_Lambda_Olift'( 'c_Lambda_Osubst'( X, Y, Z ), T ),
% 1.02/1.45 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, T ), 'c_Lambda_Olift'( Y, T ),
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.02/1.45 'tc_nat' ) ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.02/1.45 'tc_nat' ), 'tc_nat' ) ) ],
% 1.02/1.45 [ =( 'c_Lambda_Olift'( 'c_Lambda_Osubst'( X, Y, Z ), T ),
% 1.02/1.45 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, 'c_HOL_Oplus__class_Oplus'( T,
% 1.02/1.45 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ), 'c_Lambda_Olift'( Y,
% 1.02/1.45 T ), Z ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.45 T, 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.02/1.45 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.02/1.45 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.02/1.45 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.02/1.45 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ), =( Z,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.02/1.45 ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~( =(
% 1.02/1.45 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.02/1.45 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.02/1.45 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), =(
% 1.02/1.45 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.02/1.45 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.02/1.45 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~( =(
% 1.02/1.45 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.02/1.45 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.02/1.45 ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.02/1.45 ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 1.02/1.45 =( 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.45 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Osgn__if'( X ) ), =(
% 1.02/1.45 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.02/1.45 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.02/1.45 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.02/1.45 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.02/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.02/1.45 , X ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.02/1.45 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.02/1.45 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.02/1.45 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.02/1.45 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.02/1.45 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.02/1.45 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.02/1.45 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.02/1.45 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.02/1.45 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.02/1.45 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.02/1.45 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.02/1.45 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.02/1.45 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ],
% 1.02/1.45 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 1.02/1.45 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 1.02/1.45 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 1.02/1.45 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =(
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.02/1.45 ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.02/1.45 , Y, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.02/1.45 , T, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.02/1.45 , T, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.02/1.45 , Y, X ), X ) ) ],
% 1.02/1.45 [ ~( =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ) ) ), =( Y, Z )
% 1.02/1.45 ],
% 1.02/1.45 [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.02/1.45 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.02/1.45 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.02/1.45 'tc_nat' ), X ), 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.45 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.02/1.45 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 1.02/1.45 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.02/1.45 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.02/1.45 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.02/1.45 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 1.02/1.45 X ), X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 1.02/1.45 Y, Z, X ), 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ), X ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.02/1.45 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.02/1.45 , U, X ) ) ), 'c_lessequals'( U, T, X ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 1.02/1.45 ,
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.02/1.45 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.02/1.45 , U, X ) ) ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( U, T, X ) ) ]
% 1.02/1.45 ,
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.02/1.45 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.02/1.45 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( T, U, X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.02/1.45 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.02/1.45 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( T, U, X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.02/1.45 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.02/1.45 T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y,
% 1.02/1.45 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.45 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.02/1.45 T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y,
% 1.02/1.45 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.02/1.45 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.45 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 1.02/1.45 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 1.02/1.45 ) ) ],
% 1.02/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.02/1.45 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 1.02/1.45 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ),
% 1.02/1.45 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.02/1.45 ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.45 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.45 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.02/1.45 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, X,
% 1.02/1.45 'tc_nat' ), 'tc_nat' ), Y ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' )
% 1.02/1.45 ],
% 1.02/1.45 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'( Y
% 1.02/1.45 ), 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 1.02/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 1.02/1.45 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Z,
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( U, W, X ), X ), T, X ), X ) ), ~(
% 1.02/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, W, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 1.02/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.45 'c_HOL_Ominus__class_Ominus'( Z, 'c_HOL_Otimes__class_Otimes'( T, U, X )
% 1.02/1.45 , X ), W, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( Z, W, X ), X ) ), ~(
% 1.02/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, U, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.02/1.45 , U, X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( U,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 1.02/1.45 , U, X ), 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ) ), =( U,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.02/1.45 ), =( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( T, Z, X ) ) ],
% 1.02/1.45 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.02/1.45 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.02/1.45 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 1.02/1.45 , T, X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 1.02/1.45 Y, T, X ), 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.02/1.45 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 1.02/1.45 X ), X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 1.02/1.45 Y, Z, X ), 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.02/1.45 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T,
% 1.02/1.45 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'(
% 1.02/1.45 'c_Power_Opower__class_Opower'( Y, Z, X ), T, X ) ) ],
% 1.02/1.45 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.02/1.45 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.02/1.45 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.02/1.45 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 1.02/1.45 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 1.02/1.45 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.02/1.45 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.02/1.45 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.02/1.45 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 1.02/1.45 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.02/1.45 ,
% 1.02/1.45 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.02/1.45 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.02/1.45 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.02/1.45 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.02/1.45 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.02/1.45 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 1.02/1.45 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 1.02/1.45 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.02/1.45 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.02/1.45 ,
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'( Z,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.02/1.45 ,
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.02/1.45 ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.02/1.45 'c_HOL_Oinverse__class_Oinverse'( 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.02/1.45 ), X ), 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Oinverse'(
% 1.02/1.45 Y, X ), Z, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.02/1.45 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 1.02/1.45 , X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Oinverse'(
% 1.02/1.45 Y, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.02/1.45 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Osgn__class_Osgn'( Y, X ),
% 1.02/1.45 'c_HOL_Osgn__class_Osgn'( Z, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.02/1.45 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.02/1.45 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.02/1.45 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.02/1.45 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.02/1.45 , X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.02/1.45 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.02/1.45 , X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.02/1.45 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.02/1.45 , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.02/1.45 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.02/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.02/1.45 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z
% 1.02/1.45 , X ) ) ],
% 1.02/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.02/1.45 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Omod'( Z, T, X )
% 1.02/1.45 , X ) ) ],
% 1.02/1.45 [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OAbs'( X ), Y ),
% 1.02/1.45 'c_Lambda_OdB_OAbs'( 'c_Lambda_Olift'( X, 'c_HOL_Oplus__class_Oplus'( Y,
% 1.02/1.45 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 1.02/1.45 ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 1.02/1.45 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.02/1.45 ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.02/1.45 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.02/1.45 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oabs__class_Oabs'(
% 1.02/1.45 Y, X ), X ) ],
% 1.02/1.45 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ouminus__class_Ouminus'(
% 1.02/1.45 Y, X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.02/1.45 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ],
% 1.02/1.45 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( X ),
% 1.02/1.45 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.02/1.45 [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.02/1.45 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y, X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.02/1.45 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.02/1.45 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ), ~(
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.02/1.45 ,
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.02/1.45 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oabs__class_Oabs'( Y
% 1.02/1.45 , X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), 'c_HOL_Oabs__class_Oabs'(
% 1.02/1.45 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), X ) ],
% 1.02/1.45 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( X,
% 1.02/1.45 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( Y,
% 1.02/1.45 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.02/1.45 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 1.02/1.45 T, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.02/1.45 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.02/1.45 X ), Z, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.02/1.45 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 1.02/1.45 T, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.02/1.45 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.02/1.45 X ), T, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.02/1.45 , X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.02/1.45 T, X ), X ) ) ],
% 1.02/1.45 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.02/1.45 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.02/1.45 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.02/1.45 X ), T, X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.02/1.45 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 1.02/1.45 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ],
% 1.02/1.45 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 1.02/1.45 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.02/1.45 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 1.02/1.45 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 1.02/1.45 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.02/1.45 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) ),
% 1.02/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.02/1.45 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X
% 1.02/1.45 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 1.02/1.45 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.02/1.45 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X
% 1.02/1.45 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 1.02/1.45 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.02/1.45 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 1.02/1.45 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 1.02/1.45 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.02/1.45 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.02/1.45 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.02/1.45 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.02/1.45 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.02/1.45 [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X, 'tc_nat' ) ]
% 1.02/1.45 ,
% 1.02/1.45 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.02/1.45 'c_lessequals'( Z, Y, X ) ],
% 1.02/1.45 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.02/1.45 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.02/1.45 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.02/1.45 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =(
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.02/1.45 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.02/1.45 X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y, X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.02/1.45 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.02/1.45 ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.02/1.45 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.02/1.45 ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.02/1.45 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.02/1.45 ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.02/1.45 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.02/1.45 ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.02/1.45 X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ), =( Z,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.02/1.45 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.02/1.45 ) ],
% 1.02/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.02/1.45 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.02/1.45 ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 1.02/1.45 'c_OrderedGroup_Olordered__ab__group__add__class_Opprt'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.02/1.45 ,
% 1.02/1.45 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.02/1.45 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.02/1.45 ,
% 1.02/1.45 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =(
% 1.02/1.45 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 1.02/1.45 ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 1.02/1.45 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 1.02/1.45 ), X ), Y ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( Y,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.02/1.45 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.02/1.45 , X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.02/1.45 X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.02/1.45 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.02/1.45 ) ), =( Y, Z ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.02/1.45 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.02/1.45 ) ), =( Y, Z ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.02/1.45 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.02/1.45 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.02/1.45 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.02/1.45 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.02/1.45 ,
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.02/1.45 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.02/1.45 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.02/1.45 ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.02/1.45 ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.02/1.45 X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.02/1.45 ), X ) ) ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 1.02/1.45 ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.02/1.45 ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 1.02/1.45 ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 1.02/1.45 ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.02/1.45 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 1.02/1.45 ],
% 1.02/1.45 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), ~( =(
% 1.02/1.45 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y ) ), =( Y,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.02/1.45 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.02/1.45 X ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.02/1.45 [ =( 'c_Nat_Osize__class_Osize'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.02/1.45 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.02/1.45 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ],
% 1.02/1.45 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.45 'tc_nat' ), 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.02/1.45 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.02/1.45 ), X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.02/1.45 [ =( 'c_Lambda_Oliftn'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, Y ),
% 1.02/1.45 X ) ],
% 1.02/1.45 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.02/1.45 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.02/1.45 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.02/1.45 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 1.02/1.45 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ],
% 1.02/1.45 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.02/1.45 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.45 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.02/1.45 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.02/1.45 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.02/1.45 [ =( 'c_Orderings_Oord__class_Omin'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.45 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.02/1.45 [ =( 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.45 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 1.02/1.45 ,
% 1.02/1.45 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ), =( Y,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 1.02/1.45 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( X,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 1.02/1.45 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.02/1.45 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( Y, Z ), =( X,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.02/1.45 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.45 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.02/1.45 [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( =( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X ) ), =( Y,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.02/1.45 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.02/1.45 [ =( 'c_Nitpick_Onat__gcd'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.02/1.45 , X ) ],
% 1.02/1.45 [ =( 'c_nat_Onat__size'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.02/1.45 [ =( 'c_String_Ochar_Ochar__size'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.45 'tc_nat' ) ) ],
% 1.02/1.45 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.02/1.45 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.02/1.45 ), 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.02/1.45 ), 'tc_nat' ) ) ],
% 1.02/1.45 [ =( 'c_Orderings_Obot__class_Obot'( 'tc_nat' ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.02/1.45 [ =( 'c_List_Odrop'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, Y ), X )
% 1.02/1.45 ],
% 1.02/1.45 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.02/1.45 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.02/1.45 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' )
% 1.02/1.45 ],
% 1.02/1.45 [ =( 'c_Nat_Osize__class_Osize'( X, 'tc_String_Ochar' ),
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.02/1.45 [ =( 'c_List_Oreplicate'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, Y )
% 1.02/1.45 , 'c_List_Oreplicate'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, Y ) ) ]
% 1.02/1.45 ,
% 1.02/1.45 [ =( 'c_Orderings_Oord__class_Omax'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.45 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.02/1.45 [ =( 'c_Orderings_Oord__class_Omax'( 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.45 'tc_nat' ), X, 'tc_nat' ), X ) ],
% 1.02/1.45 [ ~( =( 'c_List_Oreplicate'( X, Y, Z ), 'c_List_Oreplicate'( T, U, Z ) )
% 1.02/1.45 ), =( Y, U ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.02/1.45 [ =( X, 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.45 'tc_nat' ), 'tc_nat' ) ) ],
% 1.02/1.45 [ =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.02/1.45 , X, 'tc_nat' ), X ) ],
% 1.02/1.45 [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.02/1.45 ), 'tc_nat' ), X ) ],
% 1.02/1.45 [ =( 'c_Lambda_Osubstn'( X, Y, Z ), 'c_Lambda_Osubst'( X,
% 1.02/1.45 'c_Lambda_Oliftn'( Z, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ) )
% 1.02/1.45 ],
% 1.02/1.45 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OAbs'( X ), Y, Z ),
% 1.02/1.45 'c_Lambda_OdB_OAbs'( 'c_Lambda_Osubst'( X, 'c_Lambda_Olift'( Y,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oplus__class_Oplus'( Z,
% 1.02/1.45 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ) ) ],
% 1.02/1.45 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OApp'( X, Y ), Z, T ),
% 1.02/1.45 'c_Lambda_OdB_OApp'( 'c_Lambda_Osubst'( X, Z, T ), 'c_Lambda_Osubst'( Y,
% 1.02/1.45 Z, T ) ) ) ],
% 1.02/1.45 [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, X ), Y ) ],
% 1.02/1.45 [ 'c_Lambda_Obeta'( 'c_Lambda_Osubst'( X, Y, Z ), 'c_Lambda_Osubst'( T,
% 1.02/1.45 Y, Z ) ), ~( 'c_Lambda_Obeta'( X, T ) ) ],
% 1.02/1.45 [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OApp'( X, Y ), Z ),
% 1.02/1.45 'c_Lambda_OdB_OApp'( 'c_Lambda_Olift'( X, Z ), 'c_Lambda_Olift'( Y, Z ) )
% 1.02/1.45 ) ],
% 1.02/1.45 [ 'c_Lambda_Obeta'( 'c_Lambda_Olift'( X, Y ), 'c_Lambda_Olift'( Z, Y ) )
% 1.02/1.45 , ~( 'c_Lambda_Obeta'( X, Z ) ) ],
% 1.02/1.45 [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OVar'( X ) ) ],
% 1.02/1.45 [ 'c_InductTermi_OIT'( 'v_ua______' ) ],
% 1.02/1.45 [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OAbs'( X ) ), ~(
% 1.02/1.45 'c_InductTermi_OIT'( X ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.02/1.45 ), =( 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.02/1.45 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.02/1.45 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.02/1.45 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.02/1.45 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.02/1.45 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.02/1.45 ), ~( =( 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.45 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.02/1.45 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.02/1.45 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 1.02/1.45 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.02/1.45 [ =( 'c_Lambda_Osubstn'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.02/1.45 , 'c_Lambda_Osubst'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.02/1.45 ,
% 1.02/1.45 [ 'c_InductTermi_OIT'( 'c_Lambda_Osubst'( X, 'c_Lambda_OdB_OVar'( Y ), Z
% 1.02/1.45 ) ), ~( 'c_InductTermi_OIT'( X ) ) ],
% 1.02/1.45 [ =( 'v_n____', 'v_i____' ) ],
% 1.02/1.45 [ 'c_InductTermi_OIT'( 'c_Lambda_Olift'( X, Y ) ), ~(
% 1.02/1.45 'c_InductTermi_OIT'( X ) ) ],
% 1.02/1.45 [ 'c_InductTermi_OIT'( 'v_u____' ) ],
% 1.02/1.45 [ =( 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, Y ), Z, Y ), X ) ],
% 1.02/1.45 [ 'c_InductTermi_OIT'( 'c_Lambda_Osubst'( 'v_b____', 'v_u____',
% 1.02/1.45 'v_i____' ) ) ],
% 1.02/1.45 [ ~( 'c_InductTermi_OIT'( 'c_Lambda_Olift'( 'c_Lambda_Osubst'( 'v_b____'
% 1.02/1.45 , 'v_u____', 'v_i____' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ]
% 1.02/1.45 ,
% 1.02/1.45 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.02/1.45 ],
% 1.02/1.45 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.02/1.45 ) ],
% 1.02/1.45 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.02/1.45 ],
% 1.02/1.45 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 1.02/1.45 ,
% 1.02/1.45 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.02/1.45 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 1.02/1.45 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.02/1.45 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.02/1.45 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.02/1.45 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 1.02/1.45 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 1.02/1.45 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.02/1.45 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.02/1.45 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.02/1.45 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.02/1.45 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.02/1.45 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.02/1.45 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.02/1.45 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.02/1.45 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.02/1.45 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.02/1.45 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.02/1.45 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.02/1.45 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.02/1.45 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.02/1.45 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.02/1.45 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.02/1.45 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.02/1.45 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 1.02/1.45 [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ],
% 1.02/1.45 [ 'class_Ring__and__Field_Odvd'( 'tc_nat' ) ],
% 1.02/1.45 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.02/1.45 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.02/1.45 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.02/1.45 [ 'class_Orderings_Obot'( 'tc_nat' ) ],
% 1.02/1.45 [ 'class_Power_Opower'( 'tc_nat' ) ]
% 1.02/1.45 ] .
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 percentage equality = 0.221831, percentage horn = 0.858813
% 1.02/1.45 This is a problem with some equality
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45
% 1.02/1.45 Options Used:
% 1.02/1.45
% 1.02/1.45 useres = 1
% 1.02/1.45 useparamod = 1
% 1.02/1.45 useeqrefl = 1
% 1.02/1.45 useeqfact = 1
% 1.02/1.45 usefactor = 1
% 1.02/1.45 usesimpsplitting = 0
% 1.02/1.45 usesimpdemod = 5
% 1.02/1.45 usesimpres = 3
% 1.02/1.45
% 1.02/1.45 resimpinuse = 1000
% 1.02/1.45 resimpclauses = 20000
% 1.02/1.45 substype = eqrewr
% 1.02/1.45 backwardsubs = 1
% 1.02/1.45 selectoldest = 5
% 1.02/1.45
% 1.02/1.45 litorderings [0] = split
% 1.02/1.45 litorderings [1] = extend the termordering, first sorting on arguments
% 1.02/1.45
% 1.02/1.45 termordering = kbo
% 1.02/1.45
% 1.02/1.45 litapriori = 0
% 1.02/1.45 termapriori = 1
% 1.02/1.45 litaposteriori = 0
% 1.02/1.45 termaposteriori = 0
% 1.02/1.45 demodaposteriori = 0
% 1.02/1.45 ordereqreflfact = 0
% 1.02/1.45
% 1.02/1.45 litselect = negord
% 1.02/1.45
% 1.02/1.45 maxweight = 15
% 1.02/1.45 maxdepth = 30000
% 1.02/1.45 maxlength = 115
% 1.02/1.45 maxnrvars = 195
% 1.02/1.45 excuselevel = 1
% 1.02/1.45 increasemaxweight = 1
% 1.02/1.45
% 1.02/1.45 maxselected = 10000000
% 1.02/1.45 maxnrclauses = 10000000
% 1.02/1.45
% 1.02/1.45 showgenerated = 0
% 1.02/1.45 showkept = 0
% 1.02/1.45 showselected = 0
% 1.02/1.45 showdeleted = 0
% 1.02/1.45 showresimp = 1
% 1.02/1.45 showstatus = 2000
% 1.02/1.45
% 1.02/1.45 prologoutput = 1
% 1.02/1.46 nrgoals = 5000000
% 1.02/1.46 totalproof = 1
% 1.02/1.46
% 1.02/1.46 Symbols occurring in the translation:
% 1.02/1.46
% 1.02/1.46 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.02/1.46 . [1, 2] (w:1, o:138, a:1, s:1, b:0),
% 1.02/1.46 ! [4, 1] (w:0, o:59, a:1, s:1, b:0),
% 1.02/1.46 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.02/1.46 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.02/1.46 'class_Ring__and__Field_Oordered__field' [40, 1] (w:1, o:66, a:1, s:1
% 1.02/1.46 , b:0),
% 1.02/1.46 'c_HOL_Oinverse__class_Odivide' [43, 3] (w:1, o:174, a:1, s:1, b:0),
% 1.02/1.46
% 1.02/1.46 'c_lessequals' [45, 3] (w:1, o:175, a:1, s:1, b:0),
% 1.02/1.46 'c_HOL_Ozero__class_Ozero' [46, 1] (w:1, o:67, a:1, s:1, b:0),
% 1.02/1.46 'c_HOL_Otimes__class_Otimes' [47, 3] (w:1, o:176, a:1, s:1, b:0),
% 1.02/1.46 'c_HOL_Oord__class_Oless' [48, 3] (w:1, o:177, a:1, s:1, b:0),
% 1.02/1.46 'class_Ring__and__Field_Oidom' [49, 1] (w:1, o:68, a:1, s:1, b:0),
% 1.02/1.46 'c_Ring__and__Field_Odvd__class_Odvd' [50, 3] (w:1, o:178, a:1, s:1
% 1.02/1.46 , b:0),
% 1.02/1.46 'class_Divides_Osemiring__div' [51, 1] (w:1, o:70, a:1, s:1, b:0),
% 1.02/1.46 'c_Divides_Odiv__class_Omod' [52, 3] (w:1, o:179, a:1, s:1, b:0),
% 1.02/1.46 'class_Ring__and__Field_Ofield' [53, 1] (w:1, o:71, a:1, s:1, b:0),
% 1.02/1.46 'c_HOL_Oinverse__class_Oinverse' [54, 2] (w:1, o:163, a:1, s:1, b:0)
% 1.02/1.46 ,
% 1.02/1.46 'c_HOL_Oone__class_Oone' [55, 1] (w:1, o:72, a:1, s:1, b:0),
% 1.02/1.46 'class_Int_Onumber__ring' [56, 1] (w:1, o:73, a:1, s:1, b:0),
% 1.02/1.46 'class_Ring__and__Field_Oordered__semiring__strict' [58, 1] (w:1, o:
% 1.02/1.46 75, a:1, s:1, b:0),
% 1.02/1.46 'class_OrderedGroup_Opordered__ab__group__add__abs' [60, 1] (w:1, o:
% 1.02/1.46 78, a:1, s:1, b:0),
% 1.02/1.46 'c_HOL_Oabs__class_Oabs' [61, 2] (w:1, o:164, a:1, s:1, b:0),
% 1.02/1.46 'class_Ring__and__Field_Oordered__semidom' [62, 1] (w:1, o:79, a:1
% 1.02/1.46 , s:1, b:0),
% 1.02/1.46 'c_Power_Opower__class_Opower' [64, 3] (w:1, o:182, a:1, s:1, b:0),
% 1.02/1.46 'class_Ring__and__Field_Osemiring__0' [65, 1] (w:1, o:84, a:1, s:1
% 1.02/1.46 , b:0),
% 1.02/1.46 'class_Power_Opower' [66, 1] (w:1, o:107, a:1, s:1, b:0),
% 1.02/1.46 'c_Suc' [67, 1] (w:1, o:109, a:1, s:1, b:0),
% 1.02/1.46 'tc_nat' [69, 0] (w:1, o:24, a:1, s:1, b:0),
% 1.02/1.46 'c_HOL_Oplus__class_Oplus' [70, 3] (w:1, o:183, a:1, s:1, b:0),
% 1.02/1.46 'class_Ring__and__Field_Olordered__ring' [71, 1] (w:1, o:110, a:1, s:
% 1.02/1.46 1, b:0),
% 1.02/1.46 'class_OrderedGroup_Opordered__ab__group__add' [72, 1] (w:1, o:85, a:
% 1.02/1.46 1, s:1, b:0),
% 1.02/1.46 'c_HOL_Ouminus__class_Ouminus' [73, 2] (w:1, o:165, a:1, s:1, b:0),
% 1.02/1.46 'class_Ring__and__Field_Oring' [74, 1] (w:1, o:80, a:1, s:1, b:0),
% 1.02/1.46 'c_HOL_Ominus__class_Ominus' [76, 3] (w:1, o:184, a:1, s:1, b:0),
% 1.02/1.46 'class_Orderings_Olinorder' [81, 1] (w:1, o:86, a:1, s:1, b:0),
% 1.02/1.46 'c_Orderings_Oord__class_Omax' [83, 3] (w:1, o:180, a:1, s:1, b:0),
% 1.02/1.46 'class_Orderings_Obot' [85, 1] (w:1, o:87, a:1, s:1, b:0),
% 1.02/1.46 'c_Orderings_Obot__class_Obot' [86, 1] (w:1, o:111, a:1, s:1, b:0),
% 1.02/1.46 'c_Orderings_Oord__class_Omin' [87, 3] (w:1, o:181, a:1, s:1, b:0),
% 1.02/1.46 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [89, 1]
% 1.02/1.46 (w:1, o:88, a:1, s:1, b:0),
% 1.02/1.46 'class_OrderedGroup_Ocomm__monoid__add' [90, 1] (w:1, o:89, a:1, s:1
% 1.02/1.46 , b:0),
% 1.02/1.46 'class_Ring__and__Field_Ocomm__semiring__1' [91, 1] (w:1, o:114, a:1
% 1.02/1.46 , s:1, b:0),
% 1.02/1.46 'class_OrderedGroup_Olordered__ab__group__add' [92, 1] (w:1, o:90, a:
% 1.02/1.46 1, s:1, b:0),
% 1.02/1.46 'c_OrderedGroup_Olordered__ab__group__add__class_Opprt' [93, 2] (w:1
% 1.02/1.46 , o:169, a:1, s:1, b:0),
% 1.02/1.46 'class_Ring__and__Field_Odivision__by__zero' [94, 1] (w:1, o:116, a:1
% 1.02/1.46 , s:1, b:0),
% 1.02/1.46 'class_Ring__and__Field_Opordered__ring' [95, 1] (w:1, o:120, a:1, s:
% 1.02/1.46 1, b:0),
% 1.02/1.46 'c_Lambda_OdB_OAbs' [97, 1] (w:1, o:121, a:1, s:1, b:0),
% 1.02/1.46 'c_Lambda_Osubstn' [99, 3] (w:1, o:185, a:1, s:1, b:0),
% 1.02/1.46 'class_Ring__and__Field_Oordered__ring__strict' [100, 1] (w:1, o:74
% 1.02/1.46 , a:1, s:1, b:0),
% 1.02/1.46 'class_Ring__and__Field_Oordered__idom' [102, 1] (w:1, o:117, a:1, s:
% 1.02/1.46 1, b:0),
% 1.02/1.46 'c_HOL_Osgn__class_Osgn' [103, 2] (w:1, o:170, a:1, s:1, b:0),
% 1.02/1.46 'class_Ring__and__Field_Oring__1' [104, 1] (w:1, o:81, a:1, s:1, b:0)
% 1.02/1.46 ,
% 1.02/1.46 'class_Nat_Osemiring__char__0' [105, 1] (w:1, o:76, a:1, s:1, b:0),
% 1.02/1.46 'c_Nat_Osemiring__1__class_Oof__nat' [106, 2] (w:1, o:166, a:1, s:1
% 2.35/2.75 , b:0),
% 2.35/2.75 'class_Ring__and__Field_Oordered__semiring' [107, 1] (w:1, o:118, a:1
% 2.35/2.75 , s:1, b:0),
% 2.35/2.75 'class_OrderedGroup_Oordered__ab__group__add' [108, 1] (w:1, o:77, a:
% 2.35/2.75 1, s:1, b:0),
% 2.35/2.75 'c_List_Oreplicate' [109, 3] (w:1, o:186, a:1, s:1, b:0),
% 2.35/2.75 'class_OrderedGroup_Ocomm__monoid__mult' [110, 1] (w:1, o:91, a:1, s:
% 2.35/2.75 1, b:0),
% 2.35/2.75 'class_OrderedGroup_Omonoid__mult' [111, 1] (w:1, o:93, a:1, s:1, b:0
% 2.35/2.75 ),
% 2.35/2.75 'class_Ring__and__Field_Odvd' [112, 1] (w:1, o:122, a:1, s:1, b:0),
% 2.35/2.75 'c_Lambda_OdB_OVar' [114, 1] (w:1, o:123, a:1, s:1, b:0),
% 2.35/2.75 'c_Lambda_Osubst' [115, 3] (w:1, o:187, a:1, s:1, b:0),
% 2.35/2.75 'class_OrderedGroup_Ogroup__add' [116, 1] (w:1, o:94, a:1, s:1, b:0)
% 2.35/2.75 ,
% 2.35/2.75 'class_Ring__and__Field_Odivision__ring' [117, 1] (w:1, o:124, a:1
% 2.35/2.75 , s:1, b:0),
% 2.35/2.75 'class_OrderedGroup_Opordered__ab__semigroup__add' [120, 1] (w:1, o:
% 2.35/2.75 95, a:1, s:1, b:0),
% 2.35/2.75 'class_OrderedGroup_Opordered__comm__monoid__add' [121, 1] (w:1, o:96
% 2.35/2.75 , a:1, s:1, b:0),
% 2.35/2.75 'class_Orderings_Opreorder' [122, 1] (w:1, o:98, a:1, s:1, b:0),
% 2.35/2.75 'class_Orderings_Oorder' [123, 1] (w:1, o:97, a:1, s:1, b:0),
% 2.35/2.75 'class_Ring__and__Field_Osgn__if' [124, 1] (w:1, o:125, a:1, s:1, b:0
% 2.35/2.75 ),
% 2.35/2.75 'class_OrderedGroup_Olordered__ab__group__add__abs' [125, 1] (w:1, o:
% 2.35/2.75 92, a:1, s:1, b:0),
% 2.35/2.75 'class_Ring__and__Field_Oabs__if' [126, 1] (w:1, o:126, a:1, s:1, b:0
% 2.35/2.75 ),
% 2.35/2.75 'class_Divides_Oring__div' [127, 1] (w:1, o:69, a:1, s:1, b:0),
% 2.35/2.75 'class_Ring__and__Field_Ocomm__ring__1' [129, 1] (w:1, o:112, a:1, s:
% 2.35/2.75 1, b:0),
% 2.35/2.75 'c_Lambda_Oliftn' [130, 3] (w:1, o:188, a:1, s:1, b:0),
% 2.35/2.75 'c_Lambda_Olift' [131, 2] (w:1, o:171, a:1, s:1, b:0),
% 2.35/2.75 'class_Ring__and__Field_Osemiring__1' [137, 1] (w:1, o:127, a:1, s:1
% 2.35/2.75 , b:0),
% 2.35/2.75 'class_OrderedGroup_Oab__group__add' [138, 1] (w:1, o:99, a:1, s:1
% 2.35/2.75 , b:0),
% 2.35/2.75 'class_OrderedGroup_Oab__semigroup__add' [139, 1] (w:1, o:100, a:1
% 2.35/2.75 , s:1, b:0),
% 2.35/2.75 'c_Nat_Osize__class_Osize' [143, 2] (w:1, o:167, a:1, s:1, b:0),
% 2.35/2.75 'c_Lambda_OdB_OApp' [146, 2] (w:1, o:172, a:1, s:1, b:0),
% 2.35/2.75 'c_Lambda_Obeta' [151, 2] (w:1, o:173, a:1, s:1, b:0),
% 2.35/2.75 'class_Lattices_Oboolean__algebra' [152, 1] (w:1, o:128, a:1, s:1, b:
% 2.35/2.75 0),
% 2.35/2.75 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [155, 1]
% 2.35/2.75 (w:1, o:101, a:1, s:1, b:0),
% 2.35/2.75 'class_Ring__and__Field_Osemiring' [156, 1] (w:1, o:129, a:1, s:1, b:
% 2.35/2.75 0),
% 2.35/2.75 'class_Ring__and__Field_Opordered__cancel__semiring' [157, 1] (w:1
% 2.35/2.75 , o:130, a:1, s:1, b:0),
% 2.35/2.75 'class_OrderedGroup_Ocancel__ab__semigroup__add' [158, 1] (w:1, o:102
% 2.35/2.75 , a:1, s:1, b:0),
% 2.35/2.75 'class_OrderedGroup_Ocancel__semigroup__add' [159, 1] (w:1, o:103, a:
% 2.35/2.75 1, s:1, b:0),
% 2.35/2.75 'class_Ring__and__Field_Opordered__ring__abs' [161, 1] (w:1, o:131
% 2.35/2.75 , a:1, s:1, b:0),
% 2.35/2.75 'c_List_Odrop' [163, 3] (w:1, o:189, a:1, s:1, b:0),
% 2.35/2.75 'class_OrderedGroup_Oab__semigroup__idem__mult' [164, 1] (w:1, o:104
% 2.35/2.75 , a:1, s:1, b:0),
% 2.35/2.75 'c_nat_Onat__size' [165, 1] (w:1, o:132, a:1, s:1, b:0),
% 2.35/2.75 'class_Ring__and__Field_Oordered__comm__semiring__strict' [166, 1]
% 2.35/2.75 (w:1, o:119, a:1, s:1, b:0),
% 2.35/2.75 'c_InductTermi_OIT' [167, 1] (w:1, o:133, a:1, s:1, b:0),
% 2.35/2.75 'class_Ring__and__Field_Omult__mono' [168, 1] (w:1, o:134, a:1, s:1
% 2.35/2.75 , b:0),
% 2.35/2.75 'class_Ring__and__Field_Omult__mono1' [169, 1] (w:1, o:135, a:1, s:1
% 2.35/2.75 , b:0),
% 2.35/2.75 'class_Ring__and__Field_Opordered__semiring' [171, 1] (w:1, o:136, a:
% 2.35/2.75 1, s:1, b:0),
% 2.35/2.75 'class_Ring__and__Field_Ozero__neq__one' [172, 1] (w:1, o:137, a:1
% 2.35/2.75 , s:1, b:0),
% 2.35/2.75 'class_Ring__and__Field_Ono__zero__divisors' [173, 1] (w:1, o:65, a:1
% 2.35/2.75 , s:1, b:0),
% 2.35/2.75 'class_Ring__and__Field_Omult__zero' [174, 1] (w:1, o:64, a:1, s:1
% 2.35/2.75 , b:0),
% 2.35/2.75 'class_Ring__and__Field_Oring__1__no__zero__divisors' [175, 1] (w:1
% 2.35/2.75 , o:82, a:1, s:1, b:0),
% 2.35/2.75 'class_Ring__and__Field_Oring__no__zero__divisors' [176, 1] (w:1, o:
% 2.35/2.75 83, a:1, s:1, b:0),
% 2.35/2.75 'class_Ring__and__Field_Ocomm__ring' [177, 1] (w:1, o:113, a:1, s:1
% 2.35/2.75 , b:0),
% 2.35/2.75 'class_OrderedGroup_Oab__semigroup__mult' [179, 1] (w:1, o:105, a:1
% 2.35/2.75 , s:1, b:0),
% 2.35/2.75 'class_Ring__and__Field_Ocomm__semiring' [180, 1] (w:1, o:115, a:1
% 2.35/2.75 , s:1, b:0),
% 2.35/2.75 'class_OrderedGroup_Omonoid__add' [181, 1] (w:1, o:106, a:1, s:1, b:0
% 2.35/2.75 ),
% 2.35/2.75 'c_Nitpick_Onat__gcd' [182, 2] (w:1, o:168, a:1, s:1, b:0),
% 2.35/2.75 'c_String_Ochar_Ochar__size' [183, 1] (w:1, o:108, a:1, s:1, b:0),
% 2.35/2.75 'tc_String_Ochar' [184, 0] (w:1, o:53, a:1, s:1, b:0),
% 2.35/2.75 'v_ua______' [185, 0] (w:1, o:54, a:1, s:1, b:0),
% 2.35/2.75 'v_n____' [186, 0] (w:1, o:55, a:1, s:1, b:0),
% 2.35/2.75 'v_i____' [187, 0] (w:1, o:56, a:1, s:1, b:0),
% 2.35/2.75 'v_u____' [188, 0] (w:1, o:57, a:1, s:1, b:0),
% 2.35/2.75 'v_b____' [189, 0] (w:1, o:58, a:1, s:1, b:0).
% 2.35/2.75
% 2.35/2.75
% 2.35/2.75 Starting Search:
% 2.35/2.75
% 2.35/2.75 Resimplifying inuse:
% 2.35/2.75 Done
% 2.35/2.75
% 2.35/2.75
% 2.35/2.75 Intermediate Status:
% 2.35/2.75 Generated: 4313
% 2.35/2.75 Kept: 2127
% 2.35/2.75 Inuse: 146
% 2.35/2.75 Deleted: 0
% 2.35/2.75 Deletedinuse: 0
% 2.35/2.75
% 2.35/2.75 Resimplifying inuse:
% 2.35/2.75 Done
% 2.35/2.75
% 2.35/2.75 Resimplifying inuse:
% 2.35/2.75 Done
% 2.35/2.75
% 2.35/2.75
% 2.35/2.75 Intermediate Status:
% 2.35/2.75 Generated: 10106
% 2.35/2.75 Kept: 4156
% 2.35/2.75 Inuse: 308
% 2.35/2.75 Deleted: 3
% 2.35/2.75 Deletedinuse: 0
% 2.35/2.75
% 2.35/2.75 Resimplifying inuse:
% 2.35/2.75 Done
% 2.35/2.75
% 2.35/2.75 Resimplifying inuse:
% 2.35/2.75 Done
% 2.35/2.75
% 2.35/2.75
% 2.35/2.75 Intermediate Status:
% 2.35/2.75 Generated: 17596
% 2.35/2.75 Kept: 6161
% 2.35/2.75 Inuse: 416
% 2.35/2.75 Deleted: 8
% 2.35/2.75 Deletedinuse: 0
% 2.35/2.75
% 2.35/2.75 Resimplifying inuse:
% 2.35/2.75 Done
% 2.35/2.75
% 2.35/2.75 Resimplifying inuse:
% 2.35/2.75 Done
% 2.35/2.75
% 2.35/2.75
% 2.35/2.75 Intermediate Status:
% 2.35/2.75 Generated: 27125
% 2.35/2.75 Kept: 8828
% 2.35/2.75 Inuse: 532
% 2.35/2.75 Deleted: 9
% 2.35/2.75 Deletedinuse: 0
% 2.35/2.75
% 2.35/2.75 Resimplifying inuse:
% 2.35/2.75 Done
% 2.35/2.75
% 2.35/2.75 Resimplifying inuse:
% 2.35/2.75 Done
% 2.35/2.75
% 2.35/2.75
% 2.35/2.75 Intermediate Status:
% 2.35/2.75 Generated: 36964
% 2.35/2.75 Kept: 10860
% 2.35/2.75 Inuse: 623
% 2.35/2.75 Deleted: 14
% 2.35/2.75 Deletedinuse: 1
% 2.35/2.75
% 2.35/2.75 Resimplifying inuse:
% 2.35/2.75 Done
% 2.35/2.75
% 2.35/2.75 Resimplifying inuse:
% 2.35/2.75 Done
% 2.35/2.75
% 2.35/2.75
% 2.35/2.75 Intermediate Status:
% 2.35/2.75 Generated: 45292
% 2.35/2.75 Kept: 12946
% 2.35/2.75 Inuse: 641
% 2.35/2.75 Deleted: 16
% 2.35/2.75 Deletedinuse: 3
% 2.35/2.75
% 2.35/2.75
% 2.35/2.75 Intermediate Status:
% 2.35/2.75 Generated: 53331
% 2.35/2.75 Kept: 15233
% 2.35/2.75 Inuse: 663
% 2.35/2.75 Deleted: 18
% 2.35/2.75 Deletedinuse: 3
% 2.35/2.75
% 2.35/2.75 Resimplifying inuse:
% 2.35/2.75 Done
% 2.35/2.75
% 2.35/2.75 Resimplifying inuse:
% 2.35/2.75 Done
% 2.35/2.75
% 2.35/2.75
% 2.35/2.75 Intermediate Status:
% 2.35/2.75 Generated: 62348
% 2.35/2.75 Kept: 17235
% 2.35/2.75 Inuse: 723
% 2.35/2.75 Deleted: 26
% 2.35/2.75 Deletedinuse: 3
% 2.35/2.75
% 2.35/2.75
% 2.35/2.75 Intermediate Status:
% 2.35/2.75 Generated: 70329
% 2.35/2.75 Kept: 19476
% 2.35/2.75 Inuse: 736
% 2.35/2.75 Deleted: 26
% 2.35/2.75 Deletedinuse: 3
% 2.35/2.75
% 2.35/2.75 Resimplifying inuse:
% 2.35/2.75 Done
% 2.35/2.75
% 2.35/2.75 Resimplifying clauses:
% 2.35/2.75
% 2.35/2.75 Bliksems!, er is een bewijs:
% 2.35/2.75 % SZS status Unsatisfiable
% 2.35/2.75 % SZS output start Refutation
% 2.35/2.75
% 2.35/2.75 clause( 1017, [ =( 'v_i____', 'v_n____' ) ] )
% 2.35/2.75 .
% 2.35/2.75 clause( 1018, [ 'c_InductTermi_OIT'( 'c_Lambda_Olift'( X, Y ) ), ~(
% 2.35/2.75 'c_InductTermi_OIT'( X ) ) ] )
% 2.35/2.75 .
% 2.35/2.75 clause( 1021, [ 'c_InductTermi_OIT'( 'c_Lambda_Osubst'( 'v_b____',
% 2.35/2.75 'v_u____', 'v_n____' ) ) ] )
% 2.35/2.75 .
% 2.35/2.75 clause( 1022, [ ~( 'c_InductTermi_OIT'( 'c_Lambda_Olift'( 'c_Lambda_Osubst'(
% 2.35/2.75 'v_b____', 'v_u____', 'v_n____' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 2.35/2.75 ) ) ) ] )
% 2.35/2.75 .
% 2.35/2.75 clause( 2175, [ 'c_InductTermi_OIT'( 'c_Lambda_Olift'( 'c_Lambda_Osubst'(
% 2.35/2.75 'v_b____', 'v_u____', 'v_n____' ), X ) ) ] )
% 2.35/2.75 .
% 2.35/2.75 clause( 20129, [] )
% 2.35/2.75 .
% 2.35/2.75
% 2.35/2.75
% 2.35/2.75 % SZS output end Refutation
% 2.35/2.75 found a proof!
% 2.35/2.75
% 2.35/2.75 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 2.35/2.75
% 2.35/2.75 initialclauses(
% 2.35/2.75 [ clause( 20131, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.35/2.75 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 2.35/2.75 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 2.35/2.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~( 'c_lessequals'(
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z, X ) )
% 2.35/2.75 ] )
% 2.35/2.75 , clause( 20132, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 2.35/2.75 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 2.35/2.75 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 2.35/2.75 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 2.35/2.75 , clause( 20133, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 2.35/2.75 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 2.35/2.75 , X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 2.35/2.75 'c_Ring__and__Field_Odvd__class_Odvd'( Z, T, X ) ) ] )
% 2.35/2.75 , clause( 20134, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.35/2.75 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.75 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 2.35/2.75 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z
% 2.35/2.75 , X ) ) ] )
% 2.35/2.75 , clause( 20135, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 2.35/2.75 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 2.35/2.75 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 2.35/2.75 , clause( 20136, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.35/2.75 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y
% 2.35/2.75 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y
% 2.35/2.75 , X ) ) ] )
% 2.35/2.75 , clause( 20137, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.35/2.75 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.35/2.75 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.75 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 2.35/2.75 , clause( 20138, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.35/2.75 X ) ), 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 2.35/2.75 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ] )
% 2.35/2.75 , clause( 20139, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.75 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ),
% 2.35/2.75 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 2.35/2.75 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 2.35/2.75 , clause( 20140, [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 2.35/2.75 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), 'c_Suc'( Y ), X ),
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.75 , clause( 20141, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.35/2.75 X ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X )
% 2.35/2.75 , 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ] )
% 2.35/2.75 , clause( 20142, [ =( 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat'
% 2.35/2.75 ), 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ] )
% 2.35/2.75 , clause( 20143, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat'
% 2.35/2.75 ), 'c_Suc'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ) ] )
% 2.35/2.75 , clause( 20144, [ ~( 'class_Ring__and__Field_Olordered__ring'( X ) ),
% 2.35/2.75 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y
% 2.35/2.75 , Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y
% 2.35/2.75 , X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ) ] )
% 2.35/2.75 , clause( 20145, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.35/2.75 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 2.35/2.75 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 2.35/2.75 , X ), X ) ) ] )
% 2.35/2.75 , clause( 20146, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.35/2.75 , 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 2.35/2.75 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_lessequals'( Z, Y, X )
% 2.35/2.75 ) ] )
% 2.35/2.75 , clause( 20147, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.75 'c_HOL_Ominus__class_Ominus'( T, Y, X ), Z, X ), U, X ), X ),
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 2.35/2.75 ) ) ] )
% 2.35/2.75 , clause( 20148, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 2.35/2.75 'tc_nat' ), Z, 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), ~(
% 2.35/2.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), T, 'tc_nat' ),
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat'
% 2.35/2.75 ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 2.35/2.75 )
% 2.35/2.75 , clause( 20149, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 2.35/2.75 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.75 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 2.35/2.75 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ] )
% 2.35/2.75 , clause( 20150, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 2.35/2.75 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ), ~(
% 2.35/2.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), X, 'tc_nat' ),
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat'
% 2.35/2.75 ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 2.35/2.75 )
% 2.35/2.75 , clause( 20151, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 2.35/2.75 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.75 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 2.35/2.75 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ] )
% 2.35/2.75 , clause( 20152, [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 2.35/2.75 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 2.35/2.75 W, X ) ) ), =( T, 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 2.35/2.75 , X ), W, X ) ) ] )
% 2.35/2.75 , clause( 20153, [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =(
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 2.35/2.75 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 2.35/2.75 W, X ) ) ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.75 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W ) ] )
% 2.35/2.75 , clause( 20154, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'(
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ), 'tc_nat' ) ] )
% 2.35/2.75 , clause( 20155, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'(
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ), 'tc_nat' ) ] )
% 2.35/2.75 , clause( 20156, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'(
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ), 'tc_nat' ) ] )
% 2.35/2.75 , clause( 20157, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 2.35/2.75 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_lessequals'( X,
% 2.35/2.75 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 2.35/2.75 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 2.35/2.75 , clause( 20158, [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 2.35/2.75 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X
% 2.35/2.75 , Z, 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 2.35/2.75 )
% 2.35/2.75 , clause( 20159, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 2.35/2.75 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 2.35/2.75 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 2.35/2.75 , clause( 20160, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 2.35/2.75 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 2.35/2.75 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 2.35/2.75 , clause( 20161, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 2.35/2.75 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 2.35/2.75 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 2.35/2.75 , clause( 20162, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.35/2.75 , 'c_Orderings_Oord__class_Omax'( Y, Z, X ), X ) ] )
% 2.35/2.75 , clause( 20163, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.35/2.75 , 'c_Orderings_Oord__class_Omax'( Z, Y, X ), X ) ] )
% 2.35/2.75 , clause( 20164, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.35/2.75 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.75 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.75 X ) ) ] )
% 2.35/2.75 , clause( 20165, [ ~( 'class_Orderings_Obot'( X ) ), 'c_lessequals'(
% 2.35/2.75 'c_Orderings_Obot__class_Obot'( X ), Y, X ) ] )
% 2.35/2.75 , clause( 20166, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.35/2.75 X ) ), 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'(
% 2.35/2.75 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 2.35/2.75 ) ] )
% 2.35/2.75 , clause( 20167, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 2.35/2.75 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'( Y, Z, X )
% 2.35/2.75 , T, X ), 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'(
% 2.35/2.75 Y, T, X ), 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ] )
% 2.35/2.75 , clause( 20168, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 2.35/2.75 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 2.35/2.75 X ), X ), 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'(
% 2.35/2.75 Y, Z, X ), 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ) ) ] )
% 2.35/2.75 , clause( 20169, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.75 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 2.35/2.75 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 2.35/2.75 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 2.35/2.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 2.35/2.75 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ] )
% 2.35/2.75 , clause( 20170, [ ~(
% 2.35/2.75 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 2.35/2.75 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 2.35/2.75 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 2.35/2.75 , clause( 20171, [ ~(
% 2.35/2.75 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 2.35/2.75 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z, X )
% 2.35/2.75 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ] )
% 2.35/2.75 , clause( 20172, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.75 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 2.35/2.75 , Z, X ), 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 2.35/2.75 'c_lessequals'( Z, T, 'tc_nat' ) ) ] )
% 2.35/2.75 , clause( 20173, [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 2.35/2.75 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 2.35/2.75 , clause( 20174, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 2.35/2.75 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 2.35/2.75 , clause( 20175, [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 2.35/2.75 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 2.35/2.75 , clause( 20176, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 2.35/2.75 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 2.35/2.75 , clause( 20177, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.35/2.75 , ~( =( 'c_OrderedGroup_Olordered__ab__group__add__class_Opprt'( Y, X ),
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_lessequals'( Y,
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ] )
% 2.35/2.75 , clause( 20178, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.35/2.75 , =( 'c_OrderedGroup_Olordered__ab__group__add__class_Opprt'( Y, X ),
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( Y,
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.75 , clause( 20179, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.75 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 2.35/2.75 'tc_nat' ) ) ] )
% 2.35/2.75 , clause( 20180, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.75 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 2.35/2.75 'tc_nat' ) ) ] )
% 2.35/2.75 , clause( 20181, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 2.35/2.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 2.35/2.75 Y, 'tc_nat' ) ) ] )
% 2.35/2.75 , clause( 20182, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.75 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 2.35/2.75 'tc_nat' ) ) ] )
% 2.35/2.75 , clause( 20183, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.75 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 2.35/2.75 'tc_nat' ) ) ] )
% 2.35/2.75 , clause( 20184, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.75 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 2.35/2.75 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~( 'c_lessequals'( Y,
% 2.35/2.75 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_lessequals'(
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z,
% 2.35/2.75 'tc_nat' ) ) ] )
% 2.35/2.75 , clause( 20185, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ),
% 2.35/2.75 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 2.35/2.75 , clause( 20186, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 2.35/2.75 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 2.35/2.75 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 2.35/2.75 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.75 , clause( 20187, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 2.35/2.75 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 2.35/2.75 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 2.35/2.75 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.75 , clause( 20188, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.35/2.75 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.75 Y, Z, X ), T, X ), 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X ), X ), ~( 'c_lessequals'(
% 2.35/2.75 T, 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.75 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z, X ), W, X ), X ) ) ] )
% 2.35/2.75 , clause( 20189, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.35/2.75 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 2.35/2.75 , X ), W, X ), X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X ),
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ), W, X
% 2.35/2.75 ), X ) ) ] )
% 2.35/2.75 , clause( 20190, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.35/2.75 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.75 Y, Z, X ), T, X ), 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X ), X ), ~( 'c_lessequals'(
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.75 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), W, X ) ) ] )
% 2.35/2.75 , clause( 20191, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.35/2.75 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.75 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ), U, X ), W, X ), ~(
% 2.35/2.75 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.75 Y, T, X ), U, X ), 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( Z, T, X ), W, X ), X ) ) ] )
% 2.35/2.75 , clause( 20192, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 2.35/2.75 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 2.35/2.75 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 2.35/2.75 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 2.35/2.75 , T, X ), X ) ) ] )
% 2.35/2.75 , clause( 20193, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 2.35/2.75 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 2.35/2.75 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ), ~(
% 2.35/2.75 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 2.35/2.75 , clause( 20194, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 2.35/2.75 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 2.35/2.75 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 2.35/2.75 , T, X ), X ) ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ]
% 2.35/2.75 )
% 2.35/2.75 , clause( 20195, [ ~( 'class_Divides_Osemiring__div'( X ) ),
% 2.35/2.75 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Divides_Odiv__class_Omod'( Z
% 2.35/2.75 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 2.35/2.75 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 2.35/2.75 , clause( 20196, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y,
% 2.35/2.75 'tc_nat' ), 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ),
% 2.35/2.75 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 2.35/2.75 , clause( 20197, [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 2.35/2.75 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.35/2.75 , clause( 20198, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 2.35/2.75 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ), ~( 'c_lessequals'(
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.75 , clause( 20199, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 2.35/2.75 'c_HOL_Oone__class_Oone'( X ), Y, X ), X ) ) ] )
% 2.35/2.75 , clause( 20200, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OAbs'( X ), Y, Z )
% 2.35/2.75 , 'c_Lambda_OdB_OAbs'( 'c_Lambda_Osubstn'( X, Y,
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 2.35/2.75 'tc_nat' ) ) ) ) ] )
% 2.35/2.75 , clause( 20201, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.75 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ) ] )
% 2.35/2.75 , clause( 20202, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 2.35/2.75 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 2.35/2.75 X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.75 , clause( 20203, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.75 =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z,
% 2.35/2.75 Y, X ) ) ] )
% 2.35/2.75 , clause( 20204, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z, Y,
% 2.35/2.75 X ) ) ] )
% 2.35/2.75 , clause( 20205, [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ] )
% 2.35/2.75 , clause( 20206, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ) ) ), ~(
% 2.35/2.75 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 2.35/2.75 X, T, 'tc_nat' ) ] )
% 2.35/2.75 , clause( 20207, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.75 =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Z,
% 2.35/2.75 Y, X ) ) ] )
% 2.35/2.75 , clause( 20208, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 2.35/2.75 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 2.35/2.75 ), X ) ) ] )
% 2.35/2.75 , clause( 20209, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 2.35/2.75 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 2.35/2.75 ), X ) ) ] )
% 2.35/2.75 , clause( 20210, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( Z,
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 2.35/2.75 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 2.35/2.75 ), X ) ) ] )
% 2.35/2.75 , clause( 20211, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( Y,
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 2.35/2.75 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 2.35/2.75 ), X ) ) ] )
% 2.35/2.75 , clause( 20212, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 2.35/2.75 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 2.35/2.75 , clause( 20213, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 2.35/2.75 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 2.35/2.75 , clause( 20214, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Osgn__class_Osgn'( Y, X ),
% 2.35/2.75 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), Y ) ] )
% 2.35/2.75 , clause( 20215, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 2.35/2.75 X, Y, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 2.35/2.75 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 2.35/2.75 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ] )
% 2.35/2.75 , clause( 20216, [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =(
% 2.35/2.75 'c_Power_Opower__class_Opower'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z
% 2.35/2.75 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'(
% 2.35/2.75 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oone__class_Oone'( X ), X ), Z, X
% 2.35/2.75 ), 'c_Power_Opower__class_Opower'( Y, Z, X ), X ) ) ] )
% 2.35/2.75 , clause( 20217, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.75 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ),
% 2.35/2.75 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 2.35/2.75 ) ] )
% 2.35/2.75 , clause( 20218, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.35/2.75 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 2.35/2.75 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 2.35/2.75 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 2.35/2.75 'c_lessequals'( Z, Y, X ) ) ] )
% 2.35/2.75 , clause( 20219, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.35/2.75 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 2.35/2.75 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 2.35/2.75 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ] )
% 2.35/2.75 , clause( 20220, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.35/2.75 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 2.35/2.75 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 2.35/2.75 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ] )
% 2.35/2.75 , clause( 20221, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.35/2.75 'c_lessequals'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 2.35/2.75 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 2.35/2.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 2.35/2.75 'c_lessequals'( Z, Y, X ) ) ] )
% 2.35/2.75 , clause( 20222, [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 2.35/2.75 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 2.35/2.75 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ] )
% 2.35/2.75 , clause( 20223, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), ~(
% 2.35/2.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 2.35/2.75 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), Z, X ) ) ] )
% 2.35/2.75 , clause( 20224, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 2.35/2.75 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 2.35/2.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 2.35/2.75 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ] )
% 2.35/2.75 , clause( 20225, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ), ~(
% 2.35/2.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 2.35/2.75 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ] )
% 2.35/2.75 , clause( 20226, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 2.35/2.75 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 2.35/2.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 2.35/2.75 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ] )
% 2.35/2.75 , clause( 20227, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.35/2.75 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 2.35/2.75 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ), ~(
% 2.35/2.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 2.35/2.75 , clause( 20228, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.35/2.75 'c_lessequals'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 2.35/2.75 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ), ~(
% 2.35/2.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ] )
% 2.35/2.75 , clause( 20229, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.35/2.75 X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 2.35/2.75 , T, X ), X ) ) ] )
% 2.35/2.75 , clause( 20230, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.35/2.75 X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.35/2.75 , Z, X ), X ) ) ] )
% 2.35/2.75 , clause( 20231, [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 2.35/2.75 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 2.35/2.75 , T, X ), X ) ) ] )
% 2.35/2.75 , clause( 20232, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 2.35/2.75 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 2.35/2.75 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 2.35/2.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~( 'c_lessequals'( Y,
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, T, X ) ) ]
% 2.35/2.75 )
% 2.35/2.75 , clause( 20233, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 2.35/2.75 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y, X ) ] )
% 2.35/2.75 , clause( 20234, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 2.35/2.75 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z, X ) ] )
% 2.35/2.75 , clause( 20235, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.35/2.75 , 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T
% 2.35/2.75 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 2.35/2.75 , clause( 20236, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.35/2.75 , 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T
% 2.35/2.75 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 2.35/2.75 , clause( 20237, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.35/2.75 , 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T
% 2.35/2.75 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 2.35/2.75 , clause( 20238, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 2.35/2.75 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ),
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.75 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ), T, X ), X ) ) ] )
% 2.35/2.75 , clause( 20239, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.35/2.75 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.35/2.75 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 2.35/2.75 , clause( 20240, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.35/2.75 , 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 2.35/2.75 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.75 , clause( 20241, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.35/2.75 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.35/2.75 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ] )
% 2.35/2.75 , clause( 20242, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.35/2.75 , 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 2.35/2.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.75 , clause( 20243, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) )
% 2.35/2.75 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.35/2.75 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 2.35/2.75 , clause( 20244, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) )
% 2.35/2.75 , 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~(
% 2.35/2.75 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.75 , clause( 20245, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) )
% 2.35/2.75 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.35/2.75 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ) ) ] )
% 2.35/2.75 , clause( 20246, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) )
% 2.35/2.75 , 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X ), ~(
% 2.35/2.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.75 , clause( 20247, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.75 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.75 , clause( 20248, [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 2.35/2.75 'tc_nat' ) ) ] )
% 2.35/2.75 , clause( 20249, [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X, Y,
% 2.35/2.75 'tc_nat' ) ] )
% 2.35/2.75 , clause( 20250, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.35/2.75 , =( 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omin'( Y, Z,
% 2.35/2.75 X ), T, X ), 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ominus__class_Ominus'(
% 2.35/2.75 Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ), X ) ) ] )
% 2.35/2.75 , clause( 20251, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.35/2.75 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T,
% 2.35/2.75 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~(
% 2.35/2.75 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 2.35/2.75 , clause( 20252, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 2.35/2.75 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z, 'tc_nat' ),
% 2.35/2.75 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'( Y
% 2.35/2.75 , Z, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 2.35/2.75 , clause( 20253, [ ~( =( 'c_List_Oreplicate'( X, Y, Z ),
% 2.35/2.75 'c_List_Oreplicate'( T, U, Z ) ) ), =( X, T ) ] )
% 2.35/2.75 , clause( 20254, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.75 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y
% 2.35/2.75 ) ] )
% 2.35/2.75 , clause( 20255, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 2.35/2.75 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 2.35/2.75 , clause( 20256, [ =( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.75 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X, 'tc_nat' ), X ) ] )
% 2.35/2.75 , clause( 20257, [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 2.35/2.75 ] )
% 2.35/2.75 , clause( 20258, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y )
% 2.35/2.75 ] )
% 2.35/2.75 , clause( 20259, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 2.35/2.75 ] )
% 2.35/2.75 , clause( 20260, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.75 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y
% 2.35/2.75 ) ] )
% 2.35/2.75 , clause( 20261, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.75 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), Y
% 2.35/2.75 ) ] )
% 2.35/2.75 , clause( 20262, [ ~(
% 2.35/2.75 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 2.35/2.75 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_HOL_Oord__class_Oless'(
% 2.35/2.75 Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T, X
% 2.35/2.75 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X
% 2.35/2.75 ) ) ] )
% 2.35/2.75 , clause( 20263, [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.75 Y, Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~(
% 2.35/2.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 2.35/2.75 'tc_nat' ) ) ] )
% 2.35/2.75 , clause( 20264, [ ~( 'class_Ring__and__Field_Odvd'( X ) ),
% 2.35/2.75 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 2.35/2.75 , Z, X ), X ) ] )
% 2.35/2.75 , clause( 20265, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.75 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Y
% 2.35/2.75 , Z, X ), X ) ] )
% 2.35/2.75 , clause( 20266, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.75 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 2.35/2.75 , Y, X ), X ) ] )
% 2.35/2.75 , clause( 20267, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.35/2.75 X ) ), 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'(
% 2.35/2.75 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), X ),
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'(
% 2.35/2.75 'c_HOL_Ominus__class_Ominus'( Y, T, X ), X ), 'c_HOL_Oabs__class_Oabs'(
% 2.35/2.75 'c_HOL_Ominus__class_Ominus'( Z, U, X ), X ), X ), X ) ] )
% 2.35/2.75 , clause( 20268, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.35/2.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 2.35/2.75 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~(
% 2.35/2.75 'c_HOL_Oord__class_Oless'( U, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 2.35/2.75 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 2.35/2.75 ] )
% 2.35/2.75 , clause( 20269, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.35/2.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.35/2.75 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ),
% 2.35/2.75 'c_Power_Opower__class_Opower'( Y, Z, X ), X ),
% 2.35/2.75 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'(
% 2.35/2.75 'c_HOL_Oone__class_Oone'( X ), Y, X ), Z, X ) ) ] )
% 2.35/2.75 , clause( 20270, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'(
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.75 'tc_nat' ), 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 2.35/2.75 ) ] )
% 2.35/2.75 , clause( 20271, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.35/2.75 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 2.35/2.75 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 2.35/2.75 , clause( 20272, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.75 'c_lessequals'( Y, Z, 'tc_nat' ), ~( 'c_lessequals'(
% 2.35/2.75 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 2.35/2.75 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ] )
% 2.35/2.75 , clause( 20273, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.75 'c_lessequals'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 2.35/2.75 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~( 'c_lessequals'( Y,
% 2.35/2.75 Z, 'tc_nat' ) ) ] )
% 2.35/2.75 , clause( 20274, [ =( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.75 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 2.35/2.75 , clause( 20275, [ =( 'c_Suc'( X ), 'c_HOL_Oplus__class_Oplus'( X,
% 2.35/2.75 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.35/2.75 , clause( 20276, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 2.35/2.75 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 2.35/2.75 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 2.35/2.75 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ), =( Z,
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.75 , clause( 20277, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 2.35/2.75 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 2.35/2.75 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 2.35/2.75 ) ] )
% 2.35/2.75 , clause( 20278, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.75 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.35/2.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 2.35/2.75 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 2.35/2.75 ) ) ] )
% 2.35/2.75 , clause( 20279, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.35/2.75 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.35/2.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.75 , clause( 20280, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.35/2.75 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.75 , clause( 20281, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.35/2.75 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X ),
% 2.35/2.75 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 2.35/2.75 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 2.35/2.75 , clause( 20282, [ =( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 2.35/2.75 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.35/2.75 , clause( 20283, [ =( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 2.35/2.75 ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.35/2.75 , clause( 20284, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 2.35/2.75 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 2.35/2.75 , T, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.75 Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 2.35/2.75 , clause( 20285, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 2.35/2.75 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 2.35/2.75 , T, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.75 Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 2.35/2.75 , clause( 20286, [ =( 'c_Orderings_Oord__class_Omax'( 'c_Suc'( X ), 'c_Suc'(
% 2.35/2.75 Y ), 'tc_nat' ), 'c_Suc'( 'c_Orderings_Oord__class_Omax'( X, Y, 'tc_nat'
% 2.35/2.75 ) ) ) ] )
% 2.35/2.75 , clause( 20287, [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 2.35/2.75 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.75 'tc_nat' ) ), 'tc_nat' ) ) ] )
% 2.35/2.75 , clause( 20288, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.35/2.75 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.35/2.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ] )
% 2.35/2.75 , clause( 20289, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.35/2.75 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_lessequals'(
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.75 , clause( 20290, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.35/2.75 X ) ), 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'(
% 2.35/2.75 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 2.35/2.75 'c_HOL_Oabs__class_Oabs'( Z, X ), X ), X ), 'c_HOL_Oabs__class_Oabs'(
% 2.35/2.75 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), X ) ] )
% 2.35/2.75 , clause( 20291, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 2.35/2.75 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Y, Z,
% 2.35/2.75 X ), X ), 'c_Orderings_Oord__class_Omin'( Y, Z, X ) ) ] )
% 2.35/2.75 , clause( 20292, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 2.35/2.75 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'( Z, X,
% 2.35/2.75 'tc_nat' ) ] )
% 2.35/2.75 , clause( 20293, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.35/2.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.75 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 2.35/2.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Z, X ), U, X ) ),
% 2.35/2.75 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), T, X ) )
% 2.35/2.75 ] )
% 2.35/2.75 , clause( 20294, [ =( 'c_HOL_Ominus__class_Ominus'(
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 2.35/2.75 ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 2.35/2.75 , 'c_HOL_Ominus__class_Ominus'( Z, 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( T, X,
% 2.35/2.75 'tc_nat' ), Y, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'(
% 2.35/2.75 X, T, 'tc_nat' ) ) ] )
% 2.35/2.75 , clause( 20295, [ =( 'c_HOL_Ominus__class_Ominus'(
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 2.35/2.75 ), Z, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 2.35/2.75 , 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, T,
% 2.35/2.75 'tc_nat' ), Y, 'tc_nat' ), Z, 'tc_nat' ), U, 'tc_nat' ) ), ~(
% 2.35/2.75 'c_lessequals'( T, X, 'tc_nat' ) ) ] )
% 2.35/2.75 , clause( 20296, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), Z, X
% 2.35/2.75 ), Y ) ] )
% 2.35/2.75 , clause( 20297, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 2.35/2.75 , X ) ) ] )
% 2.35/2.75 , clause( 20298, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 2.35/2.75 , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.75 , clause( 20299, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 2.35/2.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.35/2.75 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 2.35/2.75 ), X ), Y ) ] )
% 2.35/2.75 , clause( 20300, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 2.35/2.75 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 2.35/2.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 2.35/2.75 'tc_nat' ) ] )
% 2.35/2.75 , clause( 20301, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 2.35/2.75 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 2.35/2.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 2.35/2.75 'tc_nat' ) ] )
% 2.35/2.75 , clause( 20302, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.75 =( 'c_Power_Opower__class_Opower'( 'c_Power_Opower__class_Opower'( Y, Z,
% 2.35/2.75 X ), T, X ), 'c_Power_Opower__class_Opower'( Y,
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), X ) ) ] )
% 2.35/2.75 , clause( 20303, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 2.35/2.75 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 2.35/2.75 Y, X ) ) ] )
% 2.35/2.75 , clause( 20304, [ ~( 'class_Power_Opower'( X ) ), =(
% 2.35/2.75 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 2.35/2.75 ), X ) ) ] )
% 2.35/2.75 , clause( 20305, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.75 =( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 2.35/2.75 ), X ) ) ] )
% 2.35/2.75 , clause( 20306, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.75 =( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 2.35/2.75 ), X ) ) ] )
% 2.35/2.75 , clause( 20307, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 2.35/2.75 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 2.35/2.75 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) )
% 2.35/2.75 ] )
% 2.35/2.75 , clause( 20308, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X
% 2.35/2.75 ) ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 2.35/2.75 ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 2.35/2.75 , clause( 20309, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 2.35/2.75 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 2.35/2.75 , clause( 20310, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 2.35/2.75 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 2.35/2.75 , clause( 20311, [ ~( 'c_lessequals'( X, X, 'tc_nat' ) ),
% 2.35/2.75 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ] )
% 2.35/2.75 , clause( 20312, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.75 =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.75 Z, Y, X ) ) ] )
% 2.35/2.75 , clause( 20313, [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ) ) ] )
% 2.35/2.75 , clause( 20314, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 2.35/2.75 ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 2.35/2.75 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 2.35/2.75 )
% 2.35/2.75 , clause( 20315, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.75 =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.75 Z, Y, X ) ) ] )
% 2.35/2.75 , clause( 20316, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 2.35/2.75 X, Y, 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 2.35/2.75 , clause( 20317, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.35/2.75 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 2.35/2.75 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.75 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 2.35/2.75 , T, X ), X ), T, X ) ) ] )
% 2.35/2.75 , clause( 20318, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 2.35/2.75 ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.75 , clause( 20319, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.35/2.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.75 'c_Power_Opower__class_Opower'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 2.35/2.75 , X ) ] )
% 2.35/2.75 , clause( 20320, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.35/2.75 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.75 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 2.35/2.75 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ] )
% 2.35/2.75 , clause( 20321, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.35/2.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 2.35/2.75 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 2.35/2.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 2.35/2.75 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ] )
% 2.35/2.75 , clause( 20322, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.35/2.75 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.75 'c_HOL_Oinverse__class_Oinverse'( Z, X ),
% 2.35/2.75 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ] )
% 2.35/2.75 , clause( 20323, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.35/2.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 2.35/2.75 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ), ~(
% 2.35/2.75 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 2.35/2.75 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ] )
% 2.35/2.75 , clause( 20324, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.35/2.75 , =( 'c_OrderedGroup_Olordered__ab__group__add__class_Opprt'( Y, X ), Y )
% 2.35/2.75 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.75 , clause( 20325, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.35/2.75 , ~( =( 'c_OrderedGroup_Olordered__ab__group__add__class_Opprt'( Y, X ),
% 2.35/2.75 Y ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ] )
% 2.35/2.75 , clause( 20326, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.75 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z
% 2.35/2.75 ), X ), 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.75 Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.75 , clause( 20327, [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.75 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 2.35/2.75 'tc_nat' ), Y, 'tc_nat' ), 'tc_nat' ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.75 'tc_nat' ) ) ] )
% 2.35/2.75 , clause( 20328, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 2.35/2.75 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 2.35/2.75 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 2.35/2.75 , clause( 20329, [ ~( 'class_Orderings_Oorder'( X ) ),
% 2.35/2.75 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 2.35/2.75 , X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 2.35/2.75 , clause( 20330, [ ~( 'class_Ring__and__Field_Osgn__if'( X ) ), =(
% 2.35/2.75 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'(
% 2.35/2.75 'c_HOL_Oone__class_Oone'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.75 X ) ) ] )
% 2.35/2.75 , clause( 20331, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 2.35/2.75 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Z ), ~( 'c_lessequals'( Y, Z,
% 2.35/2.75 X ) ) ] )
% 2.35/2.75 , clause( 20332, [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 2.35/2.75 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.35/2.75 , Z, X ), X ) ) ] )
% 2.35/2.75 , clause( 20333, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =(
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 2.35/2.75 , Z, X ) ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ), =( Y, Z ) ]
% 2.35/2.75 )
% 2.35/2.75 , clause( 20334, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.35/2.75 X ) ), =( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 2.35/2.75 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 2.35/2.75 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.75 , clause( 20335, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 2.35/2.75 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 2.35/2.75 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 2.35/2.75 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 2.35/2.75 ) ] )
% 2.35/2.75 , clause( 20336, [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 2.35/2.75 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 2.35/2.75 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 2.35/2.75 ) ] )
% 2.35/2.75 , clause( 20337, [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 2.35/2.75 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 2.35/2.75 , Z, X ) ) ), =( 'c_Divides_Odiv__class_Omod'(
% 2.35/2.75 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 2.35/2.75 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'( T, X ), Z,
% 2.35/2.75 X ) ) ] )
% 2.35/2.75 , clause( 20338, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.35/2.75 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 2.35/2.75 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.75 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 2.35/2.75 , T, X ), X ), T, X ) ) ] )
% 2.35/2.75 , clause( 20339, [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 2.35/2.75 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ominus__class_Ominus'( Z
% 2.35/2.75 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 2.35/2.75 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 2.35/2.75 , clause( 20340, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 2.35/2.75 Y, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'(
% 2.35/2.75 Y, Z, X ), X ) ) ] )
% 2.35/2.75 , clause( 20341, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.35/2.75 , Z, X ), 'c_lessequals'( Y, T, X ), ~( 'c_lessequals'( Y,
% 2.35/2.75 'c_Orderings_Oord__class_Omax'( T, Z, X ), X ) ) ] )
% 2.35/2.75 , clause( 20342, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.75 =( 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X
% 2.35/2.75 ), 'c_Power_Opower__class_Opower'( Y, T, X ), X ),
% 2.35/2.75 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T,
% 2.35/2.75 'tc_nat' ), X ) ) ] )
% 2.35/2.75 , clause( 20343, [ =( 'c_Lambda_Oliftn'( 'c_Suc'( X ), Y, Z ),
% 2.35/2.75 'c_Lambda_Olift'( 'c_Lambda_Oliftn'( X, Y, Z ), Z ) ) ] )
% 2.35/2.75 , clause( 20344, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =(
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat'
% 2.35/2.75 ), T, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.75 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), T,
% 2.35/2.75 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.35/2.75 , clause( 20345, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.35/2.75 , Z, X ), ~( 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X )
% 2.35/2.75 , X ) ) ] )
% 2.35/2.75 , clause( 20346, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.35/2.75 , Z, X ), ~( 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X )
% 2.35/2.75 , X ) ) ] )
% 2.35/2.75 , clause( 20347, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 2.35/2.75 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 2.35/2.75 T, X ) ) ] )
% 2.35/2.75 , clause( 20348, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 2.35/2.75 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 2.35/2.75 T, X ) ) ] )
% 2.35/2.75 , clause( 20349, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 2.35/2.75 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 2.35/2.75 T, X ) ) ] )
% 2.35/2.75 , clause( 20350, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 2.35/2.75 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Y,
% 2.35/2.75 T, X ) ) ] )
% 2.35/2.75 , clause( 20351, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.35/2.75 , Z, X ), ~( 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( T, Z, X )
% 2.35/2.75 , X ) ) ] )
% 2.35/2.75 , clause( 20352, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.35/2.75 , Z, X ), ~( 'c_lessequals'( Y, 'c_Orderings_Oord__class_Omin'( Z, T, X )
% 2.35/2.75 , X ) ) ] )
% 2.35/2.75 , clause( 20353, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.35/2.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.75 'c_HOL_Osgn__class_Osgn'( Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.75 , clause( 20354, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.35/2.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.35/2.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.75 'c_HOL_Osgn__class_Osgn'( Y, X ), X ) ) ] )
% 2.35/2.75 , clause( 20355, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 2.35/2.75 ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 2.35/2.75 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 2.35/2.75 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 2.35/2.75 , Y, X ) ) ] )
% 2.35/2.75 , clause( 20356, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 2.35/2.75 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.75 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 2.35/2.75 X ), Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 2.35/2.75 , Z, X ) ] )
% 2.35/2.75 , clause( 20357, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 2.35/2.75 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 2.35/2.75 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 2.35/2.75 X ), Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 2.35/2.75 , Z, X ) ] )
% 2.35/2.75 , clause( 20358, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 2.35/2.75 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 2.35/2.75 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 2.35/2.75 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T, Z, X
% 2.35/2.75 ), X ) ) ] )
% 2.35/2.75 , clause( 20359, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.75 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X
% 2.35/2.75 ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 2.35/2.75 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ),
% 2.35/2.75 ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oinverse__class_Odivide'( Y, T, X
% 2.35/2.75 ), X ) ) ] )
% 2.35/2.75 , clause( 20360, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.75 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 2.35/2.75 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.75 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 2.35/2.75 T, X ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 2.35/2.75 , T, X ) ] )
% 2.35/2.75 , clause( 20361, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.75 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 2.35/2.75 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.75 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 2.35/2.75 T, X ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 2.35/2.75 , T, X ) ] )
% 2.35/2.75 , clause( 20362, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.75 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 2.35/2.75 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.75 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 2.35/2.75 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 2.35/2.75 Z, X ) ) ] )
% 2.35/2.75 , clause( 20363, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.75 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 2.35/2.75 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 2.35/2.75 X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 2.35/2.75 , clause( 20364, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.75 =( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 2.35/2.75 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ] )
% 2.35/2.75 , clause( 20365, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 2.35/2.75 ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.75 , clause( 20366, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 2.35/2.75 ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.75 , clause( 20367, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 2.35/2.75 , clause( 20368, [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ] )
% 2.35/2.75 , clause( 20369, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.35/2.75 X ) ), 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 2.35/2.75 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ] )
% 2.35/2.75 , clause( 20370, [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_Suc'(
% 2.35/2.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 2.35/2.75 , clause( 20371, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 2.35/2.75 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 2.35/2.75 , T, X ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'(
% 2.35/2.75 Y, T, X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ] )
% 2.35/2.75 , clause( 20372, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.35/2.75 X ) ), 'c_lessequals'( Y, 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ] )
% 2.35/2.75 , clause( 20373, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OAbs'( Y )
% 2.35/2.75 ) ) ] )
% 2.35/2.75 , clause( 20374, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.35/2.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 2.35/2.75 ), X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 2.35/2.75 , X ), W, X ), X ) ) ] )
% 2.35/2.75 , clause( 20375, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.35/2.75 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.75 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 2.35/2.75 , X ), W, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.75 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, U, X ), Y, X
% 2.35/2.75 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, U, X ),
% 2.35/2.75 W, X ), X ) ) ] )
% 2.35/2.75 , clause( 20376, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.35/2.75 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( U, Z, X ), W, X
% 2.35/2.76 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z
% 2.35/2.76 , X ), T, X ), W, X ) ) ] )
% 2.35/2.76 , clause( 20377, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 2.35/2.76 , X ), U, X ), W, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), U, X
% 2.35/2.76 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, X ),
% 2.35/2.76 W, X ), X ) ) ] )
% 2.35/2.76 , clause( 20378, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 2.35/2.76 ), U, 'tc_nat' ) ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ), =(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 2.35/2.76 'tc_nat' ), U ) ] )
% 2.35/2.76 , clause( 20379, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 2.35/2.76 ), U, 'tc_nat' ) ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ), =( Z,
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 2.35/2.76 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20380, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.76 =( 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 2.35/2.76 ), X ), Y ) ] )
% 2.35/2.76 , clause( 20381, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 2.35/2.76 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 2.35/2.76 X ), Y ) ] )
% 2.35/2.76 , clause( 20382, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.35/2.76 , Z, X ), 'c_lessequals'( T, Z, X ), ~( 'c_lessequals'(
% 2.35/2.76 'c_Orderings_Oord__class_Omin'( T, Y, X ), Z, X ) ) ] )
% 2.35/2.76 , clause( 20383, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 2.35/2.76 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), T,
% 2.35/2.76 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), T, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20384, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 2.35/2.76 , X ) ) ] )
% 2.35/2.76 , clause( 20385, [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 2.35/2.76 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 2.35/2.76 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 2.35/2.76 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 2.35/2.76 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( U, Y, X ), Z, X
% 2.35/2.76 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( W, T, X ),
% 2.35/2.76 Z, X ) ) ] )
% 2.35/2.76 , clause( 20386, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.76 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' )
% 2.35/2.76 ] )
% 2.35/2.76 , clause( 20387, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.35/2.76 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20388, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.35/2.76 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20389, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20390, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20391, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 2.35/2.76 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 2.35/2.76 , clause( 20392, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 2.35/2.76 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20393, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.35/2.76 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 2.35/2.76 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 2.35/2.76 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 2.35/2.76 , clause( 20394, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.35/2.76 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 2.35/2.76 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 2.35/2.76 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ] )
% 2.35/2.76 , clause( 20395, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.35/2.76 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 20396, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.76 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20397, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.76 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 2.35/2.76 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 2.35/2.76 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.76 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20398, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 2.35/2.76 Z, T, X ), X ) ) ] )
% 2.35/2.76 , clause( 20399, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.35/2.76 , Z, X ), ~( 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z
% 2.35/2.76 , X ) ) ] )
% 2.35/2.76 , clause( 20400, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.35/2.76 , Z, X ), ~( 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z
% 2.35/2.76 , X ) ) ] )
% 2.35/2.76 , clause( 20401, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.35/2.76 , 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T
% 2.35/2.76 , X ) ) ] )
% 2.35/2.76 , clause( 20402, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.35/2.76 , 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z
% 2.35/2.76 , X ) ) ] )
% 2.35/2.76 , clause( 20403, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.35/2.76 , 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T
% 2.35/2.76 , X ) ) ] )
% 2.35/2.76 , clause( 20404, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.35/2.76 , 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z
% 2.35/2.76 , X ) ) ] )
% 2.35/2.76 , clause( 20405, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.35/2.76 , Z, X ), ~( 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z
% 2.35/2.76 , X ) ) ] )
% 2.35/2.76 , clause( 20406, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.35/2.76 , Z, X ), ~( 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z
% 2.35/2.76 , X ) ) ] )
% 2.35/2.76 , clause( 20407, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 2.35/2.76 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'(
% 2.35/2.76 X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20408, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 2.35/2.76 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_lessequals'( X,
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20409, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 20410, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Y, T, X
% 2.35/2.76 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omax'( T, Z
% 2.35/2.76 , X ), X ) ) ] )
% 2.35/2.76 , clause( 20411, [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( Y ),
% 2.35/2.76 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.76 X, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20412, [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y,
% 2.35/2.76 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.76 X, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20413, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 2.35/2.76 ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ) ) ] )
% 2.35/2.76 , clause( 20414, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 2.35/2.76 ), =( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z ) ] )
% 2.35/2.76 , clause( 20415, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 2.35/2.76 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 2.35/2.76 ) ] )
% 2.35/2.76 , clause( 20416, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, Z )
% 2.35/2.76 , 'c_Lambda_OdB_OVar'( X ) ), =( X, Z ), 'c_HOL_Oord__class_Oless'( Z, X
% 2.35/2.76 , 'tc_nat' ) ] )
% 2.35/2.76 , clause( 20417, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.76 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20418, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ] )
% 2.35/2.76 , clause( 20419, [ ~( 'class_Ring__and__Field_Osgn__if'( X ) ), =(
% 2.35/2.76 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =(
% 2.35/2.76 Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.76 , clause( 20420, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y )
% 2.35/2.76 ) ), =( X, Y ) ] )
% 2.35/2.76 , clause( 20421, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.76 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 2.35/2.76 , Z, X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20422, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 2.35/2.76 'tc_nat' ), Z, 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), ~(
% 2.35/2.76 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.76 X, Z, 'tc_nat' ), T, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 2.35/2.76 ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20423, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 2.35/2.76 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ), Z,
% 2.35/2.76 'tc_nat' ), U, 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20424, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 2.35/2.76 'tc_nat' ), T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat'
% 2.35/2.76 ), X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ), U, 'tc_nat' ), 'tc_nat' )
% 2.35/2.76 ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20425, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat'
% 2.35/2.76 ), U, 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( Z,
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ), U,
% 2.35/2.76 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20426, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 2.35/2.76 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ), ~(
% 2.35/2.76 'c_lessequals'( Y, 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ] )
% 2.35/2.76 , clause( 20427, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 2.35/2.76 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ), ~(
% 2.35/2.76 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ] )
% 2.35/2.76 , clause( 20428, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 2.35/2.76 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 2.35/2.76 , 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.76 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 2.35/2.76 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ] )
% 2.35/2.76 , clause( 20429, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( T, Z, X
% 2.35/2.76 ), ~( 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( T, Y, X
% 2.35/2.76 ), Z, X ) ) ] )
% 2.35/2.76 , clause( 20430, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 2.35/2.76 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.35/2.76 , U, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.76 Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ),
% 2.35/2.76 =( Y, T ) ] )
% 2.35/2.76 , clause( 20431, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 2.35/2.76 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.35/2.76 , U, X ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.76 Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ), =( Z, U ),
% 2.35/2.76 =( Y, T ) ] )
% 2.35/2.76 , clause( 20432, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 2.35/2.76 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Z ) ), 'c_lessequals'( Y, Z, X
% 2.35/2.76 ) ] )
% 2.35/2.76 , clause( 20433, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 2.35/2.76 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Y ), ~( 'c_lessequals'( Z, Y,
% 2.35/2.76 X ) ) ] )
% 2.35/2.76 , clause( 20434, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.76 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 2.35/2.76 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 2.35/2.76 , X ) ) ] )
% 2.35/2.76 , clause( 20435, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 2.35/2.76 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 2.35/2.76 ) ) ] )
% 2.35/2.76 , clause( 20436, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 2.35/2.76 ), 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20437, [ =( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat'
% 2.35/2.76 ), 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20438, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 2.35/2.76 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 2.35/2.76 ) ) ] )
% 2.35/2.76 , clause( 20439, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 2.35/2.76 , 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X
% 2.35/2.76 ) ) ] )
% 2.35/2.76 , clause( 20440, [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X )
% 2.35/2.76 , 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X
% 2.35/2.76 ) ) ] )
% 2.35/2.76 , clause( 20441, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.76 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 2.35/2.76 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 2.35/2.76 , X ) ) ] )
% 2.35/2.76 , clause( 20442, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.76 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T,
% 2.35/2.76 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z
% 2.35/2.76 , X ) ) ] )
% 2.35/2.76 , clause( 20443, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.76 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ),
% 2.35/2.76 X ), 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oplus__class_Oplus'( Y, T, X )
% 2.35/2.76 , X ) ) ] )
% 2.35/2.76 , clause( 20444, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.76 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T,
% 2.35/2.76 X ), 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X )
% 2.35/2.76 , X ) ) ] )
% 2.35/2.76 , clause( 20445, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.76 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20446, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 2.35/2.76 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T,
% 2.35/2.76 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.76 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 2.35/2.76 Y, T, X ), X ) ) ] )
% 2.35/2.76 , clause( 20447, [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.76 'tc_nat' ) ), X, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( Y
% 2.35/2.76 , X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20448, [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.76 'tc_nat' ) ), X, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X
% 2.35/2.76 , Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20449, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 2.35/2.76 , 'c_HOL_Oplus__class_Oplus'( Z, U, X ) ) ), =(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Y, T, X ), U ) ] )
% 2.35/2.76 , clause( 20450, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.35/2.76 X ) ), 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 2.35/2.76 X ) ] )
% 2.35/2.76 , clause( 20451, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 2.35/2.76 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20452, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 2.35/2.76 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20453, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20454, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20455, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 2.35/2.76 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20456, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 2.35/2.76 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20457, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 2.35/2.76 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 2.35/2.76 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 2.35/2.76 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ] )
% 2.35/2.76 , clause( 20458, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 2.35/2.76 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 2.35/2.76 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y,
% 2.35/2.76 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ] )
% 2.35/2.76 , clause( 20459, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), =( Y
% 2.35/2.76 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 2.35/2.76 , X ) ) ] )
% 2.35/2.76 , clause( 20460, [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OVar'( X ), Y ),
% 2.35/2.76 'c_Lambda_OdB_OVar'( 'c_HOL_Oplus__class_Oplus'( X,
% 2.35/2.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ] )
% 2.35/2.76 , clause( 20461, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 2.35/2.76 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 2.35/2.76 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 2.35/2.76 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.76 X ) ) ] )
% 2.35/2.76 , clause( 20462, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 2.35/2.76 'c_Power_Opower__class_Opower'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 2.35/2.76 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 2.35/2.76 , clause( 20463, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =(
% 2.35/2.76 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 2.35/2.76 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) )
% 2.35/2.76 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.76 , clause( 20464, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 2.35/2.76 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ), ~( 'c_lessequals'( Y, Z,
% 2.35/2.76 X ) ) ] )
% 2.35/2.76 , clause( 20465, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 2.35/2.76 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ) ), 'c_lessequals'( Y, Z, X
% 2.35/2.76 ) ] )
% 2.35/2.76 , clause( 20466, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 2.35/2.76 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z ), ~( 'c_lessequals'( Z, Y,
% 2.35/2.76 X ) ) ] )
% 2.35/2.76 , clause( 20467, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.35/2.76 , =( 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omax'( Y, Z,
% 2.35/2.76 X ), T, X ), 'c_Orderings_Oord__class_Omax'( 'c_HOL_Ominus__class_Ominus'(
% 2.35/2.76 Y, T, X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ), X ) ) ] )
% 2.35/2.76 , clause( 20468, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 2.35/2.76 , clause( 20469, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'(
% 2.35/2.76 Y, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 2.35/2.76 , clause( 20470, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, Y, X ), 'c_lessequals'( Y, Y, X ) ] )
% 2.35/2.76 , clause( 20471, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 2.35/2.76 )
% 2.35/2.76 , clause( 20472, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.35/2.76 , Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 2.35/2.76 , clause( 20473, [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'(
% 2.35/2.76 Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ] )
% 2.35/2.76 , clause( 20474, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 2.35/2.76 , clause( 20475, [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'(
% 2.35/2.76 Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ] )
% 2.35/2.76 , clause( 20476, [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =(
% 2.35/2.76 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, X ), Y ) ] )
% 2.35/2.76 , clause( 20477, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.35/2.76 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.35/2.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 2.35/2.76 , clause( 20478, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.35/2.76 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_lessequals'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20479, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 2.35/2.76 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.76 , clause( 20480, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 2.35/2.76 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.76 , clause( 20481, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 2.35/2.76 , Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 2.35/2.76 , clause( 20482, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.35/2.76 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 2.35/2.76 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ] )
% 2.35/2.76 , clause( 20483, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.35/2.76 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 2.35/2.76 ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 2.35/2.76 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ] )
% 2.35/2.76 , clause( 20484, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 2.35/2.76 ), X ) ) ] )
% 2.35/2.76 , clause( 20485, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 2.35/2.76 ), X ) ) ] )
% 2.35/2.76 , clause( 20486, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X
% 2.35/2.76 ), X ) ) ] )
% 2.35/2.76 , clause( 20487, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 2.35/2.76 ), X ) ) ] )
% 2.35/2.76 , clause( 20488, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 2.35/2.76 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 2.35/2.76 , T, X ), 'c_Orderings_Oord__class_Omin'( Y,
% 2.35/2.76 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ] )
% 2.35/2.76 , clause( 20489, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 2.35/2.76 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 2.35/2.76 X ), X ), 'c_Orderings_Oord__class_Omin'( Z,
% 2.35/2.76 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ) ) ] )
% 2.35/2.76 , clause( 20490, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 2.35/2.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 2.35/2.76 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20491, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 2.35/2.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 2.35/2.76 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20492, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 2.35/2.76 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20493, [ ~(
% 2.35/2.76 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), ~(
% 2.35/2.76 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 2.35/2.76 , clause( 20494, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.76 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 2.35/2.76 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T,
% 2.35/2.76 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20495, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 2.35/2.76 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 2.35/2.76 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20496, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 2.35/2.76 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 2.35/2.76 ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20497, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 2.35/2.76 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 2.35/2.76 ~( 'c_lessequals'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat'
% 2.35/2.76 ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20498, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 2.35/2.76 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 2.35/2.76 ] )
% 2.35/2.76 , clause( 20499, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20500, [ =( 'c_HOL_Ominus__class_Ominus'(
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 2.35/2.76 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20501, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.76 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 2.35/2.76 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 2.35/2.76 ] )
% 2.35/2.76 , clause( 20502, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 2.35/2.76 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 2.35/2.76 ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 2.35/2.76 , clause( 20503, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 2.35/2.76 , T, X ) ) ), =( Y, Z ) ] )
% 2.35/2.76 , clause( 20504, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 2.35/2.76 , T, X ) ) ), =( Z, T ) ] )
% 2.35/2.76 , clause( 20505, [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 2.35/2.76 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), =( X, Z ) ] )
% 2.35/2.76 , clause( 20506, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 2.35/2.76 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Y, Z,
% 2.35/2.76 X ), X ), Y ) ] )
% 2.35/2.76 , clause( 20507, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 2.35/2.76 'tc_nat' ) ), =( Y, Z ) ] )
% 2.35/2.76 , clause( 20508, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 2.35/2.76 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( Y, 'c_Suc'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20509, [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 2.35/2.76 , 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) ) ), =( X,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 2.35/2.76 , clause( 20510, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.76 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20511, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.76 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20512, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 2.35/2.76 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Suc'( Y ), X ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 2.35/2.76 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ] )
% 2.35/2.76 , clause( 20513, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 2.35/2.76 'c_HOL_Oone__class_Oone'( X ), Y, X ), 'c_lessequals'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ),
% 2.35/2.76 X ) ) ] )
% 2.35/2.76 , clause( 20514, [ =( 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( X ), Y, 'tc_nat'
% 2.35/2.76 ), 'c_HOL_Oplus__class_Oplus'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20515, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 2.35/2.76 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Z,
% 2.35/2.76 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) )
% 2.35/2.76 ] )
% 2.35/2.76 , clause( 20516, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 2.35/2.76 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Z, X,
% 2.35/2.76 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) )
% 2.35/2.76 ] )
% 2.35/2.76 , clause( 20517, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 2.35/2.76 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20518, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 2.35/2.76 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 2.35/2.76 ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20519, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.76 ), 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.35/2.76 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20520, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.76 ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( T, Z, X
% 2.35/2.76 ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 2.35/2.76 ) ) ] )
% 2.35/2.76 , clause( 20521, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.76 ), 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.35/2.76 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.76 X ), T, X ) ) ] )
% 2.35/2.76 , clause( 20522, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.76 ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X
% 2.35/2.76 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 2.35/2.76 ) ) ] )
% 2.35/2.76 , clause( 20523, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.35/2.76 X ) ), 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.35/2.76 , Z, X ), X ) ) ] )
% 2.35/2.76 , clause( 20524, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.35/2.76 X ) ), 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 2.35/2.76 , T, X ), X ) ) ] )
% 2.35/2.76 , clause( 20525, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X
% 2.35/2.76 , Y, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 2.35/2.76 ) ), Y, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20526, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ] )
% 2.35/2.76 , clause( 20527, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z,
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ] )
% 2.35/2.76 , clause( 20528, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ] )
% 2.35/2.76 , clause( 20529, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ] )
% 2.35/2.76 , clause( 20530, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 2.35/2.76 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ) ] )
% 2.35/2.76 , clause( 20531, [ =( 'c_HOL_Ominus__class_Ominus'(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 Z, Y, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z,
% 2.35/2.76 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20532, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 2.35/2.76 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 2.35/2.76 , T ), =( X, Z ) ] )
% 2.35/2.76 , clause( 20533, [ ~( =( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, T, 'tc_nat'
% 2.35/2.76 ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ), =( Y
% 2.35/2.76 , T ), =( X, Z ) ] )
% 2.35/2.76 , clause( 20534, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X )
% 2.35/2.76 , 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X
% 2.35/2.76 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X
% 2.35/2.76 ) ) ] )
% 2.35/2.76 , clause( 20535, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 2.35/2.76 'c_HOL_Oabs__class_Oabs'( Y, X ), X ), 'c_HOL_Otimes__class_Otimes'( Y, Y
% 2.35/2.76 , X ) ) ] )
% 2.35/2.76 , clause( 20536, [ =( 'c_Nat_Osize__class_Osize'( X, 'tc_nat' ), X ) ] )
% 2.35/2.76 , clause( 20537, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 2.35/2.76 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 2.35/2.76 , X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Oinverse'(
% 2.35/2.76 Y, X ), X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.76 , clause( 20538, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 2.35/2.76 'c_HOL_Oinverse__class_Oinverse'( 'c_Power_Opower__class_Opower'( Y, Z, X
% 2.35/2.76 ), X ), 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Oinverse'(
% 2.35/2.76 Y, X ), Z, X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.76 , clause( 20539, [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_Suc'(
% 2.35/2.76 Y ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20540, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OApp'( Y,
% 2.35/2.76 Z ) ) ) ] )
% 2.35/2.76 , clause( 20541, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.35/2.76 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 2.35/2.76 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 Z, Y, X ) ) ] )
% 2.35/2.76 , clause( 20542, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.35/2.76 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Ouminus__class_Ouminus'( Z, X ), 'c_HOL_Ouminus__class_Ouminus'( Y
% 2.35/2.76 , X ), X ) ) ] )
% 2.35/2.76 , clause( 20543, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 2.35/2.76 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20544, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 2.35/2.76 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20545, [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 2.35/2.76 ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20546, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X )
% 2.35/2.76 , 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 2.35/2.76 , clause( 20547, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y )
% 2.35/2.76 , 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ] )
% 2.35/2.76 , clause( 20548, [ ~( =( X, 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' )
% 2.35/2.76 ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 2.35/2.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20549, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.76 ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), X
% 2.35/2.76 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ] )
% 2.35/2.76 , clause( 20550, [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 2.35/2.76 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 2.35/2.76 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 2.35/2.76 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 2.35/2.76 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( U, Y, X ), Z
% 2.35/2.76 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( W, T,
% 2.35/2.76 X ), Z, X ) ) ] )
% 2.35/2.76 , clause( 20551, [ =( 'c_HOL_Ominus__class_Ominus'(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 2.35/2.76 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20552, [ =( 'c_HOL_Ominus__class_Ominus'(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat'
% 2.35/2.76 ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20553, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.35/2.76 , Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ), =( U,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 2.35/2.76 ) ] )
% 2.35/2.76 , clause( 20554, [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 2.35/2.76 , clause( 20555, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.76 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.35/2.76 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ] )
% 2.35/2.76 , clause( 20556, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.76 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.35/2.76 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ] )
% 2.35/2.76 , clause( 20557, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.76 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.35/2.76 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ] )
% 2.35/2.76 , clause( 20558, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 2.35/2.76 , Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.76 , clause( 20559, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 2.35/2.76 , Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.76 , clause( 20560, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'(
% 2.35/2.76 X ), X ) ] )
% 2.35/2.76 , clause( 20561, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 2.35/2.76 'c_HOL_Oabs__class_Oabs'( 'c_Power_Opower__class_Opower'(
% 2.35/2.76 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), X ),
% 2.35/2.76 'c_HOL_Oabs__class_Oabs'( 'c_Power_Opower__class_Opower'( Y, Z, X ), X )
% 2.35/2.76 ) ] )
% 2.35/2.76 , clause( 20562, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.76 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 2.35/2.76 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y,
% 2.35/2.76 'c_HOL_Oone__class_Oone'( X ), X ), Z, X ) ) ] )
% 2.35/2.76 , clause( 20563, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.76 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 2.35/2.76 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Z,
% 2.35/2.76 'c_HOL_Oone__class_Oone'( X ), X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 20564, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 2.35/2.76 ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20565, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 2.35/2.76 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20566, [ =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_Suc'(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( X,
% 2.35/2.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Y, 'tc_nat' ) ) ), =( X
% 2.35/2.76 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20567, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 2.35/2.76 X, Y, 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 2.35/2.76 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20568, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.35/2.76 X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 2.35/2.76 ] )
% 2.35/2.76 , clause( 20569, [ =( 'c_Nat_Osize__class_Osize'( 'c_Suc'( X ), 'tc_nat' )
% 2.35/2.76 , 'c_HOL_Oplus__class_Oplus'( 'c_Nat_Osize__class_Osize'( X, 'tc_nat' ),
% 2.35/2.76 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20570, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.35/2.76 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.76 , clause( 20571, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ),
% 2.35/2.76 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) )
% 2.35/2.76 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 2.35/2.76 , clause( 20572, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20573, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20574, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 2.35/2.76 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 2.35/2.76 X ) ) ] )
% 2.35/2.76 , clause( 20575, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 2.35/2.76 ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 2.35/2.76 , clause( 20576, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oabs__class_Oabs'( Z, X
% 2.35/2.76 ), X ) ) ] )
% 2.35/2.76 , clause( 20577, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 2.35/2.76 Z, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 2.35/2.76 , clause( 20578, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 2.35/2.76 Z, X ) ) ] )
% 2.35/2.76 , clause( 20579, [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 2.35/2.76 ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20580, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_lessequals'( Z, Y, X ), ~(
% 2.35/2.76 'c_lessequals'( Y, Z, X ) ) ] )
% 2.35/2.76 , clause( 20581, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20582, [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20583, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 2.35/2.76 , clause( 20584, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 2.35/2.76 , clause( 20585, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ] )
% 2.35/2.76 , clause( 20586, [ ~( 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X,
% 2.35/2.76 'tc_nat' ), 'tc_nat' ) ), =( 'c_HOL_Ominus__class_Ominus'(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), X, 'tc_nat' ), Y ) ] )
% 2.35/2.76 , clause( 20587, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 2.35/2.76 'c_Orderings_Oord__class_Omin'( Y, Y, X ), Y ) ] )
% 2.35/2.76 , clause( 20588, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Oinverse__class_Odivide'(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 20589, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), Y, X ), Z ) ] )
% 2.35/2.76 , clause( 20590, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.35/2.76 , Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.76 , clause( 20591, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y,
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.35/2.76 , Z, X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.76 , clause( 20592, [ ~( 'class_OrderedGroup_Olordered__ab__group__add__abs'(
% 2.35/2.76 X ) ), 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 2.35/2.76 'c_HOL_Oabs__class_Oabs'( T, X ), X ), X ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ) ) ] )
% 2.35/2.76 , clause( 20593, [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OVar'( Y ), Z ),
% 2.35/2.76 'c_Lambda_OdB_OVar'( 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ) ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ] )
% 2.35/2.76 , clause( 20594, [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OApp'(
% 2.35/2.76 'c_Lambda_OdB_OAbs'( X ), Y ), 'c_Lambda_Osubst'( X, Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 2.35/2.76 , clause( 20595, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 2.35/2.76 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 20596, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 2.35/2.76 'tc_nat' ), 'tc_nat' ) ] )
% 2.35/2.76 , clause( 20597, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( Y, X,
% 2.35/2.76 'tc_nat' ), 'tc_nat' ) ] )
% 2.35/2.76 , clause( 20598, [ 'c_lessequals'( X, 'c_HOL_Oplus__class_Oplus'( X, Y,
% 2.35/2.76 'tc_nat' ), 'tc_nat' ) ] )
% 2.35/2.76 , clause( 20599, [ =( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Y, 'tc_nat' ),
% 2.35/2.76 'c_Orderings_Oord__class_Omax'( X, Y, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20600, [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =(
% 2.35/2.76 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 2.35/2.76 , X ) ) ), =( Y, Z ) ] )
% 2.35/2.76 , clause( 20601, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 2.35/2.76 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'( Z
% 2.35/2.76 , X ) ) ), =( Y, Z ) ] )
% 2.35/2.76 , clause( 20602, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.35/2.76 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 2.35/2.76 ), T, X ), 'c_HOL_Oinverse__class_Odivide'(
% 2.35/2.76 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 2.35/2.76 Z, T, X ), X ) ) ] )
% 2.35/2.76 , clause( 20603, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.76 ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20604, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20605, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20606, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20607, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 2.35/2.76 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 2.35/2.76 , Y, X ) ) ] )
% 2.35/2.76 , clause( 20608, [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OAbs'( Y ), Z ),
% 2.35/2.76 'c_Lambda_OdB_OAbs'( 'c_Lambda_Oliftn'( X, Y, 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 Z, 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ) ) ] )
% 2.35/2.76 , clause( 20609, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 2.35/2.76 ), =( Z, Y ) ] )
% 2.35/2.76 , clause( 20610, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 2.35/2.76 ) ] )
% 2.35/2.76 , clause( 20611, [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~(
% 2.35/2.76 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20612, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 2.35/2.76 , clause( 20613, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), =( Y, X ) ] )
% 2.35/2.76 , clause( 20614, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 2.35/2.76 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 2.35/2.76 , clause( 20615, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 2.35/2.76 ), =( Z, Y ) ] )
% 2.35/2.76 , clause( 20616, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 2.35/2.76 'c_lessequals'( Z, Y, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 2.35/2.76 , clause( 20617, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~(
% 2.35/2.76 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ] )
% 2.35/2.76 , clause( 20618, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Z, Y, X ) ] )
% 2.35/2.76 , clause( 20619, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 2.35/2.76 ) ] )
% 2.35/2.76 , clause( 20620, [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 2.35/2.76 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 2.35/2.76 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 2.35/2.76 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 2.35/2.76 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 2.35/2.76 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( W, T,
% 2.35/2.76 X ), Z, X ) ) ] )
% 2.35/2.76 , clause( 20621, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.35/2.76 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.35/2.76 , X ) ) ] )
% 2.35/2.76 , clause( 20622, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.35/2.76 , 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 2.35/2.76 , clause( 20623, [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X,
% 2.35/2.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 2.35/2.76 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20624, [ =( X, 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X,
% 2.35/2.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 2.35/2.76 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20625, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 2.35/2.76 'c_Orderings_Oord__class_Omax'( Y, Y, X ), Y ) ] )
% 2.35/2.76 , clause( 20626, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.35/2.76 X ) ), =( 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 20627, [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OApp'(
% 2.35/2.76 Z, T ) ) ), =( Y, T ) ] )
% 2.35/2.76 , clause( 20628, [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OApp'(
% 2.35/2.76 Z, T ) ) ), =( X, Z ) ] )
% 2.35/2.76 , clause( 20629, [ ~(
% 2.35/2.76 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 2.35/2.76 , clause( 20630, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 2.35/2.76 , Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, T, 'tc_nat' ), 'tc_nat' )
% 2.35/2.76 , ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20631, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20632, [ =( 'c_HOL_Ominus__class_Ominus'(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 X, Z, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 2.35/2.76 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20633, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.76 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 2.35/2.76 , clause( 20634, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.76 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ] )
% 2.35/2.76 , clause( 20635, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.35/2.76 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ),
% 2.35/2.76 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ] )
% 2.35/2.76 , clause( 20636, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omax'( Z, T, X ),
% 2.35/2.76 X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 2.35/2.76 , clause( 20637, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omax'( Z, T, X ),
% 2.35/2.76 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 2.35/2.76 , clause( 20638, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omax'( Z, T, X ),
% 2.35/2.76 X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 2.35/2.76 , clause( 20639, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, 'c_Orderings_Oord__class_Omax'( Z, T, X ),
% 2.35/2.76 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 2.35/2.76 , clause( 20640, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z, X ) ) ] )
% 2.35/2.76 , clause( 20641, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z, X ) ) ] )
% 2.35/2.76 , clause( 20642, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 2.35/2.76 'c_Orderings_Oord__class_Omin'( Y, Z, X ), 'c_Orderings_Oord__class_Omin'(
% 2.35/2.76 Z, Y, X ) ) ] )
% 2.35/2.76 , clause( 20643, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 2.35/2.76 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 2.35/2.76 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 2.35/2.76 , Y, X ) ) ] )
% 2.35/2.76 , clause( 20644, [ =( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat'
% 2.35/2.76 ), T, 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 2.35/2.76 ), Y, 'tc_nat' ), T, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20645, [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), U, X
% 2.35/2.76 ), X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X ), U, X ) ) ] )
% 2.35/2.76 , clause( 20646, [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 2.35/2.76 'tc_nat' ), X, 'tc_nat' ) ] )
% 2.35/2.76 , clause( 20647, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 2.35/2.76 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.76 , clause( 20648, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 2.35/2.76 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.76 , clause( 20649, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 2.35/2.76 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.76 , clause( 20650, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y, X
% 2.35/2.76 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.76 , clause( 20651, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.76 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 2.35/2.76 X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20652, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.76 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 2.35/2.76 Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20653, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 2.35/2.76 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20654, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 2.35/2.76 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 2.35/2.76 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 2.35/2.76 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 2.35/2.76 , clause( 20655, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.76 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.76 X ), X ) ) ] )
% 2.35/2.76 , clause( 20656, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.76 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Z, Z, X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.76 X ), X ) ) ] )
% 2.35/2.76 , clause( 20657, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 2.35/2.76 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) )
% 2.35/2.76 ] )
% 2.35/2.76 , clause( 20658, [ =( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Otimes__class_Otimes'( X, Z,
% 2.35/2.76 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) )
% 2.35/2.76 ] )
% 2.35/2.76 , clause( 20659, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 2.35/2.76 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ominus__class_Ominus'( Z, T,
% 2.35/2.76 'tc_nat' ), X ), 'c_HOL_Oinverse__class_Odivide'(
% 2.35/2.76 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 2.35/2.76 Y, T, X ), X ) ), ~( 'c_lessequals'( T, Z, 'tc_nat' ) ), =( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.76 , clause( 20660, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.35/2.76 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.35/2.76 ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ) ] )
% 2.35/2.76 , clause( 20661, [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 2.35/2.76 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.35/2.76 ) ), 'c_Ring__and__Field_Odvd__class_Odvd'( Z, Y, X ) ] )
% 2.35/2.76 , clause( 20662, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T,
% 2.35/2.76 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 2.35/2.76 , clause( 20663, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T,
% 2.35/2.76 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 2.35/2.76 , clause( 20664, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 2.35/2.76 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ] )
% 2.35/2.76 , clause( 20665, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 2.35/2.76 'c_Orderings_Oord__class_Omin'( T, Z, X ), X ) ) ] )
% 2.35/2.76 , clause( 20666, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T,
% 2.35/2.76 X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 2.35/2.76 , clause( 20667, [ ~( 'class_Orderings_Olinorder'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T,
% 2.35/2.76 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 2.35/2.76 , clause( 20668, [ =( 'c_HOL_Ominus__class_Ominus'(
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 2.35/2.76 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20669, [ =( 'c_HOL_Ominus__class_Ominus'(
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Z,
% 2.35/2.76 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20670, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.35/2.76 , X ) ) ] )
% 2.35/2.76 , clause( 20671, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 2.35/2.76 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.35/2.76 , X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20672, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 2.35/2.76 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 20673, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 2.35/2.76 ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 20674, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.35/2.76 X ) ), 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 2.35/2.76 ) ] )
% 2.35/2.76 , clause( 20675, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.35/2.76 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.35/2.76 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y
% 2.35/2.76 , X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ) ] )
% 2.35/2.76 , clause( 20676, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 2.35/2.76 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.35/2.76 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Z
% 2.35/2.76 , X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ), =( Z,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 2.35/2.76 ) ] )
% 2.35/2.76 , clause( 20677, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 2.35/2.76 X, Y, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ),
% 2.35/2.76 'tc_nat' ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20678, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.76 ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 20679, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.76 ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20680, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 2.35/2.76 X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 20681, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 2.35/2.76 X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20682, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 2.35/2.76 X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 20683, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 2.35/2.76 X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20684, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 2.35/2.76 X ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 2.35/2.76 , clause( 20685, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.76 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X )
% 2.35/2.76 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20686, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.76 'c_Suc'( X ), Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ),
% 2.35/2.76 Z, 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 2.35/2.76 ) ] )
% 2.35/2.76 , clause( 20687, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X
% 2.35/2.76 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ),
% 2.35/2.76 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20688, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 2.35/2.76 =( 'c_Suc'( X ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ]
% 2.35/2.76 )
% 2.35/2.76 , clause( 20689, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'(
% 2.35/2.76 'c_Suc'( Y ), X, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20690, [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 2.35/2.76 'c_lessequals'( Y, X, 'tc_nat' ) ] )
% 2.35/2.76 , clause( 20691, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ] )
% 2.35/2.76 , clause( 20692, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ) ) ), =( X, Z ) ] )
% 2.35/2.76 , clause( 20693, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ) ) ), =( Y, Z ) ] )
% 2.35/2.76 , clause( 20694, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 2.35/2.76 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z
% 2.35/2.76 , X ), 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ] )
% 2.35/2.76 , clause( 20695, [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X )
% 2.35/2.76 ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Y, T, X ) ) ), =( Z, T ) ] )
% 2.35/2.76 , clause( 20696, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 2.35/2.76 ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 Y, T, X ) ) ), =( Z, T ) ] )
% 2.35/2.76 , clause( 20697, [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ),
% 2.35/2.76 ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 T, Z, X ) ) ), =( Y, T ) ] )
% 2.35/2.76 , clause( 20698, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.35/2.76 X ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 2.35/2.76 ), X ), 'c_HOL_Oabs__class_Oabs'( Y, X ) ) ] )
% 2.35/2.76 , clause( 20699, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 2.35/2.76 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 2.35/2.76 ), =( Y, 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 2.35/2.76 , clause( 20700, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ),
% 2.35/2.76 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 2.35/2.76 'c_HOL_Oone__class_Oone'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20701, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.35/2.76 X ) ), 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 2.35/2.76 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ), ~(
% 2.35/2.76 'c_lessequals'( Y, Z, X ) ) ] )
% 2.35/2.76 , clause( 20702, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.35/2.76 X ) ), 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 2.35/2.76 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ) ), ~(
% 2.35/2.76 'c_lessequals'( Y, Z, X ) ) ] )
% 2.35/2.76 , clause( 20703, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y
% 2.35/2.76 ) ] )
% 2.35/2.76 , clause( 20704, [ ~(
% 2.35/2.76 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), =(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_Orderings_Oord__class_Omin'( Y, Z, X ), T
% 2.35/2.76 , X ), 'c_Orderings_Oord__class_Omin'( 'c_HOL_Oplus__class_Oplus'( Y, T,
% 2.35/2.76 X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ] )
% 2.35/2.76 , clause( 20705, [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat' ),
% 2.35/2.76 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20706, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.35/2.76 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z, X ), ~(
% 2.35/2.76 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 2.35/2.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 2.35/2.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 2.35/2.76 , clause( 20707, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.35/2.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 2.35/2.76 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20708, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.35/2.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 2.35/2.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 20709, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.35/2.76 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y, X ), ~(
% 2.35/2.76 'c_lessequals'( Z, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 2.35/2.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 2.35/2.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 20710, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 2.35/2.76 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 2.35/2.76 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ominus__class_Ominus'(
% 2.35/2.76 'c_Divides_Odiv__class_Omod'( Y, T, X ), 'c_Divides_Odiv__class_Omod'( Z
% 2.35/2.76 , T, X ), X ), T, X ) ) ] )
% 2.35/2.76 , clause( 20711, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 2.35/2.76 'c_HOL_Oabs__class_Oabs'( 'c_Power_Opower__class_Opower'( Y, Z, X ), X )
% 2.35/2.76 , 'c_Power_Opower__class_Opower'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X
% 2.35/2.76 ) ) ] )
% 2.35/2.76 , clause( 20712, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 2.35/2.76 'c_HOL_Oabs__class_Oabs'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X
% 2.35/2.76 ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ] )
% 2.35/2.76 , clause( 20713, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 2.35/2.76 , Z, X ), 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~(
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 2.35/2.76 , clause( 20714, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.35/2.76 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ),
% 2.35/2.76 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) )
% 2.35/2.76 ] )
% 2.35/2.76 , clause( 20715, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 2.35/2.76 , clause( 20716, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ] )
% 2.35/2.76 , clause( 20717, [ =( 'c_Lambda_Osubst'( 'c_Lambda_Osubst'( X,
% 2.35/2.76 'c_Lambda_Olift'( Y, Z ), 'c_Suc'( T ) ), 'c_Lambda_Osubst'( U, Y, T ), Z
% 2.35/2.76 ), 'c_Lambda_Osubst'( 'c_Lambda_Osubst'( X, U, Z ), Y, T ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oplus__class_Oplus'( T,
% 2.35/2.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20718, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.35/2.76 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X )
% 2.35/2.76 , 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 2.35/2.76 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ] )
% 2.35/2.76 , clause( 20719, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.35/2.76 X ) ), =( 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 20720, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ] )
% 2.35/2.76 , clause( 20721, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 20722, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 20723, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.35/2.76 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 2.35/2.76 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.76 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z, X ), T, X ) ) ] )
% 2.35/2.76 , clause( 20724, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.35/2.76 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 2.35/2.76 , X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y,
% 2.35/2.76 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ) ) ] )
% 2.35/2.76 , clause( 20725, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 2.35/2.76 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20726, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 2.35/2.76 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 2.35/2.76 , clause( 20727, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Osgn__class_Osgn'( Y, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20728, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Osgn__class_Osgn'( Y, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20729, [ =( 'c_HOL_Ominus__class_Ominus'(
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'( Z ),
% 2.35/2.76 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X
% 2.35/2.76 , Y, 'tc_nat' ), Z, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20730, [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 2.35/2.76 Z, X ), X ) ) ] )
% 2.35/2.76 , clause( 20731, [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ouminus__class_Ouminus'(
% 2.35/2.76 Z, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 2.35/2.76 , clause( 20732, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20733, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z
% 2.35/2.76 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 2.35/2.76 , clause( 20734, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y
% 2.35/2.76 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 2.35/2.76 , clause( 20735, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X ), Z ) ] )
% 2.35/2.76 , clause( 20736, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Z, Y, X ), X ), Z ) ] )
% 2.35/2.76 , clause( 20737, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 2.35/2.76 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 2.35/2.76 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 2.35/2.76 , clause( 20738, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 2.35/2.76 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 20739, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.35/2.76 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 2.35/2.76 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 2.35/2.76 , clause( 20740, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ), ~(
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 2.35/2.76 , clause( 20741, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Y, X ) ] )
% 2.35/2.76 , clause( 20742, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 2.35/2.76 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 2.35/2.76 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 20743, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 2.35/2.76 ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 2.35/2.76 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20744, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.35/2.76 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 2.35/2.76 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 2.35/2.76 , X ) ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 20745, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 2.35/2.76 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 20746, [ ~( 'c_Lambda_Obeta'( 'c_Lambda_OdB_OVar'( X ), Y ) ) ]
% 2.35/2.76 )
% 2.35/2.76 , clause( 20747, [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), 'tc_nat' ),
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 2.35/2.76 ), 'c_Suc'( Y ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ]
% 2.35/2.76 )
% 2.35/2.76 , clause( 20748, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.35/2.76 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.35/2.76 , X ) ) ] )
% 2.35/2.76 , clause( 20749, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.35/2.76 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 2.35/2.76 , X ) ) ] )
% 2.35/2.76 , clause( 20750, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.35/2.76 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20751, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 2.35/2.76 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20752, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 2.35/2.76 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ] )
% 2.35/2.76 , clause( 20753, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Otimes__class_Otimes'( Z,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ] )
% 2.35/2.76 , clause( 20754, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), X ) ] )
% 2.35/2.76 , clause( 20755, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ]
% 2.35/2.76 )
% 2.35/2.76 , clause( 20756, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ]
% 2.35/2.76 )
% 2.35/2.76 , clause( 20757, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 2.35/2.76 ~( 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20758, [ ~(
% 2.35/2.76 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 2.35/2.76 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 2.35/2.76 ) ] )
% 2.35/2.76 , clause( 20759, [ ~(
% 2.35/2.76 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 2.35/2.76 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ] )
% 2.35/2.76 , clause( 20760, [ ~(
% 2.35/2.76 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 2.35/2.76 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 2.35/2.76 ) ] )
% 2.35/2.76 , clause( 20761, [ ~(
% 2.35/2.76 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 2.35/2.76 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ) ) ] )
% 2.35/2.76 , clause( 20762, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X
% 2.35/2.76 ) ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_lessequals'( Y, T, X )
% 2.35/2.76 ) ] )
% 2.35/2.76 , clause( 20763, [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X
% 2.35/2.76 ) ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X )
% 2.35/2.76 ) ] )
% 2.35/2.76 , clause( 20764, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 2.35/2.76 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 2.35/2.76 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20765, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20766, [ 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( X, Y,
% 2.35/2.76 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 2.35/2.76 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20767, [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) )
% 2.35/2.76 , =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X
% 2.35/2.76 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 2.35/2.76 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'( Z,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20768, [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) )
% 2.35/2.76 , =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X
% 2.35/2.76 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 2.35/2.76 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20769, [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) )
% 2.35/2.76 , =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X
% 2.35/2.76 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 2.35/2.76 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'( Z,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 20770, [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) )
% 2.35/2.76 , =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X
% 2.35/2.76 ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 2.35/2.76 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 20771, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 2.35/2.76 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 2.35/2.76 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ] )
% 2.35/2.76 , clause( 20772, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_HOL_Oone__class_Oone'( X ), X ) ] )
% 2.35/2.76 , clause( 20773, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 2.35/2.76 , 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, T, X )
% 2.35/2.76 , 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ] )
% 2.35/2.76 , clause( 20774, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 2.35/2.76 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.35/2.76 X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 2.35/2.76 X ), X ) ) ] )
% 2.35/2.76 , clause( 20775, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 2.35/2.76 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.35/2.76 X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 2.35/2.76 , Z, X ) ) ] )
% 2.35/2.76 , clause( 20776, [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( Y,
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat'
% 2.35/2.76 ), X, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20777, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ), Y ), ~(
% 2.35/2.76 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20778, [ =( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Y, 'tc_nat' ), X ), ~(
% 2.35/2.76 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20779, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 2.35/2.76 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20780, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' )
% 2.35/2.76 , 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20781, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.35/2.76 , 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 2.35/2.76 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20782, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.35/2.76 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 2.35/2.76 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ] )
% 2.35/2.76 , clause( 20783, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 2.35/2.76 , clause( 20784, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 2.35/2.76 , clause( 20785, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Y,
% 2.35/2.76 'c_HOL_Oone__class_Oone'( X ), X ), X ) ] )
% 2.35/2.76 , clause( 20786, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat'
% 2.35/2.76 ), Z, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20787, [ =( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat'
% 2.35/2.76 ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20788, [ =( 'c_List_Odrop'( X, 'c_List_Odrop'( Y, Z, T ), T ),
% 2.35/2.76 'c_List_Odrop'( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, T ) ) ]
% 2.35/2.76 )
% 2.35/2.76 , clause( 20789, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.76 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.76 X ), Z, X ) ), ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y,
% 2.35/2.76 'c_Suc'( T ), X ), 'c_Power_Opower__class_Opower'( Z, 'c_Suc'( T ), X ),
% 2.35/2.76 X ) ) ] )
% 2.35/2.76 , clause( 20790, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X )
% 2.35/2.76 ), =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y,
% 2.35/2.76 Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ] )
% 2.35/2.76 , clause( 20791, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 2.35/2.76 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ] )
% 2.35/2.76 , clause( 20792, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.35/2.76 , 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 20793, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.35/2.76 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.35/2.76 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20794, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 2.35/2.76 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20795, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 2.35/2.76 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 2.35/2.76 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ] )
% 2.35/2.76 , clause( 20796, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.35/2.76 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.35/2.76 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 2.35/2.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 2.35/2.76 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 2.35/2.76 )
% 2.35/2.76 , clause( 20797, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.35/2.76 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.35/2.76 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 2.35/2.76 , clause( 20798, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 2.35/2.76 X ) ] )
% 2.35/2.76 , clause( 20799, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.76 ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 2.35/2.76 'c_Power_Opower__class_Opower'( Y, T, X ) ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Z
% 2.35/2.76 , T ) ] )
% 2.35/2.76 , clause( 20800, [ ~( 'class_Power_Opower'( X ) ), =(
% 2.35/2.76 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 2.35/2.76 , X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 2.35/2.76 , clause( 20801, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.76 =( 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.76 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 2.35/2.76 , clause( 20802, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 2.35/2.76 'c_Lambda_OdB_OVar'( 'c_HOL_Ominus__class_Ominus'( X,
% 2.35/2.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20803, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 2.35/2.76 'c_Lambda_OdB_OVar'( 'c_HOL_Ominus__class_Ominus'( X,
% 2.35/2.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20804, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 2.35/2.76 =( 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'(
% 2.35/2.76 'c_HOL_Oone__class_Oone'( X ), X ) ) ), 'c_HOL_Oord__class_Oless'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ] )
% 2.35/2.76 , clause( 20805, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 2.35/2.76 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Ouminus__class_Ouminus'(
% 2.35/2.76 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20806, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.76 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z
% 2.35/2.76 , X ), X ), 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ) ) ] )
% 2.35/2.76 , clause( 20807, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.76 =( 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X
% 2.35/2.76 ), Y, X ), 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ) ) ] )
% 2.35/2.76 , clause( 20808, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 2.35/2.76 X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z,
% 2.35/2.76 X ), X ) ) ] )
% 2.35/2.76 , clause( 20809, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X )
% 2.35/2.76 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 2.35/2.76 , clause( 20810, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.35/2.76 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 2.35/2.76 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 2.35/2.76 , clause( 20811, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.35/2.76 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Y, X
% 2.35/2.76 ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ] )
% 2.35/2.76 , clause( 20812, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.35/2.76 X ) ), 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'(
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 2.35/2.76 X ) ] )
% 2.35/2.76 , clause( 20813, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 2.35/2.76 , Z, X ), 'c_Power_Opower__class_Opower'( T, U, X ), X ), ~(
% 2.35/2.76 'c_lessequals'( Z, U, 'tc_nat' ) ), ~(
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 2.35/2.76 , clause( 20814, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.76 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 2.35/2.76 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.35/2.76 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20815, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.76 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.35/2.76 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.35/2.76 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20816, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.76 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 2.35/2.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 2.35/2.76 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20817, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.76 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.35/2.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.35/2.76 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20818, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.35/2.76 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.35/2.76 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 2.35/2.76 , clause( 20819, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.35/2.76 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.35/2.76 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 20820, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.35/2.76 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.35/2.76 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20821, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.35/2.76 X ) ), 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ),
% 2.35/2.76 ~( 'c_lessequals'( 'c_HOL_Oabs__class_Oabs'( Y, X ), Z, X ) ) ] )
% 2.35/2.76 , clause( 20822, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 2.35/2.76 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20823, [ 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 2.35/2.76 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20824, [ 'c_HOL_Oord__class_Oless'( X,
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 2.35/2.76 ) ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20825, [ 'c_HOL_Oord__class_Oless'( X,
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 2.35/2.76 ) ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20826, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), X ), Z ) ] )
% 2.35/2.76 , clause( 20827, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.35/2.76 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y,
% 2.35/2.76 Z, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oinverse__class_Oinverse'(
% 2.35/2.76 Z, X ), X ) ) ] )
% 2.35/2.76 , clause( 20828, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.76 Y, 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ) ] )
% 2.35/2.76 , clause( 20829, [ ~( 'c_lessequals'( 'c_Suc'( X ), X, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20830, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 2.35/2.76 , X ), Z, X ) ) ] )
% 2.35/2.76 , clause( 20831, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 2.35/2.76 , X ), Z, X ) ) ] )
% 2.35/2.76 , clause( 20832, [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), ~(
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ouminus__class_Ouminus'( Y
% 2.35/2.76 , X ), Z, X ) ) ] )
% 2.35/2.76 , clause( 20833, [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ),
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ouminus__class_Ouminus'( Y
% 2.35/2.76 , X ), Z, X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 2.35/2.76 , clause( 20834, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 2.35/2.76 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ),
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ) ), =( Z,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.76 , clause( 20835, [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 2.35/2.76 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ] )
% 2.35/2.76 , clause( 20836, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 2.35/2.76 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ] )
% 2.35/2.76 , clause( 20837, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 2.35/2.76 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ] )
% 2.35/2.76 , clause( 20838, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 2.35/2.76 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ] )
% 2.35/2.76 , clause( 20839, [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'( Y ),
% 2.35/2.76 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X
% 2.35/2.76 , 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20840, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X
% 2.35/2.76 ), Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z,
% 2.35/2.76 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20841, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X, 'tc_nat' ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ), 'tc_nat' ) ) ]
% 2.35/2.76 )
% 2.35/2.76 , clause( 20842, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.76 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.76 , clause( 20843, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.76 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ), X ), =( Z,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.76 , clause( 20844, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.76 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, U,
% 2.35/2.76 X ), X ) ) ] )
% 2.35/2.76 , clause( 20845, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 2.35/2.76 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Z,
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), T, X ) ), =( T,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.76 , clause( 20846, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 2.35/2.76 , X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y,
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), Z, X ) ), =( Z,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.76 , clause( 20847, [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OApp'( X, Y ),
% 2.35/2.76 'c_Lambda_OdB_OApp'( X, Z ) ), ~( 'c_Lambda_Obeta'( Y, Z ) ) ] )
% 2.35/2.76 , clause( 20848, [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OApp'( X, Y ),
% 2.35/2.76 'c_Lambda_OdB_OApp'( Z, Y ) ), ~( 'c_Lambda_Obeta'( X, Z ) ) ] )
% 2.35/2.76 , clause( 20849, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.76 ~( 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X
% 2.35/2.76 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20850, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20851, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20852, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20853, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20854, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oone__class_Oone'( X ), X ), X ), X
% 2.35/2.76 ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 2.35/2.76 , clause( 20855, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oone__class_Oone'( X ), X ), X ), Z
% 2.35/2.76 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 2.35/2.76 , clause( 20856, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 2.35/2.76 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ) ] )
% 2.35/2.76 , clause( 20857, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, Z )
% 2.35/2.76 , 'c_Lambda_OdB_OVar'( 'c_HOL_Ominus__class_Ominus'( X,
% 2.35/2.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20858, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 2.35/2.76 'c_Orderings_Oord__class_Omax'( Y, Z, X ), 'c_Orderings_Oord__class_Omax'(
% 2.35/2.76 Z, Y, X ) ) ] )
% 2.35/2.76 , clause( 20859, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.76 ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 2.35/2.76 'c_Power_Opower__class_Opower'( T, Z, X ) ) ), =( Y, T ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 2.35/2.76 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 2.35/2.76 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 20860, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 2.35/2.76 , Z ) ), =( Y, 'c_HOL_Ouminus__class_Ouminus'( T, X ) ) ] )
% 2.35/2.76 , clause( 20861, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 2.35/2.76 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Otimes__class_Otimes'( Y,
% 2.35/2.76 'c_HOL_Osgn__class_Osgn'( Y, X ), X ) ) ] )
% 2.35/2.76 , clause( 20862, [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OVar'( Y ), Z ),
% 2.35/2.76 'c_Lambda_OdB_OVar'( Y ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat'
% 2.35/2.76 ) ) ] )
% 2.35/2.76 , clause( 20863, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.35/2.76 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( Z, T, X ) ), =( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.76 , clause( 20864, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.35/2.76 , 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( Y, T, X ) ), =( Z,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.76 , clause( 20865, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 2.35/2.76 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.76 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oplus__class_Oplus'( Y,
% 2.35/2.76 Z, X ), X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ), =( Z,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 2.35/2.76 ) ] )
% 2.35/2.76 , clause( 20866, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 2.35/2.76 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), 'c_HOL_Oinverse__class_Oinverse'(
% 2.35/2.76 Y, X ), X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ), =( Z,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 2.35/2.76 ) ] )
% 2.35/2.76 , clause( 20867, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 2.35/2.76 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ), ~(
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 2.35/2.76 , clause( 20868, [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( X ), 'tc_nat' ) ]
% 2.35/2.76 )
% 2.35/2.76 , clause( 20869, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 2.35/2.76 'c_HOL_Oinverse__class_Oinverse'( Y, X ), X ) ) ] )
% 2.35/2.76 , clause( 20870, [ =( 'c_List_Odrop'( X, 'c_List_Oreplicate'( Y, Z, T ), T
% 2.35/2.76 ), 'c_List_Oreplicate'( 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 2.35/2.76 Z, T ) ) ] )
% 2.35/2.76 , clause( 20871, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 2.35/2.76 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 2.35/2.76 , 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ),
% 2.35/2.76 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 2.35/2.76 X ), X ), X ) ] )
% 2.35/2.76 , clause( 20872, [ =( 'c_Lambda_Oliftn'( X, 'c_Lambda_OdB_OApp'( Y, Z ), T
% 2.35/2.76 ), 'c_Lambda_OdB_OApp'( 'c_Lambda_Oliftn'( X, Y, T ), 'c_Lambda_Oliftn'(
% 2.35/2.76 X, Z, T ) ) ) ] )
% 2.35/2.76 , clause( 20873, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.35/2.76 , 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_OrderedGroup_Olordered__ab__group__add__class_Opprt'( Y, X ), X ) ] )
% 2.35/2.76 , clause( 20874, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 20875, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20876, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 20877, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20878, [ =( 'c_nat_Onat__size'( 'c_Suc'( X ) ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_nat_Onat__size'( X ), 'c_Suc'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20879, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 2.35/2.76 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Y, Z,
% 2.35/2.76 X ), X ), Y ) ] )
% 2.35/2.76 , clause( 20880, [ ~( 'class_Divides_Oring__div'( X ) ), =(
% 2.35/2.76 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z,
% 2.35/2.76 X ), 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ouminus__class_Ouminus'(
% 2.35/2.76 'c_Divides_Odiv__class_Omod'( Y, Z, X ), X ), Z, X ) ) ] )
% 2.35/2.76 , clause( 20881, [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X, X,
% 2.35/2.76 'tc_nat' ), 'tc_nat' ) ] )
% 2.35/2.76 , clause( 20882, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.76 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 2.35/2.76 , clause( 20883, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.76 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y
% 2.35/2.76 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 2.35/2.76 X ), 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ] )
% 2.35/2.76 , clause( 20884, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.76 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ] )
% 2.35/2.76 , clause( 20885, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.76 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y
% 2.35/2.76 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T,
% 2.35/2.76 X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 2.35/2.76 , clause( 20886, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 2.35/2.76 , T, X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.76 Y, T, X ), Z, X ) ) ] )
% 2.35/2.76 , clause( 20887, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), Y ), ~(
% 2.35/2.76 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20888, [ =( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 2.35/2.76 ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20889, [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OVar'( X ), Y ),
% 2.35/2.76 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat'
% 2.35/2.76 ) ) ] )
% 2.35/2.76 , clause( 20890, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y,
% 2.35/2.76 'c_Power_Opower__class_Opower'( Y, Z, X ), X ),
% 2.35/2.76 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 20891, [ =( 'c_Orderings_Oord__class_Omin'( 'c_Suc'( X ), 'c_Suc'(
% 2.35/2.76 Y ), 'tc_nat' ), 'c_Suc'( 'c_Orderings_Oord__class_Omin'( X, Y, 'tc_nat'
% 2.35/2.76 ) ) ) ] )
% 2.35/2.76 , clause( 20892, [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), =(
% 2.35/2.76 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OVar'( X ), Y, X ), 'c_Lambda_Oliftn'(
% 2.35/2.76 X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 2.35/2.76 , clause( 20893, [ =( X, 'c_Suc'( Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ),
% 2.35/2.76 ~( 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20894, [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ] )
% 2.35/2.76 , clause( 20895, [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20896, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 2.35/2.76 , clause( 20897, [ =( 'c_Lambda_Olift'( 'c_Lambda_Olift'( X, Y ), 'c_Suc'(
% 2.35/2.76 Z ) ), 'c_Lambda_Olift'( 'c_Lambda_Olift'( X, Z ), Y ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 2.35/2.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20898, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.35/2.76 X ) ), =( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 2.35/2.76 'c_HOL_Ouminus__class_Ouminus'( Y, X ) ), ~( 'c_lessequals'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20899, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.76 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ),
% 2.35/2.76 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 2.35/2.76 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20900, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.76 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 2.35/2.76 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 2.35/2.76 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20901, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.76 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 2.35/2.76 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.76 'tc_nat' ), X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat'
% 2.35/2.76 ) ) ] )
% 2.35/2.76 , clause( 20902, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.76 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ),
% 2.35/2.76 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.76 'tc_nat' ), Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat'
% 2.35/2.76 ) ) ] )
% 2.35/2.76 , clause( 20903, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 2.35/2.76 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 2.35/2.76 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20904, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.76 X, Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 2.35/2.76 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 2.35/2.76 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20905, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.76 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.35/2.76 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20906, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.76 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20907, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.76 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.35/2.76 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.76 X ), T, X ) ) ] )
% 2.35/2.76 , clause( 20908, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.76 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 20909, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.76 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 2.35/2.76 , clause( 20910, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.35/2.76 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.35/2.76 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 2.35/2.76 , clause( 20911, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.76 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 20912, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.76 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20913, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.76 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ] )
% 2.35/2.76 , clause( 20914, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.35/2.76 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.35/2.76 , 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 2.35/2.76 , clause( 20915, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.76 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 2.35/2.76 , clause( 20916, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.76 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20917, [ ~(
% 2.35/2.76 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ] )
% 2.35/2.76 , clause( 20918, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 2.35/2.76 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 2.35/2.76 T, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.76 Y, T, X ), Z, X ) ) ] )
% 2.35/2.76 , clause( 20919, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 2.35/2.76 , X ), ~( 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 2.35/2.76 T, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.76 Y, T, X ), Z, X ) ) ] )
% 2.35/2.76 , clause( 20920, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 2.35/2.76 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 2.35/2.76 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ] )
% 2.35/2.76 , clause( 20921, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T, Z, X )
% 2.35/2.76 , X ) ) ] )
% 2.35/2.76 , clause( 20922, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 2.35/2.76 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 2.35/2.76 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 2.35/2.76 X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ] )
% 2.35/2.76 , clause( 20923, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 2.35/2.76 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z,
% 2.35/2.76 X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ] )
% 2.35/2.76 , clause( 20924, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 2.35/2.76 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 2.35/2.76 X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 2.35/2.76 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ] )
% 2.35/2.76 , clause( 20925, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y
% 2.35/2.76 , X ) ) ] )
% 2.35/2.76 , clause( 20926, [ ~(
% 2.35/2.76 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ), =(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T
% 2.35/2.76 , X ), 'c_Orderings_Oord__class_Omax'( 'c_HOL_Oplus__class_Oplus'( Y, T,
% 2.35/2.76 X ), 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ) ) ] )
% 2.35/2.76 , clause( 20927, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 2.35/2.76 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Osgn__class_Osgn'( Y, X ), X ),
% 2.35/2.76 'c_HOL_Osgn__class_Osgn'( Y, X ) ) ] )
% 2.35/2.76 , clause( 20928, [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OApp'( X,
% 2.35/2.76 'c_Lambda_OdB_OVar'( Y ) ) ), ~( 'c_InductTermi_OIT'( X ) ) ] )
% 2.35/2.76 , clause( 20929, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.76 ~( =( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 2.35/2.76 'c_Power_Opower__class_Opower'( T, 'c_Suc'( Z ), X ) ) ), =( Y, T ), ~(
% 2.35/2.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 2.35/2.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 20930, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 2.35/2.76 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ),
% 2.35/2.76 ~( 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat'
% 2.35/2.76 ) ) ] )
% 2.35/2.76 , clause( 20931, [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X,
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( X, X, 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ]
% 2.35/2.76 )
% 2.35/2.76 , clause( 20932, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 2.35/2.76 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ) ] )
% 2.35/2.76 , clause( 20933, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Otimes__class_Otimes'( Z
% 2.35/2.76 , T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 2.35/2.76 , clause( 20934, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' )
% 2.35/2.76 , 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 2.35/2.76 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 2.35/2.76 ] )
% 2.35/2.76 , clause( 20935, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 2.35/2.76 X, Y, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ),
% 2.35/2.76 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 2.35/2.76 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) )
% 2.35/2.76 ] )
% 2.35/2.76 , clause( 20936, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X )
% 2.35/2.76 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ] )
% 2.35/2.76 , clause( 20937, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, Z ),
% 2.35/2.76 'c_Lambda_OdB_OVar'( X ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat'
% 2.35/2.76 ) ) ] )
% 2.35/2.76 , clause( 20938, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.35/2.76 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T
% 2.35/2.76 , X ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), ~(
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( T, Z, X ) ) ] )
% 2.35/2.76 , clause( 20939, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 2.35/2.76 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 2.35/2.76 ) ] )
% 2.35/2.76 , clause( 20940, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oone__class_Oone'( X ), Y, X ), X
% 2.35/2.76 ) ) ] )
% 2.35/2.76 , clause( 20941, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.35/2.76 , 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20942, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.35/2.76 , 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.35/2.76 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20943, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 2.35/2.76 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =(
% 2.35/2.76 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ] )
% 2.35/2.76 , clause( 20944, [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =(
% 2.35/2.76 'c_HOL_Oabs__class_Oabs'( Y, X ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ] )
% 2.35/2.76 , clause( 20945, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 2.35/2.76 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 20946, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 2.35/2.76 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 2.35/2.76 X ), T, X ) ) ] )
% 2.35/2.76 , clause( 20947, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 2.35/2.76 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20948, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 2.35/2.76 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 2.35/2.76 X ), T, X ) ) ] )
% 2.35/2.76 , clause( 20949, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 X, Y, 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20950, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 X, Y, 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20951, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 2.35/2.76 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 2.35/2.76 ), T, X ), 'c_HOL_Oinverse__class_Odivide'(
% 2.35/2.76 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 2.35/2.76 Z, T, X ), X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.76 , clause( 20952, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), =( Y
% 2.35/2.76 , 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.35/2.76 , X ) ) ] )
% 2.35/2.76 , clause( 20953, [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =(
% 2.35/2.76 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ominus__class_Ominus'( Y, Z
% 2.35/2.76 , 'tc_nat' ), X ), 'c_HOL_Ominus__class_Ominus'(
% 2.35/2.76 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 2.35/2.76 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ), ~( 'c_lessequals'( Z
% 2.35/2.76 , Y, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20954, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 2.35/2.76 ), X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 2.35/2.76 , Y, X ) ) ] )
% 2.35/2.76 , clause( 20955, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.35/2.76 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Odivide'( Y, Z,
% 2.35/2.76 X ), X ), 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ) ) ] )
% 2.35/2.76 , clause( 20956, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 2.35/2.76 , X ), 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( Z, U, X ) ), ~(
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( Y, T, X ) ) ] )
% 2.35/2.76 , clause( 20957, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.35/2.76 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~( 'c_lessequals'( Z,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 2.35/2.76 )
% 2.35/2.76 , clause( 20958, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.35/2.76 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 2.35/2.76 )
% 2.35/2.76 , clause( 20959, [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ),
% 2.35/2.76 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 2.35/2.76 ] )
% 2.35/2.76 , clause( 20960, [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ),
% 2.35/2.76 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 2.35/2.76 ] )
% 2.35/2.76 , clause( 20961, [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ),
% 2.35/2.76 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 2.35/2.76 ] )
% 2.35/2.76 , clause( 20962, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 2.35/2.76 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Oplus__class_Oplus'( Y,
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 Y, 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ), =( T, U ), =( Z,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.76 , clause( 20963, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X,
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( X, 'c_HOL_Otimes__class_Otimes'( Y, T,
% 2.35/2.76 'tc_nat' ), 'tc_nat' ) ) ), =( Z, T ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.76 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20964, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.76 ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y
% 2.35/2.76 , X ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 2.35/2.76 ) ) ] )
% 2.35/2.76 , clause( 20965, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.76 ), ~( =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Y
% 2.35/2.76 , X ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ), X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 2.35/2.76 ) ) ] )
% 2.35/2.76 , clause( 20966, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.35/2.76 X ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 2.35/2.76 X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oabs__class_Oabs'( Y, X ),
% 2.35/2.76 'c_HOL_Oabs__class_Oabs'( Z, X ), X ) ) ] )
% 2.35/2.76 , clause( 20967, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 2.35/2.76 , Y, 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20968, [ 'c_HOL_Oord__class_Oless'( X,
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ),
% 2.35/2.76 Y, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20969, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 2.35/2.76 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 20970, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 2.35/2.76 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ] )
% 2.35/2.76 , clause( 20971, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~(
% 2.35/2.76 'c_lessequals'( Z, 'c_HOL_Oinverse__class_Odivide'( Y, T, X ), X ) ) ] )
% 2.35/2.76 , clause( 20972, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 2.35/2.76 'c_lessequals'( Z, 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ] )
% 2.35/2.76 , clause( 20973, [ ~( =( 'c_Suc'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20974, [ ~( =( X, 'c_Suc'( X ) ) ) ] )
% 2.35/2.76 , clause( 20975, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 2.35/2.76 =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X )
% 2.35/2.76 ) ), =( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Z ) ] )
% 2.35/2.76 , clause( 20976, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.35/2.76 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X ), X ) ) ]
% 2.35/2.76 )
% 2.35/2.76 , clause( 20977, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 2.35/2.76 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 2.35/2.76 X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.76 X ), T, X ) ) ] )
% 2.35/2.76 , clause( 20978, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 2.35/2.76 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 2.35/2.76 Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.76 X ), Z, X ) ) ] )
% 2.35/2.76 , clause( 20979, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X
% 2.35/2.76 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 2.35/2.76 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, T,
% 2.35/2.76 X ), Z, X ) ) ] )
% 2.35/2.76 , clause( 20980, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T
% 2.35/2.76 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 2.35/2.76 X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( T,
% 2.35/2.76 Z, X ), X ) ) ] )
% 2.35/2.76 , clause( 20981, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T, X
% 2.35/2.76 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 2.35/2.76 ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( T,
% 2.35/2.76 Z, X ), X ) ) ] )
% 2.35/2.76 , clause( 20982, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oinverse__class_Odivide'( Z, T, X )
% 2.35/2.76 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T,
% 2.35/2.76 X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 2.35/2.76 X ), Z, X ) ) ] )
% 2.35/2.76 , clause( 20983, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20984, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 20985, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 20986, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 20987, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_Power_Opower__class_Opower'(
% 2.35/2.76 Y, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.76 'tc_nat' ), Z, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20988, [ ~(
% 2.35/2.76 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 Y, T, X ) ) ] )
% 2.35/2.76 , clause( 20989, [ ~(
% 2.35/2.76 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( T, Z, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 Y, T, X ) ) ] )
% 2.35/2.76 , clause( 20990, [ ~(
% 2.35/2.76 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Y, T, X ), 'c_HOL_Oplus__class_Oplus'( Z, T,
% 2.35/2.76 X ), X ) ) ] )
% 2.35/2.76 , clause( 20991, [ ~(
% 2.35/2.76 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 Z, T, X ) ) ] )
% 2.35/2.76 , clause( 20992, [ ~(
% 2.35/2.76 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Y, T, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 Z, T, X ) ) ] )
% 2.35/2.76 , clause( 20993, [ ~(
% 2.35/2.76 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( T, Y, X ), 'c_HOL_Oplus__class_Oplus'( T, Z,
% 2.35/2.76 X ), X ) ) ] )
% 2.35/2.76 , clause( 20994, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 2.35/2.76 , Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' )
% 2.35/2.76 , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20995, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Z, X, 'tc_nat' ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20996, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( X
% 2.35/2.76 , Y, 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Z, 'tc_nat' ), 'tc_nat' )
% 2.35/2.76 , ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20997, [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.76 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' )
% 2.35/2.76 , ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y
% 2.35/2.76 , 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.76 'tc_nat' ) ), X, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 20998, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z
% 2.35/2.76 , X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 2.35/2.76 )
% 2.35/2.76 , clause( 20999, [ ~( 'class_Orderings_Oorder'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ] )
% 2.35/2.76 , clause( 21000, [ ~( 'class_Orderings_Oorder'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 2.35/2.76 , X ) ), ~( 'c_lessequals'( T, Z, X ) ) ] )
% 2.35/2.76 , clause( 21001, [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X
% 2.35/2.76 ) ), 'c_lessequals'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 21002, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 2.35/2.76 , Z, X ), T, X ), ~( 'c_lessequals'( Z, U, 'tc_nat' ) ), ~(
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_Power_Opower__class_Opower'( Y
% 2.35/2.76 , U, X ), T, X ) ) ] )
% 2.35/2.76 , clause( 21003, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y
% 2.35/2.76 , Z, X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 2.35/2.76 ] )
% 2.35/2.76 , clause( 21004, [ 'c_lessequals'( X, X, 'tc_nat' ) ] )
% 2.35/2.76 , clause( 21005, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z,
% 2.35/2.76 Y, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 21006, [ 'c_lessequals'( X, X, 'tc_nat' ) ] )
% 2.35/2.76 , clause( 21007, [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y
% 2.35/2.76 , X ) ] )
% 2.35/2.76 , clause( 21008, [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y
% 2.35/2.76 , Y, X ) ] )
% 2.35/2.76 , clause( 21009, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, Z
% 2.35/2.76 , X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 2.35/2.76 , clause( 21010, [ ~( 'class_Orderings_Opreorder'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( T, Z, X ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 2.35/2.76 , clause( 21011, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.35/2.76 , 'c_lessequals'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X ), X ), ~(
% 2.35/2.76 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y,
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Z, U, X ), X ) ) ] )
% 2.35/2.76 , clause( 21012, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OApp'( Y,
% 2.35/2.76 Z ) ) ) ] )
% 2.35/2.76 , clause( 21013, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 2.35/2.76 'c_HOL_Oone__class_Oone'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 21014, [ =( 'c_Orderings_Oord__class_Omin'(
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omin'( X, Z,
% 2.35/2.76 'tc_nat' ), Y, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 21015, [ =( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), 'c_Suc'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 2.35/2.76 , clause( 21016, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ] )
% 2.35/2.76 , clause( 21017, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ] )
% 2.35/2.76 , clause( 21018, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( Z, Y, X ), X ) ) ] )
% 2.35/2.76 , clause( 21019, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), X ) ) ] )
% 2.35/2.76 , clause( 21020, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.35/2.76 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 21021, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.35/2.76 'c_lessequals'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 21022, [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X )
% 2.35/2.76 ), =( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ] )
% 2.35/2.76 , clause( 21023, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.35/2.76 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 2.35/2.76 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.76 , clause( 21024, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.35/2.76 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 2.35/2.76 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.76 , clause( 21025, [ ~( =( 'c_Lambda_OdB_OVar'( X ), 'c_Lambda_OdB_OVar'( Y )
% 2.35/2.76 ) ), =( X, Y ) ] )
% 2.35/2.76 , clause( 21026, [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.35/2.76 X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.35/2.76 , 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 2.35/2.76 , clause( 21027, [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y )
% 2.35/2.76 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 21028, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 2.35/2.76 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.76 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 2.35/2.76 , Y, X ), X ), 'c_HOL_Oinverse__class_Oinverse'( Z, X ), X ) ), =( Z,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 2.35/2.76 ) ] )
% 2.35/2.76 , clause( 21029, [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OAbs'(
% 2.35/2.76 Z ) ) ) ] )
% 2.35/2.76 , clause( 21030, [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OVar'( Y )
% 2.35/2.76 ) ) ] )
% 2.35/2.76 , clause( 21031, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 2.35/2.76 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 2.35/2.76 ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 21032, [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ),
% 2.35/2.76 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 2.35/2.76 , ~( 'c_lessequals'( Y, T, X ) ) ] )
% 2.35/2.76 , clause( 21033, [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ),
% 2.35/2.76 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 2.35/2.76 , ~( 'c_lessequals'( Y, T, X ) ) ] )
% 2.35/2.76 , clause( 21034, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Y
% 2.35/2.76 , X ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.76 X ) ) ] )
% 2.35/2.76 , clause( 21035, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), Y
% 2.35/2.76 , X ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.76 X ) ) ] )
% 2.35/2.76 , clause( 21036, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oinverse__class_Oinverse'( Y, X )
% 2.35/2.76 , X ), 'c_HOL_Oone__class_Oone'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.76 X ) ) ] )
% 2.35/2.76 , clause( 21037, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 2.35/2.76 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.76 Y, Y, X ) ) ] )
% 2.35/2.76 , clause( 21038, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 2.35/2.76 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omax'( Y, Z, X )
% 2.35/2.76 , T, X ), 'c_Orderings_Oord__class_Omax'( Y,
% 2.35/2.76 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ) ) ] )
% 2.35/2.76 , clause( 21039, [ ~( 'class_Ring__and__Field_Oring'( X ) ), =(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 2.35/2.76 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.76 Y, Z, X ) ) ] )
% 2.35/2.76 , clause( 21040, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 2.35/2.76 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 2.35/2.76 X ), X ), 'c_Orderings_Oord__class_Omax'( Z,
% 2.35/2.76 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ) ) ] )
% 2.35/2.76 , clause( 21041, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 2.35/2.76 X ), 'c_HOL_Oplus__class_Oplus'( Y, Z, X ) ) ] )
% 2.35/2.76 , clause( 21042, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oone__class_Oone'( X ),
% 2.35/2.76 'c_HOL_Oone__class_Oone'( X ), X ), X ) ] )
% 2.35/2.76 , clause( 21043, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.35/2.76 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), T, X ),
% 2.35/2.76 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ] )
% 2.35/2.76 , clause( 21044, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.35/2.76 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ), Z, X ),
% 2.35/2.76 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ] )
% 2.35/2.76 , clause( 21045, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X )
% 2.35/2.76 , 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ),
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ominus__class_Ominus'(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, U, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.35/2.76 , Z, X ), X ), 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ), =( U,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 2.35/2.76 ) ] )
% 2.35/2.76 , clause( 21046, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.76 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 2.35/2.76 ) ) ] )
% 2.35/2.76 , clause( 21047, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( T, Y
% 2.35/2.76 , X ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ] )
% 2.35/2.76 , clause( 21048, [ ~( 'class_Ring__and__Field_Oidom'( X ) ),
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ), =( T,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 2.35/2.76 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Otimes__class_Otimes'( Y, T
% 2.35/2.76 , X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 2.35/2.76 , clause( 21049, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 2.35/2.76 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 2.35/2.76 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 2.35/2.76 , clause( 21050, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ] )
% 2.35/2.76 , clause( 21051, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ] )
% 2.35/2.76 , clause( 21052, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 2.35/2.76 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Oinverse__class_Odivide'(
% 2.35/2.76 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.76 X ) ) ] )
% 2.35/2.76 , clause( 21053, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.76 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), X ) ) ] )
% 2.35/2.76 , clause( 21054, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z,
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, T, X ), Z, X ) ) ] )
% 2.35/2.76 , clause( 21055, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ), ~( 'c_lessequals'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ] )
% 2.35/2.76 , clause( 21056, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( Z,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( Y,
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ) ) ] )
% 2.35/2.76 , clause( 21057, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( T, Z, X ), Y, X ) ), ~( 'c_lessequals'( Y,
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ) ) ] )
% 2.35/2.76 , clause( 21058, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), T, X ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ] )
% 2.35/2.76 , clause( 21059, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'( Z,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 21060, [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OAbs'( X ),
% 2.35/2.76 'c_Lambda_OdB_OAbs'( Y ) ), ~( 'c_Lambda_Obeta'( X, Y ) ) ] )
% 2.35/2.76 , clause( 21061, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 2.35/2.76 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omax'( Y, Z,
% 2.35/2.76 X ), X ), 'c_Orderings_Oord__class_Omax'( Y, Z, X ) ) ] )
% 2.35/2.76 , clause( 21062, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.76 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.35/2.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.35/2.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 2.35/2.76 , clause( 21063, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.76 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.35/2.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 2.35/2.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ] )
% 2.35/2.76 , clause( 21064, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.76 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.35/2.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 2.35/2.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ] )
% 2.35/2.76 , clause( 21065, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.76 ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.35/2.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.35/2.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ] )
% 2.35/2.76 , clause( 21066, [ =( 'c_Lambda_Osubstn'( 'c_Lambda_OdB_OApp'( X, Y ), Z, T
% 2.35/2.76 ), 'c_Lambda_OdB_OApp'( 'c_Lambda_Osubstn'( X, Z, T ),
% 2.35/2.76 'c_Lambda_Osubstn'( Y, Z, T ) ) ) ] )
% 2.35/2.76 , clause( 21067, [ =( 'c_HOL_Ominus__class_Ominus'(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Y, 'tc_nat' ), X ) ] )
% 2.35/2.76 , clause( 21068, [ =( 'c_HOL_Ominus__class_Ominus'(
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X, 'tc_nat' ), Y ) ] )
% 2.35/2.76 , clause( 21069, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.35/2.76 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), Z, X
% 2.35/2.76 ), Y ) ] )
% 2.35/2.76 , clause( 21070, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 2.35/2.76 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 2.35/2.76 X ), ~( 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 21071, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.76 'c_lessequals'( Y, Z, 'tc_nat' ), ~( 'c_lessequals'(
% 2.35/2.76 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 2.35/2.76 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 2.35/2.76 X ), T, X ) ) ] )
% 2.35/2.76 , clause( 21072, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.76 'c_lessequals'( Y, Z, 'tc_nat' ), ~( 'c_lessequals'(
% 2.35/2.76 'c_Power_Opower__class_Opower'( T, Y, X ), 'c_Power_Opower__class_Opower'(
% 2.35/2.76 T, Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 2.35/2.76 X ), T, X ) ) ] )
% 2.35/2.76 , clause( 21073, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.76 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 2.35/2.76 'c_Power_Opower__class_Opower'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T,
% 2.35/2.76 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 2.35/2.76 , Y, X ) ) ] )
% 2.35/2.76 , clause( 21074, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.35/2.76 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 2.35/2.76 ), X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 2.35/2.76 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ] )
% 2.35/2.76 , clause( 21075, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 2.35/2.76 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X
% 2.35/2.76 ), X ), 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ouminus__class_Ouminus'(
% 2.35/2.76 Y, X ), Z, X ) ) ] )
% 2.35/2.76 , clause( 21076, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 2.35/2.76 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 2.35/2.76 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Oinverse__class_Odivide'( Y, T
% 2.35/2.76 , X ), 'c_HOL_Oinverse__class_Odivide'( Z, T, X ), X ) ) ] )
% 2.35/2.76 , clause( 21077, [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 2.35/2.76 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 21078, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.35/2.76 X ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X
% 2.35/2.76 ), X ), 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Z, Y, X
% 2.35/2.76 ), X ) ) ] )
% 2.35/2.76 , clause( 21079, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.35/2.76 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 2.35/2.76 ), Y ) ] )
% 2.35/2.76 , clause( 21080, [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 2.35/2.76 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 2.35/2.76 ), Y ) ] )
% 2.35/2.76 , clause( 21081, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 2.35/2.76 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 2.35/2.76 ) ) ] )
% 2.35/2.76 , clause( 21082, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y,
% 2.35/2.76 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 2.35/2.76 ) ) ] )
% 2.35/2.76 , clause( 21083, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.35/2.76 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X
% 2.35/2.76 ), Y ) ] )
% 2.35/2.76 , clause( 21084, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 2.35/2.76 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 2.35/2.76 X ), 'c_HOL_Ominus__class_Ominus'( Z, Y, X ) ) ] )
% 2.35/2.76 , clause( 21085, [ ~(
% 2.35/2.76 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ] )
% 2.35/2.76 , clause( 21086, [ ~(
% 2.35/2.76 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( T, U, X ), X ), ~( 'c_lessequals'( Z, U, X )
% 2.35/2.76 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ] )
% 2.35/2.76 , clause( 21087, [ ~( =( 'c_Lambda_OdB_OApp'( X, Y ), 'c_Lambda_OdB_OVar'(
% 2.35/2.76 Z ) ) ) ] )
% 2.35/2.76 , clause( 21088, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 2.35/2.76 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 21089, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 21090, [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 2.35/2.76 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 21091, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.76 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 2.35/2.76 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 21092, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.76 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 2.35/2.76 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 21093, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.35/2.76 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 2.35/2.76 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ) ) ] )
% 2.35/2.76 , clause( 21094, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.35/2.76 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 21095, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.35/2.76 , 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 2.35/2.76 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 2.35/2.76 , clause( 21096, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.35/2.76 , 'c_lessequals'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ), ~(
% 2.35/2.76 'c_lessequals'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 2.35/2.76 , clause( 21097, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.35/2.76 , 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 2.35/2.76 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 21098, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.35/2.76 , 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X ), ~(
% 2.35/2.76 'c_lessequals'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ), Y, X ) ) ] )
% 2.35/2.76 , clause( 21099, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.35/2.76 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X
% 2.35/2.76 ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 2.35/2.76 ), X ) ) ] )
% 2.35/2.76 , clause( 21100, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.35/2.76 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X
% 2.35/2.76 ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ouminus__class_Ouminus'( Y, X
% 2.35/2.76 ), X ) ) ] )
% 2.35/2.76 , clause( 21101, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.35/2.76 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X
% 2.35/2.76 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X )
% 2.35/2.76 , Y, X ) ) ] )
% 2.35/2.76 , clause( 21102, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.35/2.76 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Z, X
% 2.35/2.76 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ouminus__class_Ouminus'( Z, X )
% 2.35/2.76 , Y, X ) ) ] )
% 2.35/2.76 , clause( 21103, [ =( 'c_Lambda_Olift'( 'c_Lambda_Osubst'( X, Y, Z ), T ),
% 2.35/2.76 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, T ), 'c_Lambda_Olift'( Y, T ),
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 2.35/2.76 'tc_nat' ) ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 2.35/2.76 'c_HOL_Oplus__class_Oplus'( Z, 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 2.35/2.76 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 21104, [ =( 'c_Lambda_Olift'( 'c_Lambda_Osubst'( X, Y, Z ), T ),
% 2.35/2.76 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, 'c_HOL_Oplus__class_Oplus'( T,
% 2.35/2.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ), 'c_Lambda_Olift'( Y,
% 2.35/2.76 T ), Z ) ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.76 T, 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.35/2.76 , clause( 21105, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oinverse__class_Odivide'( Y,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.76 , clause( 21106, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.35/2.76 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.76 , clause( 21107, [ ~( 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 2.35/2.76 =( 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ozero__class_Ozero'( X ), X )
% 2.35/2.76 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.76 , clause( 21108, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 2.35/2.76 =( 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 2.35/2.76 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ), =( Z,
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 2.35/2.76 ) ] )
% 2.35/2.76 , clause( 21109, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.35/2.76 X ) ), ~( =( 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.76 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.76 , clause( 21110, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.35/2.76 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.76 , clause( 21111, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) )
% 2.35/2.76 , =( 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Ozero__class_Ozero'( X ), X )
% 2.35/2.76 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.76 , clause( 21112, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 2.35/2.76 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.35/2.76 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.76 , clause( 21113, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 2.35/2.76 =( 'c_HOL_Oinverse__class_Oinverse'( Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.76 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.76 , clause( 21114, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 2.35/2.76 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 2.35/2.76 ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 2.35/2.76 ) ) ] )
% 2.35/2.76 , clause( 21115, [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 2.35/2.76 X ) ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 2.35/2.76 ) ) ] )
% 2.35/2.76 , clause( 21116, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'(
% 2.35/2.76 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.77 , clause( 21117, [ ~( 'class_Ring__and__Field_Osgn__if'( X ) ), =(
% 2.35/2.77 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.77 , clause( 21118, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 2.35/2.77 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.77 , clause( 21119, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.77 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 2.35/2.77 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.77 , clause( 21120, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 2.35/2.77 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.77 , clause( 21121, [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 2.35/2.77 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.77 , clause( 21122, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 2.35/2.77 ) ), =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 2.35/2.77 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.77 , clause( 21123, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 2.35/2.77 ) ), =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 2.35/2.77 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.77 , clause( 21124, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.77 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 2.35/2.77 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.77 , clause( 21125, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.77 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 2.35/2.77 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.77 , clause( 21126, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 2.35/2.77 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 2.35/2.77 ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.77 , clause( 21127, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.77 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 2.35/2.77 , X ) ] )
% 2.35/2.77 , clause( 21128, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 2.35/2.77 =( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ]
% 2.35/2.77 )
% 2.35/2.77 , clause( 21129, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 2.35/2.77 ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.77 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.77 , clause( 21130, [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ),
% 2.35/2.77 ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.77 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.77 , clause( 21131, [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X
% 2.35/2.77 ) ), ~( =( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 2.35/2.77 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.77 , clause( 21132, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 2.35/2.77 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 2.35/2.77 ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21133, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 2.35/2.77 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 2.35/2.77 ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21134, [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 2.35/2.77 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 2.35/2.77 ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21135, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 2.35/2.77 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 2.35/2.77 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21136, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.77 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ),
% 2.35/2.77 ~( 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21137, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 2.35/2.77 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21138, [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 2.35/2.77 ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21139, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 2.35/2.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~( =(
% 2.35/2.77 'c_HOL_Oinverse__class_Oinverse'( Y, X ),
% 2.35/2.77 'c_HOL_Oinverse__class_Oinverse'( Z, X ) ) ), =( Y, Z ) ] )
% 2.35/2.77 , clause( 21140, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.77 ), =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.35/2.77 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( X ), X ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 2.35/2.77 ) ) ] )
% 2.35/2.77 , clause( 21141, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.77 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.35/2.77 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.77 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.35/2.77 , Y, X ), X ) ) ] )
% 2.35/2.77 , clause( 21142, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.77 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.77 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 2.35/2.77 , T, X ), X ) ) ] )
% 2.35/2.77 , clause( 21143, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.77 ), 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 2.35/2.77 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.77 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 2.35/2.77 , T, X ), X ) ) ] )
% 2.35/2.77 , clause( 21144, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.77 ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.77 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.35/2.77 , Y, X ), X ) ) ] )
% 2.35/2.77 , clause( 21145, [ ~( =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y,
% 2.35/2.77 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ) ) )
% 2.35/2.77 , =( Y, Z ) ] )
% 2.35/2.77 , clause( 21146, [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 2.35/2.77 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 2.35/2.77 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21147, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 2.35/2.77 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Oplus__class_Oplus'( Y, Z,
% 2.35/2.77 'tc_nat' ), X ), 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.77 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 2.35/2.77 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ] )
% 2.35/2.77 , clause( 21148, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 2.35/2.77 X, Y, 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 2.35/2.77 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 2.35/2.77 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21149, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 2.35/2.77 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 2.35/2.77 X ), X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 2.35/2.77 Y, Z, X ), 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ), X ) ] )
% 2.35/2.77 , clause( 21150, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.35/2.77 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 2.35/2.77 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_lessequals'( U, T, X ),
% 2.35/2.77 ~( 'c_lessequals'( Z, Y, X ) ) ] )
% 2.35/2.77 , clause( 21151, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.35/2.77 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 2.35/2.77 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_lessequals'( Z, Y, X ),
% 2.35/2.77 ~( 'c_lessequals'( U, T, X ) ) ] )
% 2.35/2.77 , clause( 21152, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.35/2.77 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 2.35/2.77 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_HOL_Oord__class_Oless'( T
% 2.35/2.77 , U, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ] )
% 2.35/2.77 , clause( 21153, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.35/2.77 , ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 2.35/2.77 'c_HOL_Ominus__class_Ominus'( T, U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y
% 2.35/2.77 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, U, X ) ) ] )
% 2.35/2.77 , clause( 21154, [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 2.35/2.77 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.35/2.77 T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y,
% 2.35/2.77 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ] )
% 2.35/2.77 , clause( 21155, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.77 =( 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X
% 2.35/2.77 ), T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'(
% 2.35/2.77 Y, T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ] )
% 2.35/2.77 , clause( 21156, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.35/2.77 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.77 'c_Divides_Odiv__class_Omod'( Y, Z, X ), T, X ), Z, X ),
% 2.35/2.77 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, T, X ), Z, X
% 2.35/2.77 ) ) ] )
% 2.35/2.77 , clause( 21157, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.35/2.77 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y,
% 2.35/2.77 'c_Divides_Odiv__class_Omod'( Z, T, X ), X ), T, X ),
% 2.35/2.77 'c_Divides_Odiv__class_Omod'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 2.35/2.77 ) ) ] )
% 2.35/2.77 , clause( 21158, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.35/2.77 , 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.77 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.77 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.77 , clause( 21159, [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) )
% 2.35/2.77 , 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.35/2.77 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.77 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 2.35/2.77 , clause( 21160, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 2.35/2.77 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ), Y ),
% 2.35/2.77 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ] )
% 2.35/2.77 , clause( 21161, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'(
% 2.35/2.77 X, 'c_Suc'( Y ), 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21162, [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 2.35/2.77 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 2.35/2.77 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'( Z,
% 2.35/2.77 T, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 2.35/2.77 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ominus__class_Ominus'( Z,
% 2.35/2.77 'c_HOL_Otimes__class_Otimes'( U, W, X ), X ), T, X ), X ) ), ~(
% 2.35/2.77 'c_Ring__and__Field_Odvd__class_Odvd'( Y, W, X ) ) ] )
% 2.35/2.77 , clause( 21163, [ ~( 'class_Ring__and__Field_Odvd'( X ) ), ~(
% 2.35/2.77 'class_Ring__and__Field_Ocomm__ring'( X ) ),
% 2.35/2.77 'c_Ring__and__Field_Odvd__class_Odvd'( Y, 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.77 'c_HOL_Ominus__class_Ominus'( Z, 'c_HOL_Otimes__class_Otimes'( T, U, X )
% 2.35/2.77 , X ), W, X ), X ), ~( 'c_Ring__and__Field_Odvd__class_Odvd'( Y,
% 2.35/2.77 'c_HOL_Oplus__class_Oplus'( Z, W, X ), X ) ), ~(
% 2.35/2.77 'c_Ring__and__Field_Odvd__class_Odvd'( Y, U, X ) ) ] )
% 2.35/2.77 , clause( 21164, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 2.35/2.77 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 2.35/2.77 , U, X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( U,
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_HOL_Oinverse__class_Odivide'( Y
% 2.35/2.77 , U, X ), 'c_HOL_Oinverse__class_Odivide'( T, Z, X ) ) ] )
% 2.35/2.77 , clause( 21165, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 2.35/2.77 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 2.35/2.77 'c_HOL_Oinverse__class_Odivide'( T, U, X ) ) ), =( U,
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 2.35/2.77 ), =( 'c_HOL_Otimes__class_Otimes'( Y, U, X ),
% 2.35/2.77 'c_HOL_Otimes__class_Otimes'( T, Z, X ) ) ] )
% 2.35/2.77 , clause( 21166, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 2.35/2.77 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ] )
% 2.35/2.77 , clause( 21167, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 2.35/2.77 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21168, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 2.35/2.77 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 2.35/2.77 , T, X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 2.35/2.77 Y, T, X ), 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ) ) ] )
% 2.35/2.77 , clause( 21169, [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 2.35/2.77 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 2.35/2.77 X ), X ), 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omax'(
% 2.35/2.77 Y, Z, X ), 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ) ) ] )
% 2.35/2.77 , clause( 21170, [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 2.35/2.77 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T,
% 2.35/2.77 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'(
% 2.35/2.77 'c_Power_Opower__class_Opower'( Y, Z, X ), T, X ) ) ] )
% 2.35/2.77 , clause( 21171, [ ~( 'class_Orderings_Oorder'( X ) ),
% 2.35/2.77 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Z, Y ), ~( 'c_lessequals'( Y, Z
% 2.35/2.77 , X ) ) ] )
% 2.35/2.77 , clause( 21172, [ ~( 'class_Orderings_Oorder'( X ) ),
% 2.35/2.77 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ), =(
% 2.35/2.77 Z, Y ) ] )
% 2.35/2.77 , clause( 21173, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ),
% 2.35/2.77 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21174, [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ),
% 2.35/2.77 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21175, [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ),
% 2.35/2.77 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21176, [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 2.35/2.77 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 2.35/2.77 , clause( 21177, [ ~( 'class_Orderings_Oorder'( X ) ),
% 2.35/2.77 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 2.35/2.77 , X ) ) ] )
% 2.35/2.77 , clause( 21178, [ ~( 'class_Orderings_Oorder'( X ) ),
% 2.35/2.77 'c_HOL_Oord__class_Oless'( Y, Z, X ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 2.35/2.77 , X ) ) ] )
% 2.35/2.77 , clause( 21179, [ ~( 'class_Orderings_Oorder'( X ) ),
% 2.35/2.77 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ), =(
% 2.35/2.77 Y, Z ) ] )
% 2.35/2.77 , clause( 21180, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~(
% 2.35/2.77 'c_lessequals'( Y, Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ] )
% 2.35/2.77 , clause( 21181, [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 2.35/2.77 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ] )
% 2.35/2.77 , clause( 21182, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 2.35/2.77 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 2.35/2.77 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'( Z,
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 2.35/2.77 )
% 2.35/2.77 , clause( 21183, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 2.35/2.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 2.35/2.77 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 2.35/2.77 'c_HOL_Oinverse__class_Odivide'( T, Z, X ), X ), ~( 'c_lessequals'(
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 2.35/2.77 ] )
% 2.35/2.77 , clause( 21184, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 2.35/2.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.35/2.77 'c_HOL_Oinverse__class_Oinverse'( 'c_Power_Opower__class_Opower'( Y, Z, X
% 2.35/2.77 ), X ), 'c_Power_Opower__class_Opower'( 'c_HOL_Oinverse__class_Oinverse'(
% 2.35/2.77 Y, X ), Z, X ) ) ] )
% 2.35/2.77 , clause( 21185, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), ~(
% 2.35/2.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.35/2.77 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Ouminus__class_Ouminus'( Y, X )
% 2.35/2.77 , X ), 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oinverse__class_Oinverse'(
% 2.35/2.77 Y, X ), X ) ) ] )
% 2.35/2.77 , clause( 21186, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 2.35/2.77 'c_HOL_Osgn__class_Osgn'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ),
% 2.35/2.77 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Osgn__class_Osgn'( Y, X ),
% 2.35/2.77 'c_HOL_Osgn__class_Osgn'( Z, X ), X ) ) ] )
% 2.35/2.77 , clause( 21187, [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 2.35/2.77 X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.77 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.77 , clause( 21188, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.77 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.77 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.77 , clause( 21189, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.77 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.77 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.77 , clause( 21190, [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X )
% 2.35/2.77 ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.77 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ) ] )
% 2.35/2.77 , clause( 21191, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.35/2.77 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.77 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.77 , clause( 21192, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.35/2.77 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.77 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.77 , clause( 21193, [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 2.35/2.77 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.77 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.77 , clause( 21194, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.35/2.77 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.35/2.77 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 2.35/2.77 'c_HOL_Otimes__class_Otimes'( 'c_Divides_Odiv__class_Omod'( Y, T, X ), Z
% 2.35/2.77 , X ) ) ] )
% 2.35/2.77 , clause( 21195, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.35/2.77 'c_Divides_Odiv__class_Omod'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 2.35/2.77 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 2.35/2.77 'c_HOL_Otimes__class_Otimes'( Y, 'c_Divides_Odiv__class_Omod'( Z, T, X )
% 2.35/2.77 , X ) ) ] )
% 2.35/2.77 , clause( 21196, [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OAbs'( X ), Y ),
% 2.35/2.77 'c_Lambda_OdB_OAbs'( 'c_Lambda_Olift'( X, 'c_HOL_Oplus__class_Oplus'( Y,
% 2.35/2.77 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ) ) ] )
% 2.35/2.77 , clause( 21197, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.35/2.77 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 2.35/2.77 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 2.35/2.77 ) ] )
% 2.35/2.77 , clause( 21198, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 2.35/2.77 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X )
% 2.35/2.77 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 2.35/2.77 ] )
% 2.35/2.77 , clause( 21199, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =(
% 2.35/2.77 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ), 'c_HOL_Oone__class_Oone'( X )
% 2.35/2.77 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ] )
% 2.35/2.77 , clause( 21200, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.35/2.77 X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.77 'c_HOL_Oabs__class_Oabs'( Y, X ), X ) ] )
% 2.35/2.77 , clause( 21201, [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 2.35/2.77 'c_HOL_Ouminus__class_Ouminus'( Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.77 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oone__class_Oone'( X ), X ), Y, X
% 2.35/2.77 ) ) ] )
% 2.35/2.77 , clause( 21202, [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 2.35/2.77 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21203, [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ),
% 2.35/2.77 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21204, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.35/2.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.35/2.77 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y, X ),
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.77 , clause( 21205, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 2.35/2.77 =( 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 2.35/2.77 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ] )
% 2.35/2.77 , clause( 21206, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 2.35/2.77 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ), ~(
% 2.35/2.77 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.77 , clause( 21207, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.35/2.77 X ) ), 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'(
% 2.35/2.77 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ), X ),
% 2.35/2.77 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), X ), X
% 2.35/2.77 ) ] )
% 2.35/2.77 , clause( 21208, [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 2.35/2.77 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( X,
% 2.35/2.77 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21209, [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 2.35/2.77 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ), =( Y,
% 2.35/2.77 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21210, [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 2.35/2.77 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 2.35/2.77 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 2.35/2.77 T, X ), X ) ) ] )
% 2.35/2.77 , clause( 21211, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.77 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.35/2.77 , T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y,
% 2.35/2.77 T, X ), Z, X ) ) ] )
% 2.35/2.77 , clause( 21212, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.77 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 2.35/2.77 , T, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.77 Z, T, X ), X ) ) ] )
% 2.35/2.77 , clause( 21213, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.77 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 2.35/2.77 ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 2.35/2.77 , X ), T, X ) ) ] )
% 2.35/2.77 , clause( 21214, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.77 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 2.35/2.77 ), X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y
% 2.35/2.77 , T, X ), X ) ) ] )
% 2.35/2.77 , clause( 21215, [ =( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.77 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 2.35/2.77 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 2.35/2.77 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21216, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.77 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X
% 2.35/2.77 ), X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 2.35/2.77 , X ), T, X ) ) ] )
% 2.35/2.77 , clause( 21217, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.77 =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T
% 2.35/2.77 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X
% 2.35/2.77 ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 2.35/2.77 , clause( 21218, [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 2.35/2.77 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), T, X
% 2.35/2.77 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 2.35/2.77 'c_HOL_Otimes__class_Otimes'( Z, T, X ), X ) ) ] )
% 2.35/2.77 , clause( 21219, [ =( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.77 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), Z, 'tc_nat' ),
% 2.35/2.77 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat'
% 2.35/2.77 ), 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21220, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 2.35/2.77 'c_HOL_Oplus__class_Oplus'( Y, Z, 'tc_nat' ), 'tc_nat' ),
% 2.35/2.77 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat'
% 2.35/2.77 ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21221, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.77 =( 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Oplus__class_Oplus'( Z, T, X )
% 2.35/2.77 , X ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X
% 2.35/2.77 ), 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ] )
% 2.35/2.77 , clause( 21222, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 2.35/2.77 =( 'c_HOL_Oabs__class_Oabs'( Y, X ), 'c_HOL_Oabs__class_Oabs'( Z, X ) ) )
% 2.35/2.77 , 'c_Ring__and__Field_Odvd__class_Odvd'( Y, Z, X ) ] )
% 2.35/2.77 , clause( 21223, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 2.35/2.77 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X
% 2.35/2.77 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Y, X ),
% 2.35/2.77 'c_HOL_Ouminus__class_Ouminus'( Z, X ), X ) ) ] )
% 2.35/2.77 , clause( 21224, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.35/2.77 'c_HOL_Ouminus__class_Ouminus'( 'c_HOL_Oplus__class_Oplus'( Y, Z, X ), X
% 2.35/2.77 ), 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ouminus__class_Ouminus'( Z, X ),
% 2.35/2.77 'c_HOL_Ouminus__class_Ouminus'( Y, X ), X ) ) ] )
% 2.35/2.77 , clause( 21225, [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 2.35/2.77 'c_HOL_Oord__class_Oless'( 'c_HOL_Oinverse__class_Odivide'( Y, Z, X ),
% 2.35/2.77 'c_HOL_Oinverse__class_Odivide'( T, U, X ), X ), ~( 'c_lessequals'( U, Z
% 2.35/2.77 , X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U
% 2.35/2.77 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'(
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ] )
% 2.35/2.77 , clause( 21226, [ ~( 'class_Orderings_Oorder'( X ) ), ~(
% 2.35/2.77 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 2.35/2.77 Y, X ) ) ] )
% 2.35/2.77 , clause( 21227, [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 2.35/2.77 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 2.35/2.77 Y, X ) ) ] )
% 2.35/2.77 , clause( 21228, [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X,
% 2.35/2.77 'tc_nat' ) ] )
% 2.35/2.77 , clause( 21229, [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y
% 2.35/2.77 , Z, X ), 'c_lessequals'( Z, Y, X ) ] )
% 2.35/2.77 , clause( 21230, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 2.35/2.77 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 2.35/2.77 Y, X ) ) ] )
% 2.35/2.77 , clause( 21231, [ ~( 'class_Orderings_Opreorder'( X ) ), ~(
% 2.35/2.77 'c_HOL_Oord__class_Oless'( Y, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 2.35/2.77 Y, X ) ) ] )
% 2.35/2.77 , clause( 21232, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.35/2.77 , ~( =( 'c_HOL_Oplus__class_Oplus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.77 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.77 , clause( 21233, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 2.35/2.77 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y,
% 2.35/2.77 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.77 , clause( 21234, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.35/2.77 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.35/2.77 ) ] )
% 2.35/2.77 , clause( 21235, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.35/2.77 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 2.35/2.77 ) ] )
% 2.35/2.77 , clause( 21236, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 2.35/2.77 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.35/2.77 ) ] )
% 2.35/2.77 , clause( 21237, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 2.35/2.77 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.35/2.77 ) ] )
% 2.35/2.77 , clause( 21238, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 2.35/2.77 'class_Int_Onumber__ring'( X ) ), ~( =( Y, 'c_HOL_Oplus__class_Oplus'( Y
% 2.35/2.77 , Z, X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.77 , clause( 21239, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.35/2.77 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.35/2.77 ) ] )
% 2.35/2.77 , clause( 21240, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.35/2.77 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 2.35/2.77 ) ] )
% 2.35/2.77 , clause( 21241, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.35/2.77 , =( 'c_OrderedGroup_Olordered__ab__group__add__class_Opprt'(
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 2.35/2.77 )
% 2.35/2.77 , clause( 21242, [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 2.35/2.77 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.77 , clause( 21243, [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) )
% 2.35/2.77 , =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 2.35/2.77 )
% 2.35/2.77 , clause( 21244, [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'(
% 2.35/2.77 X ) ), =( 'c_HOL_Oabs__class_Oabs'( 'c_HOL_Ozero__class_Ozero'( X ), X )
% 2.35/2.77 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.77 , clause( 21245, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ouminus__class_Ouminus'( Y, X ) )
% 2.35/2.77 ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ] )
% 2.35/2.77 , clause( 21246, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 2.35/2.77 =( 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ]
% 2.35/2.77 )
% 2.35/2.77 , clause( 21247, [ ~( 'class_Ring__and__Field_Odivision__ring'( X ) ), =(
% 2.35/2.77 'c_HOL_Oinverse__class_Oinverse'( 'c_HOL_Oinverse__class_Oinverse'( Y, X
% 2.35/2.77 ), X ), Y ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.77 , clause( 21248, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.77 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 2.35/2.77 'c_Ring__and__Field_Odvd__class_Odvd'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 2.35/2.77 , X ) ) ] )
% 2.35/2.77 , clause( 21249, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 2.35/2.77 'class_Int_Onumber__ring'( X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y,
% 2.35/2.77 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ] )
% 2.35/2.77 , clause( 21250, [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 2.35/2.77 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.35/2.77 ) ), =( Y, Z ) ] )
% 2.35/2.77 , clause( 21251, [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 2.35/2.77 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.35/2.77 ) ), =( Y, Z ) ] )
% 2.35/2.77 , clause( 21252, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.35/2.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.35/2.77 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 2.35/2.77 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.77 , clause( 21253, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.35/2.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.35/2.77 'c_HOL_Oinverse__class_Odivide'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 2.35/2.77 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.77 , clause( 21254, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =(
% 2.35/2.77 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 2.35/2.77 , 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.77 , clause( 21255, [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 2.35/2.77 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 2.35/2.77 'c_HOL_Oinverse__class_Odivide'( 'c_HOL_Ozero__class_Ozero'( X ),
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 2.35/2.77 )
% 2.35/2.77 , clause( 21256, [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 2.35/2.77 =( 'c_HOL_Osgn__class_Osgn'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 2.35/2.77 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.77 , clause( 21257, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.77 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 2.35/2.77 ) ] )
% 2.35/2.77 , clause( 21258, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 2.35/2.77 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 2.35/2.77 ] )
% 2.35/2.77 , clause( 21259, [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~(
% 2.35/2.77 'class_Int_Onumber__ring'( X ) ), =( Y, 'c_HOL_Oplus__class_Oplus'( Y,
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ] )
% 2.35/2.77 , clause( 21260, [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 2.35/2.77 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 2.35/2.77 ] )
% 2.35/2.77 , clause( 21261, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 2.35/2.77 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y )
% 2.35/2.77 ] )
% 2.35/2.77 , clause( 21262, [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =(
% 2.35/2.77 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 2.35/2.77 ] )
% 2.35/2.77 , clause( 21263, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.77 =( 'c_HOL_Oplus__class_Oplus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 2.35/2.77 ) ] )
% 2.35/2.77 , clause( 21264, [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 2.35/2.77 =( 'c_HOL_Oplus__class_Oplus'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), Y
% 2.35/2.77 ) ] )
% 2.35/2.77 , clause( 21265, [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) )
% 2.35/2.77 , ~( =( 'c_HOL_Ouminus__class_Ouminus'( Y, X ), Y ) ), =( Y,
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.77 , clause( 21266, [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 2.35/2.77 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 2.35/2.77 X ), 'c_HOL_Oone__class_Oone'( X ) ) ] )
% 2.35/2.77 , clause( 21267, [ =( 'c_Nat_Osize__class_Osize'(
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21268, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ] )
% 2.35/2.77 , clause( 21269, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 2.35/2.77 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 2.35/2.77 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21270, [ =( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 2.35/2.77 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 2.35/2.77 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21271, [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.77 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21272, [ =( 'c_Lambda_Oliftn'( 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.77 'tc_nat' ), X, Y ), X ) ] )
% 2.35/2.77 , clause( 21273, [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.77 'tc_nat' ), X, 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 2.35/2.77 ] )
% 2.35/2.77 , clause( 21274, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 2.35/2.77 ) ) ) ] )
% 2.35/2.77 , clause( 21275, [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 2.35/2.77 ) ) ) ] )
% 2.35/2.77 , clause( 21276, [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 2.35/2.77 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ] )
% 2.35/2.77 , clause( 21277, [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 2.35/2.77 'c_lessequals'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ]
% 2.35/2.77 )
% 2.35/2.77 , clause( 21278, [ =( 'c_HOL_Otimes__class_Otimes'( X,
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21279, [ =( 'c_HOL_Otimes__class_Otimes'(
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21280, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21281, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21282, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ),
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21283, [ =( 'c_Orderings_Oord__class_Omin'( X,
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21284, [ =( 'c_Orderings_Oord__class_Omin'(
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21285, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 2.35/2.77 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ), =( Y,
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ] )
% 2.35/2.77 , clause( 21286, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 2.35/2.77 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( X,
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ] )
% 2.35/2.77 , clause( 21287, [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 2.35/2.77 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( Y, Z ), =( X,
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21288, [ =( 'c_HOL_Ominus__class_Ominus'( X,
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 2.35/2.77 , clause( 21289, [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21290, [ ~( =( X, 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ) )
% 2.35/2.77 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21291, [ ~( =( 'c_HOL_Oplus__class_Oplus'( X, Y, 'tc_nat' ), X )
% 2.35/2.77 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21292, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X
% 2.35/2.77 ) ) ) ] )
% 2.35/2.77 , clause( 21293, [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X
% 2.35/2.77 ) ) ) ] )
% 2.35/2.77 , clause( 21294, [ =( 'c_Nitpick_Onat__gcd'( X, 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.77 'tc_nat' ) ), X ) ] )
% 2.35/2.77 , clause( 21295, [ =( 'c_nat_Onat__size'( 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.77 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21296, [ =( 'c_String_Ochar_Ochar__size'( X ),
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21297, [ =( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.77 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21298, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21299, [ ~( 'c_HOL_Oord__class_Oless'( X,
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21300, [ =( 'c_Orderings_Obot__class_Obot'( 'tc_nat' ),
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21301, [ =( 'c_List_Odrop'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 2.35/2.77 ), X, Y ), X ) ] )
% 2.35/2.77 , clause( 21302, [ =( 'c_HOL_Ominus__class_Ominus'(
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21303, [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 2.35/2.77 X, 'tc_nat' ) ] )
% 2.35/2.77 , clause( 21304, [ =( 'c_Nat_Osize__class_Osize'( X, 'tc_String_Ochar' ),
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21305, [ =( 'c_List_Oreplicate'( 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.77 'tc_nat' ), X, Y ), 'c_List_Oreplicate'( 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.77 'tc_nat' ), Z, Y ) ) ] )
% 2.35/2.77 , clause( 21306, [ =( 'c_Orderings_Oord__class_Omax'( X,
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 2.35/2.77 , clause( 21307, [ =( 'c_Orderings_Oord__class_Omax'(
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ), X ) ] )
% 2.35/2.77 , clause( 21308, [ ~( =( 'c_List_Oreplicate'( X, Y, Z ),
% 2.35/2.77 'c_List_Oreplicate'( T, U, Z ) ) ), =( Y, U ), =( X,
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21309, [ =( X, 'c_HOL_Oplus__class_Oplus'( X,
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21310, [ =( 'c_HOL_Oplus__class_Oplus'(
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ), X ) ] )
% 2.35/2.77 , clause( 21311, [ =( 'c_HOL_Oplus__class_Oplus'( X,
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ] )
% 2.35/2.77 , clause( 21312, [ =( 'c_Lambda_Osubstn'( X, Y, Z ), 'c_Lambda_Osubst'( X,
% 2.35/2.77 'c_Lambda_Oliftn'( Z, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ) )
% 2.35/2.77 ] )
% 2.35/2.77 , clause( 21313, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OAbs'( X ), Y, Z ),
% 2.35/2.77 'c_Lambda_OdB_OAbs'( 'c_Lambda_Osubst'( X, 'c_Lambda_Olift'( Y,
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oplus__class_Oplus'( Z,
% 2.35/2.77 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat' ) ) ) ) ] )
% 2.35/2.77 , clause( 21314, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OApp'( X, Y ), Z, T
% 2.35/2.77 ), 'c_Lambda_OdB_OApp'( 'c_Lambda_Osubst'( X, Z, T ), 'c_Lambda_Osubst'(
% 2.35/2.77 Y, Z, T ) ) ) ] )
% 2.35/2.77 , clause( 21315, [ =( 'c_Lambda_Osubst'( 'c_Lambda_OdB_OVar'( X ), Y, X ),
% 2.35/2.77 Y ) ] )
% 2.35/2.77 , clause( 21316, [ 'c_Lambda_Obeta'( 'c_Lambda_Osubst'( X, Y, Z ),
% 2.35/2.77 'c_Lambda_Osubst'( T, Y, Z ) ), ~( 'c_Lambda_Obeta'( X, T ) ) ] )
% 2.35/2.77 , clause( 21317, [ =( 'c_Lambda_Olift'( 'c_Lambda_OdB_OApp'( X, Y ), Z ),
% 2.35/2.77 'c_Lambda_OdB_OApp'( 'c_Lambda_Olift'( X, Z ), 'c_Lambda_Olift'( Y, Z ) )
% 2.35/2.77 ) ] )
% 2.35/2.77 , clause( 21318, [ 'c_Lambda_Obeta'( 'c_Lambda_Olift'( X, Y ),
% 2.35/2.77 'c_Lambda_Olift'( Z, Y ) ), ~( 'c_Lambda_Obeta'( X, Z ) ) ] )
% 2.35/2.77 , clause( 21319, [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OVar'( X ) ) ] )
% 2.35/2.77 , clause( 21320, [ 'c_InductTermi_OIT'( 'v_ua______' ) ] )
% 2.35/2.77 , clause( 21321, [ 'c_InductTermi_OIT'( 'c_Lambda_OdB_OAbs'( X ) ), ~(
% 2.35/2.77 'c_InductTermi_OIT'( X ) ) ] )
% 2.35/2.77 , clause( 21322, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 2.35/2.77 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 2.35/2.77 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 2.35/2.77 ), =( 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 2.35/2.77 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21323, [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 2.35/2.77 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 2.35/2.77 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ] )
% 2.35/2.77 , clause( 21324, [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 2.35/2.77 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 2.35/2.77 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 2.35/2.77 ), ~( =( 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.77 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ] )
% 2.35/2.77 , clause( 21325, [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 2.35/2.77 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.77 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ] )
% 2.35/2.77 , clause( 21326, [ =( 'c_Lambda_Osubstn'( X, Y, 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.77 'tc_nat' ) ), 'c_Lambda_Osubst'( X, Y, 'c_HOL_Ozero__class_Ozero'(
% 2.35/2.77 'tc_nat' ) ) ) ] )
% 2.35/2.77 , clause( 21327, [ 'c_InductTermi_OIT'( 'c_Lambda_Osubst'( X,
% 2.35/2.77 'c_Lambda_OdB_OVar'( Y ), Z ) ), ~( 'c_InductTermi_OIT'( X ) ) ] )
% 2.35/2.77 , clause( 21328, [ =( 'v_n____', 'v_i____' ) ] )
% 2.35/2.77 , clause( 21329, [ 'c_InductTermi_OIT'( 'c_Lambda_Olift'( X, Y ) ), ~(
% 2.35/2.77 'c_InductTermi_OIT'( X ) ) ] )
% 2.35/2.77 , clause( 21330, [ 'c_InductTermi_OIT'( 'v_u____' ) ] )
% 2.35/2.77 , clause( 21331, [ =( 'c_Lambda_Osubst'( 'c_Lambda_Olift'( X, Y ), Z, Y ),
% 2.35/2.77 X ) ] )
% 2.35/2.77 , clause( 21332, [ 'c_InductTermi_OIT'( 'c_Lambda_Osubst'( 'v_b____',
% 2.35/2.77 'v_u____', 'v_i____' ) ) ] )
% 2.35/2.77 , clause( 21333, [ ~( 'c_InductTermi_OIT'( 'c_Lambda_Olift'(
% 2.35/2.77 'c_Lambda_Osubst'( 'v_b____', 'v_u____', 'v_i____' ),
% 2.35/2.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 2.35/2.77 , clause( 21334, [
% 2.35/2.77 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' ) ]
% 2.35/2.77 )
% 2.35/2.77 , clause( 21335, [
% 2.35/2.77 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat' ) ]
% 2.35/2.77 )
% 2.35/2.77 , clause( 21336, [
% 2.35/2.77 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' ) ]
% 2.35/2.77 )
% 2.35/2.77 , clause( 21337, [ 'class_Ring__and__Field_Opordered__cancel__semiring'(
% 2.35/2.77 'tc_nat' ) ] )
% 2.35/2.77 , clause( 21338, [ 'class_Ring__and__Field_Oordered__semiring__strict'(
% 2.35/2.77 'tc_nat' ) ] )
% 2.35/2.77 , clause( 21339, [ 'class_OrderedGroup_Opordered__ab__semigroup__add'(
% 2.35/2.77 'tc_nat' ) ] )
% 2.35/2.77 , clause( 21340, [ 'class_OrderedGroup_Opordered__comm__monoid__add'(
% 2.35/2.77 'tc_nat' ) ] )
% 2.35/2.77 , clause( 21341, [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 2.35/2.77 'tc_nat' ) ] )
% 2.35/2.77 , clause( 21342, [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' )
% 2.35/2.77 ] )
% 2.35/2.77 , clause( 21343, [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' )
% 2.35/2.77 ] )
% 2.35/2.77 , clause( 21344, [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' )
% 2.35/2.77 ] )
% 2.35/2.77 , clause( 21345, [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' )
% 2.35/2.77 ] )
% 2.35/2.77 , clause( 21346, [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ]
% 2.35/2.77 )
% 2.35/2.77 , clause( 21347, [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' )
% 2.35/2.77 ] )
% 2.35/2.77 , clause( 21348, [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ]
% 2.35/2.77 )
% 2.35/2.77 , clause( 21349, [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ]
% 2.35/2.77 )
% 2.35/2.77 , clause( 21350, [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ]
% 2.35/2.77 )
% 2.35/2.77 , clause( 21351, [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ]
% 2.35/2.77 )
% 2.35/2.77 , clause( 21352, [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ] )
% 2.35/2.77 , clause( 21353, [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ]
% 2.35/2.77 )
% 2.35/2.77 , clause( 21354, [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ] )
% 2.35/2.77 , clause( 21355, [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ] )
% 2.35/2.77 , clause( 21356, [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ] )
% 2.35/2.77 , clause( 21357, [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ] )
% 2.35/2.77 , clause( 21358, [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ] )
% 2.35/2.77 , clause( 21359, [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ] )
% 2.35/2.77 , clause( 21360, [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ] )
% 2.35/2.77 , clause( 21361, [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ] )
% 2.35/2.77 , clause( 21362, [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ] )
% 2.35/2.77 , clause( 21363, [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ] )
% 2.35/2.77 , clause( 21364, [ 'class_Ring__and__Field_Odvd'( 'tc_nat' ) ] )
% 2.35/2.77 , clause( 21365, [ 'class_Orderings_Opreorder'( 'tc_nat' ) ] )
% 2.35/2.77 , clause( 21366, [ 'class_Orderings_Olinorder'( 'tc_nat' ) ] )
% 2.35/2.77 , clause( 21367, [ 'class_Orderings_Oorder'( 'tc_nat' ) ] )
% 2.35/2.77 , clause( 21368, [ 'class_Orderings_Obot'( 'tc_nat' ) ] )
% 2.35/2.77 , clause( 21369, [ 'class_Power_Opower'( 'tc_nat' ) ] )
% 2.35/2.77 ] ).
% 2.35/2.77
% 2.35/2.77
% 2.35/2.77
% 2.35/2.77 eqswap(
% 2.35/2.77 clause( 22637, [ =( 'v_i____', 'v_n____' ) ] )
% 2.35/2.79 , clause( 21328, [ =( 'v_n____', 'v_i____' ) ] )
% 2.35/2.79 , 0, substitution( 0, [] )).
% 2.35/2.79
% 2.35/2.79
% 2.35/2.79 subsumption(
% 2.35/2.79 clause( 1017, [ =( 'v_i____', 'v_n____' ) ] )
% 2.35/2.79 , clause( 22637, [ =( 'v_i____', 'v_n____' ) ] )
% 2.35/2.79 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.35/2.79
% 2.35/2.79
% 2.35/2.79 subsumption(
% 2.35/2.79 clause( 1018, [ 'c_InductTermi_OIT'( 'c_Lambda_Olift'( X, Y ) ), ~(
% 2.35/2.79 'c_InductTermi_OIT'( X ) ) ] )
% 2.35/2.79 , clause( 21329, [ 'c_InductTermi_OIT'( 'c_Lambda_Olift'( X, Y ) ), ~(
% 2.35/2.79 'c_InductTermi_OIT'( X ) ) ] )
% 2.35/2.79 , substitution( 0, [ :=( X, X ), :=( Y, Y )] ), permutation( 0, [ ==>( 0, 0
% 2.35/2.79 ), ==>( 1, 1 )] ) ).
% 2.35/2.79
% 2.35/2.79
% 2.35/2.79 paramod(
% 2.35/2.79 clause( 26392, [ 'c_InductTermi_OIT'( 'c_Lambda_Osubst'( 'v_b____',
% 2.35/2.79 'v_u____', 'v_n____' ) ) ] )
% 2.35/2.79 , clause( 1017, [ =( 'v_i____', 'v_n____' ) ] )
% 2.35/2.79 , 0, clause( 21332, [ 'c_InductTermi_OIT'( 'c_Lambda_Osubst'( 'v_b____',
% 2.35/2.79 'v_u____', 'v_i____' ) ) ] )
% 2.35/2.79 , 0, 4, substitution( 0, [] ), substitution( 1, [] )).
% 2.35/2.79
% 2.35/2.79
% 2.35/2.79 subsumption(
% 2.35/2.79 clause( 1021, [ 'c_InductTermi_OIT'( 'c_Lambda_Osubst'( 'v_b____',
% 2.35/2.79 'v_u____', 'v_n____' ) ) ] )
% 2.35/2.79 , clause( 26392, [ 'c_InductTermi_OIT'( 'c_Lambda_Osubst'( 'v_b____',
% 2.35/2.79 'v_u____', 'v_n____' ) ) ] )
% 2.35/2.79 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.35/2.79
% 2.35/2.79
% 2.35/2.79 paramod(
% 2.35/2.79 clause( 28881, [ ~( 'c_InductTermi_OIT'( 'c_Lambda_Olift'(
% 2.35/2.79 'c_Lambda_Osubst'( 'v_b____', 'v_u____', 'v_n____' ),
% 2.35/2.79 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 2.35/2.79 , clause( 1017, [ =( 'v_i____', 'v_n____' ) ] )
% 2.35/2.79 , 0, clause( 21333, [ ~( 'c_InductTermi_OIT'( 'c_Lambda_Olift'(
% 2.35/2.79 'c_Lambda_Osubst'( 'v_b____', 'v_u____', 'v_i____' ),
% 2.35/2.79 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 2.35/2.79 , 0, 6, substitution( 0, [] ), substitution( 1, [] )).
% 2.35/2.79
% 2.35/2.79
% 2.35/2.79 subsumption(
% 2.35/2.79 clause( 1022, [ ~( 'c_InductTermi_OIT'( 'c_Lambda_Olift'( 'c_Lambda_Osubst'(
% 2.35/2.79 'v_b____', 'v_u____', 'v_n____' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 2.35/2.79 ) ) ) ] )
% 2.35/2.79 , clause( 28881, [ ~( 'c_InductTermi_OIT'( 'c_Lambda_Olift'(
% 2.35/2.79 'c_Lambda_Osubst'( 'v_b____', 'v_u____', 'v_n____' ),
% 2.35/2.79 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 2.35/2.79 , substitution( 0, [] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.35/2.79
% 2.35/2.79
% 2.35/2.79 resolution(
% 2.35/2.79 clause( 28882, [ 'c_InductTermi_OIT'( 'c_Lambda_Olift'( 'c_Lambda_Osubst'(
% 2.35/2.79 'v_b____', 'v_u____', 'v_n____' ), X ) ) ] )
% 2.35/2.79 , clause( 1018, [ 'c_InductTermi_OIT'( 'c_Lambda_Olift'( X, Y ) ), ~(
% 2.35/2.79 'c_InductTermi_OIT'( X ) ) ] )
% 2.35/2.79 , 1, clause( 1021, [ 'c_InductTermi_OIT'( 'c_Lambda_Osubst'( 'v_b____',
% 2.35/2.79 'v_u____', 'v_n____' ) ) ] )
% 2.35/2.79 , 0, substitution( 0, [ :=( X, 'c_Lambda_Osubst'( 'v_b____', 'v_u____',
% 2.35/2.79 'v_n____' ) ), :=( Y, X )] ), substitution( 1, [] )).
% 2.35/2.79
% 2.35/2.79
% 2.35/2.79 subsumption(
% 2.35/2.79 clause( 2175, [ 'c_InductTermi_OIT'( 'c_Lambda_Olift'( 'c_Lambda_Osubst'(
% 2.35/2.79 'v_b____', 'v_u____', 'v_n____' ), X ) ) ] )
% 2.35/2.79 , clause( 28882, [ 'c_InductTermi_OIT'( 'c_Lambda_Olift'( 'c_Lambda_Osubst'(
% 2.35/2.79 'v_b____', 'v_u____', 'v_n____' ), X ) ) ] )
% 2.35/2.79 , substitution( 0, [ :=( X, X )] ), permutation( 0, [ ==>( 0, 0 )] ) ).
% 2.35/2.79
% 2.35/2.79
% 2.35/2.79 resolution(
% 2.35/2.79 clause( 28883, [] )
% 2.35/2.79 , clause( 1022, [ ~( 'c_InductTermi_OIT'( 'c_Lambda_Olift'(
% 2.35/2.79 'c_Lambda_Osubst'( 'v_b____', 'v_u____', 'v_n____' ),
% 2.35/2.79 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ] )
% 2.35/2.79 , 0, clause( 2175, [ 'c_InductTermi_OIT'( 'c_Lambda_Olift'(
% 2.35/2.79 'c_Lambda_Osubst'( 'v_b____', 'v_u____', 'v_n____' ), X ) ) ] )
% 2.35/2.79 , 0, substitution( 0, [] ), substitution( 1, [ :=( X,
% 2.35/2.79 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )] )).
% 2.35/2.79
% 2.35/2.79
% 2.35/2.79 subsumption(
% 2.35/2.79 clause( 20129, [] )
% 2.35/2.79 , clause( 28883, [] )
% 2.35/2.79 , substitution( 0, [] ), permutation( 0, [] ) ).
% 2.35/2.79
% 2.35/2.79
% 2.35/2.79 end.
% 2.35/2.79
% 2.35/2.79 % ABCDEFGHIJKLMNOPQRSTUVWXYZ
% 2.35/2.79
% 2.35/2.79 Memory use:
% 2.35/2.79
% 2.35/2.79 space for terms: 496186
% 2.35/2.79 space for clauses: 1072694
% 2.35/2.79
% 2.35/2.79
% 2.35/2.79 clauses generated: 72780
% 2.35/2.79 clauses kept: 20130
% 2.35/2.79 clauses selected: 753
% 2.35/2.79 clauses deleted: 944
% 2.35/2.79 clauses inuse deleted: 10
% 2.35/2.79
% 2.35/2.79 subsentry: 318309
% 2.35/2.79 literals s-matched: 186905
% 2.35/2.79 literals matched: 182589
% 2.35/2.79 full subsumption: 73447
% 2.35/2.79
% 2.35/2.79 checksum: -2046217270
% 2.35/2.79
% 2.35/2.79
% 2.35/2.79 Bliksem ended
%------------------------------------------------------------------------------