TSTP Solution File: LCL749-1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : LCL749-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n028.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 07:57:29 EDT 2022
% Result : Timeout 300.06s 300.49s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL749-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.13 % Command : bliksem %s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Mon Jul 4 11:57:19 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.03/1.39 *** allocated 10000 integers for termspace/termends
% 1.03/1.39 *** allocated 10000 integers for clauses
% 1.03/1.39 *** allocated 10000 integers for justifications
% 1.03/1.39 *** allocated 15000 integers for termspace/termends
% 1.03/1.39 *** allocated 22500 integers for termspace/termends
% 1.03/1.39 Bliksem 1.12
% 1.03/1.39
% 1.03/1.39
% 1.03/1.39 Automatic Strategy Selection
% 1.03/1.39
% 1.03/1.39 Clauses:
% 1.03/1.39 [
% 1.03/1.39 [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Oappend'( X, T, Z ) ) ),
% 1.03/1.39 =( Y, T ) ],
% 1.03/1.39 [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Oappend'( T, Y, Z ) ) ),
% 1.03/1.39 =( X, T ) ],
% 1.03/1.39 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.03/1.39 'tc_nat' ), X, 'tc_nat' ), Y ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.03/1.39 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.03/1.39 'tc_nat' ), Y, 'tc_nat' ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.03/1.39 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'(
% 1.03/1.39 X, Y, 'tc_nat' ) ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 1.03/1.39 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ),
% 1.03/1.39 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.03/1.39 [ =( 'c_List_Odrop'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 1.03/1.39 'c_List_Oappend'( 'c_List_Odrop'( X, Y, T ), 'c_List_Odrop'(
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( X, 'c_Nat_Osize__class_Osize'( Y,
% 1.03/1.39 'tc_List_Olist'( T ) ), 'tc_nat' ), Z, T ), T ) ) ],
% 1.03/1.39 [ ~( =( 'c_List_Oreplicate'( X, Y, Z ), 'c_List_Oreplicate'( T, U, Z ) )
% 1.03/1.39 ), =( X, T ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.03/1.39 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.03/1.39 , Z ), T ), X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.39 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ),
% 1.03/1.39 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.03/1.39 'tc_nat' ) ) ],
% 1.03/1.39 [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Olist_OCons'( X, Y, Z ),
% 1.03/1.39 'tc_List_Olist'( Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 1.03/1.39 ), 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z ) ) ), 'c_Suc'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.03/1.39 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.03/1.39 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.03/1.39 Y, X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.03/1.39 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.03/1.39 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~( 'c_lessequals'( Y,
% 1.03/1.39 Z, 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_Lambda_Obeta'( 'c_Lambda_Osubst'( X, Y, Z ), 'c_Lambda_Osubst'( T,
% 1.03/1.39 Y, Z ) ), ~( 'c_Lambda_Obeta'( X, T ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.03/1.39 hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X ), Z ), T ), X ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.03/1.39 Z, X ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 1.03/1.39 Z, 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 1.03/1.39 Z, 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.03/1.39 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 1.03/1.39 Y, T, X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, T, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 1.03/1.39 Y, Z, X ) ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.03/1.39 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.03/1.39 T, X ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), =(
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_Orderings_Oord__class_Omin'(
% 1.03/1.39 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X ),
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( Y, T, X ) ), 'c_HOL_Ominus__class_Ominus'(
% 1.03/1.39 Z, T, X ) ) ) ],
% 1.03/1.39 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X, Y,
% 1.03/1.39 'tc_nat' ) ],
% 1.03/1.39 [ =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 1.03/1.39 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.03/1.39 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.03/1.39 ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( U, Z, X ) ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'(
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ) ), T ) ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), Z ), T ), X ), ~( 'c_lessequals'( Y
% 1.03/1.39 , T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), Z ), T ), X ), ~( 'c_lessequals'( Y
% 1.03/1.39 , T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), Z ), T ), X ), ~( 'c_lessequals'( Y
% 1.03/1.39 , T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ), Z, X ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ), Y, X ) ],
% 1.03/1.39 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_Suc'(
% 1.03/1.39 'v_sko__Nat__Xnat__Xinduct__1'( X ) ) ) ) ), ~( hBOOL( hAPP( X,
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.03/1.39 [ =( 'c_List_Otake'( X, 'c_List_Olist_ONil'( Y ), Y ),
% 1.03/1.39 'c_List_Olist_ONil'( Y ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.39 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.03/1.39 [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Oappend'( T, U, Z ) ) ),
% 1.03/1.39 =( 'c_List_Oappend'( 'c_List_Odrop'( 'c_Nat_Osize__class_Osize'( T,
% 1.03/1.39 'tc_List_Olist'( Z ) ), X, Z ), Y, Z ), U ), 'c_lessequals'(
% 1.03/1.39 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Z ) ),
% 1.03/1.39 'c_Nat_Osize__class_Osize'( T, 'tc_List_Olist'( Z ) ), 'tc_nat' ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.03/1.39 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), 'c_Suc'( Y ), X ),
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'( Y
% 1.03/1.39 ) ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y
% 1.03/1.39 ) ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 1.03/1.39 , Y ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.03/1.39 Y ) ) ) ],
% 1.03/1.39 [ =( X, 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Otimes__class_Otimes'( Z, 'c_Suc'( X
% 1.03/1.39 ), 'tc_nat' ), 'tc_nat' ) ), ~( 'c_lessequals'(
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.03/1.39 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.03/1.39 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( T, Y, X ), Z
% 1.03/1.39 , X ) ), U ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( T, Z, X ) ), U ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.39 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X
% 1.03/1.39 , Y, 'tc_nat' ), Z, 'tc_nat' ) ), T ), U, 'tc_nat' ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.39 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ), T ), hAPP(
% 1.03/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ) ), U ), 'tc_nat' ) ), ~(
% 1.03/1.39 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.39 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ), Z ), hAPP(
% 1.03/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ) ), U ), 'tc_nat' ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.39 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X
% 1.03/1.39 , T, 'tc_nat' ), Y, 'tc_nat' ) ), Z ), U, 'tc_nat' ) ), ~( 'c_lessequals'(
% 1.03/1.39 T, X, 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.39 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y
% 1.03/1.39 , Z, 'tc_nat' ), T, 'tc_nat' ) ), U ), 'tc_nat' ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.39 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ) ), X ), hAPP(
% 1.03/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ) ), U ), 'tc_nat' ) ), ~(
% 1.03/1.39 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.39 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ), Z ), hAPP(
% 1.03/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ) ), U ), 'tc_nat' ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.39 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( T
% 1.03/1.39 , X, 'tc_nat' ), Y, 'tc_nat' ) ), U ), 'tc_nat' ) ), ~( 'c_lessequals'( X
% 1.03/1.39 , T, 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.03/1.39 ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( U, Z, X ) ), W ) ) ), =( T, hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'(
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z, X ) ), W ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.03/1.39 ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( U, Z, X ) ), W ) ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'(
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ) ), T ), W ) ],
% 1.03/1.39 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Z,
% 1.03/1.39 'c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1'( X ), 'tc_nat' ) ),
% 1.03/1.39 ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), 'tc_nat' ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.03/1.39 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.03/1.39 ), Y ), Z, 'tc_nat' ), ~( 'c_lessequals'( X,
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.03/1.39 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ),
% 1.03/1.39 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.39 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat'
% 1.03/1.39 ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.03/1.39 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 1.03/1.39 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.03/1.39 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 1.03/1.39 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.03/1.39 'c_Orderings_Oord__class_Omax'( Y, Z, X ), T, X ), ~( 'c_lessequals'( Z,
% 1.03/1.39 T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.03/1.39 'c_Orderings_Oord__class_Omax'( Y, Z, X ), X ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.03/1.39 'c_Orderings_Oord__class_Omax'( Z, Y, X ), X ) ],
% 1.03/1.39 [ =( 'c_List_Oappend'( X, 'c_List_Olist_ONil'( Y ), Y ), X ) ],
% 1.03/1.39 [ =( X, 'c_List_Oappend'( 'c_List_Olist_ONil'( Y ), X, Y ) ) ],
% 1.03/1.39 [ =( X, 'c_List_Oappend'( X, 'c_List_Olist_ONil'( Y ), Y ) ) ],
% 1.03/1.39 [ =( 'c_List_Oappend'( 'c_List_Olist_ONil'( X ), Y, X ), Y ) ],
% 1.03/1.39 [ =( X, 'c_List_Oappend'( 'c_List_Olist_ONil'( Y ), X, Y ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Obot'( X ) ), 'c_lessequals'(
% 1.03/1.39 'c_Orderings_Obot__class_Obot'( X ), Y, X ) ],
% 1.03/1.39 [ =( 'c_Nat_Onat_Onat__rec'( X, Y, 'c_Suc'( Z ), T ), hAPP( hAPP( Y, Z )
% 1.03/1.39 , 'c_Nat_Onat_Onat__rec'( X, Y, Z, T ) ) ) ],
% 1.03/1.39 [ 'c_List_Odistinct'( X, Y ), ~( 'c_List_Odistinct'( 'c_List_Oappend'( X
% 1.03/1.39 , Z, Y ), Y ) ) ],
% 1.03/1.39 [ 'c_List_Odistinct'( X, Y ), ~( 'c_List_Odistinct'( 'c_List_Oappend'( Z
% 1.03/1.39 , X, Y ), Y ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ) ) ), ~(
% 1.03/1.39 'c_Groebner__Basis_Ogb__semiring'( U, W, X, V0, V1, V2 ) ) ],
% 1.03/1.39 [ =( X, 'c_List_Orev'( 'c_List_Orev'( X, Y ), Y ) ) ],
% 1.03/1.39 [ =( 'c_List_Orev'( 'c_List_Orev'( X, Y ), Y ), X ) ],
% 1.03/1.39 [ =( 'c_List_Orev'( 'c_List_Orev'( X, Y ), Y ), X ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), 'c_Orderings_Oord__class_Omax'( Y, Z
% 1.03/1.39 , X ) ), T ), 'c_Orderings_Oord__class_Omax'( hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), Y ), T ), hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), Z ), T ), X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), Y ), 'c_Orderings_Oord__class_Omax'(
% 1.03/1.39 Z, T, X ) ), 'c_Orderings_Oord__class_Omax'( hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ), hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), Y ), T ), X ) ) ],
% 1.03/1.39 [ =( X, 'c_List_Otake'( 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'(
% 1.03/1.39 Y ) ), 'c_List_Oappend'( X, Z, Y ), Y ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.03/1.39 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.03/1.39 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.03/1.39 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.03/1.39 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.03/1.39 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.03/1.39 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 1.03/1.39 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_Suc'(
% 1.03/1.39 'v_sko__List__Xupt__Xinduct__1'( X ) ) ) ) ), ~( hBOOL( hAPP( X,
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.03/1.39 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_Suc'(
% 1.03/1.39 'v_sko__List__Xreplicate__Xinduct__1'( X ) ) ) ) ), ~( hBOOL( hAPP( X,
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.03/1.39 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.03/1.39 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.03/1.39 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.39 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.03/1.39 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.39 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.03/1.39 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.39 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.39 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.03/1.39 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.39 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.03/1.39 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.03/1.39 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'(
% 1.03/1.39 Y, Z, X ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( U, Z, X ) ), W ), X ), ~( 'c_lessequals'( T
% 1.03/1.39 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z
% 1.03/1.39 , X ) ), W ), X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( Y
% 1.03/1.39 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ), U
% 1.03/1.39 , X ) ), W ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( T, U, X )
% 1.03/1.39 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Z, U, X ) ), W ), X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.03/1.39 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'(
% 1.03/1.39 Y, Z, X ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( U, Z, X ) ), W ), X ), ~( 'c_lessequals'(
% 1.03/1.39 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'(
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ) ), T ), W, X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.03/1.39 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'(
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T, X ) ), U ), W, X ), ~(
% 1.03/1.39 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, T, X ) ), U ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.03/1.39 ), W ), X ) ) ],
% 1.03/1.39 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 1.03/1.39 , X, 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.03/1.39 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Y, X )
% 1.03/1.39 ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ) ), X ) ],
% 1.03/1.39 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ),
% 1.03/1.39 'c_Orderings_Obot__class_Obot'( X ) ), 'c_Orderings_Obot__class_Obot'( X
% 1.03/1.39 ) ) ],
% 1.03/1.39 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ),
% 1.03/1.39 'c_Orderings_Obot__class_Obot'( X ) ), Y ),
% 1.03/1.39 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 1.03/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 1.03/1.39 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.03/1.39 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 1.03/1.39 X, T, 'tc_nat' ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.03/1.39 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.03/1.39 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Osemigroup__add'( X ) ), =( 'c_List_Ofoldl'(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.39 X ), Y ), Z ), T, X, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.03/1.39 ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Z, T, X, X ) ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ =( 'c_List_Orev'( 'c_List_Oreplicate'( X, Y, Z ), Z ),
% 1.03/1.39 'c_List_Oreplicate'( X, Y, Z ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.03/1.39 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.03/1.39 ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' ) ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ],
% 1.03/1.39 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_Suc'(
% 1.03/1.39 'c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1'( X ) ) ) ) ), ~( hBOOL(
% 1.03/1.39 hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.03/1.39 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 1.03/1.39 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.03/1.39 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ],
% 1.03/1.39 [ ~( =( 'c_List_Orev'( X, Y ), 'c_List_Olist_OCons'( Z,
% 1.03/1.39 'c_List_Olist_ONil'( Y ), Y ) ) ), =( X, 'c_List_Olist_OCons'( Z,
% 1.03/1.39 'c_List_Olist_ONil'( Y ), Y ) ) ],
% 1.03/1.39 [ 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.03/1.39 'c_Divides_Odiv__class_Odiv'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.03/1.39 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.03/1.39 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.03/1.39 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.03/1.39 , T, X ), X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.03/1.39 , Z, X ), X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.03/1.39 , T, X ), X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.03/1.39 , Z, X ), X ) ) ],
% 1.03/1.39 [ =( 'c_List_Otake'( 'c_Suc'( X ), 'c_List_Olist_OCons'( Y, Z, T ), T )
% 1.03/1.39 , 'c_List_Olist_OCons'( Y, 'c_List_Otake'( X, Z, T ), T ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.03/1.39 Y, X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'(
% 1.03/1.39 Y, Z, X ), X ) ) ],
% 1.03/1.39 [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.03/1.39 ~( hBOOL( hAPP( X, T ) ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Z, 'c_Suc'( T ), 'tc_nat' ), 'tc_nat' ) ),
% 1.03/1.39 ~( 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), Y,
% 1.03/1.39 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.03/1.39 'c_lessequals'( Y, T, X ), ~( 'c_lessequals'( Y,
% 1.03/1.39 'c_Orderings_Oord__class_Omax'( T, Z, X ), X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.03/1.39 'c_Power_Opower__class_Opower'( Y, T, X ), X ),
% 1.03/1.39 'c_Power_Opower__class_Opower'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.39 'tc_nat' ), Z ), T ), X ) ) ],
% 1.03/1.39 [ =( 'c_List_Odrop'( X, 'c_List_Olist_ONil'( Y ), Y ),
% 1.03/1.39 'c_List_Olist_ONil'( Y ) ) ],
% 1.03/1.39 [ 'c_lessequals'( 'c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1'(
% 1.03/1.39 X, Y ), Y, 'tc_nat' ), ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.03/1.39 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 1.03/1.39 Y, T, X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, T, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 1.03/1.39 Y, Z, X ) ) ) ],
% 1.03/1.39 [ =( 'c_Orderings_Oord__class_Omax'( 'c_Suc'( X ), 'c_Suc'( Y ),
% 1.03/1.39 'tc_nat' ), 'c_Suc'( 'c_Orderings_Oord__class_Omax'( X, Y, 'tc_nat' ) ) )
% 1.03/1.39 ],
% 1.03/1.39 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.03/1.39 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.03/1.39 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.03/1.39 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.03/1.39 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~( 'c_lessequals'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.03/1.39 [ 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), X,
% 1.03/1.39 'tc_nat' ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), Y ), hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ) ) ],
% 1.03/1.39 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 1.03/1.39 Y, 'tc_nat' ) ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.03/1.39 , 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ) ), U ), 'tc_nat' ),
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( Z, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.39 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( T
% 1.03/1.39 , X, 'tc_nat' ), Y, 'tc_nat' ) ), U ), 'tc_nat' ) ), ~( 'c_lessequals'( X
% 1.03/1.39 , T, 'tc_nat' ) ) ],
% 1.03/1.39 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 1.03/1.39 Y, 'tc_nat' ) ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.03/1.39 , 'c_HOL_Otimes__class_Otimes'( T, Y, 'tc_nat' ) ), U ), 'tc_nat' ),
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.39 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X
% 1.03/1.39 , T, 'tc_nat' ), Y, 'tc_nat' ) ), Z ), U, 'tc_nat' ) ), ~( 'c_lessequals'(
% 1.03/1.39 T, X, 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ominus__class_Ominus'( Y, Z, X )
% 1.03/1.39 ), Z ), Y ) ],
% 1.03/1.39 [ =( 'c_Suc'( 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y ) ) ),
% 1.03/1.39 'c_Nat_Osize__class_Osize'( 'c_List_Olist_OCons'( Z, X, Y ),
% 1.03/1.39 'tc_List_Olist'( Y ) ) ) ],
% 1.03/1.39 [ ~( hBOOL( hAPP( X, 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), Y, 'tc_nat' ) ) ) ),
% 1.03/1.39 hBOOL( hAPP( X, Z ) ) ],
% 1.03/1.39 [ ~( hBOOL( hAPP( X, 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), Y, 'tc_nat' ) ) ) ),
% 1.03/1.39 hBOOL( hAPP( X, Z ) ) ],
% 1.03/1.39 [ =( 'c_List_Otake'( X, 'c_List_Otake'( Y, Z, T ), T ), 'c_List_Otake'(
% 1.03/1.39 hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( 'tc_nat' ), X ), Y ), Z, T )
% 1.03/1.39 ) ],
% 1.03/1.39 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.03/1.39 'tc_nat' ) ],
% 1.03/1.39 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.03/1.39 'tc_nat' ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.03/1.39 'c_Power_Opower__class_Opower'( 'c_Power_Opower__class_Opower'( Y, Z, X )
% 1.03/1.39 , T, X ), 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'(
% 1.03/1.39 Z, T, 'tc_nat' ), X ) ) ],
% 1.03/1.39 [ ~( =( 'c_List_Olist_OCons'( X, 'c_List_Olist_ONil'( Y ), Y ),
% 1.03/1.39 'c_List_Orev'( Z, Y ) ) ), =( Z, 'c_List_Olist_OCons'( X,
% 1.03/1.39 'c_List_Olist_ONil'( Y ), Y ) ) ],
% 1.03/1.39 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_Suc'(
% 1.03/1.39 'v_sko__Nat__Xnat__Xinducts__1'( X ) ) ) ) ), ~( hBOOL( hAPP( X,
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.03/1.39 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.03/1.39 Y, X ) ) ],
% 1.03/1.39 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( Y,
% 1.03/1.39 'c_Suc'( Z ), X ), 'c_HOL_Otimes__class_Otimes'( Y,
% 1.03/1.39 'c_Power_Opower__class_Opower'( Y, Z, X ), X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.03/1.39 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.03/1.39 ), X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.03/1.39 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.03/1.39 ), X ) ) ],
% 1.03/1.39 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.03/1.39 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ),
% 1.03/1.39 'tc_nat' ), ~( 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 1.03/1.39 Z, 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.03/1.39 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.03/1.39 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.03/1.39 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.03/1.39 [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Olist_OCons'( X, Y, Z ),
% 1.03/1.39 'tc_List_Olist'( Z ) ), 'c_Suc'( 'c_Nat_Osize__class_Osize'( Y,
% 1.03/1.39 'tc_List_Olist'( Z ) ) ) ) ],
% 1.03/1.39 [ =( 'c_List_Olist__update'( 'c_List_Oappend'( X, Y, Z ), T, U, Z ),
% 1.03/1.39 'c_List_Oappend'( X, 'c_List_Olist__update'( Y,
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( T, 'c_Nat_Osize__class_Osize'( X,
% 1.03/1.39 'tc_List_Olist'( Z ) ), 'tc_nat' ), U, Z ), Z ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( T, 'c_Nat_Osize__class_Osize'( X,
% 1.03/1.39 'tc_List_Olist'( Z ) ), 'tc_nat' ) ],
% 1.03/1.39 [ =( 'c_List_Otake'( X, Y, Z ), Y ), ~( 'c_lessequals'(
% 1.03/1.39 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z ) ), X, 'tc_nat' ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.03/1.39 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.03/1.39 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( 'c_lessequals'( X, X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X,
% 1.03/1.39 'c_Suc'( X ), 'tc_nat' ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( 'c_List_Olistsum'( Y,
% 1.03/1.39 X ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), Y, X, X ) ) ],
% 1.03/1.39 [ ~( =( X, 'c_List_Otake'( 'c_Nat_Osize__class_Osize'( X,
% 1.03/1.39 'tc_List_Olist'( Y ) ), Z, Y ) ) ), =( 'c_List_Oappend'( X,
% 1.03/1.39 'c_List_Oappend'( 'c_List_Odrop'( 'c_Nat_Osize__class_Osize'( X,
% 1.03/1.39 'tc_List_Olist'( Y ) ), Z, Y ), T, Y ), Y ), 'c_List_Oappend'( Z, T, Y )
% 1.03/1.39 ), ~( 'c_lessequals'( 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y
% 1.03/1.39 ) ), 'c_Nat_Osize__class_Osize'( Z, 'tc_List_Olist'( Y ) ), 'tc_nat' ) )
% 1.03/1.39 ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.03/1.39 , Y, X ) ) ],
% 1.03/1.39 [ =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 1.03/1.39 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.03/1.39 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.03/1.39 , Y, X ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.03/1.39 'tc_nat' ), 'c_Suc'( X ), 'tc_nat' ) ],
% 1.03/1.39 [ =( 'c_List_Odrop'( X, 'c_List_Otake'( Y, Z, T ), T ), 'c_List_Otake'(
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'c_List_Odrop'( X, Z, T )
% 1.03/1.39 , T ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.03/1.39 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.03/1.39 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.03/1.39 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.03/1.39 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Z ), ~( 'c_lessequals'( Y, Z,
% 1.03/1.39 X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 1.03/1.39 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Z ) ), 'c_lessequals'( Y, Z, X
% 1.03/1.39 ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.03/1.39 'c_Orderings_Oord__class_Omax'( Y, Z, X ), Y ), ~( 'c_lessequals'( Z, Y,
% 1.03/1.39 X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.39 X ), Y ), Z ) ), T ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.39 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.03/1.39 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.39 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.03/1.39 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.39 X ), Y ), Z ) ), T ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.39 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.03/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.39 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.03/1.39 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.03/1.39 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.03/1.39 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.03/1.39 'c_Power_Opower__class_Opower'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.39 'tc_nat' ), Z ), T ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.03/1.39 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.03/1.39 Y, T, X ), X ) ) ],
% 1.03/1.39 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X,
% 1.03/1.39 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.03/1.39 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' )
% 1.03/1.39 ) ],
% 1.03/1.39 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X,
% 1.03/1.39 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.03/1.39 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' )
% 1.03/1.39 ) ],
% 1.03/1.39 [ =( 'c_List_Odrop'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.03/1.39 'c_List_Olist_OCons'( X, Y, Z ), Z ), 'c_List_Olist_OCons'( X, Y, Z ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ =( 'c_List_Otake'( X, 'c_List_Odrop'( Y, Z, T ), T ), 'c_List_Odrop'(
% 1.03/1.39 Y, 'c_List_Otake'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.03/1.39 ), Y ), Z, T ), T ) ) ],
% 1.03/1.39 [ =( 'c_List_Oreplicate'( 'c_Suc'( X ), Y, Z ), 'c_List_Olist_OCons'( Y
% 1.03/1.39 , 'c_List_Oreplicate'( X, Y, Z ), Z ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 1.03/1.39 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.03/1.39 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.03/1.39 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ), Y, 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.03/1.39 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.03/1.39 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.03/1.39 [ =( 'c_List_Orev'( 'c_List_Otake'( X, Y, Z ), Z ), 'c_List_Odrop'(
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( 'c_Nat_Osize__class_Osize'( Y,
% 1.03/1.39 'tc_List_Olist'( Z ) ), X, 'tc_nat' ), 'c_List_Orev'( Y, Z ), Z ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.03/1.39 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ),
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ), Y ), ~( 'c_lessequals'( Y
% 1.03/1.39 , Z, X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =( hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ), Y ) ), 'c_lessequals'( Y,
% 1.03/1.39 Z, X ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ), Z ), ~( 'c_lessequals'( Z
% 1.03/1.39 , Y, X ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), =(
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( 'c_Orderings_Oord__class_Omax'( Y, Z, X ),
% 1.03/1.39 T, X ), 'c_Orderings_Oord__class_Omax'( 'c_HOL_Ominus__class_Ominus'( Y,
% 1.03/1.39 T, X ), 'c_HOL_Ominus__class_Ominus'( Z, T, X ), X ) ) ],
% 1.03/1.39 [ =( hAPP( 'c_COMBK'( X, Y, Z ), T ), X ) ],
% 1.03/1.39 [ =( 'c_List_Orev'( 'c_List_Odrop'( X, Y, Z ), Z ), 'c_List_Otake'(
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( 'c_Nat_Osize__class_Osize'( Y,
% 1.03/1.39 'tc_List_Olist'( Z ) ), X, 'tc_nat' ), 'c_List_Orev'( Y, Z ), Z ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.03/1.39 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 1.03/1.39 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 1.03/1.39 , X ), 'c_lessequals'( Y, Y, X ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.03/1.39 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.03/1.39 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.03/1.39 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.03/1.39 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.03/1.39 [ hBOOL( hAPP( X, Y ) ), 'c_HOL_Oord__class_Oless'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.03/1.39 'c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1'( X ), 'tc_nat' ),
% 1.03/1.39 ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__meet'( X ) ), =(
% 1.03/1.39 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ), hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__meet'( X ) ), =(
% 1.03/1.39 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), T ), hAPP(
% 1.03/1.39 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.03/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ), hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.03/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), T ), hAPP(
% 1.03/1.39 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.03/1.39 'c_Nat_Osemiring__1__class_Oof__nat__aux'( Y, 'c_Suc'( Z ), T, X ),
% 1.03/1.39 'c_Nat_Osemiring__1__class_Oof__nat__aux'( Y, Z, hAPP( Y, T ), X ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), Y ), hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), Z ), T ) ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), Y ), hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), Z ), T ) ), hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), Z ), hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), Y ), T ) ) ) ],
% 1.03/1.39 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.03/1.39 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.03/1.39 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.03/1.39 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.03/1.39 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.03/1.39 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.03/1.39 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.03/1.39 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.03/1.39 'c_lessequals'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) )
% 1.03/1.39 , ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ),
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.03/1.39 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 1.03/1.39 ],
% 1.03/1.39 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, Z ), U ) )
% 1.03/1.39 , hAPP( hAPP( Y, Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.03/1.39 , T ), U ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, Y, V0, V1, V2
% 1.03/1.39 ) ) ],
% 1.03/1.39 [ =( 'c_Lambda_Oliftn'( 'c_Suc'( X ), Y, Z ), hAPP( hAPP(
% 1.03/1.39 'c_Lambda_Olift', 'c_Lambda_Oliftn'( X, Y, Z ) ), Z ) ) ],
% 1.03/1.39 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 1.03/1.39 Z, 'tc_nat' ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.03/1.39 , 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, 'tc_nat' ) ), T ) ) )
% 1.03/1.39 ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.03/1.39 'c_lessequals'( Y, hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X ), T ),
% 1.03/1.39 Z ), X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.03/1.39 'c_lessequals'( Y, hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X ), Z ),
% 1.03/1.39 T ), X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ), T, X ), ~( 'c_lessequals'(
% 1.03/1.39 Z, T, X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ), T, X ), ~( 'c_lessequals'(
% 1.03/1.39 Y, T, X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ), T, X ), ~( 'c_lessequals'(
% 1.03/1.39 Z, T, X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ), T, X ), ~( 'c_lessequals'(
% 1.03/1.39 Y, T, X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.03/1.39 'c_lessequals'( Y, hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X ), T ),
% 1.03/1.39 Z ), X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.03/1.39 'c_lessequals'( Y, hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X ), Z ),
% 1.03/1.39 T ), X ) ) ],
% 1.03/1.39 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.03/1.39 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.03/1.39 , Y ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ) ), Z, X ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), T ), 'c_Divides_Odiv__class_Odiv'( Y, Z
% 1.03/1.39 , X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.03/1.39 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.03/1.39 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.03/1.39 , Y ), 'c_HOL_Otimes__class_Otimes'( Z, T, X ) ), T, X ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Z ), 'c_Divides_Odiv__class_Odiv'( Y, T
% 1.03/1.39 , X ) ) ), =( T, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.03/1.39 [ =( 'c_Type_Oshift'( 'c_Type_Oshift'( X, Y, Z, T ),
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), U, T ), 'c_Type_Oshift'(
% 1.03/1.39 'c_Type_Oshift'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), U, T ),
% 1.03/1.39 'c_Suc'( Y ), Z, T ) ) ],
% 1.03/1.39 [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Oappend'( T, U, Z ) ) ),
% 1.03/1.39 =( Y, 'c_List_Oappend'( 'c_List_Odrop'( 'c_Nat_Osize__class_Osize'( X,
% 1.03/1.39 'tc_List_Olist'( Z ) ), T, Z ), U, Z ) ), ~( 'c_lessequals'(
% 1.03/1.39 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Z ) ),
% 1.03/1.39 'c_Nat_Osize__class_Osize'( T, 'tc_List_Olist'( Z ) ), 'tc_nat' ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.03/1.39 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.03/1.39 'tc_nat' ), Y, 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat'
% 1.03/1.39 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.03/1.39 , Y, 'tc_nat' ) ) ],
% 1.03/1.39 [ =( hAPP( 'c_Fun_Ocomp'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) )
% 1.03/1.39 ) ],
% 1.03/1.39 [ =( hAPP( X, hAPP( Y, Z ) ), hAPP( 'c_Fun_Ocomp'( X, Y, T, U, W ), Z )
% 1.03/1.39 ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.03/1.39 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.03/1.39 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.03/1.39 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.03/1.39 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.03/1.39 [ =( 'c_List_Otake'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.03/1.39 , X ), Y ), Z, T ), 'c_List_Oappend'( 'c_List_Otake'( X, Z, T ),
% 1.03/1.39 'c_List_Otake'( Y, 'c_List_Odrop'( X, Z, T ), T ), T ) ), ~(
% 1.03/1.39 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.03/1.39 Y ), 'c_Nat_Osize__class_Osize'( Z, 'tc_List_Olist'( T ) ), 'tc_nat' ) )
% 1.03/1.39 ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ), T ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( U, Z, X )
% 1.03/1.39 ), W ), X ), ~( 'c_HOL_Oord__class_Oless'( T, hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'(
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( U, Y, X ), Z, X ) ), W ), X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.03/1.39 , 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Z, T, X ),
% 1.03/1.39 U, X ) ), W ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( T, U, X )
% 1.03/1.39 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Z, U, X ) ), W ), X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ), T ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( U, Z, X )
% 1.03/1.39 ), W ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'(
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( Y, U, X ), Z, X ) ), T ), W, X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), T
% 1.03/1.39 , X ) ), U ), W, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, T, X )
% 1.03/1.39 ), U ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Z, T, X ) ), W ), X ) ) ],
% 1.03/1.39 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ), Z ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( T,
% 1.03/1.39 Y, 'tc_nat' ) ), U ) ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ), =( hAPP(
% 1.03/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, T,
% 1.03/1.39 'tc_nat' ), Y, 'tc_nat' ) ), Z ), U ) ],
% 1.03/1.39 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ), Z ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( T,
% 1.03/1.39 Y, 'tc_nat' ) ), U ) ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ), =( Z,
% 1.03/1.39 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( T, X,
% 1.03/1.39 'tc_nat' ), Y, 'tc_nat' ) ), U ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.03/1.39 'c_lessequals'( T, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), T ), Y ), Z, X ) ) ],
% 1.03/1.39 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 1.03/1.39 Z, 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, X,
% 1.03/1.39 'tc_nat' ), Z, 'tc_nat' ) ), T ) ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 1.03/1.39 Z, 'tc_nat' ) ), T ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.03/1.39 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.03/1.39 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.03/1.39 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.03/1.39 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.03/1.39 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.03/1.39 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.03/1.39 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.03/1.39 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.39 'c_Power_Opower__class_Opower'( Y, T, X ), 'c_Power_Opower__class_Opower'(
% 1.03/1.39 Z, T, X ), X ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldl'(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ), Z, X, X
% 1.03/1.39 ) ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.03/1.39 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z, X ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.03/1.39 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z, X ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.03/1.39 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 1.03/1.39 X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.03/1.39 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z,
% 1.03/1.39 X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.03/1.39 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, T,
% 1.03/1.39 X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y,
% 1.03/1.39 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~( 'c_lessequals'( Y, Z,
% 1.03/1.39 X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.03/1.39 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( T, Y, X ), Z, X ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.03/1.39 'c_lessequals'( 'c_Orderings_Oord__class_Omax'( Y, T, X ), Z, X ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.03/1.39 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'(
% 1.03/1.39 X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), Z,
% 1.03/1.39 'tc_nat' ), ~( 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.39 'tc_nat' ), Z ), Y ), 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.03/1.39 'c_Power_Opower__class_Opower'( Y, Z, X ), X ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.03/1.39 , X ), 'c_HOL_Oord__class_Oless'( Y, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.39 Y, 'c_Orderings_Oord__class_Omax'( T, Z, X ), X ) ) ],
% 1.03/1.39 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( Y ), 'tc_nat' ), hAPP(
% 1.03/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ) ],
% 1.03/1.39 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ), hAPP(
% 1.03/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ) ) ],
% 1.03/1.39 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.03/1.39 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.39 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, T, 'tc_nat' ) ), X ), Y,
% 1.03/1.39 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, T ) ) ],
% 1.03/1.39 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 1.03/1.39 , hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ) ), Y ), Z,
% 1.03/1.39 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), ~( hBOOL( hAPP(
% 1.03/1.39 'c_InductTermi_OIT', Y ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT',
% 1.03/1.39 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_Osubst'( X, Y,
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z, 'tc_Lambda_OdB',
% 1.03/1.39 'tc_Lambda_OdB' ) ) ) ) ],
% 1.03/1.39 [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Olist_ONil'( Z ), T, Z ), Y ) ],
% 1.03/1.39 [ =( hAPP( 'c_Type_Oshift'( X, Y, Z, T ), Y ), Z ) ],
% 1.03/1.39 [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), T ), hAPP(
% 1.03/1.39 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ) ) ],
% 1.03/1.39 [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ), hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), T ) ) ) ],
% 1.03/1.39 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ), hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), T ) ) ) ],
% 1.03/1.39 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), T ), hAPP(
% 1.03/1.39 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ) ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.03/1.39 X, 'tc_bool' ) ), hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.03/1.39 , Y ), Z ) ), T ), hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.03/1.39 , Y ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.03/1.39 X, 'tc_bool' ) ), Z ), T ) ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.03/1.39 X, 'tc_bool' ) ), Y ), hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.03/1.39 , Z ), T ) ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.03/1.39 'tc_fun'( X, 'tc_bool' ) ), Z ), hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.03/1.39 , Y ), T ) ) ) ],
% 1.03/1.39 [ =( 'c_Nat_Onat_Onat__case'( X, Y, 'c_Suc'( Z ), T ), hAPP( Y, Z ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Oappend'( Y, Z, X ) ) ), =( Y
% 1.03/1.39 , 'c_List_Olist_ONil'( X ) ) ],
% 1.03/1.39 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Oappend'( Y, Z, X ) ) ), =( Z
% 1.03/1.39 , 'c_List_Olist_ONil'( X ) ) ],
% 1.03/1.39 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y ) ) ), =( X, Y
% 1.03/1.39 ) ],
% 1.03/1.39 [ ~( 'c_lessequals'( 'c_Nat_Osize__class_Osize'( 'c_List_Olist_OCons'( X
% 1.03/1.39 , Y, Z ), 'tc_List_Olist'( Z ) ), 'c_Nat_Osize__class_Osize'( Y,
% 1.03/1.39 'tc_List_Olist'( Z ) ), 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, Y, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 1.03/1.39 Z, Z, X ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.03/1.39 [ ~( =( 'c_List_Otake'( 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'(
% 1.03/1.39 Y ) ), Z, Y ), X ) ), 'c_lessequals'( 'c_Nat_Osize__class_Osize'( Z,
% 1.03/1.39 'tc_List_Olist'( Y ) ), 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y
% 1.03/1.39 ) ), 'tc_nat' ), =( 'c_List_Oappend'( Z, T, Y ), 'c_List_Oappend'( X,
% 1.03/1.39 'c_List_Oappend'( 'c_List_Odrop'( 'c_Nat_Osize__class_Osize'( X,
% 1.03/1.39 'tc_List_Olist'( Y ) ), Z, Y ), T, Y ), Y ) ) ],
% 1.03/1.39 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.03/1.39 'tc_nat' ), Z, 'tc_nat' ) ), T ), U, 'tc_nat' ), ~( 'c_lessequals'( hAPP(
% 1.03/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ), T ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 1.03/1.39 Z, 'tc_nat' ) ), U ), 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) )
% 1.03/1.39 ],
% 1.03/1.39 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ), Z ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( T,
% 1.03/1.39 Y, 'tc_nat' ) ), U ), 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( X, T, 'tc_nat' ), Y, 'tc_nat' ) ), Z ), U,
% 1.03/1.39 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.03/1.39 , 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.03/1.39 'tc_nat' ), T, 'tc_nat' ) ), U ), 'tc_nat' ), ~( 'c_lessequals'( hAPP(
% 1.03/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 1.03/1.39 T, 'tc_nat' ) ), U ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) )
% 1.03/1.39 ],
% 1.03/1.39 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ), Z ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( T,
% 1.03/1.39 Y, 'tc_nat' ) ), U ), 'tc_nat' ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( T, X, 'tc_nat' ), Y, 'tc_nat' ) ), U ),
% 1.03/1.39 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.03/1.39 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.03/1.39 , 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.03/1.39 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.03/1.39 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 1.03/1.39 [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ), =( X
% 1.03/1.39 , 'c_List_Olist_ONil'( Z ) ) ],
% 1.03/1.39 [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ), =( Y
% 1.03/1.39 , 'c_List_Olist_ONil'( Z ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.03/1.39 , X ), 'c_HOL_Oord__class_Oless'( T, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.39 hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( X ), T ), Y ), Z, X ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.03/1.39 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 1.03/1.39 T, U, X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, U, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 1.03/1.39 T, Z, X ) ) ) ), =( Z, U ), =( Y, T ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.03/1.39 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 1.03/1.39 T, U, X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, U, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 1.03/1.39 T, Z, X ) ) ) ), =( Z, U ), =( Y, T ) ],
% 1.03/1.39 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ) ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 1.03/1.39 T, 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ) ),
% 1.03/1.39 =( Y, T ), =( X, Z ) ],
% 1.03/1.39 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ) ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 1.03/1.39 T, 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ) ),
% 1.03/1.39 =( Y, T ), =( X, Z ) ],
% 1.03/1.39 [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Olist_ONil'( X ),
% 1.03/1.39 'tc_List_Olist'( X ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( =( X, 'c_List_Otake'( 'c_Nat_Osize__class_Osize'( X,
% 1.03/1.39 'tc_List_Olist'( Y ) ), Z, Y ) ) ), =( 'c_List_Oappend'( X,
% 1.03/1.39 'c_List_Odrop'( 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y ) ), Z
% 1.03/1.39 , Y ), Y ), Z ) ],
% 1.03/1.39 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat'
% 1.03/1.39 ), 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.03/1.39 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.03/1.39 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.03/1.39 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.03/1.39 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.03/1.39 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Z
% 1.03/1.39 , X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.03/1.39 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.03/1.39 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), Y
% 1.03/1.39 , X ), Z ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.03/1.39 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.03/1.39 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) )
% 1.03/1.39 , 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.03/1.39 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 1.03/1.39 , 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.03/1.39 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Otimes__class_Otimes'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.03/1.39 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.03/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ), ~( 'c_lessequals'( Z
% 1.03/1.39 , Y, 'tc_nat' ) ) ],
% 1.03/1.39 [ =( 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.03/1.39 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.03/1.39 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X, hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.03/1.39 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.03/1.39 T, Z, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 1.03/1.39 ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.03/1.39 , T, X ) ) ), =( Y, Z ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ominus__class_Ominus'( Z
% 1.03/1.39 , T, X ) ) ), =( Z, T ) ],
% 1.03/1.39 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y
% 1.03/1.39 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), =( X, Z ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), Y ), 'c_Orderings_Oord__class_Omax'(
% 1.03/1.39 Y, Z, X ) ), Y ) ],
% 1.03/1.39 [ =( 'c_List_Orev'( 'c_List_Olist_OCons'( X, Y, Z ), Z ),
% 1.03/1.39 'c_List_Oappend'( 'c_List_Orev'( Y, Z ), 'c_List_Olist_OCons'( X,
% 1.03/1.39 'c_List_Olist_ONil'( Z ), Z ), Z ) ) ],
% 1.03/1.39 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.03/1.39 'tc_nat' ) ), =( Y, Z ) ],
% 1.03/1.39 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.03/1.39 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y
% 1.03/1.39 , X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ), 'tc_nat'
% 1.03/1.39 ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.03/1.39 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X
% 1.03/1.39 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat'
% 1.03/1.39 ) ) ],
% 1.03/1.39 [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Olist_OCons'( Z, T, U ), W, U ),
% 1.03/1.39 'c_List_Ofoldl'( X, hAPP( hAPP( X, Y ), Z ), T, W, U ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 1.03/1.39 , Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'(
% 1.03/1.39 Y ) ) ) ],
% 1.03/1.39 [ =( 'c_List_Odrop'( 'c_Suc'( X ), 'c_List_Olist_OCons'( Y, Z, T ), T )
% 1.03/1.39 , 'c_List_Odrop'( X, Z, T ) ) ],
% 1.03/1.39 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.03/1.39 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.03/1.39 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.03/1.39 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.03/1.39 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.03/1.39 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.03/1.39 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.03/1.39 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( T, Z, X
% 1.03/1.39 ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.03/1.39 ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.03/1.39 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.03/1.39 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.03/1.39 X ), T, X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.03/1.39 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~( 'c_lessequals'( Z, T, X
% 1.03/1.39 ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X
% 1.03/1.39 ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.03/1.39 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.03/1.39 , Z, X ), X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.03/1.39 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'(
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, T, X ), 'c_HOL_Otimes__class_Otimes'( Z
% 1.03/1.39 , T, X ), X ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.03/1.39 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' )
% 1.03/1.39 , ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.03/1.39 'tc_nat' ) ), X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.03/1.39 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ),
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ) ],
% 1.03/1.39 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), Y ), ~(
% 1.03/1.39 'c_lessequals'( Y, Z, X ) ) ],
% 1.03/1.39 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), ~( =( hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), Y ) ),
% 1.03/1.39 'c_lessequals'( Y, Z, X ) ],
% 1.03/1.39 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), Z ), ~(
% 1.03/1.39 'c_lessequals'( Z, Y, X ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.03/1.39 'c_Suc'( X ), 'tc_nat' ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.03/1.39 'c_Suc'( X ), 'tc_nat' ) ],
% 1.03/1.39 [ =( 'c_List_Orev'( 'c_List_Olist_OCons'( X, 'c_List_Olist_ONil'( Y ), Y
% 1.03/1.39 ), Y ), 'c_List_Olist_OCons'( X, 'c_List_Olist_ONil'( Y ), Y ) ) ],
% 1.03/1.39 [ ~( =( 'c_List_Orev'( X, Y ), 'c_List_Olist_OCons'( Z, T, Y ) ) ), =( X
% 1.03/1.39 , 'c_List_Oappend'( 'c_List_Orev'( T, Y ), 'c_List_Olist_OCons'( Z,
% 1.03/1.39 'c_List_Olist_ONil'( Y ), Y ), Y ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.03/1.39 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.03/1.39 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.03/1.39 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.03/1.39 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.03/1.39 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omax'( Y, T
% 1.03/1.39 , X ), Z, X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.03/1.39 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Orderings_Oord__class_Omax'( T, Y
% 1.03/1.39 , X ), Z, X ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.03/1.39 X, 'tc_bool' ) ), Y ), Z ), hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.03/1.39 , Z ), Y ) ) ],
% 1.03/1.39 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), Y ) ) ],
% 1.03/1.39 [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), Y ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( 'c_List_Olistsum'(
% 1.03/1.39 'c_List_Olist_ONil'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ), hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), Z ), Y ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ) ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z,
% 1.03/1.39 Y, 'tc_nat' ) ), T ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 1.03/1.39 ), 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.39 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), T ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.03/1.39 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( T, Z, X ) ), U ) ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), Z, X ) ), U ) ) ],
% 1.03/1.39 [ 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), X,
% 1.03/1.39 'tc_nat' ) ],
% 1.03/1.39 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp',
% 1.03/1.39 Y, Z, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( 'c_Lambda_OdB_OAbs'( X )
% 1.03/1.39 , Y ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.03/1.39 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.03/1.39 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y, X, 'tc_nat' ), 'tc_nat' ) )
% 1.03/1.39 ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.03/1.39 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.03/1.39 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ) )
% 1.03/1.39 ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.03/1.39 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.03/1.39 'c_Power_Opower__class_Opower'( T, Z, X ), X ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.03/1.39 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.03/1.39 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Y, X )
% 1.03/1.39 ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.03/1.39 X ), X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X )
% 1.03/1.39 ), 'c_HOL_Otimes__class_Otimes'( Y, Y, X ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.03/1.39 X ), X ) ) ],
% 1.03/1.39 [ =( 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, Z ), T, Z ),
% 1.03/1.39 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ],
% 1.03/1.39 [ =( 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, Z ), T, Z ),
% 1.03/1.39 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ],
% 1.03/1.39 [ ~( hBOOL( hAPP( X, 'c_Nat_Onat_Onat__case'( Y, Z, 'c_Suc'( T ), 't_a'
% 1.03/1.39 ) ) ) ), hBOOL( hAPP( X, hAPP( Z, T ) ) ) ],
% 1.03/1.39 [ ~( hBOOL( hAPP( X, 'c_Nat_Onat_Onat__case'( Y, Z, 'c_Suc'( T ), 't_a'
% 1.03/1.39 ) ) ) ), hBOOL( hAPP( X, hAPP( Z, T ) ) ) ],
% 1.03/1.39 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 1.03/1.39 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.03/1.39 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.03/1.39 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.03/1.39 [ =( X, 'c_List_Odrop'( 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'(
% 1.03/1.39 Z ) ), 'c_List_Oappend'( Y, X, Z ), Z ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP(
% 1.03/1.39 hAPP( 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ), T, X ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP(
% 1.03/1.39 hAPP( 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ), T, X ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.03/1.39 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), Z ), T ), X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.03/1.39 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), T ), Z ), X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP(
% 1.03/1.39 hAPP( 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ), T, X ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP(
% 1.03/1.39 hAPP( 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ), T, X ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.03/1.39 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.03/1.39 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 1.03/1.39 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.03/1.39 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.03/1.39 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'(
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( =( 'c_List_Otake'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ), =( Y,
% 1.03/1.39 'c_List_Olist_ONil'( Z ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.03/1.39 ) ],
% 1.03/1.39 [ =( 'c_List_Omap'( 'c_COMBK'( X, Y, Z ), T, Z, Y ), 'c_List_Oreplicate'(
% 1.03/1.39 'c_Nat_Osize__class_Osize'( T, 'tc_List_Olist'( Z ) ), X, Y ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.03/1.39 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.03/1.39 [ =( 'c_List_Olist__update'( 'c_List_Olist_ONil'( X ), Y, Z, X ),
% 1.03/1.39 'c_List_Olist_ONil'( X ) ) ],
% 1.03/1.39 [ =( 'c_List_Olist__update'( 'c_List_Olist_ONil'( X ), Y, Z, X ),
% 1.03/1.39 'c_List_Olist_ONil'( X ) ) ],
% 1.03/1.39 [ =( 'c_List_Olist__update'( 'c_List_Olist_ONil'( X ), Y, Z, X ),
% 1.03/1.39 'c_List_Olist_ONil'( X ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.03/1.39 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.03/1.39 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z
% 1.03/1.39 , 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.03/1.39 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.03/1.39 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.03/1.39 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.03/1.39 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.03/1.39 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.03/1.39 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.03/1.39 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Y, X ),
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X )
% 1.03/1.39 , Y, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat'
% 1.03/1.39 ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X
% 1.03/1.39 , 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ),
% 1.03/1.39 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), =( 'c_Suc'( X
% 1.03/1.39 ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( Y )
% 1.03/1.39 , X, 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_lessequals'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_lessequals'( Y, X,
% 1.03/1.39 'tc_nat' ) ],
% 1.03/1.39 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.03/1.39 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.03/1.39 ) ],
% 1.03/1.39 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.03/1.39 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 1.03/1.39 ) ],
% 1.03/1.39 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.03/1.39 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.03/1.39 ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.03/1.39 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 1.03/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 1.03/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.03/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.03/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 1.03/1.39 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.03/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' ) ), Y ) ), ~(
% 1.03/1.39 'c_lessequals'( Z, X, 'tc_nat' ) ) ],
% 1.03/1.39 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.03/1.39 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat'
% 1.03/1.39 ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T, X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Z, U, X ), X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( T, 'c_HOL_Otimes__class_Otimes'(
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), U, X ), X ) ) ],
% 1.03/1.39 [ =( 'c_List_Olist__update'( 'c_List_Oappend'( X, Y, Z ), T, U, Z ),
% 1.03/1.39 'c_List_Oappend'( 'c_List_Olist__update'( X, T, U, Z ), Y, Z ) ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( T, 'c_Nat_Osize__class_Osize'( X,
% 1.03/1.39 'tc_List_Olist'( Z ) ), 'tc_nat' ) ) ],
% 1.03/1.39 [ =( 'c_List_Olist__update'( 'c_List_Oappend'( X, Y, Z ), T, U, Z ),
% 1.03/1.39 'c_List_Oappend'( 'c_List_Olist__update'( X, T, U, Z ), Y, Z ) ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( T, 'c_Nat_Osize__class_Osize'( X,
% 1.03/1.39 'tc_List_Olist'( Z ) ), 'tc_nat' ) ) ],
% 1.03/1.39 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z
% 1.03/1.39 , 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), ~(
% 1.03/1.39 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.03/1.39 'tc_nat' ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 1.03/1.39 ) ],
% 1.03/1.39 [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Otake'( X, Y, Z ),
% 1.03/1.39 'tc_List_Olist'( Z ) ), hAPP( hAPP( 'c_Orderings_Oord__class_Omin'(
% 1.03/1.39 'tc_nat' ), 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z ) ) ), X )
% 1.03/1.39 ) ],
% 1.03/1.39 [ 'c_Lambda_Obeta'( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y,
% 1.03/1.39 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 1.03/1.39 , Z, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), ~( 'c_Lambda_Obeta'( X, Z )
% 1.03/1.39 ) ],
% 1.03/1.39 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X, 'c_Suc'(
% 1.03/1.39 'v_sko__List__Xlexn__Xinduct__1'( X ) ) ) ) ), ~( hBOOL( hAPP( X,
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.03/1.39 [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Orotate'( X, Y, Z ),
% 1.03/1.39 'tc_List_Olist'( Z ) ), 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z
% 1.03/1.39 ) ) ) ],
% 1.03/1.39 [ =( 'c_List_Olist_ONil'( X ), 'c_List_Oreplicate'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, X ) ) ],
% 1.03/1.39 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.03/1.39 'tc_nat' ) ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.03/1.39 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.03/1.39 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 1.03/1.39 , X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.03/1.39 , Y, X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.03/1.39 , Y, X ) ) ],
% 1.03/1.39 [ ~( 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 1.03/1.39 ), Y ), X ), 'tc_nat' ) ), =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), X, 'tc_nat' ), Y ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), Y ), Y ), Y ) ],
% 1.03/1.39 [ 'c_Lambda_Obeta'( hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'(
% 1.03/1.39 X ) ), Y ), 'c_Lambda_Osubst'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.03/1.39 ) ) ) ],
% 1.03/1.39 [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Oappend'( X, Y, Z ),
% 1.03/1.39 'tc_List_Olist'( Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 1.03/1.39 ), 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Z ) ) ),
% 1.03/1.39 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z ) ) ) ) ],
% 1.03/1.39 [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Odrop'( X, Y, Z ),
% 1.03/1.39 'tc_List_Olist'( Z ) ), 'c_HOL_Ominus__class_Ominus'(
% 1.03/1.39 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z ) ), X, 'tc_nat' ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.03/1.39 , X ), Y ), 'tc_nat' ) ],
% 1.03/1.39 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.03/1.39 , Y ), X ), 'tc_nat' ) ],
% 1.03/1.39 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.03/1.39 , X ), Y ), 'tc_nat' ) ],
% 1.03/1.39 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Y ),
% 1.03/1.39 'c_Orderings_Oord__class_Omax'( X, Y, 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( 'c_List_Olistsum'(
% 1.03/1.39 'c_List_Olist_OCons'( Y, Z, X ), X ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Olistsum'( Z, X ) ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.03/1.39 ), =( Z, Y ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.03/1.39 ) ],
% 1.03/1.39 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 1.03/1.39 , Y, 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.03/1.39 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.03/1.39 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 1.03/1.39 'tc_nat' ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.03/1.39 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.03/1.39 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.03/1.39 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.03/1.39 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.03/1.39 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.03/1.39 [ =( 'c_List_Oappend'( 'c_List_Oreplicate'( X, Y, Z ),
% 1.03/1.39 'c_List_Oreplicate'( T, Y, Z ), Z ), 'c_List_Oappend'(
% 1.03/1.39 'c_List_Oreplicate'( T, Y, Z ), 'c_List_Oreplicate'( X, Y, Z ), Z ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.03/1.39 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.03/1.39 ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.03/1.39 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'(
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.03/1.39 , X ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.03/1.39 'c_lessequals'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.03/1.39 'c_Orderings_Oord__class_Omax'( Y, Y, X ), Y ) ],
% 1.03/1.39 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP( hAPP(
% 1.03/1.39 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( Y, T ) ],
% 1.03/1.39 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP( hAPP(
% 1.03/1.39 'c_Lambda_OdB_OApp', Z ), T ) ) ), =( X, Z ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.03/1.39 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.03/1.39 T, X ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.39 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.03/1.39 , Z ), T ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) )
% 1.03/1.39 , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), T, X ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.03/1.39 [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), T, X ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.03/1.39 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.03/1.39 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.03/1.39 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.03/1.39 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ),
% 1.03/1.39 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 1.03/1.39 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T, 'tc_Lambda_OdB',
% 1.03/1.39 'tc_Lambda_OdB' ) ) ), =( Y, T ) ],
% 1.03/1.39 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( X ),
% 1.03/1.39 Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), 'c_List_Ofoldl'(
% 1.03/1.39 'c_Lambda_OdB_OApp', 'c_Lambda_OdB_OAbs'( Z ), T, 'tc_Lambda_OdB',
% 1.03/1.39 'tc_Lambda_OdB' ) ) ), =( X, Z ) ],
% 1.03/1.39 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB',
% 1.03/1.39 'tc_Lambda_OdB' ), 'c_Lambda_OdB_OAbs'( Z ) ) ), =( X,
% 1.03/1.39 'c_Lambda_OdB_OAbs'( Z ) ) ],
% 1.03/1.39 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Olist_OCons'( Y, Z, X ) ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ 'c_List_Odistinct'( 'c_List_Olist_ONil'( X ), X ) ],
% 1.03/1.39 [ =( 'c_List_Olist__update'( X, Y, Z, T ), 'c_List_Oappend'(
% 1.03/1.39 'c_List_Otake'( Y, X, T ), 'c_List_Olist_OCons'( Z, 'c_List_Odrop'(
% 1.03/1.39 'c_Suc'( Y ), X, T ), T ), T ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.03/1.39 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( T ) ), 'tc_nat' ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ), 'tc_nat' ),
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.39 'tc_nat' ), X ), Z ), 'c_Suc'( Y ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y
% 1.03/1.39 , 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.03/1.39 , X ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.03/1.39 , X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.03/1.39 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.39 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.03/1.39 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.03/1.39 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.03/1.39 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.03/1.39 'c_lessequals'( Y, T, X ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.03/1.39 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.03/1.39 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.03/1.39 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.03/1.39 'c_lessequals'( Z, T, X ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.03/1.39 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.03/1.39 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.03/1.39 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.03/1.39 'c_lessequals'( Y, T, X ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.03/1.39 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.03/1.39 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.03/1.39 'c_lessequals'( Z, T, X ) ) ],
% 1.03/1.39 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.03/1.39 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ),
% 1.03/1.39 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.03/1.39 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ),
% 1.03/1.39 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.03/1.39 [ =( 'c_List_Olist__update'( X, Y, Z, T ), X ), ~( 'c_lessequals'(
% 1.03/1.39 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( T ) ), Y, 'tc_nat' ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( Y, hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Y,
% 1.03/1.39 X, 'tc_nat' ) ), X ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ) ), Y ), ~( 'c_lessequals'(
% 1.03/1.39 X, Y, 'tc_nat' ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Y ), X ), ~(
% 1.03/1.39 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ), hAPP( hAPP( Z, Y ),
% 1.03/1.39 'c_Suc'( T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Z, W, V0,
% 1.03/1.39 V1 ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ), hAPP( hAPP( Y, Z ),
% 1.03/1.39 'c_Suc'( T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Y, W, V0,
% 1.03/1.39 V1 ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( X, Y ), 'c_Suc'( Z ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.03/1.39 X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1
% 1.03/1.39 ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( X, Y ), 'c_Suc'( Z ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.03/1.39 X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1
% 1.03/1.39 ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 1.03/1.39 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' )
% 1.03/1.39 , 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ),
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.39 'tc_nat' ), X ), Y ), Z, 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat'
% 1.03/1.39 ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ), Z ),
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.39 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat'
% 1.03/1.39 ) ) ],
% 1.03/1.39 [ =( 'c_List_Odrop'( X, 'c_List_Odrop'( Y, Z, T ), T ), 'c_List_Odrop'(
% 1.03/1.39 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, T ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.03/1.39 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.03/1.39 ~( 'c_lessequals'( 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( T ), X ),
% 1.03/1.39 'c_Power_Opower__class_Opower'( Z, 'c_Suc'( T ), X ), X ) ) ],
% 1.03/1.39 [ =( 'c_List_Oreplicate'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.39 'tc_nat' ), X ), Y ), Z, T ), 'c_List_Oappend'( 'c_List_Oreplicate'( X, Z
% 1.03/1.39 , T ), 'c_List_Oreplicate'( Y, Z, T ), T ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.03/1.39 , X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ) ],
% 1.03/1.39 [ =( 'c_List_Otake'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, Y ),
% 1.03/1.39 'c_List_Olist_ONil'( Y ) ) ],
% 1.03/1.39 [ =( 'c_List_Otake'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 1.03/1.39 'c_List_Oappend'( 'c_List_Otake'( X, Y, T ), 'c_List_Otake'(
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( X, 'c_Nat_Osize__class_Osize'( Y,
% 1.03/1.39 'tc_List_Olist'( T ) ), 'tc_nat' ), Z, T ), T ) ) ],
% 1.03/1.39 [ ~( =( 'c_List_Orev'( X, Y ), 'c_List_Orev'( Z, Y ) ) ), =( X, Z ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ =( 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 1.03/1.39 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, T ), Z, T ) ) ],
% 1.03/1.39 [ =( 'c_List_Olist_OCons'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 1.03/1.39 'c_List_Oappend'( 'c_List_Olist_OCons'( X, Y, T ), Z, T ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.03/1.39 , =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.03/1.39 [ 'c_lessequals'( X, 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), Z, 'tc_nat' ), 'tc_nat'
% 1.03/1.39 ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.03/1.39 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y ) ), 'tc_nat' ), =( X,
% 1.03/1.39 'c_List_Olist_ONil'( Y ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.03/1.39 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.03/1.39 'c_Groebner__Basis_Ogb__semiring'( W, Y, X, V0, V1, V2 ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 1.03/1.39 hAPP( X, Y ), T ) ), hAPP( hAPP( X, Y ), U ) ) ), ~(
% 1.03/1.39 'c_Groebner__Basis_Ogb__semiring'( Z, X, W, V0, V1, V2 ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.03/1.39 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.03/1.39 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.03/1.39 , V0, V1, V2 ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.03/1.39 T, X, U, W, Y, V0 ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.03/1.39 T, X, U, Y, W, V0 ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.03/1.39 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.03/1.39 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.03/1.39 , V0, V1, V2 ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.03/1.39 X, T, U, Y, W, V0 ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.03/1.39 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.03/1.39 , V0, V1, V2 ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.03/1.39 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.03/1.39 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.03/1.39 , V0, V1, V2 ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.03/1.39 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.03/1.39 W, V0, V1, V2 ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.03/1.39 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.03/1.39 W, V0, V1, V2 ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.03/1.39 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.03/1.39 ~( 'c_Groebner__Basis_Ogb__semiring'( X, W, V0, V1, V2, V3 ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.03/1.39 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.03/1.39 W, V0, V1, V2 ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.03/1.39 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.03/1.39 , V0, V1, V2 ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.03/1.39 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.03/1.39 W, V0, V1, V2 ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.03/1.39 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.03/1.39 , V0, V1, V2 ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.03/1.39 , hAPP( hAPP( X, T ), hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), U ) ) ),
% 1.03/1.39 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.03/1.39 , hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), hAPP( hAPP( X, T ), U ) ) ) ),
% 1.03/1.39 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.03/1.39 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.03/1.39 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.03/1.39 T, X, U, W, Z, V0 ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.03/1.39 T, X, U, W, Y, V0 ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.03/1.39 T, X, U, Z, W, V0 ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.03/1.39 T, X, U, Y, W, V0 ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.03/1.39 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.03/1.39 'c_Groebner__Basis_Ogb__semiring'( Y, X, W, V0, V1, V2 ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.03/1.39 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.03/1.39 X, T, U, Z, W, V0 ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.03/1.39 X, T, U, Y, W, V0 ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, hAPP( hAPP( X, T ), T ) ),
% 1.03/1.39 Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, U, W, T, V0 ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ), hAPP( hAPP( Z, hAPP(
% 1.03/1.39 hAPP( X, T ), U ) ), Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, W
% 1.03/1.39 , V0, U, V1 ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ), hAPP( hAPP( Y, hAPP(
% 1.03/1.39 hAPP( X, Z ), U ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Y, W
% 1.03/1.39 , V0, U, V1 ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), T ) )
% 1.03/1.39 , hAPP( hAPP( Y, hAPP( hAPP( X, Z ), U ) ), T ) ), ~(
% 1.03/1.39 'c_Groebner__Basis_Ogb__semiring'( X, Y, W, V0, V1, V2 ) ) ],
% 1.03/1.39 [ ~( =( 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', X, Y, 'tc_Lambda_OdB',
% 1.03/1.39 'tc_Lambda_OdB' ), 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp', Z, Y,
% 1.03/1.39 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ), =( X, Z ) ],
% 1.03/1.39 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.03/1.39 X ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ), X ) ) ],
% 1.03/1.39 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.03/1.39 X ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), T ), Z ), X ) ) ],
% 1.03/1.39 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( hAPP(
% 1.03/1.39 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), T, X )
% 1.03/1.39 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.03/1.39 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( hAPP(
% 1.03/1.39 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), T, X )
% 1.03/1.39 , ~( 'c_lessequals'( Z, T, X ) ) ],
% 1.03/1.39 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.03/1.39 X ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ), X ) ) ],
% 1.03/1.39 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.03/1.39 X ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), T ), Z ), X ) ) ],
% 1.03/1.39 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.03/1.39 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.03/1.39 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.03/1.39 [ =( 'c_List_Oappend'( 'c_List_Otake'( X, Y, Z ), 'c_List_Odrop'( X, Y,
% 1.03/1.39 Z ), Z ), Y ) ],
% 1.03/1.39 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( 'c_Suc'(
% 1.03/1.39 X ), Y, 'tc_nat' ), 'c_Suc'( Z ), 'tc_nat' ),
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.03/1.39 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.03/1.39 'c_Divides_Odiv__class_Odiv'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.03/1.39 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.03/1.39 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.03/1.39 , Y, 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y,
% 1.03/1.39 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ),
% 1.03/1.39 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'(
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), X, 'tc_nat' ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( Z ), Y, 'tc_nat' ), 'tc_nat' ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Y, X )
% 1.03/1.39 ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ) ), X ), =( Y,
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Y, X )
% 1.03/1.39 ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ) ), X ), =( Z,
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.39 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.03/1.39 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 1.03/1.39 [ 'c_Lambda_Obeta'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP(
% 1.03/1.39 hAPP( 'c_Lambda_OdB_OApp', X ), Z ) ), ~( 'c_Lambda_Obeta'( Y, Z ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ 'c_Lambda_Obeta'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), hAPP(
% 1.03/1.39 hAPP( 'c_Lambda_OdB_OApp', Z ), Y ) ), ~( 'c_Lambda_Obeta'( X, Z ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ =( 'c_List_Orev'( 'c_List_Oappend'( 'c_List_Orev'( X, Y ),
% 1.03/1.39 'c_List_Olist_OCons'( Z, 'c_List_Olist_ONil'( Y ), Y ), Y ), Y ),
% 1.03/1.39 'c_List_Olist_OCons'( Z, X, Y ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.03/1.39 'c_Orderings_Oord__class_Omax'( Y, Z, X ), 'c_Orderings_Oord__class_Omax'(
% 1.03/1.39 Z, Y, X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 1.03/1.39 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_Power_Opower__class_Opower'(
% 1.03/1.39 T, Z, X ) ) ), =( Y, T ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.03/1.39 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.03/1.39 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.03/1.39 [ ~( =( 'c_List_Odrop'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ),
% 1.03/1.39 'c_lessequals'( 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z ) ), X
% 1.03/1.39 , 'tc_nat' ) ],
% 1.03/1.39 [ =( 'c_List_Odrop'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ), ~(
% 1.03/1.39 'c_lessequals'( 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z ) ), X
% 1.03/1.39 , 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( X ), 'tc_nat' ) ],
% 1.03/1.39 [ 'c_List_Odistinct'( 'c_List_Odrop'( X, Y, Z ), Z ), ~(
% 1.03/1.39 'c_List_Odistinct'( Y, Z ) ) ],
% 1.03/1.39 [ 'c_List_Odistinct'( 'c_List_Orev'( X, Y ), Y ), ~( 'c_List_Odistinct'(
% 1.03/1.39 X, Y ) ) ],
% 1.03/1.39 [ 'c_List_Odistinct'( X, Y ), ~( 'c_List_Odistinct'( 'c_List_Orev'( X, Y
% 1.03/1.39 ), Y ) ) ],
% 1.03/1.39 [ =( 'c_List_Odrop'( X, 'c_List_Oreplicate'( Y, Z, T ), T ),
% 1.03/1.39 'c_List_Oreplicate'( 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), Z, T
% 1.03/1.39 ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.03/1.39 'c_Orderings_Oord__class_Omax'( hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ), hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), Y ), T ), X ), hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), Y ), 'c_Orderings_Oord__class_Omax'(
% 1.03/1.39 Z, T, X ) ), X ) ],
% 1.03/1.39 [ =( 'c_Lambda_Oliftn'( X, hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ), Z ), T
% 1.03/1.39 ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Oliftn'( X, Y, T ) ),
% 1.03/1.39 'c_Lambda_Oliftn'( X, Z, T ) ) ) ],
% 1.03/1.39 [ =( 'c_List_Oreplicate'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, Y )
% 1.03/1.39 , 'c_List_Olist_ONil'( Y ) ) ],
% 1.03/1.39 [ =( 'c_nat_Onat__size'( 'c_Suc'( X ) ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_nat_Onat__size'( X ) ),
% 1.03/1.39 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.03/1.39 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.03/1.39 'c_Orderings_Oord__class_Omax'( Y, hAPP( hAPP(
% 1.03/1.39 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ), X ), Y ) ],
% 1.03/1.39 [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X, X, 'tc_nat' ),
% 1.03/1.39 'tc_nat' ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.03/1.39 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( T, Z, X )
% 1.03/1.39 , 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, Y, X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( T, Y, X ), X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.03/1.39 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.03/1.39 , 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ) ) ],
% 1.03/1.39 [ ~( =( 'c_List_Orev'( X, Y ), 'c_List_Olist_ONil'( Y ) ) ), =( X,
% 1.03/1.39 'c_List_Olist_ONil'( Y ) ) ],
% 1.03/1.39 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ominus__class_Ominus'( X, Y
% 1.03/1.39 , 'tc_nat' ), 'tc_nat' ), Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ =( 'c_List_Orotate'( X, 'c_List_Olist_ONil'( Y ), Y ),
% 1.03/1.39 'c_List_Olist_ONil'( Y ) ) ],
% 1.03/1.39 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), Y ) ) ],
% 1.03/1.39 [ ~( =( X, 'c_List_Olist_OCons'( Y, X, Z ) ) ) ],
% 1.03/1.39 [ =( 'c_List_Olist__update'( 'c_List_Olist_OCons'( X, Y, Z ),
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), T, Z ), 'c_List_Olist_OCons'( T,
% 1.03/1.39 Y, Z ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( 'tc_nat' ), 'c_Suc'( X
% 1.03/1.39 ) ), 'c_Suc'( Y ) ), 'c_Suc'( hAPP( hAPP( 'c_Orderings_Oord__class_Omin'(
% 1.03/1.39 'tc_nat' ), X ), Y ) ) ) ],
% 1.03/1.39 [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Olist__update'( X, Y, Z, T ),
% 1.03/1.39 'tc_List_Olist'( T ) ), 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( T
% 1.03/1.39 ) ) ) ],
% 1.03/1.39 [ =( X, 'c_Suc'( Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 1.03/1.39 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.03/1.39 X, 'c_Suc'( X ), 'tc_nat' ) ],
% 1.03/1.39 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Y, 'c_Suc'( X ), 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.03/1.39 [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Oappend'( T, U, Z ) ) ),
% 1.03/1.39 =( X, 'c_List_Otake'( 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Z )
% 1.03/1.39 ), T, Z ) ), ~( 'c_lessequals'( 'c_Nat_Osize__class_Osize'( X,
% 1.03/1.39 'tc_List_Olist'( Z ) ), 'c_Nat_Osize__class_Osize'( T, 'tc_List_Olist'( Z
% 1.03/1.39 ) ), 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.03/1.39 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.03/1.39 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.03/1.39 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.03/1.39 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.03/1.39 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.03/1.39 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.03/1.39 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.03/1.39 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.03/1.39 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.03/1.39 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.03/1.39 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.03/1.39 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Z, X, 'tc_nat' )
% 1.03/1.39 , 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.03/1.39 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.03/1.39 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.03/1.39 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.03/1.39 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.03/1.39 , 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.03/1.39 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.03/1.39 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.39 Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.03/1.39 [ =( 'c_List_Otake'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.03/1.39 'c_List_Olist_OCons'( X, Y, Z ), Z ), 'c_List_Olist_ONil'( Z ) ) ],
% 1.03/1.39 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.03/1.39 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.03/1.39 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.03/1.39 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_List_Odistinct'( X, Y ), ~( 'c_List_Odistinct'( 'c_List_Orotate'( Z
% 1.03/1.39 , X, Y ), Y ) ) ],
% 1.03/1.39 [ 'c_List_Odistinct'( 'c_List_Orotate'( X, Y, Z ), Z ), ~(
% 1.03/1.39 'c_List_Odistinct'( Y, Z ) ) ],
% 1.03/1.39 [ ~( =( 'c_List_Oreplicate'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ),
% 1.03/1.39 =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.03/1.39 'c_List_Olistsum'( 'c_List_Orev'( Y, X ), X ), 'c_List_Olistsum'( Y, X )
% 1.03/1.39 ) ],
% 1.03/1.39 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), Y, X ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), Z, X ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.03/1.39 hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ),
% 1.03/1.39 X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.03/1.39 hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ),
% 1.03/1.39 X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.03/1.39 hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Z ), T ),
% 1.03/1.39 X ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( hAPP(
% 1.03/1.39 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), Z, X )
% 1.03/1.39 ],
% 1.03/1.39 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( hAPP(
% 1.03/1.39 hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ), Y, X )
% 1.03/1.39 ],
% 1.03/1.39 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.03/1.39 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Otimes__class_Otimes'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.03/1.39 X ) ) ],
% 1.03/1.39 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.03/1.39 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.03/1.39 [ =( 'c_Fun_Ocomp'( X, 'c_Fun_Ocomp'( Y, Z, T, U, W ), U, V0, W ),
% 1.03/1.39 'c_Fun_Ocomp'( 'c_Fun_Ocomp'( X, Y, U, V0, T ), Z, T, V0, W ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, 'c_Power_Opower__class_Opower'( Y, Z, X
% 1.03/1.39 ), X ), 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.03/1.39 Y, X ), 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ) ) ],
% 1.03/1.39 [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Oreplicate'( X, Y, Z ),
% 1.03/1.39 'tc_List_Olist'( Z ) ), X ) ],
% 1.03/1.39 [ =( hAPP( 'c_Type_Oshift'( X, Y, Z, T ), U ), hAPP( X, U ) ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( U, Y, 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Oreplicate'( Y, Z, X ) ) ),
% 1.03/1.39 =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.03/1.39 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.03/1.39 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.03/1.39 , X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.03/1.39 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.03/1.39 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.03/1.39 , X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.03/1.39 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.03/1.39 , X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.03/1.39 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.03/1.39 , X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.39 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.03/1.39 [ ~( =( 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y ) ),
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_List_Olist_ONil'( Y
% 1.03/1.39 ) ) ],
% 1.03/1.39 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Orev'( Y, X ) ) ), =( Y,
% 1.03/1.39 'c_List_Olist_ONil'( X ) ) ],
% 1.03/1.39 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( X ), Y,
% 1.03/1.39 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_lessequals'( X, 'c_Suc'( Y ), 'tc_nat' ), ~( 'c_lessequals'( X, Y,
% 1.03/1.39 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( Y, X,
% 1.03/1.39 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.03/1.39 ) ), X, 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.03/1.39 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Suc'(
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.03/1.39 ) ), X, 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( 'c_lessequals'( 'c_Suc'( X ), X, 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Z, 'tc_nat' )
% 1.03/1.39 , 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.03/1.39 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 1.03/1.39 ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.03/1.39 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ),
% 1.03/1.39 ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, Z
% 1.03/1.39 , 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.03/1.39 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.03/1.39 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.03/1.39 ,
% 1.03/1.39 [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ) ],
% 1.03/1.39 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Z ) ) ],
% 1.03/1.39 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.03/1.39 X, 'tc_bool' ) ), Y ), hAPP( hAPP(
% 1.03/1.39 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.03/1.39 , Y ), Z ) ), hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.03/1.39 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ) ) ],
% 1.03/1.39 [ ~( =( 'c_List_Orotate'( X, Y, Z ), 'c_List_Olist_ONil'( Z ) ) ), =( Y
% 1.03/1.39 , 'c_List_Olist_ONil'( Z ) ) ],
% 1.03/1.39 [ =( 'c_List_Otake'( X, 'c_List_Oreplicate'( Y, Z, T ), T ),
% 1.03/1.39 'c_List_Oreplicate'( hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( 'tc_nat'
% 1.03/1.39 ), X ), Y ), Z, T ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.03/1.39 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.03/1.39 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.03/1.39 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.03/1.39 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.03/1.39 [ =( 'c_List_Olist__update'( 'c_List_Oappend'( X, 'c_List_Olist_OCons'(
% 1.03/1.39 Y, Z, T ), T ), 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( T ) ), U
% 1.03/1.39 , T ), 'c_List_Oappend'( X, 'c_List_Olist_OCons'( U, Z, T ), T ) ) ],
% 1.03/1.39 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.39 'tc_nat' ), X ), Y ), X, 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.39 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =(
% 1.03/1.39 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ominus__class_Ominus'( Y, Z
% 1.03/1.39 , 'tc_nat' ), X ), 'c_HOL_Ominus__class_Ominus'(
% 1.03/1.39 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.03/1.39 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ), X ) ), ~( 'c_lessequals'( Z
% 1.03/1.39 , Y, 'tc_nat' ) ) ],
% 1.03/1.39 [ =( 'c_Divides_Odiv__class_Odiv'( X, 'c_HOL_Otimes__class_Otimes'( Y, Z
% 1.03/1.39 , 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'(
% 1.03/1.39 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.03/1.39 , Z, X ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.03/1.39 ), ~( 'c_lessequals'( T, Y, X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.03/1.39 , T, X ), X ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.03/1.39 ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'(
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.03/1.39 , Z, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.03/1.39 ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'(
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.03/1.39 , T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.03/1.39 ), ~( 'c_lessequals'( Z, T, X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'(
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.03/1.39 , T, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.03/1.39 ), ~( 'c_lessequals'( Z, T, X ) ) ],
% 1.03/1.39 [ ~( =( 'c_List_Oappend'( X, Y, Z ), X ) ), =( Y, 'c_List_Olist_ONil'( Z
% 1.03/1.39 ) ) ],
% 1.03/1.39 [ ~( =( X, 'c_List_Oappend'( X, Y, Z ) ) ), =( Y, 'c_List_Olist_ONil'( Z
% 1.03/1.39 ) ) ],
% 1.03/1.39 [ ~( =( 'c_List_Oappend'( X, Y, Z ), Y ) ), =( X, 'c_List_Olist_ONil'( Z
% 1.03/1.39 ) ) ],
% 1.03/1.39 [ ~( =( X, 'c_List_Oappend'( Y, X, Z ) ) ), =( Y, 'c_List_Olist_ONil'( Z
% 1.03/1.39 ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.03/1.39 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Z, T, X ) ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Otimes__class_Otimes'( Z, U
% 1.03/1.39 , X ) ) ) ), =( T, U ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.03/1.39 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.03/1.39 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ) ), hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Otimes__class_Otimes'(
% 1.03/1.39 Y, T, 'tc_nat' ) ) ) ), =( Z, T ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.03/1.39 'tc_nat' ) ) ],
% 1.03/1.39 [ =( 'c_List_Oappend'( 'c_List_Olist_ONil'( X ), 'c_List_Olist_OCons'( Y
% 1.03/1.39 , Z, X ), X ), 'c_List_Olist_OCons'( Y, Z, X ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.03/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Y
% 1.03/1.39 , X ) ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ) ),
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.03/1.39 ) ) ],
% 1.03/1.39 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.03/1.39 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Y
% 1.03/1.39 , X ) ), 'c_HOL_Otimes__class_Otimes'( Z, Z, X ) ),
% 1.03/1.39 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.03/1.39 ) ) ],
% 1.03/1.39 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.03/1.39 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.03/1.39 'tc_nat' ), Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~(
% 1.03/1.39 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.03/1.39 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.39 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.03/1.39 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.03/1.39 [ 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ominus__class_Ominus'( Y, Z,
% 1.03/1.39 'tc_nat' ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.03/1.39 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.03/1.40 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 1.03/1.40 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 1.03/1.40 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =( hAPP( hAPP(
% 1.03/1.40 'c_Lattices_Olower__semilattice__class_Oinf'( X ), Y ), Y ), Y ) ],
% 1.03/1.40 [ =( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'(
% 1.03/1.40 X, 'tc_bool' ) ), Y ), Y ), Y ) ],
% 1.03/1.40 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.03/1.40 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.03/1.40 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.03/1.40 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.03/1.40 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.03/1.40 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.03/1.40 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ),
% 1.03/1.40 ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.03/1.40 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.03/1.40 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.40 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.03/1.40 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.03/1.40 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.03/1.40 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.03/1.40 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.03/1.40 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.03/1.40 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.03/1.40 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.03/1.40 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ),
% 1.03/1.40 ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.03/1.40 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.03/1.40 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.40 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.03/1.40 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.03/1.40 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.40 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.03/1.40 , Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.03/1.40 ],
% 1.03/1.40 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.03/1.40 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.40 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.03/1.40 , Z ), Y ), 'tc_nat' ) ) ],
% 1.03/1.40 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.40 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.03/1.40 , X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) )
% 1.03/1.40 ],
% 1.03/1.40 [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hBOOL(
% 1.03/1.40 hAPP( X, 'c_Suc'( 'c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1'( X ) ) )
% 1.03/1.40 ), ~( hBOOL( hAPP( X, Y ) ) ) ],
% 1.03/1.40 [ 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.03/1.40 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y,
% 1.03/1.40 'tc_nat' ) ), ~( 'c_lessequals'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.03/1.40 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.03/1.40 [ ~( =( 'c_List_Oappend'( 'c_List_Odrop'( 'c_Nat_Osize__class_Osize'( X
% 1.03/1.40 , 'tc_List_Olist'( Y ) ), Z, Y ), 'c_List_Oappend'( 'c_List_Odrop'(
% 1.03/1.40 'c_Nat_Osize__class_Osize'( Z, 'tc_List_Olist'( Y ) ), X, Y ), T, Y ), Y
% 1.03/1.40 ), T ) ), ~( =( 'c_List_Otake'( 'c_Nat_Osize__class_Osize'( X,
% 1.03/1.40 'tc_List_Olist'( Y ) ), Z, Y ), X ) ), ~( =( Z, 'c_List_Otake'(
% 1.03/1.40 'c_Nat_Osize__class_Osize'( Z, 'tc_List_Olist'( Y ) ), X, Y ) ) ), =(
% 1.03/1.40 'c_List_Oappend'( Z, 'c_List_Oappend'( 'c_List_Odrop'(
% 1.03/1.40 'c_Nat_Osize__class_Osize'( Z, 'tc_List_Olist'( Y ) ), X, Y ), T, Y ), Y
% 1.03/1.40 ), 'c_List_Oappend'( X, T, Y ) ) ],
% 1.03/1.40 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.03/1.40 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.03/1.40 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.03/1.40 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 1.03/1.40 ) ) ],
% 1.03/1.40 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.03/1.40 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 1.03/1.40 ) ) ],
% 1.03/1.40 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.03/1.40 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.03/1.40 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.03/1.40 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.03/1.40 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 1.03/1.40 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z, Y, 'tc_nat' )
% 1.03/1.40 ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.03/1.40 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 1.03/1.40 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 1.03/1.40 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 1.03/1.40 ,
% 1.03/1.40 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.03/1.40 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 1.03/1.40 , X ) ) ],
% 1.03/1.40 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.03/1.40 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.03/1.40 , X ) ) ],
% 1.03/1.40 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.03/1.40 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.03/1.40 , X ), ~( 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.03/1.40 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ), X ) ) ],
% 1.03/1.40 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.03/1.40 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.03/1.40 ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~(
% 1.03/1.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.03/1.40 'tc_nat' ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.03/1.40 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.03/1.40 , Y, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.03/1.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.03/1.40 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.03/1.40 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( T, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.03/1.40 , Z, X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.03/1.40 X ), T, X ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.03/1.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.03/1.40 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.03/1.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.03/1.40 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.03/1.40 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.03/1.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.03/1.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.03/1.40 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.03/1.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.03/1.40 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.03/1.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.03/1.40 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.03/1.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.03/1.40 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.03/1.40 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.03/1.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.03/1.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.03/1.40 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.03/1.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.03/1.40 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.03/1.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ), ~(
% 1.03/1.40 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.03/1.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ), ~(
% 1.03/1.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.03/1.40 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.03/1.40 [ =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Oappend'(
% 1.03/1.40 'c_List_Olist_ONil'( Z ), 'c_List_Olist_OCons'( X, Y, Z ), Z ) ) ],
% 1.03/1.40 [ =( 'c_List_Olist_OCons'( X, 'c_List_Olist_ONil'( Y ), Y ),
% 1.03/1.40 'c_List_Orev'( 'c_List_Olist_OCons'( X, 'c_List_Olist_ONil'( Y ), Y ), Y
% 1.03/1.40 ) ) ],
% 1.03/1.40 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.03/1.40 , =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.03/1.40 'c_Orderings_Oord__class_Omax'( Y, Z, X ) ), T ),
% 1.03/1.40 'c_Orderings_Oord__class_Omax'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.03/1.40 ), Y ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X )
% 1.03/1.40 ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =(
% 1.03/1.40 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ),
% 1.03/1.40 'c_Power_Opower__class_Opower'( T, 'c_Suc'( Z ), X ) ) ), =( Y, T ), ~(
% 1.03/1.40 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.03/1.40 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.03/1.40 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.03/1.40 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( Y, T, X ), X ),
% 1.03/1.40 'c_Divides_Odiv__class_Odiv'( Z, T, X ) ), =( Y,
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.03/1.40 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.03/1.40 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( T, Z, X ), X ),
% 1.03/1.40 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), =( Z,
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.03/1.40 [ =( 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.03/1.40 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ),
% 1.03/1.40 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), =( X,
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.03/1.40 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( Z, T, 'tc_nat' ), 'tc_nat' ), ~(
% 1.03/1.40 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) )
% 1.03/1.40 ],
% 1.03/1.40 [ 'c_lessequals'( X, 'c_HOL_Otimes__class_Otimes'( X,
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( X, X, 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ]
% 1.03/1.40 ,
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.03/1.40 , U, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.03/1.40 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.03/1.40 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.03/1.40 , U, X ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.03/1.40 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.03/1.40 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.03/1.40 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.03/1.40 'c_Orderings_Oord__class_Omax'( 'c_Orderings_Oord__class_Omax'( Y, Z, X )
% 1.03/1.40 , T, X ), 'c_Orderings_Oord__class_Omax'( Y,
% 1.03/1.40 'c_Orderings_Oord__class_Omax'( Z, T, X ), X ) ) ],
% 1.03/1.40 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.03/1.40 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omax'( Z, T,
% 1.03/1.40 X ), X ), 'c_Orderings_Oord__class_Omax'( Z,
% 1.03/1.40 'c_Orderings_Oord__class_Omax'( Y, T, X ), X ) ) ],
% 1.03/1.40 [ =( 'c_List_Olist_ONil'( X ), 'c_List_Oappend'( 'c_List_Olist_ONil'( X
% 1.03/1.40 ), 'c_List_Olist_ONil'( X ), X ) ) ],
% 1.03/1.40 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( hAPP(
% 1.03/1.40 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.03/1.40 , T ), X ), Y ) ) ) ],
% 1.03/1.40 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( hAPP(
% 1.03/1.40 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.03/1.40 , X ), T ), Y ) ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.03/1.40 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.03/1.40 ), 'c_HOL_Otimes__class_Otimes'( T, Z, X ) ),
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.03/1.40 , Y ), T ), Z, X ) ) ],
% 1.03/1.40 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.03/1.40 X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( X, 'c_Suc'( 'c_Divides_Odiv__class_Odiv'( Y
% 1.03/1.40 , X, 'tc_nat' ) ), 'tc_nat' ), 'tc_nat' ) ],
% 1.03/1.40 [ 'c_List_Odistinct'( 'c_List_Otake'( X, Y, Z ), Z ), ~(
% 1.03/1.40 'c_List_Odistinct'( Y, Z ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.03/1.40 , X ), X ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.03/1.40 , X ), X ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.03/1.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.03/1.40 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'(
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ), X ) ), X ) ) ],
% 1.03/1.40 [ 'c_Lambda_Obeta'( 'c_Lambda_OdB_OAbs'( X ), 'c_Lambda_OdB_OAbs'( Y ) )
% 1.03/1.40 , ~( 'c_Lambda_Obeta'( X, Y ) ) ],
% 1.03/1.40 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.03/1.40 'c_Orderings_Oord__class_Omax'( Y, 'c_Orderings_Oord__class_Omax'( Y, Z,
% 1.03/1.40 X ), X ), 'c_Orderings_Oord__class_Omax'( Y, Z, X ) ) ],
% 1.03/1.40 [ =( 'c_List_Oappend'( 'c_List_Oreplicate'( X, Y, Z ),
% 1.03/1.40 'c_List_Olist_OCons'( Y, 'c_List_Olist_ONil'( Z ), Z ), Z ),
% 1.03/1.40 'c_List_Olist_OCons'( Y, 'c_List_Oreplicate'( X, Y, Z ), Z ) ) ],
% 1.03/1.40 [ =( 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'(
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.03/1.40 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.03/1.40 , X ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.03/1.40 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 1.03/1.40 , X ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.03/1.40 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.03/1.40 , X ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.03/1.40 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Z, Y, X )
% 1.03/1.40 , X ) ) ],
% 1.03/1.40 [ =( 'c_List_Orev'( 'c_List_Olist_ONil'( X ), X ), 'c_List_Olist_ONil'(
% 1.03/1.40 X ) ) ],
% 1.03/1.40 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.03/1.40 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ), X ) ]
% 1.03/1.40 ,
% 1.03/1.40 [ =( 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP(
% 1.03/1.40 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ), Y ) ]
% 1.03/1.40 ,
% 1.03/1.40 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.03/1.40 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.03/1.40 , Y ), Z ), Z, X ), Y ) ],
% 1.03/1.40 [ =( 'c_List_Orev'( 'c_List_Oappend'( X, Y, Z ), Z ), 'c_List_Oappend'(
% 1.03/1.40 'c_List_Orev'( Y, Z ), 'c_List_Orev'( X, Z ), Z ) ) ],
% 1.03/1.40 [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Oappend'( Z, T, U ), W, U ),
% 1.03/1.40 'c_List_Ofoldl'( X, 'c_List_Ofoldl'( X, Y, Z, W, U ), T, W, U ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( 'c_List_Olistsum'(
% 1.03/1.40 'c_List_Omap'( 'c_COMBK'( Y, X, Z ), T, Z, X ), X ),
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.03/1.40 'c_Nat_Osize__class_Osize'( T, 'tc_List_Olist'( Z ) ), X ), Y, X ) ) ]
% 1.03/1.40 ,
% 1.03/1.40 [ =( 'c_List_Orotate'( X, 'c_List_Orotate'( Y, Z, T ), T ),
% 1.03/1.40 'c_List_Orotate'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X )
% 1.03/1.40 , Y ), Z, T ) ) ],
% 1.03/1.40 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.03/1.40 'c_Nat_Osize__class_Osize'( 'c_List_Olist_ONil'( X ), 'tc_List_Olist'( X
% 1.03/1.40 ) ), 'tc_nat' ) ) ],
% 1.03/1.40 [ 'c_List_Odistinct'( X, Y ), ~( 'c_List_Odistinct'(
% 1.03/1.40 'c_List_Olist_OCons'( Z, X, Y ), Y ) ) ],
% 1.03/1.40 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.03/1.40 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.03/1.40 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.03/1.40 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.03/1.40 ,
% 1.03/1.40 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.03/1.40 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.03/1.40 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.03/1.40 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.03/1.40 ,
% 1.03/1.40 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.03/1.40 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.03/1.40 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.03/1.40 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ) ) ]
% 1.03/1.40 ,
% 1.03/1.40 [ 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.03/1.40 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.03/1.40 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.03/1.40 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.03/1.40 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 1.03/1.40 , 'tc_nat' ) ) ],
% 1.03/1.40 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.03/1.40 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.03/1.40 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 1.03/1.40 , 'tc_nat' ) ) ],
% 1.03/1.40 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.03/1.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.03/1.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.03/1.40 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.03/1.40 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.03/1.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.03/1.40 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 1.03/1.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.03/1.40 ,
% 1.03/1.40 [ ~( =( 'c_List_Olist__update'( X, Y, Z, T ), 'c_List_Olist_ONil'( T ) )
% 1.03/1.40 ), =( X, 'c_List_Olist_ONil'( T ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.03/1.40 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.03/1.40 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.03/1.40 ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.03/1.40 ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 1.03/1.40 =( 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 1.03/1.40 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =(
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =(
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.03/1.40 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z,
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =(
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.03/1.40 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.03/1.40 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.03/1.40 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.03/1.40 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.03/1.40 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.03/1.40 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.03/1.40 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.03/1.40 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.03/1.40 ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.03/1.40 X ) ), =( 'c_HOL_Ominus__class_Ominus'( Y, Y, X ),
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.03/1.40 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.03/1.40 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.03/1.40 ) ],
% 1.03/1.40 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.03/1.40 'c_HOL_Ominus__class_Ominus'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.03/1.40 ) ],
% 1.03/1.40 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.03/1.40 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.03/1.40 ) ],
% 1.03/1.40 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.03/1.40 'c_HOL_Ominus__class_Ominus'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.03/1.40 ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.03/1.40 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 1.03/1.40 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.03/1.40 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.03/1.40 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.03/1.40 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.03/1.40 ,
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.03/1.40 X ) ), ~( =( 'c_HOL_Ominus__class_Ominus'( Y, Z, X ),
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 1.03/1.40 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.03/1.40 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.03/1.40 ) ), =( Y, Z ) ],
% 1.03/1.40 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =(
% 1.03/1.40 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.03/1.40 ) ), =( Y, Z ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.03/1.40 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.03/1.40 Y ) ],
% 1.03/1.40 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.03/1.40 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.03/1.40 Y ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.03/1.40 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.03/1.40 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.03/1.40 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.03/1.40 Y ) ],
% 1.03/1.40 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.03/1.40 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.03/1.40 Y ) ],
% 1.03/1.40 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.03/1.40 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.03/1.40 Y ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.03/1.40 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.03/1.40 Y ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.03/1.40 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.03/1.40 Y ) ],
% 1.03/1.40 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ],
% 1.03/1.40 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.03/1.40 'tc_nat' ), 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( Y,
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.03/1.40 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.03/1.40 ), X, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'(
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.03/1.40 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_OCons'( T, U, Z )
% 1.03/1.40 ) ), =( X, T ) ],
% 1.03/1.40 [ ~( =( 'c_List_Olist_OCons'( X, Y, Z ), 'c_List_Olist_OCons'( T, U, Z )
% 1.03/1.40 ) ), =( Y, U ) ],
% 1.03/1.40 [ ~( =( 'c_Lambda_OdB_OAbs'( X ), hAPP( hAPP( 'c_Lambda_OdB_OApp', Y ),
% 1.03/1.40 Z ) ) ) ],
% 1.03/1.40 [ =( hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( 'tc_nat' ),
% 1.03/1.40 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ) ),
% 1.03/1.40 'c_HOL_Ominus__class_Ominus'( Z, Y, 'tc_nat' ) ),
% 1.03/1.40 'c_HOL_Ominus__class_Ominus'( hAPP( hAPP( 'c_Orderings_Oord__class_Omin'(
% 1.03/1.40 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.03/1.40 [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~(
% 1.03/1.40 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~( hBOOL( hAPP( X,
% 1.03/1.40 'c_HOL_Ominus__class_Ominus'( Y, Z, 'tc_nat' ) ) ) ) ],
% 1.03/1.40 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.03/1.40 [ =( 'c_List_Olist__update'( 'c_List_Olist__update'( X, Y, Z, T ), U, W
% 1.03/1.40 , T ), 'c_List_Olist__update'( 'c_List_Olist__update'( X, U, W, T ), Y, Z
% 1.03/1.40 , T ) ), =( Y, U ) ],
% 1.03/1.40 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =(
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), Y ) ],
% 1.03/1.40 [ ~( hBOOL( hAPP( X, Y ) ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.03/1.40 'c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1'( X, Z ), 'tc_nat' )
% 1.03/1.40 ), ~( hBOOL( hAPP( X, Z ) ) ), hBOOL( hAPP( X,
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.03/1.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( T, U, X ), X ), ~( 'c_lessequals'(
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.40 Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.03/1.40 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ) )
% 1.03/1.40 , ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.03/1.40 [ ~( =( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), 'c_Lambda_OdB_OAbs'(
% 1.03/1.40 Z ) ) ) ],
% 1.03/1.40 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.03/1.40 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.03/1.40 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.03/1.40 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.03/1.40 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.03/1.40 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.03/1.40 [ 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.03/1.40 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.03/1.40 [ =( 'c_List_Oappend'( 'c_List_Oreplicate'( X, Y, Z ),
% 1.03/1.40 'c_List_Olist_OCons'( Y, T, Z ), Z ), 'c_List_Olist_OCons'( Y,
% 1.03/1.40 'c_List_Oappend'( 'c_List_Oreplicate'( X, Y, Z ), T, Z ), Z ) ) ],
% 1.03/1.40 [ ~( =( 'c_Fun_Ocomp'( X, Y, Z, T, U ), 'c_Fun_Ocomp'( W, V0, V1, T, U )
% 1.03/1.40 ) ), =( hAPP( X, hAPP( Y, V2 ) ), hAPP( W, hAPP( V0, V2 ) ) ) ],
% 1.03/1.40 [ ~( =( hAPP( X, hAPP( Y, Z ) ), hAPP( T, hAPP( U, W ) ) ) ), =( hAPP(
% 1.03/1.40 'c_Fun_Ocomp'( X, Y, V0, V1, V2 ), Z ), hAPP( 'c_Fun_Ocomp'( T, U, V3, V1
% 1.03/1.40 , V4 ), W ) ) ],
% 1.03/1.40 [ =( 'c_List_Olist_ONil'( X ), 'c_List_Orev'( 'c_List_Olist_ONil'( X ),
% 1.03/1.40 X ) ) ],
% 1.03/1.40 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.03/1.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.03/1.40 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.03/1.40 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.03/1.40 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.03/1.40 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ],
% 1.03/1.40 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.03/1.40 'c_HOL_Oord__class_Oless'( 'c_Suc'( X ), Y, 'tc_nat' ) ) ],
% 1.03/1.40 [ 'c_HOL_Oord__class_Oless'( X, 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.03/1.40 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( hAPP(
% 1.03/1.40 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Otimes__class_Otimes'(
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.03/1.40 ],
% 1.03/1.40 [ ~( =( 'c_List_Oappend'( X, Y, Z ), 'c_List_Oappend'( T, U, Z ) ) ),
% 1.03/1.40 =( 'c_List_Otake'( 'c_Nat_Osize__class_Osize'( T, 'tc_List_Olist'( Z ) )
% 1.03/1.40 , X, Z ), T ), 'c_lessequals'( 'c_Nat_Osize__class_Osize'( X,
% 1.03/1.40 'tc_List_Olist'( Z ) ), 'c_Nat_Osize__class_Osize'( T, 'tc_List_Olist'( Z
% 1.03/1.40 ) ), 'tc_nat' ) ],
% 1.03/1.40 [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Orev'( X, Y ), 'tc_List_Olist'(
% 1.03/1.40 Y ) ), 'c_Nat_Osize__class_Osize'( X, 'tc_List_Olist'( Y ) ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.03/1.40 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.03/1.40 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( Z, Y, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.03/1.40 , Y, X ), X ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.03/1.40 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( Z, T, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.03/1.40 , T, X ), X ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.03/1.40 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.03/1.40 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), 'c_HOL_Otimes__class_Otimes'( Y
% 1.03/1.40 , T, X ), X ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.03/1.40 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( T, Z, X ), 'c_HOL_Otimes__class_Otimes'( T
% 1.03/1.40 , Y, X ), X ) ) ],
% 1.03/1.40 [ =( 'c_Lambda_Osubst'( hAPP( hAPP( 'c_Lambda_OdB_OApp', X ), Y ), Z, T
% 1.03/1.40 ), hAPP( hAPP( 'c_Lambda_OdB_OApp', 'c_Lambda_Osubst'( X, Z, T ) ),
% 1.03/1.40 'c_Lambda_Osubst'( Y, Z, T ) ) ) ],
% 1.03/1.40 [ ~( =( 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( 'c_Suc'( X ), Z, 'tc_nat' ) ) ), =( Y, Z )
% 1.03/1.40 ],
% 1.03/1.40 [ =( 'c_Suc'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'(
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ), X ), ~(
% 1.03/1.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.03/1.40 'tc_nat' ) ) ],
% 1.03/1.40 [ =( 'c_List_Olist__update'( 'c_List_Olist_OCons'( X, Y, Z ), 'c_Suc'( T
% 1.03/1.40 ), U, Z ), 'c_List_Olist_OCons'( X, 'c_List_Olist__update'( Y, T, U, Z )
% 1.03/1.40 , Z ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.03/1.40 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 1.03/1.40 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 1.03/1.40 'c_HOL_Oplus__class_Oplus'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.03/1.40 , X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ],
% 1.03/1.40 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, Y,
% 1.03/1.40 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.03/1.40 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.03/1.40 'tc_nat' ) ) ],
% 1.03/1.40 [ hBOOL( hAPP( hAPP( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.03/1.40 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ), T ) ), ~( hBOOL( hAPP( Z, T ) ) ),
% 1.03/1.40 ~( hBOOL( hAPP( Y, T ) ) ) ],
% 1.03/1.40 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'(
% 1.03/1.40 'c_Orderings_Oord__class_Omax'( Y, hAPP( hAPP(
% 1.03/1.40 'c_Orderings_Oord__class_Omin'( X ), Z ), T ), X ), hAPP( hAPP(
% 1.03/1.40 'c_Orderings_Oord__class_Omin'( X ), 'c_Orderings_Oord__class_Omax'( Y, Z
% 1.03/1.40 , X ) ), 'c_Orderings_Oord__class_Omax'( Y, T, X ) ), X ) ],
% 1.03/1.40 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.03/1.40 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.03/1.40 , U, X ) ) ), 'c_lessequals'( U, T, X ), ~( 'c_lessequals'( Z, Y, X ) ) ]
% 1.03/1.40 ,
% 1.03/1.40 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.03/1.40 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.03/1.40 , U, X ) ) ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( U, T, X ) ) ]
% 1.03/1.40 ,
% 1.03/1.40 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.03/1.40 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.03/1.40 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( T, U, X ), ~(
% 1.03/1.40 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.03/1.40 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =(
% 1.03/1.40 'c_HOL_Ominus__class_Ominus'( Y, Z, X ), 'c_HOL_Ominus__class_Ominus'( T
% 1.03/1.40 , U, X ) ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~(
% 1.03/1.40 'c_HOL_Oord__class_Oless'( T, U, X ) ) ],
% 1.03/1.40 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.03/1.40 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.03/1.40 T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y,
% 1.03/1.40 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.03/1.40 'c_Power_Opower__class_Opower'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ),
% 1.03/1.40 T, X ), 'c_HOL_Otimes__class_Otimes'( 'c_Power_Opower__class_Opower'( Y,
% 1.03/1.40 T, X ), 'c_Power_Opower__class_Opower'( Z, T, X ), X ) ) ],
% 1.03/1.40 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( 'c_List_Olistsum'(
% 1.03/1.40 'c_List_Oappend'( Y, Z, X ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.40 X ), 'c_List_Olistsum'( Y, X ) ), 'c_List_Olistsum'( Z, X ) ) ) ],
% 1.03/1.40 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.03/1.40 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ) ), Y ),
% 1.03/1.40 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.03/1.40 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ominus__class_Ominus'( X, 'c_Suc'( Y
% 1.03/1.40 ), 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.03/1.40 [ ~( =( 'c_List_Oappend'( X, 'c_List_Olist_OCons'( Y,
% 1.03/1.40 'c_List_Olist_ONil'( Z ), Z ), Z ), 'c_List_Oappend'( T,
% 1.03/1.40 'c_List_Olist_OCons'( U, 'c_List_Olist_ONil'( Z ), Z ), Z ) ) ), =( X, T
% 1.03/1.40 ) ],
% 1.03/1.40 [ ~( =( 'c_List_Oappend'( X, 'c_List_Olist_OCons'( Y,
% 1.03/1.40 'c_List_Olist_ONil'( Z ), Z ), Z ), 'c_List_Oappend'( T,
% 1.03/1.40 'c_List_Olist_OCons'( U, 'c_List_Olist_ONil'( Z ), Z ), Z ) ) ), =( Y, U
% 1.03/1.40 ) ],
% 1.03/1.40 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.03/1.40 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.03/1.40 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.03/1.40 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.03/1.40 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.03/1.40 'c_Orderings_Oord__class_Omax'( hAPP( hAPP(
% 1.03/1.40 'c_Orderings_Oord__class_Omin'( X ), Y ), Z ), T, X ), hAPP( hAPP(
% 1.03/1.40 'c_Orderings_Oord__class_Omin'( X ), 'c_Orderings_Oord__class_Omax'( Y, T
% 1.03/1.40 , X ) ), 'c_Orderings_Oord__class_Omax'( Z, T, X ) ) ) ],
% 1.03/1.40 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.03/1.40 'c_Orderings_Oord__class_Omax'( Y, hAPP( hAPP(
% 1.03/1.40 'c_Orderings_Oord__class_Omin'( X ), Z ), T ), X ), hAPP( hAPP(
% 1.03/1.40 'c_Orderings_Oord__class_Omin'( X ), 'c_Orderings_Oord__class_Omax'( Y, Z
% 1.03/1.40 , X ) ), 'c_Orderings_Oord__class_Omax'( Y, T, X ) ) ) ],
% 1.03/1.40 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.03/1.40 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T,
% 1.03/1.40 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'(
% 1.03/1.40 'c_Power_Opower__class_Opower'( Y, Z, X ), T, X ) ) ],
% 1.03/1.40 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.03/1.40 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.03/1.40 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.03/1.40 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 1.03/1.40 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 1.03/1.40 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.03/1.40 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.03/1.40 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.03/1.40 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 1.03/1.40 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.03/1.40 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 1.03/1.40 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.03/1.40 ,
% 1.03/1.40 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.03/1.40 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.03/1.40 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.03/1.40 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.03/1.40 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.03/1.40 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 1.03/1.40 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 1.03/1.40 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.03/1.40 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.03/1.40 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.03/1.40 ,
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.03/1.40 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.03/1.40 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'( Z,
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.03/1.40 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), X ), ~( 'c_lessequals'(
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.03/1.40 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( Y, Y, X ), X ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.03/1.40 , X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.03/1.40 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.03/1.40 , X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.03/1.40 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Otimes__class_Otimes'( Y, Z, X )
% 1.03/1.40 , X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.03/1.40 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.03/1.40 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.03/1.40 X, 'tc_nat' ) ), 'c_lessequals'( 'c_HOL_Otimes__class_Otimes'( X,
% 1.03/1.40 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ), 'tc_nat' ), Y, 'tc_nat' )
% 1.03/1.40 ],
% 1.03/1.40 [ =( 'c_List_Oappend'( 'c_List_Olist_ONil'( X ), 'c_List_Olist_ONil'( X
% 1.03/1.40 ), X ), 'c_List_Olist_ONil'( X ) ) ],
% 1.03/1.40 [ =( 'c_List_Olist__update'( 'c_List_Olist__update'( X, Y, Z, T ), Y, U
% 1.03/1.40 , T ), 'c_List_Olist__update'( X, Y, U, T ) ) ],
% 1.03/1.40 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( 'c_Suc'( X ),
% 1.03/1.40 'c_Suc'( Y ), 'tc_nat' ) ) ],
% 1.03/1.40 [ 'c_lessequals'( 'c_Suc'( X ), 'c_Suc'( Y ), 'tc_nat' ), ~(
% 1.03/1.40 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.03/1.40 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =(
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.03/1.40 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 1.03/1.40 T, X ), X ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.03/1.40 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, T,
% 1.03/1.40 X ), Z, X ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z, X ), T
% 1.03/1.40 , X ), 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z,
% 1.03/1.40 T, X ), X ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.03/1.40 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.03/1.40 X ), T, X ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.03/1.40 , X ), 'c_HOL_Otimes__class_Otimes'( Z, 'c_HOL_Otimes__class_Otimes'( Y,
% 1.03/1.40 T, X ), X ) ) ],
% 1.03/1.40 [ =( 'c_List_Oappend'( 'c_List_Oappend'( X, Y, Z ), T, Z ),
% 1.03/1.40 'c_List_Oappend'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ],
% 1.03/1.40 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( X, Y,
% 1.03/1.40 'tc_nat' ), Z, 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.03/1.40 [ =( 'c_List_Oappend'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 1.03/1.40 'c_List_Oappend'( 'c_List_Oappend'( X, Y, T ), Z, T ) ) ],
% 1.03/1.40 [ =( 'c_List_Oappend'( 'c_List_Oappend'( X, Y, Z ), T, Z ),
% 1.03/1.40 'c_List_Oappend'( X, 'c_List_Oappend'( Y, T, Z ), Z ) ) ],
% 1.03/1.40 [ =( 'c_List_Oappend'( X, 'c_List_Oappend'( Y, Z, T ), T ),
% 1.03/1.40 'c_List_Oappend'( 'c_List_Oappend'( X, Y, T ), Z, T ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( Y, 'c_HOL_Otimes__class_Otimes'( Z, T, X )
% 1.03/1.40 , X ), 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Otimes__class_Otimes'( Y, Z,
% 1.03/1.40 X ), T, X ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.03/1.40 , Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( Y, T, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 1.03/1.40 Z, T, X ) ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =(
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.03/1.40 , Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( Y, T, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 1.03/1.40 Z, T, X ) ) ) ],
% 1.03/1.40 [ =( 'c_HOL_Otimes__class_Otimes'( hAPP( hAPP(
% 1.03/1.40 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.03/1.40 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ),
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( Y, Z, 'tc_nat' ) ) ) ],
% 1.03/1.40 [ =( 'c_HOL_Otimes__class_Otimes'( X, hAPP( hAPP(
% 1.03/1.40 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), hAPP( hAPP(
% 1.03/1.40 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X,
% 1.03/1.40 Y, 'tc_nat' ) ), 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ) ]
% 1.03/1.40 ,
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.03/1.40 X ), Z ), T ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( Y, Z, X ) ), 'c_HOL_Otimes__class_Otimes'(
% 1.03/1.40 Y, T, X ) ) ) ],
% 1.03/1.40 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.03/1.40 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.03/1.40 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.03/1.40 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.03/1.40 [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X, 'tc_nat' ) ]
% 1.03/1.40 ,
% 1.03/1.40 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.03/1.40 'c_lessequals'( Z, Y, X ) ],
% 1.03/1.40 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.03/1.40 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.03/1.40 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.03/1.40 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.03/1.40 'c_Nat_Osemiring__1__class_Oof__nat__aux'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.03/1.40 'tc_nat' ), Z, X ), Z ) ],
% 1.03/1.40 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 1.03/1.40 'v_sko__List__Xlexn__Xinduct__1'( X ) ) ), ~( hBOOL( hAPP( X,
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.03/1.40 [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( hBOOL(
% 1.03/1.40 hAPP( X, 'c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1'( X ) ) ) ), ~(
% 1.03/1.40 hBOOL( hAPP( X, Y ) ) ) ],
% 1.03/1.40 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.03/1.40 [ =( 'c_Lambda_Oliftn'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, Y ),
% 1.03/1.40 X ) ],
% 1.03/1.40 [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ), ~( hBOOL( hAPP( X
% 1.03/1.40 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.03/1.40 [ ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), hBOOL(
% 1.03/1.40 hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.03/1.40 'tc_nat' ), 'tc_nat' ) ) ) ],
% 1.03/1.40 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.03/1.40 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.03/1.40 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.03/1.40 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.03/1.40 [ =( 'c_Nat_Onat_Onat__rec'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.03/1.40 ), Z ), X ) ],
% 1.03/1.40 [ hBOOL( hAPP( X, 'c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1'(
% 1.03/1.40 X, Y ) ) ), ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.03/1.40 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.03/1.40 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.03/1.40 [ ~( =( 'c_HOL_Ominus__class_Ominus'( X, Y, 'tc_nat' ),
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =(
% 1.03/1.40 'c_HOL_Ominus__class_Ominus'( Y, X, 'tc_nat' ),
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ],
% 1.03/1.40 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.03/1.40 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 1.03/1.40 'c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1'( X ) ) ), ~( hBOOL( hAPP( X
% 1.03/1.40 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.03/1.40 [ =( 'c_HOL_Otimes__class_Otimes'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.03/1.40 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.03/1.40 [ =( 'c_HOL_Otimes__class_Otimes'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.03/1.40 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.03/1.40 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.03/1.40 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.03/1.40 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.03/1.40 [ =( 'c_Nat_Onat_Onat__case'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.03/1.40 ), Z ), X ) ],
% 1.03/1.40 [ =( 'c_Nat_Onat_Onat__case'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.03/1.40 ), Z ), X ) ],
% 1.03/1.40 [ =( hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( 'tc_nat' ), X ),
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.03/1.40 'tc_nat' ) ) ],
% 1.03/1.40 [ =( hAPP( hAPP( 'c_Orderings_Oord__class_Omin'( 'tc_nat' ),
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.03/1.40 'tc_nat' ) ) ],
% 1.03/1.40 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( Z, Y, 'tc_nat' ) ) ), =( Y,
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 1.03/1.40 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( X,
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 1.03/1.40 [ ~( =( 'c_HOL_Otimes__class_Otimes'( X, Y, 'tc_nat' ),
% 1.03/1.40 'c_HOL_Otimes__class_Otimes'( X, Z, 'tc_nat' ) ) ), =( Y, Z ), =( X,
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.03/1.40 [ =( 'c_HOL_Ominus__class_Ominus'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.03/1.40 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.03/1.40 [ =( 'c_HOL_Ominus__class_Ominus'( X, X, 'tc_nat' ),
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.03/1.40 [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 1.03/1.40 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.03/1.40 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 1.03/1.40 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.03/1.40 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X,
% 1.03/1.40 'v_sko__List__Xreplicate__Xinduct__1'( X ) ) ), ~( hBOOL( hAPP( X,
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.03/1.40 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.03/1.40 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.03/1.40 [ ~( hBOOL( hAPP( X, 'c_Nat_Onat_Onat__case'( Y, Z,
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 't_a' ) ) ) ), hBOOL( hAPP( X, Y
% 1.03/1.40 ) ) ],
% 1.03/1.40 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, 'v_sko__Nat__Xnat__Xinducts__1'(
% 1.03/1.40 X ) ) ), ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) )
% 1.03/1.40 ],
% 1.03/1.40 [ =( 'c_Nitpick_Onat__gcd'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.03/1.40 , X ) ],
% 1.03/1.40 [ =( 'c_nat_Onat__size'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.03/1.40 [ =( 'c_String_Ochar_Ochar__size'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.03/1.40 'tc_nat' ) ) ],
% 1.03/1.40 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.03/1.40 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.03/1.40 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, 'v_sko__Nat__Xnat__Xinduct__1'(
% 1.03/1.40 X ) ) ), ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) )
% 1.03/1.40 ],
% 1.03/1.40 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.03/1.40 ), 'tc_nat' ) ) ],
% 1.03/1.40 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.03/1.40 ), 'tc_nat' ) ) ],
% 1.03/1.40 [ =( 'c_Orderings_Obot__class_Obot'( 'tc_nat' ),
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.03/1.40 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, 'v_sko__List__Xupt__Xinduct__1'(
% 1.03/1.40 X ) ) ), ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) )
% 1.03/1.40 ],
% 1.03/1.40 [ =( 'c_List_Odrop'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, Y ), X )
% 1.03/1.40 ],
% 1.03/1.40 [ =( 'c_HOL_Ominus__class_Ominus'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.03/1.40 ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.03/1.40 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.03/1.40 'c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1'( X ) ) ) ), ~( hBOOL(
% 1.03/1.40 hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.03/1.40 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' )
% 1.03/1.40 ],
% 1.03/1.40 [ =( 'c_Nat_Osize__class_Osize'( X, 'tc_String_Ochar' ),
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.03/1.40 [ =( 'c_List_Oreplicate'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, Y )
% 1.03/1.40 , 'c_List_Oreplicate'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, Y ) ) ]
% 1.03/1.40 ,
% 1.03/1.40 [ =( 'c_Orderings_Oord__class_Omax'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.03/1.40 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.03/1.40 [ =( 'c_Orderings_Oord__class_Omax'( 'c_HOL_Ozero__class_Ozero'(
% 1.03/1.40 'tc_nat' ), X, 'tc_nat' ), X ) ],
% 1.03/1.40 [ ~( =( 'c_List_Oreplicate'( X, Y, Z ), 'c_List_Oreplicate'( T, U, Z ) )
% 1.03/1.40 ), =( Y, U ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.03/1.40 [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.03/1.40 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 1.03/1.40 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.03/1.40 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ),
% 1.03/1.40 ~( 'c_Groebner__Basis_Ogb__semiring'( T, U, X, W, Z, V0 ) ) ],
% 1.03/1.40 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( 'c_List_Olistsum'(
% 1.03/1.40 'c_List_Omap'( 'c_COMBK'( 'c_HOL_Ozero__class_Ozero'( X ), X, Y ), Z, Y,
% 1.03/1.40 X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.03/1.40 [ ~( =( 'c_List_Omap'( X, Y, Z, T ), 'c_List_Olist_ONil'( T ) ) ), =( Y
% 1.03/1.40 , 'c_List_Olist_ONil'( Z ) ) ],
% 1.03/1.40 [ =( 'c_List_Odrop'( X, 'c_List_Omap'( Y, Z, T, U ), U ), 'c_List_Omap'(
% 1.03/1.40 Y, 'c_List_Odrop'( X, Z, T ), T, U ) ) ],
% 1.03/1.40 [ ~( =( hAPP( X, 'c_List_Osko__List__Xmap__idI__1__1'( X, Y, Z ) ),
% 1.03/1.40 'c_List_Osko__List__Xmap__idI__1__1'( X, Y, Z ) ) ), =( 'c_List_Omap'( X
% 1.03/1.40 , Y, Z, Z ), Y ) ],
% 1.03/1.40 [ 'c_List_Odistinct'( X, Y ), ~( 'c_List_Odistinct'( 'c_List_Omap'( Z, X
% 1.03/1.40 , Y, T ), T ) ) ],
% 1.03/1.40 [ =( 'c_List_Omap'( X, 'c_List_Oappend'( Y, Z, T ), T, U ),
% 1.03/1.40 'c_List_Oappend'( 'c_List_Omap'( X, Y, T, U ), 'c_List_Omap'( X, Z, T, U
% 1.03/1.40 ), U ) ) ],
% 1.03/1.40 [ ~( =( 'c_List_Omap'( X, Y, Z, T ), 'c_List_Omap'( X, U, Z, T ) ) ),
% 1.03/1.40 =( 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z ) ),
% 1.03/1.40 'c_Nat_Osize__class_Osize'( U, 'tc_List_Olist'( Z ) ) ) ],
% 1.03/1.40 [ ~( =( 'c_List_Olist_ONil'( X ), 'c_List_Omap'( Y, Z, T, X ) ) ), =( Z
% 1.03/1.40 , 'c_List_Olist_ONil'( T ) ) ],
% 1.03/1.40 [ =( 'c_List_Omap'( X, 'c_List_Oreplicate'( Y, Z, T ), T, U ),
% 1.03/1.40 'c_List_Oreplicate'( Y, hAPP( X, Z ), U ) ) ],
% 1.03/1.40 [ =( 'c_Nat_Osize__class_Osize'( 'c_List_Omap'( X, Y, Z, T ),
% 1.03/1.40 'tc_List_Olist'( T ) ), 'c_Nat_Osize__class_Osize'( Y, 'tc_List_Olist'( Z
% 1.03/1.40 ) ) ) ],
% 1.03/1.40 [ =( 'c_List_Orotate'( X, 'c_List_Omap'( Y, Z, T, U ), U ),
% 1.03/1.40 'c_List_Omap'( Y, 'c_List_Orotate'( X, Z, T ), T, U ) ) ],
% 1.03/1.40 [ =( 'c_List_Orev'( 'c_List_Omap'( X, Y, Z, T ), T ), 'c_List_Omap'( X,
% 1.03/1.40 'c_List_Orev'( Y, Z ), Z, T ) ) ],
% 1.03/1.40 [ ~( =( hAPP( X, 'c_List_Osko__List__Xmap__ext__1__1'( X, Y, Z, T, U ) )
% 1.03/1.40 , hAPP( Y, 'c_List_Osko__List__Xmap__ext__1__1'( X, Y, Z, T, U ) ) ) ),
% 1.03/1.40 =( 'c_List_Omap'( X, Z, T, U ), 'c_List_Omap'( Y, Z, T, U ) ) ],
% 1.03/1.40 [ =( 'c_List_Otake'( X, 'c_List_Omap'( Y, Z, T, U ), U ), 'c_List_Omap'(
% 1.03/1.40 Y, 'c_List_Otake'( X, Z, T ), T, U ) ) ],
% 1.03/1.40 [ =( 'c_List_Omap'( X, 'c_List_Olist_ONil'( Y ), Y, Z ),
% 1.03/1.40 'c_List_Olist_ONil'( Z ) ) ],
% 1.03/1.40 [ =( 'c_List_Omap'( X, 'c_List_Omap'( Y, Z, T, U ), U, W ),
% 1.03/1.40 'c_List_Omap'( 'c_Fun_Ocomp'( X, Y, U, W, T ), Z, T, W ) ) ],
% 1.03/1.40 [ =( 'c_List_Omap'( X, 'c_List_Olist_OCons'( Y, Z, T ), T, U ),
% 1.03/1.40 'c_List_Olist_OCons'( hAPP( X, Y ), 'c_List_Omap'( X, Z, T, U ), U ) ) ]
% 1.03/1.40 ,
% 1.03/1.40 [ =( 'c_List_Olist_OCons'( hAPP( X, Y ), 'c_List_Omap'( X, Z, T, U ), U
% 1.03/1.40 ), 'c_List_Omap'( X, 'c_List_Olist_OCons'( Y, Z, T ), T, U ) ) ],
% 1.03/1.40 [ =( 'c_List_Omap'( X, 'c_List_Olist_OCons'( Y, Z, T ), T, U ),
% 1.03/1.40 'c_List_Olist_OCons'( hAPP( X, Y ), 'c_List_Omap'( X, Z, T, U ), U ) ) ]
% 1.03/1.40 ,
% 1.03/1.40 [ ~( =( hAPP( X, 'c_List_Osko__List__Xmap__cong__1__1'( X, Y, Z, T, U )
% 1.03/1.40 ), hAPP( Y, 'c_List_Osko__List__Xmap__cong__1__1'( X, Y, Z, T, U ) ) ) )
% 1.03/1.40 , =( 'c_List_Omap'( X, Z, T, U ), 'c_List_Omap'( Y, Z, T, U ) ) ],
% 1.03/1.40 [ ~( =( hAPP( X, 'c_List_Osko__List__Xmap__eq__conv__1__1'( X, Y, Z, T,
% 1.03/1.40 U ) ), hAPP( Y, 'c_List_Osko__List__Xmap__eq__conv__1__1'( X, Y, Z, T, U
% 1.03/1.40 ) ) ) ), =( 'c_List_Omap'( X, Z, T, U ), 'c_List_Omap'( Y, Z, T, U ) ) ]
% 1.03/1.40 ,
% 1.03/1.40 [ =( 'c_List_Omap'( X, 'c_List_Olist__update'( Y, Z, T, U ), U, W ),
% 1.03/1.40 'c_List_Olist__update'( 'c_List_Omap'( X, Y, U, W ), Z, hAPP( X, T ), W )
% 1.03/1.40 ) ],
% 1.03/1.40 [ =( 'c_List_Olist_ONil'( X ), 'c_List_Omap'( Y, 'c_List_Olist_ONil'( Z
% 1.03/1.40 ), Z, X ) ) ],
% 1.03/1.40 [ 'c_List_Olistsp'( X, 'c_List_Oappend'( Y, Z, T ), T ), ~(
% 1.03/1.40 'c_List_Olistsp'( X, Z, T ) ), ~( 'c_List_Olistsp'( X, Y, T ) ) ],
% 1.03/1.40 [ 'c_List_Olistsp'( X, Y, Z ), ~( hBOOL( hAPP( X,
% 1.03/1.40 'c_List_Osko__List__Xin__listsp__conv__set__1__1'( X, Y, Z ) ) ) ) ],
% 1.03/1.40 [ 'c_List_Olistsp'( hAPP( hAPP(
% 1.03/1.40 'c_Lattices_Olower__semilattice__class_Oinf'( 'tc_fun'( X, 'tc_bool' ) )
% 1.03/1.40 , Y ), Z ), T, X ), ~( 'c_List_Olistsp'( Z, T, X ) ), ~( 'c_List_Olistsp'(
% 1.03/1.40 Y, T, X ) ) ],
% 1.03/1.40 [ 'c_List_Olistsp'( X, 'c_List_Olist_ONil'( Y ), Y ) ],
% 1.03/1.40 [ 'c_List_Olistsp'( X, Y, Z ), ~( 'c_List_Olistsp'( X, 'c_List_Oappend'(
% 1.03/1.40 T, Y, Z ), Z ) ) ],
% 1.03/1.40 [ 'c_List_Olistsp'( X, Y, Z ), ~( 'c_List_Olistsp'( X, 'c_List_Oappend'(
% 1.03/1.40 Y, T, Z ), Z ) ) ],
% 1.03/1.40 [ hBOOL( hAPP( 'c_InductTermi_OIT', 'c_Lambda_OdB_OAbs'( X ) ) ), ~(
% 1.03/1.40 hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 1.03/1.40 [ =( hAPP( hAPP( 'c_Lambda_Olift', hAPP( hAPP( 'c_Lambda_OdB_OApp', X )
% 1.03/1.40 , Y ) ), Z ), hAPP( hAPP( 'c_Lambda_OdB_OApp', hAPP( hAPP(
% 1.03/1.40 'c_Lambda_Olift', X ), Z ) ), hAPP( hAPP( 'c_Lambda_Olift', Y ), Z ) ) )
% 1.03/1.40 ],
% 1.03/1.40 [ =( 'c_Lambda_Osubst'( hAPP( hAPP( 'c_Lambda_Olift', X ), Y ), Z, Y ),
% 1.03/1.40 X ) ],
% 1.03/1.40 [ 'c_Lambda_Obeta'( hAPP( hAPP( 'c_Lambda_Olift', X ), Y ), hAPP( hAPP(
% 1.03/1.40 'c_Lambda_Olift', Z ), Y ) ), ~( 'c_Lambda_Obeta'( X, Z ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.03/1.40 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.03/1.40 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.03/1.40 ), =( 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.03/1.40 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.03/1.40 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.03/1.40 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.03/1.40 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.03/1.40 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.03/1.40 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.03/1.40 ), ~( =( 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.03/1.40 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.03/1.40 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.03/1.40 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 1.03/1.40 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.03/1.40 [ =( hAPP( hAPP( 'c_Lambda_Olift', 'c_List_Ofoldl'( 'c_Lambda_OdB_OApp'
% 1.03/1.40 , X, Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ), Z ), 'c_List_Ofoldl'(
% 1.03/1.40 'c_Lambda_OdB_OApp', hAPP( hAPP( 'c_Lambda_Olift', X ), Z ),
% 1.03/1.40 'c_List_Omap'( 'c_COMBC'( 'c_Lambda_Olift', Z, 'tc_Lambda_OdB', 'tc_nat'
% 1.03/1.40 , 'tc_Lambda_OdB' ), Y, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ),
% 1.03/1.40 'tc_Lambda_OdB', 'tc_Lambda_OdB' ) ) ],
% 1.03/1.40 [ 'c_Type_Otypings'( 'c_Type_Oshift'( X, Y, Z, 'tc_Type_Otype' ),
% 1.03/1.40 'c_List_Omap'( 'c_COMBC'( 'c_Lambda_Olift', Y, 'tc_Lambda_OdB', 'tc_nat'
% 1.03/1.40 , 'tc_Lambda_OdB' ), T, 'tc_Lambda_OdB', 'tc_Lambda_OdB' ), U ), ~(
% 1.03/1.40 'c_Type_Otypings'( X, T, U ) ) ],
% 1.03/1.40 [ hBOOL( hAPP( 'c_InductTermi_OIT', hAPP( hAPP( 'c_Lambda_Olift', X ), Y
% 1.03/1.40 ) ) ), ~( hBOOL( hAPP( 'c_InductTermi_OIT', X ) ) ) ],
% 1.03/1.40 [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), Y ) ) ]
% 1.03/1.40 ,
% 1.03/1.40 [ 'c_List_Olistsp'( 'c_InductTermi_OIT', 'v_ts', 'tc_Lambda_OdB' ) ]
% 1.03/1.40 ,
% 1.03/1.40 [ ~( 'c_List_Olistsp'( 'c_InductTermi_OIT', 'c_List_Omap'( 'c_COMBC'(
% 1.03/1.40 'c_Lambda_Olift', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_Lambda_OdB'
% 1.03/1.40 , 'tc_nat', 'tc_Lambda_OdB' ), 'v_ts', 'tc_Lambda_OdB', 'tc_Lambda_OdB' )
% 1.03/1.40 , 'tc_Lambda_OdB' ) ) ],
% 1.03/1.40 [ 'class_Lattices_Olower__semilattice'( 'tc_fun'( X, Y ) ), ~(
% 1.03/1.40 'class_Lattices_Olattice'( Y ) ) ],
% 1.03/1.40 [ 'class_Lattices_Obounded__lattice'( 'tc_fun'( X, Y ) ), ~(
% 1.03/1.40 'class_Lattices_Obounded__lattice'( Y ) ) ],
% 1.03/1.40 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 1.03/1.40 'class_Orderings_Opreorder'( Y ) ) ],
% 1.03/1.40 [ 'class_Lattices_Olattice'( 'tc_fun'( X, Y ) ), ~(
% 1.03/1.40 'class_Lattices_Olattice'( Y ) ) ],
% 1.03/1.40 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 1.03/1.40 'class_Orderings_Oorder'( Y ) ) ],
% 1.03/1.40 [ 'class_Orderings_Obot'( 'tc_fun'( X, Y ) ), ~( 'class_Orderings_Obot'(
% 1.03/1.40 Y ) ) ],
% 1.03/1.40 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.03/1.40 ],
% 1.03/1.40 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.03/1.40 ) ],
% 1.03/1.40 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.03/1.40 ],
% 1.03/1.40 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 1.03/1.40 ,
% 1.03/1.40 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.03/1.40 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 1.03/1.40 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.03/1.40 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.03/1.40 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.03/1.40 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 1.03/1.40 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 1.03/1.40 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.03/1.40 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.03/1.40 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.03/1.40 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.03/1.40 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.03/1.40 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.03/1.40 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.03/1.40 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.03/1.40 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.03/1.40 [ 'class_OrderedGroup_Osemigroup__add'( 'tc_nat' ) ],
% 1.03/1.40 [ 'class_Lattices_Olower__semilattice'( 'tc_nat' ) ],
% 1.03/1.40 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.03/1.40 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.03/1.40 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.03/1.40 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.03/1.40 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.03/1.40 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.03/1.40 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.03/1.40 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.03/1.40 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 1.03/1.40 [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ],
% 1.03/1.40 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.03/1.40 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.03/1.40 [ 'class_Lattices_Olattice'( 'tc_nat' ) ],
% 1.03/1.40 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.03/1.40 [ 'class_Orderings_Obot'( 'tc_nat' ) ],
% 1.03/1.40 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 1.03/1.40 [ 'class_Lattices_Olower__semilattice'( 'tc_bool' ) ],
% 1.03/1.40 [ 'class_Lattices_Obounded__lattice'( 'tc_bool' ) ],
% 1.03/1.40 [ 'class_Orderings_Opreorder'( 'tc_bool' ) ],
% 1.03/1.40 [ 'class_Lattices_Olattice'( 'tc_bool' ) ],
% 1.03/1.40 [ 'class_Orderings_Oorder'( 'tc_bool' ) ],
% 1.03/1.40 [ 'class_Orderings_Obot'( 'tc_bool' ) ],
% 1.03/1.40 [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), Y ) ) ]
% 1.03/1.40 ,
% 1.03/1.40 [ =( 'c_COMBB'( X, Y, Z, T, U, W ), hAPP( X, hAPP( Y, Z ) ) ) ],
% 1.03/1.40 [ 'c_fequal'( X, X, Y ) ],
% 1.03/1.40 [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ]
% 1.03/1.40 ] .
% 1.03/1.40
% 1.03/1.40
% 1.03/1.40 percentage equality = 0.306227, percentage horn = 0.903704
% 1.03/1.40 This is a problem with some equality
% 1.03/1.40
% 1.03/1.40
% 1.03/1.40
% 1.03/1.40 Options Used:
% 1.03/1.40
% 1.03/1.40 useres = 1
% 1.03/1.40 useparamod = 1
% 1.03/1.40 useeqrefl = 1
% 1.03/1.40 useeqfact = 1
% 1.03/1.40 usefactor = 1
% 1.03/1.40 usesimpsplitting = 0
% 1.03/1.40 usesimpdemod = 5
% 1.03/1.40 usesimpres = 3
% 1.03/1.40
% 1.03/1.40 resimpinuse = 1000
% 1.03/1.40 resimpclauses = 20000
% 1.03/1.40 substype = eqrewr
% 1.03/1.40 backwardsubs = 1
% 1.03/1.40 selectoldest = 5
% 1.03/1.40
% 1.03/1.40 litorderings [0] = split
% 1.03/1.40 litorderings [1] = extend the termordering, first sorting on arguments
% 1.03/1.40
% 1.03/1.40 termordering = kbo
% 1.03/1.40
% 1.03/1.40 litapriori = 0
% 1.03/1.40 termapriori = 1
% 1.03/1.40 litaposteriori = 0
% 1.03/1.40 termaposteriori = 0
% 1.03/1.40 demodaposteriori = 0
% 1.03/1.40 ordereqreflfact = 0
% 1.03/1.40
% 1.03/1.40 litselect = negord
% 1.03/1.40
% 1.03/1.40 maxweight = 15
% 1.03/1.40 maxdepth = 30000
% 1.03/1.40 maxlength = 115
% 1.03/1.40 maxnrvars = 195
% 1.03/1.40 excuselevel = 1
% 1.03/1.40 increasemaxweight = 1
% 1.03/1.40
% 1.03/1.40 maxselected = 10000000
% 1.03/1.40 maxnrclauses = 10000000
% 1.03/1.40
% 1.03/1.40 showgenerated = 0
% 1.03/1.40 showkept = 0
% 1.03/1.40 showselected = 0
% 1.03/1.40 showdeleted = 0
% 1.03/1.40 showresimp = 1
% 1.03/1.40 showstatus = 2000
% 1.03/1.40
% 1.03/1.40 prologoutput = 1
% 1.03/1.40 nrgoals = 5000000
% 1.03/1.40 totalproof = 1
% 1.03/1.40
% 1.03/1.40 Symbols occurring in the translation:
% 1.03/1.40
% 1.03/1.40 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.03/1.40 . [1, 2] (w:1, o:184, a:1, s:1, b:0),
% 1.03/1.40 ! [4, 1] (w:0, o:105, a:1, s:1, b:0),
% 1.03/1.40 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.03/1.40 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.03/1.40 'c_List_Oappend' [42, 3] (w:1, o:219, a:1, s:1, b:0),
% 1.03/1.40 'tc_nat' [46, 0] (w:1, o:34, a:1, s:1, b:0),
% 1.03/1.40 'c_HOL_Otimes__class_Otimes' [47, 3] (w:1, o:220, a:1, s:1, b:0),
% 1.03/1.40 'c_Divides_Odiv__class_Odiv' [48, 3] (w:1, o:222, a:1, s:1, b:0),
% 1.03/1.40 'c_HOL_Ozero__class_Ozero' [49, 1] (w:1, o:110, a:1, s:1, b:0),
% 1.03/1.40 'c_HOL_Oord__class_Oless' [50, 3] (w:1, o:223, a:1, s:1, b:0),
% 1.03/1.40 'c_HOL_Ominus__class_Ominus' [53, 3] (w:1, o:224, a:1, s:1, b:0),
% 1.03/1.40 'c_Suc' [54, 1] (w:1, o:112, a:1, s:1, b:0),
% 1.03/1.40 'c_HOL_Oplus__class_Oplus' [55, 1] (w:1, o:113, a:1, s:1, b:0),
% 1.03/1.40 hAPP [56, 2] (w:1, o:209, a:1, s:1, b:0),
% 1.03/1.40 'c_lessequals' [57, 3] (w:1, o:225, a:1, s:1, b:0),
% 1.03/1.40 'c_List_Odrop' [58, 3] (w:1, o:226, a:1, s:1, b:0),
% 1.03/1.40 'tc_List_Olist' [59, 1] (w:1, o:114, a:1, s:1, b:0),
% 1.03/1.40 'c_Nat_Osize__class_Osize' [60, 2] (w:1, o:210, a:1, s:1, b:0),
% 1.03/1.40 'c_List_Oreplicate' [62, 3] (w:1, o:227, a:1, s:1, b:0),
% 1.03/1.40 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [64, 1]
% 1.03/1.40 (w:1, o:116, a:1, s:1, b:0),
% 1.03/1.40 'class_OrderedGroup_Ocomm__monoid__add' [65, 1] (w:1, o:117, a:1, s:1
% 1.03/1.40 , b:0),
% 1.03/1.40 'c_List_Olist_OCons' [70, 3] (w:1, o:228, a:1, s:1, b:0),
% 1.03/1.40 'class_Ring__and__Field_Oordered__semidom' [71, 1] (w:1, o:121, a:1
% 1.03/1.40 , s:1, b:0),
% 1.03/1.40 'c_Nat_Osemiring__1__class_Oof__nat' [72, 2] (w:1, o:211, a:1, s:1
% 1.03/1.40 , b:0),
% 1.03/1.40 'c_Lambda_Osubst' [76, 3] (w:1, o:229, a:1, s:1, b:0),
% 1.03/1.40 'c_Lambda_Obeta' [78, 2] (w:1, o:212, a:1, s:1, b:0),
% 1.03/1.40 'class_Orderings_Olinorder' [79, 1] (w:1, o:122, a:1, s:1, b:0),
% 1.03/1.40 'c_Orderings_Oord__class_Omin' [81, 1] (w:1, o:123, a:1, s:1, b:0),
% 1.03/1.40 'class_Ring__and__Field_Oidom' [83, 1] (w:1, o:124, a:1, s:1, b:0),
% 1.03/1.40 'class_Int_Onumber__ring' [84, 1] (w:1, o:125, a:1, s:1, b:0),
% 1.03/1.40 'c_Orderings_Oord__class_Omax' [85, 3] (w:1, o:230, a:1, s:1, b:0),
% 1.03/1.40 'class_OrderedGroup_Opordered__ab__group__add' [86, 1] (w:1, o:126
% 1.03/1.40 , a:1, s:1, b:0),
% 1.03/1.40 'c_Power_Opower__class_Opower' [87, 3] (w:1, o:231, a:1, s:1, b:0),
% 1.03/1.40 'class_Ring__and__Field_Oring' [88, 1] (w:1, o:127, a:1, s:1, b:0),
% 1.03/1.40 hBOOL [92, 1] (w:1, o:128, a:1, s:1, b:0),
% 1.03/1.40 'v_sko__Nat__Xnat__Xinduct__1' [93, 1] (w:1, o:129, a:1, s:1, b:0),
% 1.03/1.40 'c_List_Olist_ONil' [94, 1] (w:1, o:130, a:1, s:1, b:0),
% 1.03/1.40 'c_List_Otake' [95, 3] (w:1, o:234, a:1, s:1, b:0),
% 1.03/1.40 'class_Ring__and__Field_Oordered__semiring__strict' [96, 1] (w:1, o:
% 1.03/1.40 131, a:1, s:1, b:0),
% 1.03/1.40 'class_Ring__and__Field_Osemiring__0' [101, 1] (w:1, o:135, a:1, s:1
% 1.03/1.40 , b:0),
% 1.03/1.40 'class_Power_Opower' [102, 1] (w:1, o:155, a:1, s:1, b:0),
% 1.03/1.40 'c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1' [105, 1] (w:1
% 1.03/1.40 , o:156, a:1, s:1, b:0),
% 1.03/1.40 'class_Orderings_Obot' [106, 1] (w:1, o:136, a:1, s:1, b:0),
% 1.03/1.40 'c_Orderings_Obot__class_Obot' [107, 1] (w:1, o:157, a:1, s:1, b:0),
% 1.03/1.40
% 1.03/1.40 'c_Nat_Onat_Onat__rec' [110, 4] (w:1, o:240, a:1, s:1, b:0),
% 1.03/1.40 'c_List_Odistinct' [111, 2] (w:1, o:213, a:1, s:1, b:0),
% 1.03/1.40 'c_Groebner__Basis_Ogb__semiring' [118, 6] (w:1, o:252, a:1, s:1, b:0
% 1.03/1.40 ),
% 1.03/1.40 'c_List_Orev' [119, 2] (w:1, o:214, a:1, s:1, b:0),
% 1.03/1.40 'v_sko__List__Xupt__Xinduct__1' [120, 1] (w:1, o:158, a:1, s:1, b:0)
% 1.03/1.40 ,
% 1.03/1.40 'v_sko__List__Xreplicate__Xinduct__1' [121, 1] (w:1, o:159, a:1, s:1
% 1.03/1.40 , b:0),
% 1.03/1.40 'class_Ring__and__Field_Opordered__ring' [122, 1] (w:1, o:163, a:1
% 1.03/1.40 , s:1, b:0),
% 1.03/1.40 'class_Ring__and__Field_Oordered__ring__strict' [123, 1] (w:1, o:120
% 1.03/1.40 , a:1, s:1, b:0),
% 1.03/1.40 'class_Lattices_Obounded__lattice' [124, 1] (w:1, o:164, a:1, s:1, b:
% 1.03/1.40 0),
% 1.03/1.40 'c_Lattices_Olower__semilattice__class_Oinf' [125, 1] (w:1, o:165, a:
% 1.03/1.40 1, s:1, b:0),
% 1.03/1.40 'class_Ring__and__Field_Ocomm__semiring__1' [126, 1] (w:1, o:166, a:1
% 1.03/1.40 , s:1, b:0),
% 1.03/1.40 'class_OrderedGroup_Osemigroup__add' [128, 1] (w:1, o:137, a:1, s:1
% 1.03/1.40 , b:0),
% 1.03/1.40 'c_List_Ofoldl' [129, 5] (w:1, o:246, a:1, s:1, b:0),
% 1.03/1.40 'c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1' [130, 1] (w:1, o:167
% 1.03/1.40 , a:1, s:1, b:0),
% 1.03/1.40 'class_Nat_Osemiring__char__0' [131, 1] (w:1, o:115, a:1, s:1, b:0),
% 3.33/3.70
% 3.33/3.70 'class_Ring__and__Field_Oordered__semiring' [132, 1] (w:1, o:160, a:1
% 3.33/3.70 , s:1, b:0),
% 3.33/3.70 'class_OrderedGroup_Omonoid__mult' [133, 1] (w:1, o:140, a:1, s:1, b:
% 3.33/3.70 0),
% 3.33/3.70 'c_ATP__Linkup_Osko__Nat__Xex__least__nat__le__1__1' [134, 2] (w:1
% 3.33/3.70 , o:215, a:1, s:1, b:0),
% 3.33/3.70 'class_OrderedGroup_Olordered__ab__group__add' [135, 1] (w:1, o:138
% 3.33/3.70 , a:1, s:1, b:0),
% 3.33/3.70 'class_OrderedGroup_Ogroup__add' [136, 1] (w:1, o:141, a:1, s:1, b:0)
% 3.33/3.70 ,
% 3.33/3.70 'v_sko__Nat__Xnat__Xinducts__1' [138, 1] (w:1, o:168, a:1, s:1, b:0)
% 3.33/3.70 ,
% 3.33/3.70 'class_OrderedGroup_Opordered__ab__semigroup__add' [139, 1] (w:1, o:
% 3.33/3.70 142, a:1, s:1, b:0),
% 3.33/3.70 'c_List_Olist__update' [140, 4] (w:1, o:241, a:1, s:1, b:0),
% 3.33/3.70 'class_OrderedGroup_Omonoid__add' [141, 1] (w:1, o:143, a:1, s:1, b:0
% 3.33/3.70 ),
% 3.33/3.70 'c_List_Olistsum' [142, 2] (w:1, o:216, a:1, s:1, b:0),
% 3.33/3.70 'class_OrderedGroup_Opordered__comm__monoid__add' [143, 1] (w:1, o:
% 3.33/3.70 144, a:1, s:1, b:0),
% 3.33/3.70 'class_Orderings_Opreorder' [144, 1] (w:1, o:146, a:1, s:1, b:0),
% 3.33/3.70 'class_Orderings_Oorder' [145, 1] (w:1, o:145, a:1, s:1, b:0),
% 3.33/3.70 'class_OrderedGroup_Oab__group__add' [146, 1] (w:1, o:147, a:1, s:1
% 3.33/3.70 , b:0),
% 3.33/3.70 'class_OrderedGroup_Oab__semigroup__add' [147, 1] (w:1, o:148, a:1
% 3.33/3.70 , s:1, b:0),
% 3.33/3.70 'class_Lattices_Olower__semilattice' [148, 1] (w:1, o:169, a:1, s:1
% 3.33/3.70 , b:0),
% 3.33/3.70 'c_COMBK' [150, 3] (w:1, o:221, a:1, s:1, b:0),
% 3.33/3.70 'class_OrderedGroup_Olordered__ab__group__add__meet' [152, 1] (w:1
% 3.33/3.70 , o:139, a:1, s:1, b:0),
% 3.33/3.70 'class_Ring__and__Field_Osemiring__1' [153, 1] (w:1, o:170, a:1, s:1
% 3.33/3.70 , b:0),
% 3.33/3.70 'c_Nat_Osemiring__1__class_Oof__nat__aux' [155, 4] (w:1, o:242, a:1
% 3.33/3.70 , s:1, b:0),
% 3.33/3.70 'c_Lambda_Oliftn' [156, 3] (w:1, o:235, a:1, s:1, b:0),
% 3.33/3.70 'c_Lambda_Olift' [157, 0] (w:1, o:76, a:1, s:1, b:0),
% 3.33/3.70 'class_Divides_Osemiring__div' [158, 1] (w:1, o:171, a:1, s:1, b:0),
% 3.33/3.70
% 3.33/3.70 'c_Type_Oshift' [160, 4] (w:1, o:243, a:1, s:1, b:0),
% 3.33/3.70 'c_Fun_Ocomp' [165, 5] (w:1, o:247, a:1, s:1, b:0),
% 3.33/3.70 'class_Ring__and__Field_Oordered__idom' [168, 1] (w:1, o:161, a:1, s:
% 3.33/3.70 1, b:0),
% 3.33/3.70 'c_InductTermi_OIT' [169, 0] (w:1, o:87, a:1, s:1, b:0),
% 3.33/3.70 'c_Lambda_OdB_OApp' [170, 0] (w:1, o:88, a:1, s:1, b:0),
% 3.33/3.70 'c_Lambda_OdB_OAbs' [171, 1] (w:1, o:172, a:1, s:1, b:0),
% 3.33/3.70 'tc_Lambda_OdB' [173, 0] (w:1, o:89, a:1, s:1, b:0),
% 3.33/3.70 'class_Lattices_Olattice' [174, 1] (w:1, o:173, a:1, s:1, b:0),
% 3.33/3.70 'tc_bool' [175, 0] (w:1, o:90, a:1, s:1, b:0),
% 3.33/3.70 'tc_fun' [176, 2] (w:1, o:217, a:1, s:1, b:0),
% 3.33/3.70 'c_Nat_Onat_Onat__case' [180, 4] (w:1, o:244, a:1, s:1, b:0),
% 3.33/3.70 'class_Ring__and__Field_Osemiring' [186, 1] (w:1, o:174, a:1, s:1, b:
% 3.33/3.70 0),
% 3.33/3.70 't_a' [187, 0] (w:1, o:94, a:1, s:1, b:0),
% 3.33/3.70 'c_List_Omap' [189, 4] (w:1, o:245, a:1, s:1, b:0),
% 3.33/3.70 'class_Ring__and__Field_Opordered__cancel__semiring' [190, 1] (w:1
% 3.33/3.70 , o:175, a:1, s:1, b:0),
% 3.33/3.70 'class_OrderedGroup_Ocancel__ab__semigroup__add' [191, 1] (w:1, o:149
% 3.33/3.70 , a:1, s:1, b:0),
% 3.33/3.70 'class_OrderedGroup_Ocancel__semigroup__add' [192, 1] (w:1, o:150, a:
% 3.33/3.70 1, s:1, b:0),
% 3.33/3.70 'v_sko__List__Xlexn__Xinduct__1' [197, 1] (w:1, o:176, a:1, s:1, b:0)
% 3.33/3.70 ,
% 3.33/3.70 'c_List_Orotate' [198, 3] (w:1, o:236, a:1, s:1, b:0),
% 3.33/3.70 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [203, 1]
% 3.33/3.70 (w:1, o:151, a:1, s:1, b:0),
% 3.33/3.70 'class_OrderedGroup_Oab__semigroup__idem__mult' [207, 1] (w:1, o:152
% 3.33/3.70 , a:1, s:1, b:0),
% 3.33/3.70 'c_nat_Onat__size' [210, 1] (w:1, o:177, a:1, s:1, b:0),
% 3.33/3.70 'class_Ring__and__Field_Oring__1' [213, 1] (w:1, o:132, a:1, s:1, b:0
% 3.33/3.70 ),
% 3.33/3.70 'class_Ring__and__Field_Omult__mono' [214, 1] (w:1, o:178, a:1, s:1
% 3.33/3.70 , b:0),
% 3.33/3.70 'class_Ring__and__Field_Omult__mono1' [215, 1] (w:1, o:179, a:1, s:1
% 3.33/3.70 , b:0),
% 3.33/3.70 'c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1' [216, 1] (w:1, o:180
% 3.33/3.70 , a:1, s:1, b:0),
% 3.33/3.70 'class_Ring__and__Field_Oordered__comm__semiring__strict' [217, 1]
% 3.33/3.70 (w:1, o:162, a:1, s:1, b:0),
% 3.33/3.70 'class_Ring__and__Field_Opordered__semiring' [218, 1] (w:1, o:181, a:
% 3.33/3.70 1, s:1, b:0),
% 3.33/3.70 'class_Ring__and__Field_Ozero__neq__one' [219, 1] (w:1, o:182, a:1
% 20.78/21.13 , s:1, b:0),
% 20.78/21.13 'class_Ring__and__Field_Ono__zero__divisors' [220, 1] (w:1, o:119, a:
% 20.78/21.13 1, s:1, b:0),
% 20.78/21.13 'class_Ring__and__Field_Omult__zero' [221, 1] (w:1, o:118, a:1, s:1
% 20.78/21.13 , b:0),
% 20.78/21.13 'class_Ring__and__Field_Oring__1__no__zero__divisors' [222, 1] (w:1
% 20.78/21.13 , o:133, a:1, s:1, b:0),
% 20.78/21.13 'class_Ring__and__Field_Oring__no__zero__divisors' [223, 1] (w:1, o:
% 20.78/21.13 134, a:1, s:1, b:0),
% 20.78/21.13 'class_OrderedGroup_Ocomm__monoid__mult' [228, 1] (w:1, o:153, a:1
% 20.78/21.13 , s:1, b:0),
% 20.78/21.13 'class_OrderedGroup_Oab__semigroup__mult' [229, 1] (w:1, o:154, a:1
% 20.78/21.13 , s:1, b:0),
% 20.78/21.13 'class_Ring__and__Field_Ocomm__semiring' [231, 1] (w:1, o:183, a:1
% 20.78/21.13 , s:1, b:0),
% 20.78/21.13 'c_Nitpick_Onat__gcd' [232, 2] (w:1, o:218, a:1, s:1, b:0),
% 20.78/21.13 'c_String_Ochar_Ochar__size' [233, 1] (w:1, o:111, a:1, s:1, b:0),
% 20.78/21.13 'tc_String_Ochar' [234, 0] (w:1, o:97, a:1, s:1, b:0),
% 20.78/21.13 'c_List_Osko__List__Xmap__idI__1__1' [235, 3] (w:1, o:232, a:1, s:1
% 20.78/21.13 , b:0),
% 20.78/21.13 'c_List_Osko__List__Xmap__ext__1__1' [236, 5] (w:1, o:248, a:1, s:1
% 20.78/21.13 , b:0),
% 20.78/21.13 'c_List_Osko__List__Xmap__cong__1__1' [238, 5] (w:1, o:249, a:1, s:1
% 20.78/21.13 , b:0),
% 20.78/21.13 'c_List_Osko__List__Xmap__eq__conv__1__1' [239, 5] (w:1, o:250, a:1
% 20.78/21.13 , s:1, b:0),
% 20.78/21.13 'c_List_Olistsp' [240, 3] (w:1, o:237, a:1, s:1, b:0),
% 20.78/21.13 'c_List_Osko__List__Xin__listsp__conv__set__1__1' [241, 3] (w:1, o:
% 20.78/21.13 233, a:1, s:1, b:0),
% 20.78/21.13 'c_COMBC' [242, 5] (w:1, o:251, a:1, s:1, b:0),
% 20.78/21.13 'tc_Type_Otype' [243, 0] (w:1, o:98, a:1, s:1, b:0),
% 20.78/21.13 'c_Type_Otypings' [245, 3] (w:1, o:238, a:1, s:1, b:0),
% 20.78/21.13 'v_ts' [247, 0] (w:1, o:100, a:1, s:1, b:0),
% 20.78/21.13 'c_COMBB' [250, 6] (w:1, o:253, a:1, s:1, b:0),
% 20.78/21.13 'c_fequal' [251, 3] (w:1, o:239, a:1, s:1, b:0).
% 20.78/21.13
% 20.78/21.13
% 20.78/21.13 Starting Search:
% 20.78/21.13
% 20.78/21.13 Resimplifying inuse:
% 20.78/21.13 Done
% 20.78/21.13
% 20.78/21.13
% 20.78/21.13 Intermediate Status:
% 20.78/21.13 Generated: 5961
% 20.78/21.13 Kept: 2197
% 20.78/21.13 Inuse: 146
% 20.78/21.13 Deleted: 5
% 20.78/21.13 Deletedinuse: 0
% 20.78/21.13
% 20.78/21.13 Resimplifying inuse:
% 20.78/21.13 Done
% 20.78/21.13
% 20.78/21.13 Resimplifying inuse:
% 20.78/21.13 Done
% 20.78/21.13
% 20.78/21.13
% 20.78/21.13 Intermediate Status:
% 20.78/21.13 Generated: 11479
% 20.78/21.13 Kept: 4218
% 20.78/21.13 Inuse: 191
% 20.78/21.13 Deleted: 5
% 20.78/21.13 Deletedinuse: 0
% 20.78/21.13
% 20.78/21.13 Resimplifying inuse:
% 20.78/21.13 Done
% 20.78/21.13
% 20.78/21.13 Resimplifying inuse:
% 20.78/21.13 Done
% 20.78/21.13
% 20.78/21.13
% 20.78/21.13 Intermediate Status:
% 20.78/21.13 Generated: 17542
% 20.78/21.13 Kept: 6265
% 20.78/21.13 Inuse: 330
% 20.78/21.13 Deleted: 6
% 20.78/21.13 Deletedinuse: 0
% 20.78/21.13
% 20.78/21.13 Resimplifying inuse:
% 20.78/21.13 Done
% 20.78/21.13
% 20.78/21.13 Resimplifying inuse:
% 20.78/21.13 Done
% 20.78/21.13
% 20.78/21.13
% 20.78/21.13 Intermediate Status:
% 20.78/21.13 Generated: 25070
% 20.78/21.13 Kept: 8741
% 20.78/21.13 Inuse: 399
% 20.78/21.13 Deleted: 11
% 20.78/21.13 Deletedinuse: 4
% 20.78/21.13
% 20.78/21.13 Resimplifying inuse:
% 20.78/21.13 Done
% 20.78/21.13
% 20.78/21.13 Resimplifying inuse:
% 20.78/21.13 Done
% 20.78/21.13
% 20.78/21.13
% 20.78/21.13 Intermediate Status:
% 20.78/21.13 Generated: 32803
% 20.78/21.13 Kept: 10806
% 20.78/21.13 Inuse: 443
% 20.78/21.13 Deleted: 12
% 20.78/21.13 Deletedinuse: 4
% 20.78/21.13
% 20.78/21.13 Resimplifying inuse:
% 20.78/21.13 Done
% 20.78/21.13
% 20.78/21.13
% 20.78/21.13 Intermediate Status:
% 20.78/21.13 Generated: 39027
% 20.78/21.13 Kept: 12967
% 20.78/21.13 Inuse: 502
% 20.78/21.13 Deleted: 14
% 20.78/21.13 Deletedinuse: 5
% 20.78/21.13
% 20.78/21.13 Resimplifying inuse:
% 20.78/21.13 Done
% 20.78/21.13
% 20.78/21.13 Resimplifying inuse:
% 20.78/21.13 Done
% 20.78/21.13
% 20.78/21.13
% 20.78/21.13 Intermediate Status:
% 20.78/21.13 Generated: 46344
% 20.78/21.13 Kept: 15037
% 20.78/21.13 Inuse: 586
% 20.78/21.13 Deleted: 21
% 20.78/21.13 Deletedinuse: 6
% 20.78/21.13
% 20.78/21.13 Resimplifying inuse:
% 20.78/21.13 Done
% 20.78/21.13
% 20.78/21.13 Resimplifying inuse:
% 20.78/21.13 Done
% 20.78/21.13
% 20.78/21.13
% 20.78/21.13 Intermediate Status:
% 20.78/21.13 Generated: 54391
% 20.78/21.13 Kept: 17085
% 20.78/21.13 Inuse: 674
% 20.78/21.13 Deleted: 23
% 20.78/21.13 Deletedinuse: 6
% 20.78/21.13
% 20.78/21.13 Resimplifying inuse:
% 20.78/21.13 Done
% 20.78/21.13
% 20.78/21.13 Resimplifying inuse:
% 20.78/21.13 Done
% 20.78/21.13
% 20.78/21.13
% 20.78/21.13 Intermediate Status:
% 20.78/21.13 Generated: 65840
% 20.78/21.13 Kept: 19183
% 20.78/21.13 Inuse: 752
% 20.78/21.13 Deleted: 26
% 20.78/21.13 Deletedinuse: 7
% 20.78/21.13
% 20.78/21.13 Resimplifying inuse:
% 20.78/21.13 Done
% 20.78/21.13
% 20.78/21.13 Resimplifying clauses:
% 20.78/21.13 Done
% 20.78/21.13
% 20.78/21.13 Resimplifying inuse:
% 20.78/21.13 Done
% 20.78/21.13
% 20.78/21.13
% 20.78/21.13 Intermediate Status:
% 20.78/21.13 Generated: 73631
% 20.78/21.13 Kept: 21187
% 20.78/21.13 Inuse: 840
% 20.78/21.13 Deleted: 580
% 20.78/21.13 Deletedinuse: 9
% 20.78/21.13
% 20.78/21.13 Resimplifying inuse:
% 20.78/21.13 Done
% 20.78/21.13
% 20.78/21.13 Resimplifying inuse:
% 20.78/21.13 Done
% 20.78/21.13
% 20.78/21.13
% 20.78/21.13 Intermediate Status:
% 20.78/21.13 Generated: 82671
% 20.78/21.13 Kept: 23193
% 20.78/21.13 Inuse: 887
% 20.78/21.13 Deleted: 581
% 20.78/21.13 Deletedinuse: 10
% 20.78/21.13
% 20.78/21.13 Resimplifying inuse:
% 20.78/21.13 Done
% 20.78/21.13
% 20.78/21.13 Resimplifying inuse:
% 20.78/21.13 Done
% 20.78/21.13
% 20.78/21.13
% 20.78/21.13 Intermediate Status:
% 20.78/21.13 Generated: 92622
% 20.78/21.13 Kept: 25753
% 20.78/21.13 Inuse: 922
% 20.78/21.13 Deleted: 581
% 20.78/21.13 Deletedinuse: 10
% 20.78/21.13
% 20.78/21.13 Resimplifying inuse:
% 20.78/21.13 Done
% 20.78/21.13
% 20.78/21.13 Resimplifying inuse:
% 20.78/21.13 Done
% 20.78/21.13
% 20.78/21.13
% 20.78/21.13 Intermediate Status:
% 20.78/21.13 Generated: 104039
% 20.78/21.13 Kept: 27950
% 20.78/21.13 Inuse: 947
% 20.78/21.13 Deleted: 582
% 20.78/21.13 Deletedinuse: 11
% 20.78/21.13
% 20.78/21.13 Resimplifying inuse:
% 20.78/21.13 Done
% 20.78/21.13
% 20.78/21.13
% 20.78/21.13 Intermediate Status:
% 20.78/21.13 Generated: 118141
% 20.78/21.13 Kept: 31357
% 20.78/21.13 Inuse: 957
% 20.78/21.13 Deleted: 582
% 20.78/21.13 Deletedinuse: 11
% 20.78/21.13
% 20.78/21.13 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81
% 64.42/64.81 Intermediate Status:
% 64.42/64.81 Generated: 129533
% 64.42/64.81 Kept: 34553
% 64.42/64.81 Inuse: 987
% 64.42/64.81 Deleted: 582
% 64.42/64.81 Deletedinuse: 11
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81
% 64.42/64.81 Intermediate Status:
% 64.42/64.81 Generated: 144885
% 64.42/64.81 Kept: 37502
% 64.42/64.81 Inuse: 1017
% 64.42/64.81 Deleted: 582
% 64.42/64.81 Deletedinuse: 11
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81
% 64.42/64.81 Intermediate Status:
% 64.42/64.81 Generated: 157965
% 64.42/64.81 Kept: 39512
% 64.42/64.81 Inuse: 1032
% 64.42/64.81 Deleted: 582
% 64.42/64.81 Deletedinuse: 11
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81 Resimplifying clauses:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81
% 64.42/64.81 Intermediate Status:
% 64.42/64.81 Generated: 167087
% 64.42/64.81 Kept: 41670
% 64.42/64.81 Inuse: 1091
% 64.42/64.81 Deleted: 976
% 64.42/64.81 Deletedinuse: 11
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81
% 64.42/64.81 Intermediate Status:
% 64.42/64.81 Generated: 181881
% 64.42/64.81 Kept: 45292
% 64.42/64.81 Inuse: 1151
% 64.42/64.81 Deleted: 976
% 64.42/64.81 Deletedinuse: 11
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81
% 64.42/64.81 Intermediate Status:
% 64.42/64.81 Generated: 198390
% 64.42/64.81 Kept: 50488
% 64.42/64.81 Inuse: 1161
% 64.42/64.81 Deleted: 976
% 64.42/64.81 Deletedinuse: 11
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81
% 64.42/64.81 Intermediate Status:
% 64.42/64.81 Generated: 205479
% 64.42/64.81 Kept: 52576
% 64.42/64.81 Inuse: 1181
% 64.42/64.81 Deleted: 976
% 64.42/64.81 Deletedinuse: 11
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81
% 64.42/64.81 Intermediate Status:
% 64.42/64.81 Generated: 241051
% 64.42/64.81 Kept: 56966
% 64.42/64.81 Inuse: 1201
% 64.42/64.81 Deleted: 976
% 64.42/64.81 Deletedinuse: 11
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81
% 64.42/64.81 Intermediate Status:
% 64.42/64.81 Generated: 274059
% 64.42/64.81 Kept: 60181
% 64.42/64.81 Inuse: 1206
% 64.42/64.81 Deleted: 976
% 64.42/64.81 Deletedinuse: 11
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81 Resimplifying clauses:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81
% 64.42/64.81 Intermediate Status:
% 64.42/64.81 Generated: 286108
% 64.42/64.81 Kept: 62815
% 64.42/64.81 Inuse: 1236
% 64.42/64.81 Deleted: 1093
% 64.42/64.81 Deletedinuse: 11
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81
% 64.42/64.81 Intermediate Status:
% 64.42/64.81 Generated: 302732
% 64.42/64.81 Kept: 68217
% 64.42/64.81 Inuse: 1246
% 64.42/64.81 Deleted: 1093
% 64.42/64.81 Deletedinuse: 11
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81
% 64.42/64.81 Intermediate Status:
% 64.42/64.81 Generated: 320613
% 64.42/64.81 Kept: 70417
% 64.42/64.81 Inuse: 1266
% 64.42/64.81 Deleted: 1099
% 64.42/64.81 Deletedinuse: 17
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81
% 64.42/64.81 Intermediate Status:
% 64.42/64.81 Generated: 337413
% 64.42/64.81 Kept: 73137
% 64.42/64.81 Inuse: 1281
% 64.42/64.81 Deleted: 1099
% 64.42/64.81 Deletedinuse: 17
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81
% 64.42/64.81 Intermediate Status:
% 64.42/64.81 Generated: 351681
% 64.42/64.81 Kept: 75400
% 64.42/64.81 Inuse: 1286
% 64.42/64.81 Deleted: 1100
% 64.42/64.81 Deletedinuse: 18
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81
% 64.42/64.81 Intermediate Status:
% 64.42/64.81 Generated: 363486
% 64.42/64.81 Kept: 77611
% 64.42/64.81 Inuse: 1321
% 64.42/64.81 Deleted: 1102
% 64.42/64.81 Deletedinuse: 20
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81
% 64.42/64.81 Intermediate Status:
% 64.42/64.81 Generated: 373656
% 64.42/64.81 Kept: 79706
% 64.42/64.81 Inuse: 1351
% 64.42/64.81 Deleted: 1104
% 64.42/64.81 Deletedinuse: 22
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81 Resimplifying clauses:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81
% 64.42/64.81 Intermediate Status:
% 64.42/64.81 Generated: 384147
% 64.42/64.81 Kept: 81713
% 64.42/64.81 Inuse: 1394
% 64.42/64.81 Deleted: 1680
% 64.42/64.81 Deletedinuse: 23
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81
% 64.42/64.81 Intermediate Status:
% 64.42/64.81 Generated: 401558
% 64.42/64.81 Kept: 85300
% 64.42/64.81 Inuse: 1431
% 64.42/64.81 Deleted: 1680
% 64.42/64.81 Deletedinuse: 23
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81
% 64.42/64.81 Intermediate Status:
% 64.42/64.81 Generated: 415157
% 64.42/64.81 Kept: 87899
% 64.42/64.81 Inuse: 1456
% 64.42/64.81 Deleted: 1687
% 64.42/64.81 Deletedinuse: 30
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81
% 64.42/64.81 Intermediate Status:
% 64.42/64.81 Generated: 425847
% 64.42/64.81 Kept: 89901
% 64.42/64.81 Inuse: 1475
% 64.42/64.81 Deleted: 1687
% 64.42/64.81 Deletedinuse: 30
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81
% 64.42/64.81 Intermediate Status:
% 64.42/64.81 Generated: 434899
% 64.42/64.81 Kept: 91921
% 64.42/64.81 Inuse: 1506
% 64.42/64.81 Deleted: 1687
% 64.42/64.81 Deletedinuse: 30
% 64.42/64.81
% 64.42/64.81
% 64.42/64.81 Intermediate Status:
% 64.42/64.81 Generated: 455663
% 64.42/64.81 Kept: 94654
% 64.42/64.81 Inuse: 1516
% 64.42/64.81 Deleted: 1687
% 64.42/64.81 Deletedinuse: 30
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81
% 64.42/64.81 Intermediate Status:
% 64.42/64.81 Generated: 467683
% 64.42/64.81 Kept: 96676
% 64.42/64.81 Inuse: 1552
% 64.42/64.81 Deleted: 1687
% 64.42/64.81 Deletedinuse: 30
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81
% 64.42/64.81 Intermediate Status:
% 64.42/64.81 Generated: 482543
% 64.42/64.81 Kept: 99560
% 64.42/64.81 Inuse: 1576
% 64.42/64.81 Deleted: 1687
% 64.42/64.81 Deletedinuse: 30
% 64.42/64.81
% 64.42/64.81 Resimplifying inuse:
% 64.42/64.81 Done
% 64.42/64.81
% 64.42/64.81 Resimplifying clauses:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58
% 125.15/125.58 Intermediate Status:
% 125.15/125.58 Generated: 503142
% 125.15/125.58 Kept: 102530
% 125.15/125.58 Inuse: 1591
% 125.15/125.58 Deleted: 2458
% 125.15/125.58 Deletedinuse: 30
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58
% 125.15/125.58 Intermediate Status:
% 125.15/125.58 Generated: 532384
% 125.15/125.58 Kept: 105830
% 125.15/125.58 Inuse: 1601
% 125.15/125.58 Deleted: 2458
% 125.15/125.58 Deletedinuse: 30
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58
% 125.15/125.58 Intermediate Status:
% 125.15/125.58 Generated: 561812
% 125.15/125.58 Kept: 108770
% 125.15/125.58 Inuse: 1611
% 125.15/125.58 Deleted: 2458
% 125.15/125.58 Deletedinuse: 30
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58
% 125.15/125.58 Intermediate Status:
% 125.15/125.58 Generated: 580664
% 125.15/125.58 Kept: 111007
% 125.15/125.58 Inuse: 1626
% 125.15/125.58 Deleted: 2458
% 125.15/125.58 Deletedinuse: 30
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58
% 125.15/125.58 Intermediate Status:
% 125.15/125.58 Generated: 596302
% 125.15/125.58 Kept: 113824
% 125.15/125.58 Inuse: 1633
% 125.15/125.58 Deleted: 2458
% 125.15/125.58 Deletedinuse: 30
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58
% 125.15/125.58 Intermediate Status:
% 125.15/125.58 Generated: 603779
% 125.15/125.58 Kept: 115895
% 125.15/125.58 Inuse: 1646
% 125.15/125.58 Deleted: 2458
% 125.15/125.58 Deletedinuse: 30
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58
% 125.15/125.58 Intermediate Status:
% 125.15/125.58 Generated: 618397
% 125.15/125.58 Kept: 118095
% 125.15/125.58 Inuse: 1676
% 125.15/125.58 Deleted: 2458
% 125.15/125.58 Deletedinuse: 30
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58
% 125.15/125.58 Intermediate Status:
% 125.15/125.58 Generated: 631628
% 125.15/125.58 Kept: 120123
% 125.15/125.58 Inuse: 1700
% 125.15/125.58 Deleted: 2458
% 125.15/125.58 Deletedinuse: 30
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58 Resimplifying clauses:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58
% 125.15/125.58 Intermediate Status:
% 125.15/125.58 Generated: 653628
% 125.15/125.58 Kept: 122881
% 125.15/125.58 Inuse: 1716
% 125.15/125.58 Deleted: 2933
% 125.15/125.58 Deletedinuse: 31
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58
% 125.15/125.58 Intermediate Status:
% 125.15/125.58 Generated: 686803
% 125.15/125.58 Kept: 127721
% 125.15/125.58 Inuse: 1726
% 125.15/125.58 Deleted: 2933
% 125.15/125.58 Deletedinuse: 31
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58
% 125.15/125.58 Intermediate Status:
% 125.15/125.58 Generated: 703656
% 125.15/125.58 Kept: 129813
% 125.15/125.58 Inuse: 1731
% 125.15/125.58 Deleted: 2933
% 125.15/125.58 Deletedinuse: 31
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58
% 125.15/125.58 Intermediate Status:
% 125.15/125.58 Generated: 722588
% 125.15/125.58 Kept: 131813
% 125.15/125.58 Inuse: 1741
% 125.15/125.58 Deleted: 2933
% 125.15/125.58 Deletedinuse: 31
% 125.15/125.58
% 125.15/125.58
% 125.15/125.58 Intermediate Status:
% 125.15/125.58 Generated: 741983
% 125.15/125.58 Kept: 133926
% 125.15/125.58 Inuse: 1751
% 125.15/125.58 Deleted: 2933
% 125.15/125.58 Deletedinuse: 31
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58
% 125.15/125.58 Intermediate Status:
% 125.15/125.58 Generated: 762761
% 125.15/125.58 Kept: 136339
% 125.15/125.58 Inuse: 1761
% 125.15/125.58 Deleted: 2933
% 125.15/125.58 Deletedinuse: 31
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58
% 125.15/125.58 Intermediate Status:
% 125.15/125.58 Generated: 779230
% 125.15/125.58 Kept: 138356
% 125.15/125.58 Inuse: 1789
% 125.15/125.58 Deleted: 2933
% 125.15/125.58 Deletedinuse: 31
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58
% 125.15/125.58 Intermediate Status:
% 125.15/125.58 Generated: 813755
% 125.15/125.58 Kept: 141694
% 125.15/125.58 Inuse: 1796
% 125.15/125.58 Deleted: 2933
% 125.15/125.58 Deletedinuse: 31
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58 Resimplifying clauses:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58
% 125.15/125.58 Intermediate Status:
% 125.15/125.58 Generated: 824474
% 125.15/125.58 Kept: 143814
% 125.15/125.58 Inuse: 1816
% 125.15/125.58 Deleted: 3230
% 125.15/125.58 Deletedinuse: 31
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58
% 125.15/125.58 Intermediate Status:
% 125.15/125.58 Generated: 829618
% 125.15/125.58 Kept: 145943
% 125.15/125.58 Inuse: 1823
% 125.15/125.58 Deleted: 3248
% 125.15/125.58 Deletedinuse: 31
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58
% 125.15/125.58 Intermediate Status:
% 125.15/125.58 Generated: 835573
% 125.15/125.58 Kept: 148143
% 125.15/125.58 Inuse: 1828
% 125.15/125.58 Deleted: 3268
% 125.15/125.58 Deletedinuse: 31
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58
% 125.15/125.58 Intermediate Status:
% 125.15/125.58 Generated: 843071
% 125.15/125.58 Kept: 150406
% 125.15/125.58 Inuse: 1838
% 125.15/125.58 Deleted: 3288
% 125.15/125.58 Deletedinuse: 31
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58
% 125.15/125.58 Intermediate Status:
% 125.15/125.58 Generated: 854292
% 125.15/125.58 Kept: 152434
% 125.15/125.58 Inuse: 1860
% 125.15/125.58 Deleted: 3288
% 125.15/125.58 Deletedinuse: 31
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58
% 125.15/125.58 Intermediate Status:
% 125.15/125.58 Generated: 886994
% 125.15/125.58 Kept: 159424
% 125.15/125.58 Inuse: 1883
% 125.15/125.58 Deleted: 3288
% 125.15/125.58 Deletedinuse: 31
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58
% 125.15/125.58 Intermediate Status:
% 125.15/125.58 Generated: 901583
% 125.15/125.58 Kept: 162398
% 125.15/125.58 Inuse: 1893
% 125.15/125.58 Deleted: 3288
% 125.15/125.58 Deletedinuse: 31
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58 Resimplifying clauses:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 125.15/125.58 Done
% 125.15/125.58
% 125.15/125.58
% 125.15/125.58 Intermediate Status:
% 125.15/125.58 Generated: 911837
% 125.15/125.58 Kept: 164398
% 125.15/125.58 Inuse: 1906
% 125.15/125.58 Deleted: 3657
% 125.15/125.58 Deletedinuse: 31
% 125.15/125.58
% 125.15/125.58 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31
% 209.90/210.31 Intermediate Status:
% 209.90/210.31 Generated: 924657
% 209.90/210.31 Kept: 166645
% 209.90/210.31 Inuse: 1923
% 209.90/210.31 Deleted: 3657
% 209.90/210.31 Deletedinuse: 31
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31
% 209.90/210.31 Intermediate Status:
% 209.90/210.31 Generated: 939750
% 209.90/210.31 Kept: 169107
% 209.90/210.31 Inuse: 1943
% 209.90/210.31 Deleted: 3657
% 209.90/210.31 Deletedinuse: 31
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31
% 209.90/210.31 Intermediate Status:
% 209.90/210.31 Generated: 955733
% 209.90/210.31 Kept: 171349
% 209.90/210.31 Inuse: 1958
% 209.90/210.31 Deleted: 3657
% 209.90/210.31 Deletedinuse: 31
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31
% 209.90/210.31 Intermediate Status:
% 209.90/210.31 Generated: 971403
% 209.90/210.31 Kept: 173485
% 209.90/210.31 Inuse: 1973
% 209.90/210.31 Deleted: 3657
% 209.90/210.31 Deletedinuse: 31
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31
% 209.90/210.31 Intermediate Status:
% 209.90/210.31 Generated: 984247
% 209.90/210.31 Kept: 175636
% 209.90/210.31 Inuse: 1988
% 209.90/210.31 Deleted: 3657
% 209.90/210.31 Deletedinuse: 31
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31
% 209.90/210.31 Intermediate Status:
% 209.90/210.31 Generated: 996177
% 209.90/210.31 Kept: 178436
% 209.90/210.31 Inuse: 1998
% 209.90/210.31 Deleted: 3657
% 209.90/210.31 Deletedinuse: 31
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31
% 209.90/210.31 Intermediate Status:
% 209.90/210.31 Generated: 1023041
% 209.90/210.31 Kept: 181745
% 209.90/210.31 Inuse: 2008
% 209.90/210.31 Deleted: 3657
% 209.90/210.31 Deletedinuse: 31
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31 Resimplifying clauses:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31
% 209.90/210.31 Intermediate Status:
% 209.90/210.31 Generated: 1042628
% 209.90/210.31 Kept: 183749
% 209.90/210.31 Inuse: 2036
% 209.90/210.31 Deleted: 4310
% 209.90/210.31 Deletedinuse: 31
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31
% 209.90/210.31 Intermediate Status:
% 209.90/210.31 Generated: 1068786
% 209.90/210.31 Kept: 187674
% 209.90/210.31 Inuse: 2058
% 209.90/210.31 Deleted: 4312
% 209.90/210.31 Deletedinuse: 33
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31
% 209.90/210.31 Intermediate Status:
% 209.90/210.31 Generated: 1081919
% 209.90/210.31 Kept: 189929
% 209.90/210.31 Inuse: 2063
% 209.90/210.31 Deleted: 4312
% 209.90/210.31 Deletedinuse: 33
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31
% 209.90/210.31 Intermediate Status:
% 209.90/210.31 Generated: 1117905
% 209.90/210.31 Kept: 193614
% 209.90/210.31 Inuse: 2093
% 209.90/210.31 Deleted: 4312
% 209.90/210.31 Deletedinuse: 33
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31
% 209.90/210.31 Intermediate Status:
% 209.90/210.31 Generated: 1127052
% 209.90/210.31 Kept: 195615
% 209.90/210.31 Inuse: 2114
% 209.90/210.31 Deleted: 4313
% 209.90/210.31 Deletedinuse: 34
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31
% 209.90/210.31 Intermediate Status:
% 209.90/210.31 Generated: 1141247
% 209.90/210.31 Kept: 197876
% 209.90/210.31 Inuse: 2138
% 209.90/210.31 Deleted: 4313
% 209.90/210.31 Deletedinuse: 34
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31
% 209.90/210.31 Intermediate Status:
% 209.90/210.31 Generated: 1155575
% 209.90/210.31 Kept: 203881
% 209.90/210.31 Inuse: 2148
% 209.90/210.31 Deleted: 4313
% 209.90/210.31 Deletedinuse: 34
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31 Resimplifying clauses:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31
% 209.90/210.31 Intermediate Status:
% 209.90/210.31 Generated: 1169168
% 209.90/210.31 Kept: 205902
% 209.90/210.31 Inuse: 2172
% 209.90/210.31 Deleted: 4857
% 209.90/210.31 Deletedinuse: 34
% 209.90/210.31
% 209.90/210.31
% 209.90/210.31 Intermediate Status:
% 209.90/210.31 Generated: 1179571
% 209.90/210.31 Kept: 208257
% 209.90/210.31 Inuse: 2173
% 209.90/210.31 Deleted: 4857
% 209.90/210.31 Deletedinuse: 34
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31
% 209.90/210.31 Intermediate Status:
% 209.90/210.31 Generated: 1191315
% 209.90/210.31 Kept: 210567
% 209.90/210.31 Inuse: 2193
% 209.90/210.31 Deleted: 4857
% 209.90/210.31 Deletedinuse: 34
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31
% 209.90/210.31 Intermediate Status:
% 209.90/210.31 Generated: 1203655
% 209.90/210.31 Kept: 213001
% 209.90/210.31 Inuse: 2213
% 209.90/210.31 Deleted: 4860
% 209.90/210.31 Deletedinuse: 37
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31
% 209.90/210.31 Intermediate Status:
% 209.90/210.31 Generated: 1222650
% 209.90/210.31 Kept: 216753
% 209.90/210.31 Inuse: 2233
% 209.90/210.31 Deleted: 4860
% 209.90/210.31 Deletedinuse: 37
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31
% 209.90/210.31 Intermediate Status:
% 209.90/210.31 Generated: 1233618
% 209.90/210.31 Kept: 218755
% 209.90/210.31 Inuse: 2253
% 209.90/210.31 Deleted: 4860
% 209.90/210.31 Deletedinuse: 37
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31
% 209.90/210.31 Intermediate Status:
% 209.90/210.31 Generated: 1244961
% 209.90/210.31 Kept: 220773
% 209.90/210.31 Inuse: 2274
% 209.90/210.31 Deleted: 4861
% 209.90/210.31 Deletedinuse: 38
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31
% 209.90/210.31 Intermediate Status:
% 209.90/210.31 Generated: 1260254
% 209.90/210.31 Kept: 222929
% 209.90/210.31 Inuse: 2298
% 209.90/210.31 Deleted: 4861
% 209.90/210.31 Deletedinuse: 38
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31 Resimplifying clauses:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31
% 209.90/210.31 Intermediate Status:
% 209.90/210.31 Generated: 1287480
% 209.90/210.31 Kept: 227888
% 209.90/210.31 Inuse: 2323
% 209.90/210.31 Deleted: 6112
% 209.90/210.31 Deletedinuse: 38
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31 Resimplifying inuse:
% 209.90/210.31 Done
% 209.90/210.31
% 209.90/210.31
% 209.90/210.31 Intermediate Status:
% 209.90/210.31 Generated: 1303731
% 209.90/210.31 Kept: 230302
% 209.90/210.31 Inuse: Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------