TSTP Solution File: SWV584-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV584-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 16:26:54 EDT 2022
% Result : Timeout 300.03s 300.43s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV584-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : bliksem %s
% 0.13/0.33 % Computer : n013.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % DateTime : Tue Jun 14 19:38:59 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.32/1.75 *** allocated 10000 integers for termspace/termends
% 1.32/1.75 *** allocated 10000 integers for clauses
% 1.32/1.75 *** allocated 10000 integers for justifications
% 1.32/1.75 *** allocated 15000 integers for termspace/termends
% 1.32/1.75 *** allocated 22500 integers for termspace/termends
% 1.32/1.75 *** allocated 33750 integers for termspace/termends
% 1.32/1.75 *** allocated 50625 integers for termspace/termends
% 1.32/1.75 Bliksem 1.12
% 1.32/1.75
% 1.32/1.75
% 1.32/1.75 Automatic Strategy Selection
% 1.32/1.75
% 1.32/1.75 Clauses:
% 1.32/1.75 [
% 1.32/1.75 [ ~( 'class_Orderings_Oorder'( X ) ), =( hAPP(
% 1.32/1.75 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, X ), Z ),
% 1.32/1.75 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), U ), W ) ), hAPP( hAPP( Y, hAPP(
% 1.32/1.75 hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), U ) ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower_Opower'( X, Y, Z ), T ), W ) ) ), ~(
% 1.32/1.75 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.32/1.75 [ ~( =( 'c_Set_Oimage'( X, Y, Z, T ), 'c_Orderings_Obot__class_Obot'(
% 1.32/1.75 'tc_fun'( T, 'tc_bool' ) ) ) ), =( Y, 'c_Orderings_Obot__class_Obot'(
% 1.32/1.75 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( X, 'tc_bool' )
% 1.32/1.75 ), Y ), 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, 'tc_fun'( X
% 1.32/1.75 , 'tc_bool' ) ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( X, 'tc_bool' ) ), Y ), Z )
% 1.32/1.75 , hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( X, 'tc_bool' ) ), Y
% 1.32/1.75 ), T ), 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( X, 'tc_bool' )
% 1.32/1.75 ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( X,
% 1.32/1.75 'tc_bool' ) ) ), T ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( X, 'tc_bool' ) ), Z )
% 1.32/1.75 , T ), 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 1.32/1.75 'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), hAPP(
% 1.32/1.75 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, 'tc_nat' ), hAPP(
% 1.32/1.75 'c_Suc', T ) ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.32/1.75 'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), hAPP(
% 1.32/1.75 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, 'tc_nat' ), T ) ) ),
% 1.32/1.75 hAPP( Y, T ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat'
% 1.32/1.75 ), T ), Z ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_Finite__Set_Osetsum'( Y,
% 1.32/1.75 'tc_nat', X ), hAPP( 'c_SetInterval_Oord__class_OatLeastLessThan'( Z,
% 1.32/1.75 'tc_nat' ), T ) ) ), hAPP( 'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ),
% 1.32/1.75 hAPP( 'c_SetInterval_Oord__class_OatLeastLessThan'( T, 'tc_nat' ), U ) )
% 1.32/1.75 ), hAPP( 'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), hAPP(
% 1.32/1.75 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, 'tc_nat' ), U ) ) ), ~(
% 1.32/1.75 hBOOL( hAPP( 'c_lessequals'( T, 'tc_nat' ), U ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( Z, 'tc_nat' ), T ) ) ) ],
% 1.32/1.75 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.75 'c_Int_OMin', X ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.32/1.75 Z, 'tc_nat' ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z )
% 1.32/1.75 , X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ), ~(
% 1.32/1.75 hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), X ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.32/1.75 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y,
% 1.32/1.75 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( Y, T ) ) ), ~( hBOOL(
% 1.32/1.75 hAPP( X, T ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), T ), U ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), T ), U ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( Z, X ), Y ) ), ~( hBOOL( hAPP( 'c_lessequals'( U, X ), T
% 1.32/1.75 ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( U, X ), T ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), Y
% 1.32/1.75 ) ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.75 , Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ),
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.75 , Y ), Z ), T, X ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.75 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.75 , Y ), T ), Z, X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 1.32/1.75 'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), hAPP(
% 1.32/1.75 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, 'tc_nat' ), T ) ), hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( Y, Z ) ), hAPP(
% 1.32/1.75 'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), hAPP(
% 1.32/1.75 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( 'c_Suc', Z ),
% 1.32/1.75 'tc_nat' ), T ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'tc_nat' ), Z ), T ) ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( Y, hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), Y ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), Y ), 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ),
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ), Z ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.32/1.75 =( X, Y ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.32/1.75 [ =( X, Y ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X
% 1.32/1.75 ), Y ) ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.32/1.75 =( X, Y ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( Y, X ), Z ) ) ), =( Y, Z ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( Y, X ), Z ) ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( Y, X ), Z ) ) ), =( Z, Y ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), =( Z, Y ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.75 , 'tc_nat' ), 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ) ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.32/1.75 hAPP( 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.75 ) ), Y ) ) ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 'tc_nat' ) ), Y ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 'tc_nat' ) ), X ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.75 Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 X ), Y ), Y ) ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.75 Y ) ) ) ],
% 1.32/1.75 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y )
% 1.32/1.75 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.32/1.75 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( Y, 'tc_nat' ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.32/1.75 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), X ), hAPP(
% 1.32/1.75 hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ), T
% 1.32/1.75 ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( Y, 'tc_nat' ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.32/1.75 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), X ), hAPP(
% 1.32/1.75 hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ), T
% 1.32/1.75 ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z )
% 1.32/1.75 , X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~(
% 1.32/1.75 hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ) ) )
% 1.32/1.75 ],
% 1.32/1.75 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oone__class_Oone'(
% 1.32/1.75 'tc_nat' ), 'tc_nat' ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( 'c_Suc'
% 1.32/1.75 , U ) ), hAPP( hAPP( Y, hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T
% 1.32/1.75 ), U ) ), T ) ), ~( 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.75 , Y ), Z ), Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.32/1.75 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.75 , Y ), Z ), Z, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.32/1.75 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.32/1.75 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.75 Y ) ) ), 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.32/1.75 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Z, X, 'tc_fun'( T,
% 1.32/1.75 'tc_bool' ) ), Y ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 1.32/1.75 'tc_bool' ) ), Y ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X
% 1.32/1.75 ) ), 'c_HOL_Oone__class_Oone'( X ) ) ) ) ],
% 1.32/1.75 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 1.32/1.75 Z, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Z, 'tc_nat' ) ),
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z, 'tc_nat' ) ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.32/1.75 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.32/1.75 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.32/1.75 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Oorder'( X ) ), ~( =( hAPP(
% 1.32/1.75 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, X ), Z ),
% 1.32/1.75 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ), ~( hBOOL(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), hAPP( Z, Y ) ), T ), ~(
% 1.32/1.75 'c_Lattices_Oboolean__algebra'( U, Z, W, V0, V1, X, V2, T, V3 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), hAPP( Z, Y ) ), T ), ~(
% 1.32/1.75 'c_Lattices_Oboolean__algebra'( U, Z, W, V0, X, V1, T, V2, V3 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, hAPP( Y, Z ) ), Z ), T ), ~(
% 1.32/1.75 'c_Lattices_Oboolean__algebra'( U, Y, W, V0, V1, X, V2, T, V3 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, hAPP( Y, Z ) ), Z ), T ), ~(
% 1.32/1.75 'c_Lattices_Oboolean__algebra'( U, Y, W, V0, X, V1, T, V2, V3 ) ) ],
% 1.32/1.75 [ =( hAPP( X, hAPP( X, Y ) ), Y ), ~( 'c_Lattices_Oboolean__algebra'( Z
% 1.32/1.75 , X, T, U, W, V0, V1, V2, V3 ) ) ],
% 1.32/1.75 [ ~( 'c_Lattices_Oboolean__algebra'( X, Y, Z, T, U, W, hAPP( hAPP( U, V0
% 1.32/1.75 ), V1 ), hAPP( hAPP( W, V0 ), V1 ), V2 ) ), =( hAPP( Y, V0 ), V1 ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ =( hAPP( X, Y ), Z ), ~( 'c_Lattices_Oboolean__algebra'( T, X, U, W,
% 1.32/1.75 V0, V1, Z, Y, V2 ) ) ],
% 1.32/1.75 [ =( hAPP( X, Y ), Z ), ~( 'c_Lattices_Oboolean__algebra'( T, X, U, W,
% 1.32/1.75 V0, V1, Y, Z, V2 ) ) ],
% 1.32/1.75 [ =( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( U, hAPP( X, Z ) ),
% 1.32/1.75 hAPP( X, T ) ) ), ~( 'c_Lattices_Oboolean__algebra'( W, X, V0, V1, U, Y,
% 1.32/1.75 V2, V3, V4 ) ) ],
% 1.32/1.75 [ =( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( U, hAPP( X, Z ) ),
% 1.32/1.75 hAPP( X, T ) ) ), ~( 'c_Lattices_Oboolean__algebra'( W, X, V0, V1, Y, U,
% 1.32/1.75 V2, V3, V4 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( T, Y ), hAPP( U, Z ) ) ), ~(
% 1.32/1.75 'c_Lattices_Oboolean__algebra'( X, U, W, V0, T, V1, V2, V3, V4 ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.32/1.75 ), 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z )
% 1.32/1.75 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.75 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), hAPP( 'c_Suc',
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.75 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.32/1.75 Y, 'tc_nat' ), X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y ) ) ) ],
% 1.32/1.75 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.75 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ) ), T ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), T ), X ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 'tc_nat' ) ), Z ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ) ) )
% 1.32/1.75 ],
% 1.32/1.75 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.32/1.75 V3, V4 ) ), hBOOL( hAPP( hAPP( W, Z ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower_Opower'( V1, V2, V4 ), hAPP( V0, V5 ) ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.32/1.75 [ 'c_Finite__Set_Ofinite'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.75 'tc_fun'( X, 'tc_bool' ) ), Y ), 'c_Set_Oinsert'( Z, T, X ) ), X ), ~(
% 1.32/1.75 'c_Finite__Set_Ofinite'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.75 'tc_fun'( X, 'tc_bool' ) ), Y ), T ), X ) ) ],
% 1.32/1.75 [ 'c_Finite__Set_Ofinite'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.75 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ), X ), ~( 'c_Finite__Set_Ofinite'(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( X, 'tc_bool' ) ), Y )
% 1.32/1.75 , 'c_Set_Oinsert'( T, Z, X ) ), X ) ) ],
% 1.32/1.75 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ),
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.32/1.75 'tc_nat' ), Z, 'tc_nat' ) ) ), 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.32/1.75 'tc_nat' ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.32/1.75 ) ],
% 1.32/1.75 [ =( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), hAPP( U, W
% 1.32/1.75 ) ), V0 ) ), hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), W
% 1.32/1.75 ), V0 ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( V1, U, V2, V3, V4,
% 1.32/1.75 V5, X, Y, Z, V6, T ) ) ],
% 1.32/1.75 [ =( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), U ), W ) )
% 1.32/1.75 , hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), hAPP( X, U ) ), W ) ),
% 1.32/1.75 ~( 'c_Ring__and__Field_Oordered__idom'( V0, V1, V2, V3, V4, V5, X, Y, Z,
% 1.32/1.75 V6, T ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.32/1.75 ), Z ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.32/1.75 hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.75 , Y ), Z ), Z, X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.75 , Y ), Z ), Y, X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), U ), W ) ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.32/1.75 X, Y, Z ), T ), U ) ), W ) ), ~( 'c_OrderedGroup_Omonoid__mult'( X, Y, Z
% 1.32/1.75 ) ) ],
% 1.32/1.75 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( Y, X ), 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 1.32/1.75 T, X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ), ~( hBOOL(
% 1.32/1.75 hAPP( 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.32/1.75 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( Y, X ), 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 1.32/1.75 T, X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ), ~( hBOOL(
% 1.32/1.75 hAPP( 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.32/1.75 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( Y, X ), 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 1.32/1.75 T, X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ), ~( hBOOL(
% 1.32/1.75 hAPP( 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.32/1.75 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.32/1.75 X ), Z ) ) ],
% 1.32/1.75 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.32/1.75 X ), Y ) ) ],
% 1.32/1.75 [ ~( 'class_Lattices_Olattice'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ), Z ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( 'class_Lattices_Olattice'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ), Y ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ) ) )
% 1.32/1.75 ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), T ) ),
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), T ) ) ), Y ) ), ~( hBOOL(
% 1.32/1.75 hAPP( 'c_lessequals'( T, 'tc_nat' ), Z ) ) ) ],
% 1.32/1.75 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 'tc_nat' ), X ), 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z,
% 1.32/1.75 'tc_nat' ) ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), X ), T ), X ), ~(
% 1.32/1.75 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.32/1.75 , hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.32/1.75 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z )
% 1.32/1.75 ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.32/1.75 , hBOOL( hAPP( 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X
% 1.32/1.75 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.32/1.75 , hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.32/1.75 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T )
% 1.32/1.75 ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.32/1.75 , hBOOL( hAPP( 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), X
% 1.32/1.75 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ), hBOOL(
% 1.32/1.75 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z
% 1.32/1.75 ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), ~(
% 1.32/1.75 hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ), hBOOL(
% 1.32/1.75 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z
% 1.32/1.75 ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), ~(
% 1.32/1.75 hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ),
% 1.32/1.75 Z ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ),
% 1.32/1.75 X ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z )
% 1.32/1.75 , Y ) ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ),
% 1.32/1.75 Z ) ) ) ],
% 1.32/1.75 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.32/1.75 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.32/1.75 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.32/1.75 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( X, T ) ],
% 1.32/1.75 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.32/1.75 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.32/1.75 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.32/1.75 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( Y, T ), =( X, T ) ],
% 1.32/1.75 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.32/1.75 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.32/1.75 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.32/1.75 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( X, U ), =( Y, U ) ],
% 1.32/1.75 [ ~( =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.32/1.75 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.32/1.75 'c_Set_Oinsert'( T, 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'(
% 1.32/1.75 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ), =( Y, T ), =( Y, U ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 1.32/1.75 'c_Finite__Set_Osetsum'( Y, Z, X ),
% 1.32/1.75 'c_Lattices_Oupper__semilattice__class_Osup'( T, U, 'tc_fun'( Z,
% 1.32/1.75 'tc_bool' ) ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_Finite__Set_Osetsum'( Y,
% 1.32/1.75 Z, X ), T ) ), hAPP( 'c_Finite__Set_Osetsum'( Y, Z, X ), U ) ) ), hAPP(
% 1.32/1.75 'c_Finite__Set_Osetsum'( Y, Z, X ),
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( T, U, 'tc_fun'( Z,
% 1.32/1.75 'tc_bool' ) ) ) ) ), ~( 'c_Finite__Set_Ofinite'( U, Z ) ), ~(
% 1.32/1.75 'c_Finite__Set_Ofinite'( T, Z ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP(
% 1.32/1.75 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) )
% 1.32/1.75 ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), hAPP( 'c_Suc', Y ) )
% 1.32/1.75 ), ~( hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.32/1.75 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ),
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( X,
% 1.32/1.75 'tc_bool' ) ), 'tc_fun'( X, 'tc_bool' ) ), Y ) ],
% 1.32/1.75 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ),
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ), T ) ), ~(
% 1.32/1.75 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ],
% 1.32/1.75 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ),
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ), T ) ), ~(
% 1.32/1.75 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ), =( Z, Y ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), =( Z, Y ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( Y, X ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ),
% 1.32/1.75 Y ) ) ) ],
% 1.32/1.75 [ ~( 'class_RealVector_Ometric__space'( X ) ), ~(
% 1.32/1.75 'class_RealVector_Oreal__normed__algebra__1'( Y ) ), =( Z, T ), ~(
% 1.32/1.75 'c_Lim_OLIM'( U, W, T, Y, X ) ), ~( 'c_Lim_OLIM'( U, W, Z, Y, X ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ =( X, Y ), ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) ) ), ~(
% 1.32/1.75 hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.32/1.75 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), X ) ), =(
% 1.32/1.75 Y, X ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), X ), Y
% 1.32/1.75 ) ), =( Y, X ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'tc_Int_Oint' ), Y ), X ) ) ],
% 1.32/1.75 [ ~( 'class_RealVector_Ometric__space'( X ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_SEQ_OLIMSEQ'( T, X ), Z ) ) ), ~( hBOOL( hAPP( 'c_SEQ_OLIMSEQ'( T, X )
% 1.32/1.75 , Y ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), Z ) ), =( Z, Y ), hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Z ), Y ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.32/1.75 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), X ) ), =(
% 1.32/1.75 Y, X ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( Z, X ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.32/1.75 Z ) ) ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ), =( Z, Y ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( Z, X ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.32/1.75 Z ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ) ) )
% 1.32/1.75 ],
% 1.32/1.75 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.32/1.75 [ ~( 'class_RealVector_Ometric__space'( X ) ), ~(
% 1.32/1.75 'class_RealVector_Oreal__normed__vector'( Y ) ), 'c_Lim_OLIM'( hAPP( hAPP(
% 1.32/1.75 'c_COMBB'( Y, X, Y ), Z ), hAPP( 'c_COMBC'( 'c_HOL_Oplus__class_Oplus'( Y
% 1.32/1.75 ), Y, Y, Y ), T ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( Y ), U )
% 1.32/1.75 , T ), W, Y, X ), ~( 'c_Lim_OLIM'( Z, U, W, Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Oorder'( X ) ), =( hAPP(
% 1.32/1.75 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, X ), Z ),
% 1.32/1.75 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~( hBOOL(
% 1.32/1.75 hAPP( 'c_lessequals'( Z, X ), Y ) ) ) ],
% 1.32/1.75 [ ~( 'class_Lattices_Olattice'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.32/1.75 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ), X ),
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.32/1.75 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.32/1.75 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 1.32/1.75 'c_Finite__Set_Osetsum'( Y, Z, X ), 'c_Orderings_Obot__class_Obot'(
% 1.32/1.75 'tc_fun'( Z, 'tc_bool' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( Y, 'tc_bool' ) ), Z ), T ),
% 1.32/1.75 'tc_fun'( Y, 'tc_bool' ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.75 'tc_fun'( Y, 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.32/1.75 X, Z, 'tc_fun'( Y, 'tc_bool' ) ) ),
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( X, T, 'tc_fun'( Y,
% 1.32/1.75 'tc_bool' ) ) ) ) ],
% 1.32/1.75 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ), T,
% 1.32/1.75 'tc_fun'( X, 'tc_bool' ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.75 'tc_fun'( X, 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.32/1.75 Y, T, 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, 'tc_fun'( X,
% 1.32/1.75 'tc_bool' ) ) ) ) ],
% 1.32/1.75 [ ~( hBOOL( hAPP( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.32/1.75 ) ), Y ) ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ), Y ) ), ~( hBOOL(
% 1.32/1.75 hAPP( 'c_lessequals'( Z, 'tc_nat' ), X ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 1.32/1.75 'c_Finite__Set_Osetsum'( Y, Z, X ), T ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.75 ), 'c_Finite__Set_Ofinite'( T, Z ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 1.32/1.75 'c_Finite__Set_Osetsum'( Y, Z, X ), T ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.75 ), 'c_Finite__Set_Ofinite'( T, Z ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y
% 1.32/1.75 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.32/1.75 ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( X, 'tc_bool' )
% 1.32/1.75 ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), Y ),
% 1.32/1.75 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.32/1.75 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ],
% 1.32/1.75 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.32/1.75 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 1.32/1.75 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.32/1.75 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 1.32/1.75 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 1.32/1.75 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.32/1.75 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_RealVector_Oreal__normed__vector'( 't_a' ) ), =(
% 1.32/1.75 'c_Series_Osummable'( 'v_f', 't_a' ), hAPP( 'c_Ex'( 't_a' ),
% 1.32/1.75 'c_Series_Osums'( 'v_f', 't_a' ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP( X, Z ), Y ) ),
% 1.32/1.75 =( Z, Y ), ~( 'c_Ring__and__Field_Oordered__idom'( T, U, W, V0, V1, X, V2
% 1.32/1.75 , V3, V4, V5, V6 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, hAPP( Y, Z ) ), hAPP( Y, Z ) ), hAPP( hAPP( X, Z ),
% 1.32/1.75 Z ) ), ~( 'c_Ring__and__Field_Oordered__idom'( T, U, W, V0, V1, V2, Y, V3
% 1.32/1.75 , X, V4, V5 ) ) ],
% 1.32/1.75 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.32/1.75 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.32/1.75 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ],
% 1.32/1.75 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ) ) )
% 1.32/1.75 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Y ), ~( hBOOL(
% 1.32/1.75 hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.32/1.75 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP(
% 1.32/1.75 'c_Suc', Y ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ),
% 1.32/1.75 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), Y ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.32/1.75 ) ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), Y ), Z ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.75 'class_Int_Onumber__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.75 Y, X ) ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), X ), Y
% 1.32/1.75 ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.32/1.75 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( Z, Y, 'tc_nat' ) )
% 1.32/1.75 ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Z ) ) ) ],
% 1.32/1.75 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ) ) ) ) ],
% 1.32/1.75 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( T, Z, X ) ) ) ) ],
% 1.32/1.75 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.32/1.75 X ), T ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.32/1.75 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.32/1.75 X ), T ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ) ],
% 1.32/1.75 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ) ) ) ) ],
% 1.32/1.75 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( T, Z, X ) ) ) ) ],
% 1.32/1.75 [ ~( 'class_HOL_Ominus'( X ) ), =( hAPP( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( 't_a', X ) ), Y ), Z ), 'v_x' ),
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), hAPP( Y, 'v_x' ) ), hAPP(
% 1.32/1.75 Z, 'v_x' ) ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), T ) )
% 1.32/1.75 , hAPP( hAPP( Y, hAPP( hAPP( X, Z ), U ) ), T ) ), ~(
% 1.32/1.75 'c_Groebner__Basis_Ogb__semiring'( X, Y, W, V0, V1, V2 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ), hAPP( hAPP( Y, hAPP(
% 1.32/1.75 hAPP( X, Z ), U ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Y, W
% 1.32/1.75 , V0, U, V1 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ), hAPP( hAPP( Z, hAPP(
% 1.32/1.75 hAPP( X, T ), U ) ), Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, W
% 1.32/1.75 , V0, U, V1 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, hAPP( hAPP( X, T ), T ) ),
% 1.32/1.75 Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, U, W, T, V0 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.32/1.75 X, T, U, Y, W, V0 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.32/1.75 X, T, U, Z, W, V0 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.32/1.75 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.32/1.75 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.32/1.75 'c_Groebner__Basis_Ogb__semiring'( Y, X, W, V0, V1, V2 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.32/1.75 T, X, U, Y, W, V0 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.32/1.75 T, X, U, Z, W, V0 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.32/1.75 T, X, U, W, Y, V0 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.32/1.75 T, X, U, W, Z, V0 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.32/1.75 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.32/1.75 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.32/1.75 , hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), hAPP( hAPP( X, T ), U ) ) ) ),
% 1.32/1.75 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.32/1.75 , hAPP( hAPP( X, T ), hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), U ) ) ),
% 1.32/1.75 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.32/1.75 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.32/1.75 , V0, V1, V2 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.32/1.75 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.32/1.75 W, V0, V1, V2 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.32/1.75 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.32/1.75 , V0, V1, V2 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.32/1.75 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.32/1.75 W, V0, V1, V2 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.32/1.75 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.32/1.75 ~( 'c_Groebner__Basis_Ogb__semiring'( X, W, V0, V1, V2, V3 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.32/1.75 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.32/1.75 W, V0, V1, V2 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.32/1.75 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.32/1.75 W, V0, V1, V2 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.32/1.75 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.32/1.75 , V0, V1, V2 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.32/1.75 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.32/1.75 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.32/1.75 , V0, V1, V2 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.32/1.75 X, T, U, Y, W, V0 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.32/1.75 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.32/1.75 , V0, V1, V2 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.32/1.75 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.32/1.75 T, X, U, Y, W, V0 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.32/1.75 T, X, U, W, Y, V0 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.32/1.75 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.32/1.75 , V0, V1, V2 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.32/1.75 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 1.32/1.75 hAPP( X, Y ), T ) ), hAPP( hAPP( X, Y ), U ) ) ), ~(
% 1.32/1.75 'c_Groebner__Basis_Ogb__semiring'( Z, X, W, V0, V1, V2 ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.32/1.75 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.32/1.75 'c_Groebner__Basis_Ogb__semiring'( W, Y, X, V0, V1, V2 ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), T, X ),
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.32/1.75 ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ),
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.32/1.75 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 1.32/1.75 ) ],
% 1.32/1.75 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.32/1.75 ) ],
% 1.32/1.75 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.32/1.75 ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.32/1.75 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.75 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.75 ) ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 X ), X ), Y ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.75 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.32/1.75 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~(
% 1.32/1.75 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.32/1.75 [ ~( =( 'c_Set_Oinsert'( X, Y, Z ), 'c_Orderings_Obot__class_Obot'(
% 1.32/1.75 'tc_fun'( Z, 'tc_bool' ) ) ) ), hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), Y )
% 1.32/1.75 ) ],
% 1.32/1.75 [ =( 'c_Set_Oinsert'( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.75 'tc_fun'( Y, 'tc_bool' ) ), Z ), 'c_Set_Oinsert'( X,
% 1.32/1.75 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), Y ) ), Y ),
% 1.32/1.75 'c_Set_Oinsert'( X, Z, Y ) ) ],
% 1.32/1.75 [ ~( 'class_Lattices_Olattice'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.32/1.75 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ), X ),
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.32/1.75 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.32/1.75 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ), =( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.32/1.75 Z, 'tc_nat' ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.32/1.75 U ), hAPP( W, V0 ) ), V1 ) ) ), =( V0, Y ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, V4, V5, X, W, Z, T, V6, U
% 1.32/1.75 ) ) ],
% 1.32/1.75 [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y,
% 1.32/1.75 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ),
% 1.32/1.75 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'(
% 1.32/1.75 'tc_fun'( Z, 'tc_bool' ) ), Z ), Z ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z )
% 1.32/1.75 , X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~(
% 1.32/1.75 hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) )
% 1.32/1.75 , ~( hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ), T ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ), T ),
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ) ),
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__meet'( X ) ), =(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ) ),
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__meet'( X ) ), =(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ), T ),
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 'tc_nat' ) ), Y ) ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( X, 'tc_bool' )
% 1.32/1.75 ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( X, 'tc_bool' ) )
% 1.32/1.75 , Y ), Z ) ), Z ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( X
% 1.32/1.75 , 'tc_bool' ) ), Y ), Z ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y )
% 1.32/1.75 , 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), T, X ),
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.32/1.75 ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), Z ), T, X ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), T, X ),
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.32/1.75 ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ) ) ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.75 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.75 'tc_nat' ) ) ), Y ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ),
% 1.32/1.75 'c_HOL_Oone__class_Oone'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ) ) )
% 1.32/1.75 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.32/1.75 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.32/1.75 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), hAPP( 'c_Suc', X )
% 1.32/1.75 ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.32/1.75 ), Z ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.32/1.75 ), T ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.32/1.75 ), T ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Z
% 1.32/1.75 ), T ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP(
% 1.32/1.75 'c_Suc', Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) )
% 1.32/1.75 ],
% 1.32/1.75 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP( 'c_Suc', Y ) ) )
% 1.32/1.75 ) ],
% 1.32/1.75 [ ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), X ) ) ), hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP( 'c_Suc', X ) ) )
% 1.32/1.75 ],
% 1.32/1.75 [ ~( =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z
% 1.32/1.75 , 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' )
% 1.32/1.75 ) ) ), =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( Z,
% 1.32/1.75 'tc_bool' ) ), X ), Y ), X ) ],
% 1.32/1.75 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 'tc_nat' ), Z ), T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ),
% 1.32/1.75 T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Z ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ), hBOOL(
% 1.32/1.75 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z
% 1.32/1.75 ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~(
% 1.32/1.75 hBOOL( hAPP( 'c_lessequals'( Z, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.32/1.75 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), 'c_Set_Oinsert'( Y
% 1.32/1.75 , 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.32/1.75 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), Y ) )
% 1.32/1.75 ) ), hBOOL( hAPP( X, Z ) ) ],
% 1.32/1.75 [ ~( hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.32/1.75 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), Y ) )
% 1.32/1.75 ) ), hBOOL( hAPP( X, Z ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, hAPP( Y, Z ) ), hAPP( T, Z ) ), Z ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( U, W, V0, V1, V2, V3, T, V4, X, Y,
% 1.32/1.75 V5 ) ) ],
% 1.32/1.75 [ =( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, hAPP( X, Z ) ),
% 1.32/1.75 hAPP( X, T ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, V0, V1,
% 1.32/1.75 V2, V3, V4, V5, Y, X, V6 ) ) ],
% 1.32/1.75 [ =( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, hAPP( X, Z ) ),
% 1.32/1.75 hAPP( X, T ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, V0, V1,
% 1.32/1.75 V2, V3, X, V4, Y, V5, V6 ) ) ],
% 1.32/1.75 [ =( hAPP( X, hAPP( X, Y ) ), hAPP( X, Y ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( Z, T, U, W, V0, V1, V2, V3, V4, X,
% 1.32/1.75 V5 ) ) ],
% 1.32/1.75 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.32/1.75 V3, V4 ) ), =( hAPP( V3, Z ), Z ) ],
% 1.32/1.75 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, hAPP( Z, T ), U, W, V0,
% 1.32/1.75 V1, V2, V3, Z, V4 ) ), =( T, hAPP( Z, T ) ) ],
% 1.32/1.75 [ =( hAPP( X, Y ), hAPP( hAPP( Z, Y ), hAPP( T, Y ) ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( U, W, V0, V1, V2, V3, X, V4, Z, T,
% 1.32/1.75 V5 ) ) ],
% 1.32/1.75 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.75 'c_Int_OMin', X ) ), Y ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.75 'c_Int_OMin', X ) ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z,
% 1.32/1.75 T, U ), hAPP( W, Y ) ), V0 ) ) ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( V1, V2, Y, V3, V4, X, W, Z, T, V5, U
% 1.32/1.75 ) ), =( V0, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.75 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 X ) ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.32/1.75 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 X ) ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.32/1.75 ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.32/1.75 ) ],
% 1.32/1.75 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ) ), ~( hBOOL(
% 1.32/1.75 hAPP( 'c_lessequals'( X, 'tc_nat' ), T ) ) ), =( Z, hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), X ) ), Y ) ), U ) ) ],
% 1.32/1.75 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ) ), ~( hBOOL(
% 1.32/1.75 hAPP( 'c_lessequals'( T, 'tc_nat' ), X ) ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), T ) ), Y ) ), Z ), U ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.75 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y
% 1.32/1.75 , 'tc_nat' ), X ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), =( Z,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), =( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( X, 'tc_bool' )
% 1.32/1.75 ), Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), Y
% 1.32/1.75 ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( X, 'tc_bool' )
% 1.32/1.75 ), Y ), Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 1.32/1.75 ) ],
% 1.32/1.75 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), hAPP( 'c_Suc',
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.75 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 'tc_nat' ) ), Y ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( X ), hAPP( 'c_Finite__Set_Osetsum'( Y,
% 1.32/1.75 'tc_nat', X ), hAPP( 'c_SetInterval_Oord__class_OatLeastLessThan'( Z,
% 1.32/1.75 'tc_nat' ), T ) ) ), hAPP( 'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ),
% 1.32/1.75 hAPP( 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, 'tc_nat' ), U ) )
% 1.32/1.75 ), hAPP( 'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), hAPP(
% 1.32/1.75 'c_SetInterval_Oord__class_OatLeastLessThan'( U, 'tc_nat' ), T ) ) ), ~(
% 1.32/1.75 hBOOL( hAPP( 'c_lessequals'( U, 'tc_nat' ), T ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( Z, 'tc_nat' ), U ) ) ) ],
% 1.32/1.75 [ ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), Z ) ), T ) ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.32/1.75 ~( hBOOL( hAPP( X, T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), hAPP( 'c_Suc', T ) ) ) ) )
% 1.32/1.75 , ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ), 'tc_nat' ), Y ) ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 'tc_nat' ) ), Y ) ) ) ],
% 1.32/1.75 [ 'c_Finite__Set_Ofinite'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.32/1.75 'tc_bool' ) ), X ) ],
% 1.32/1.75 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( X )
% 1.32/1.75 , 'c_Power_Opower_Opower'( 'c_HOL_Oone__class_Oone'( X ),
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.75 , 'tc_nat' ), 'tc_nat' ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.75 , 'tc_nat' ), 'tc_nat' ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ) ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.32/1.75 'tc_nat' ), 'tc_nat' ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 'tc_nat' ) ), Y ) ) ) ],
% 1.32/1.75 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.32/1.75 'c_Orderings_Obot__class_Obot'( X ), X ), 'c_Orderings_Obot__class_Obot'(
% 1.32/1.75 X ) ) ],
% 1.32/1.75 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.32/1.75 'c_Orderings_Obot__class_Obot'( X ), Y, X ),
% 1.32/1.75 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.32/1.75 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.32/1.75 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 1.32/1.75 X, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.32/1.75 ) ) ) ],
% 1.32/1.75 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.32/1.75 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 1.32/1.75 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.32/1.75 ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP(
% 1.32/1.75 'c_Finite__Set_Osetsum'( Y, Z, X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( Z, 'tc_bool' ) ), T ),
% 1.32/1.75 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.32/1.75 'tc_bool' ) ), Z ) ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ),
% 1.32/1.75 hAPP( 'c_Finite__Set_Osetsum'( Y, Z, X ), T ) ), hAPP( Y, U ) ) ), ~(
% 1.32/1.75 hBOOL( hAPP( hAPP( 'c_in'( Z ), U ), T ) ) ), ~( 'c_Finite__Set_Ofinite'(
% 1.32/1.75 T, Z ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 1.32/1.75 'c_Finite__Set_Osetsum'( Y, Z, X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( Z, 'tc_bool' ) ), T ),
% 1.32/1.75 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.32/1.75 'tc_bool' ) ), Z ) ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ),
% 1.32/1.75 hAPP( 'c_Finite__Set_Osetsum'( Y, Z, X ), T ) ), hAPP( Y, U ) ) ), ~(
% 1.32/1.75 hBOOL( hAPP( hAPP( 'c_in'( Z ), U ), T ) ) ), ~( 'c_Finite__Set_Ofinite'(
% 1.32/1.75 T, Z ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.32/1.75 , X ) ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.75 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ),
% 1.32/1.75 X ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), U ), Z ) ), W ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( T, X ), hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W ) ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), U ) ), W ) ) ), ~( hBOOL(
% 1.32/1.75 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), Y ), X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), Z ), U ) ), W ) ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), U ), Z ) ), W ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T
% 1.32/1.75 ), X ), W ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ) ), U ), X ), W ) ),
% 1.32/1.75 ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.32/1.75 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), U ), X ),
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), W ) ) ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.32/1.75 , X ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.32/1.75 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ),
% 1.32/1.75 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ),
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_Suc', X ), 'tc_nat' ), Y ) ),
% 1.32/1.75 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) )
% 1.32/1.75 ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.32/1.75 ~( hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_Suc', X ), 'tc_nat' ), Y ) ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_Suc', X ), 'tc_nat' ), Y ) ),
% 1.32/1.75 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) )
% 1.32/1.75 ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.32/1.75 ~( hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_Suc', X ), 'tc_nat' ), Y ) ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ =( 'c_Relation_OImage'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y
% 1.32/1.75 , 'tc_bool' ) ), Y, Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.32/1.75 'tc_bool' ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.32/1.75 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z )
% 1.32/1.75 , T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), Z ) ) ), ~( hBOOL(
% 1.32/1.75 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.32/1.75 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z )
% 1.32/1.75 , T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ), ~( hBOOL(
% 1.32/1.75 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( =( 'c_Set_Oinsert'( X, Y, Z ), 'c_Orderings_Obot__class_Obot'(
% 1.32/1.75 'tc_fun'( Z, 'tc_bool' ) ) ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( X, 'tc_bool' )
% 1.32/1.75 ), Y ), 'c_Set_Oinsert'( Z, T, X ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( X, 'tc_bool' ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( X, 'tc_bool' ) ), Y ), T ) ),
% 1.32/1.75 'c_Set_Oinsert'( Z, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.32/1.75 'tc_bool' ) ), X ) ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( X, 'tc_bool' )
% 1.32/1.75 ), Y ), 'c_Set_Oinsert'( Z, T, X ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( X, 'tc_bool' ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( X, 'tc_bool' ) ), Y ),
% 1.32/1.75 'c_Set_Oinsert'( Z, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.32/1.75 'tc_bool' ) ), X ) ) ), T ) ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Obot'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.32/1.75 'c_Orderings_Obot__class_Obot'( X ), X ), Y ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.75 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.32/1.75 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), X ), 'c_Int_OPls' ) ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 'tc_nat' ), X ), Y ), 'tc_nat' ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.32/1.75 X, 'tc_nat' ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z )
% 1.32/1.75 , Y ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.32/1.75 Z ), 'tc_nat' ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ),
% 1.32/1.75 Y ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP(
% 1.32/1.75 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) )
% 1.32/1.75 ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP(
% 1.32/1.75 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) )
% 1.32/1.75 ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP(
% 1.32/1.75 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) )
% 1.32/1.75 ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ) ), ~( hBOOL(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), X ) ), Y ) ), U ) ) ) ),
% 1.32/1.75 ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), T ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), T ) ), U ) ) ), ~(
% 1.32/1.75 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), X ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ), U ) ) ) ), ~( hBOOL(
% 1.32/1.75 hAPP( 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ) ), ~( hBOOL(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), T ) ), Y ) ), Z ) ), U ) )
% 1.32/1.75 ), ~( hBOOL( hAPP( 'c_lessequals'( T, 'tc_nat' ), X ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ) ), T ) ), U ) )
% 1.32/1.75 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), T ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), U ) ) ) ), ~( hBOOL(
% 1.32/1.75 hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Z ), Y ) ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( X ), T ), Y ) ), Z ) ), U ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), T ), Z ) ), U ) ) ],
% 1.32/1.75 [ ~( 'class_RealVector_Ometric__space'( X ) ), 'c_SEQ_OCauchy'( Y, X ),
% 1.32/1.75 ~( hBOOL( hAPP( 'c_SEQ_OLIMSEQ'( Y, X ), Z ) ) ) ],
% 1.32/1.75 [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.32/1.75 'c_Set_Oimage'( Y, Z, T, X ) ) ), =( Z, 'c_Orderings_Obot__class_Obot'(
% 1.32/1.75 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.75 'tc_nat' ) ), Y ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.32/1.75 , 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.32/1.75 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, X, Z ), T )
% 1.32/1.75 , U ) ), T ), hAPP( hAPP( X, T ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y
% 1.32/1.75 , X, Z ), T ), U ) ) ), ~( 'c_OrderedGroup_Omonoid__mult'( Y, X, Z ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.32/1.75 , hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ) ), Z )
% 1.32/1.75 , hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc', X
% 1.32/1.75 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ),
% 1.32/1.75 ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) ) ) ],
% 1.32/1.75 [ =( hAPP( 'c_Suc', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ) ],
% 1.32/1.75 [ =( hAPP( 'c_Suc', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.32/1.75 [ ~( =( 'c_List_Ofilter'( X, Y, Z ), Y ) ), hBOOL( hAPP( X, T ) ), ~(
% 1.32/1.75 hBOOL( hAPP( hAPP( 'c_in'( Z ), T ), 'c_List_Oset'( Y, Z ) ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.32/1.75 'tc_nat' ), 'tc_nat' ), X ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.32/1.75 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), T ), ~(
% 1.32/1.75 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.75 X ), Y ), Z ) ), Z ), Y ) ],
% 1.32/1.75 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_SEQ_OZseq'(
% 1.32/1.75 hAPP( 'c_COMBC'( hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'( X, X ), 'tc_nat' ),
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( X ) ), Y ), 'tc_nat', X, X ), Z ), X ), ~(
% 1.32/1.75 hBOOL( hAPP( 'c_SEQ_OLIMSEQ'( Y, X ), Z ) ) ) ],
% 1.32/1.75 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), hBOOL( hAPP(
% 1.32/1.75 'c_SEQ_OLIMSEQ'( Y, X ), Z ) ), ~( 'c_SEQ_OZseq'( hAPP( 'c_COMBC'( hAPP(
% 1.32/1.75 hAPP( 'c_COMBB'( X, 'tc_fun'( X, X ), 'tc_nat' ),
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( X ) ), Y ), 'tc_nat', X, X ), Z ), X ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( hBOOL(
% 1.32/1.75 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.32/1.75 ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.75 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.32/1.75 ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ) ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.32/1.75 ), 'c_Parity_Oeven__odd__class_Oeven'(
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ],
% 1.32/1.75 [ ~( =( hAPP( X, Y ), hAPP( X, Z ) ) ), ~(
% 1.32/1.75 'c_Lattices_Oboolean__algebra'( T, X, U, W, V0, V1, V2, V3, V4 ) ), =( Y
% 1.32/1.75 , Z ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 X ), Y ), Z ) ), T ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), T ) ), Y ) ), Z ) ), U ) )
% 1.32/1.75 , ~( hBOOL( hAPP( 'c_lessequals'( T, 'tc_nat' ), X ) ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), X ) ), Y ) ), U ) ) ), ~(
% 1.32/1.75 hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), T ) ) ) ],
% 1.32/1.75 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 1.32/1.75 Y, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc',
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ),
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ),
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 'tc_nat' ) ), Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( X, 'tc_bool' )
% 1.32/1.75 ), 'c_Set_Oinsert'( Y, Z, X ) ), T ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( X, 'tc_bool' ) ), Z ), T ) ), ~(
% 1.32/1.75 hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP(
% 1.32/1.75 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, X ), Z ), hAPP(
% 1.32/1.75 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, X ), T ), 'tc_fun'( X,
% 1.32/1.75 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 1.32/1.75 ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.32/1.75 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ), ~( hBOOL(
% 1.32/1.75 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y
% 1.32/1.75 ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.32/1.75 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.32/1.75 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ),
% 1.32/1.75 'c_Int_OMin' ), 'c_Int_OPls' ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.32/1.75 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.75 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'tc_Int_Oint' ), X ), 'c_Int_OPls' ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.32/1.75 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( Y, X ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.32/1.75 ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Obot'( X ) ), =( hAPP(
% 1.32/1.75 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 't_a', X ) ), 'v_x' ),
% 1.32/1.75 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.32/1.75 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), hBOOL(
% 1.32/1.75 'c_Series_Osummable'( Y, X ) ), ~( hBOOL( hAPP( 'c_Series_Osums'( Y, X )
% 1.32/1.75 , Z ) ) ) ],
% 1.32/1.75 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), hBOOL(
% 1.32/1.75 'c_Series_Osummable'( Y, X ) ), ~( hBOOL( hAPP( 'c_Series_Osums'( Y, X )
% 1.32/1.75 , Z ) ) ) ],
% 1.32/1.75 [ =( hAPP( X, Y ), hAPP( Z, T ) ), ~( hBOOL( hAPP( hAPP( U, Y ), W ) ) )
% 1.32/1.75 , ~( 'c_Ring__and__Field_Oordered__idom'( V0, Z, W, V1, V2, U, V3, T, V4
% 1.32/1.75 , X, V5 ) ) ],
% 1.32/1.75 [ =( hAPP( X, Y ), Z ), ~( hBOOL( hAPP( hAPP( T, U ), Y ) ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( W, V0, U, V1, V2, T, V3, Z, V4, X,
% 1.32/1.75 V5 ) ) ],
% 1.32/1.75 [ ~( =( hAPP( X, Y ), hAPP( Z, T ) ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( U, Z, W, V0, V1, V2, V3, T, V4, X,
% 1.32/1.75 V5 ) ), hBOOL( hAPP( hAPP( V2, Y ), W ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.32/1.75 X, 'tc_nat' ), Y ) ) ) ],
% 1.32/1.75 [ ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.32/1.75 X, 'tc_nat' ), Y ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T
% 1.32/1.75 ) ) ) ],
% 1.32/1.75 [ 'c_Finite__Set_Ofinite'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.75 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ), X ), ~( 'c_Finite__Set_Ofinite'( Y
% 1.32/1.75 , X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_Finite__Set_Osetsum'( Y, Z, X )
% 1.32/1.75 , 'c_Lattices_Oupper__semilattice__class_Osup'( T, U, 'tc_fun'( Z,
% 1.32/1.75 'tc_bool' ) ) ) ), hAPP( 'c_Finite__Set_Osetsum'( Y, Z, X ),
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( T, U, 'tc_fun'( Z,
% 1.32/1.75 'tc_bool' ) ) ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.32/1.75 'c_Finite__Set_Osetsum'( Y, Z, X ), T ) ), hAPP( 'c_Finite__Set_Osetsum'(
% 1.32/1.75 Y, Z, X ), U ) ) ), ~( 'c_Finite__Set_Ofinite'( U, Z ) ), ~(
% 1.32/1.75 'c_Finite__Set_Ofinite'( T, Z ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T ), W ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( T, hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ), T ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ), 'c_Divides_Odiv__class_Omod'(
% 1.32/1.75 Z, Y, X ) ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.32/1.75 ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ),
% 1.32/1.75 'c_Int_OMin' ), X ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'tc_Int_Oint' ), 'c_Int_OMin' ), 'c_Int_OBit0'( X ) ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ),
% 1.32/1.75 'c_Int_OMin' ), 'c_Int_OBit0'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), 'c_Int_OMin' ), X ) ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ),
% 1.32/1.75 'c_Int_OMin' ), X ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'tc_Int_Oint' ), 'c_Int_OMin' ), 'c_Int_OBit1'( X ) ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ),
% 1.32/1.75 'c_Int_OMin' ), 'c_Int_OBit1'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), 'c_Int_OMin' ), X ) ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ) ) )
% 1.32/1.75 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'tc_nat' ), T ), Z ) ) ) ],
% 1.32/1.75 [ 'c_Finite__Set_Ofinite'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.75 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ), X ), ~( 'c_Finite__Set_Ofinite'( Y
% 1.32/1.75 , X ) ), ~( 'c_Finite__Set_Ofinite'( Z, X ) ) ],
% 1.32/1.75 [ 'c_Finite__Set_Ofinite'( X, Y ), ~( 'c_Finite__Set_Ofinite'( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( Y, 'tc_bool' ) ), X ), Z )
% 1.32/1.75 , Y ) ), ~( 'c_Finite__Set_Ofinite'( Z, Y ) ) ],
% 1.32/1.75 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Set_Oinsert'( X, Y
% 1.32/1.75 , Z ), 'c_Set_Oinsert'( X, T, Z ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.32/1.75 'c_Set_Oinsert'( X, 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T,
% 1.32/1.75 'tc_fun'( Z, 'tc_bool' ) ), Z ) ) ],
% 1.32/1.75 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X
% 1.32/1.75 , Y, 'tc_nat' ) ), Y ) ) ) ],
% 1.32/1.75 [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( X, Y, Z ), Z ),
% 1.32/1.75 'c_Set_Oinsert'( X, Y, Z ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z )
% 1.32/1.75 , X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~(
% 1.32/1.75 hBOOL( hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ) )
% 1.32/1.75 , ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.32/1.75 ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( T, 'tc_nat' ), Z ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( X, Y ) ), =( Z, Y ), ~( hBOOL( hAPP( 'c_Set_Oinsert'( Z,
% 1.32/1.75 X, T ), Y ) ) ) ],
% 1.32/1.75 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), X, 'tc_nat' ),
% 1.32/1.75 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 1.32/1.75 ) ), X ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.32/1.75 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.32/1.75 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Z ), Y ) ) ),
% 1.32/1.75 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), T ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Z ), X ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Z ), Y ) ) ) ],
% 1.32/1.75 [ 'c_Finite__Set_Ofinite'( 'c_Set_Oinsert'( X, Y, Z ), Z ), ~(
% 1.32/1.75 'c_Finite__Set_Ofinite'( Y, Z ) ) ],
% 1.32/1.75 [ 'c_Finite__Set_Ofinite'( X, Y ), ~( 'c_Finite__Set_Ofinite'(
% 1.32/1.75 'c_Set_Oinsert'( Z, X, Y ), Y ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.32/1.75 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X, Z, 'tc_nat' ) )
% 1.32/1.75 ), ~( hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ), ~( hBOOL(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ) ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.32/1.75 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, Z ), U ) )
% 1.32/1.75 , hAPP( hAPP( Y, Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.32/1.75 , T ), U ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, Y, V0, V1, V2
% 1.32/1.75 ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.32/1.75 Y ) ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Owellorder'( X ) ), ~( hBOOL( hAPP( Y, Z ) ) ),
% 1.32/1.75 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.32/1.75 'c_Orderings_Oord__class_OLeast'( Y, X ) ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.32/1.75 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ) ), U ) ), W ) ), ~(
% 1.32/1.75 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), Y ), T ) ), U ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), W ) ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.32/1.75 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ),
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T
% 1.32/1.75 ) ), W ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), U ) ), W
% 1.32/1.75 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), T ), U ) ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ), W ) ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.32/1.75 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ),
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W
% 1.32/1.75 ) ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), ~( =(
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 1.32/1.75 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( T, 'tc_bool' ) )
% 1.32/1.75 ) ), ~( 'c_Finite__Set_Ofinite'( Z, T ) ), ~( 'c_Finite__Set_Ofinite'( Y
% 1.32/1.75 , T ) ), =( hAPP( 'c_Finite__Set_Osetsum'( U, T, X ),
% 1.32/1.75 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 1.32/1.75 'tc_bool' ) ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.32/1.75 'c_Finite__Set_Osetsum'( U, T, X ), Y ) ), hAPP( 'c_Finite__Set_Osetsum'(
% 1.32/1.75 U, T, X ), Z ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.75 'tc_nat' ) ), Y ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.75 'tc_nat' ) ), Y ) ],
% 1.32/1.75 [ ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), Z ) ), T ) ), hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), T ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.32/1.75 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.75 , U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), W ), T ), Z, X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 1.32/1.75 'c_Finite__Set_Osetsum'( Y, Z, X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( Z, 'tc_bool' ) ), T ),
% 1.32/1.75 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.32/1.75 'tc_bool' ) ), Z ) ) ), hAPP( 'c_Finite__Set_Osetsum'( Y, Z, X ), T ) ),
% 1.32/1.75 hBOOL( hAPP( hAPP( 'c_in'( Z ), U ), T ) ), ~( 'c_Finite__Set_Ofinite'( T
% 1.32/1.75 , Z ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.75 'tc_nat' ), X ), Y ), 'tc_nat' ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.32/1.75 X, 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y
% 1.32/1.75 ) ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X )
% 1.32/1.75 , Z ), 'tc_nat' ), Y ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.75 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.75 ) ), Y ) ) ) ],
% 1.32/1.75 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y )
% 1.32/1.75 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.32/1.75 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, T ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ) ), T ),
% 1.32/1.75 'tc_nat' ), U ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), T ), 'tc_nat' ),
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), U ) ) ) ), ~( hBOOL(
% 1.32/1.75 hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.32/1.75 ) ), Z ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.32/1.75 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) )
% 1.32/1.75 ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), T ) ), Y ) ), Z ),
% 1.32/1.75 'tc_nat' ), U ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( T, 'tc_nat' ), X ) )
% 1.32/1.75 ) ],
% 1.32/1.75 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), T ) ), U ) ) ), ~(
% 1.32/1.75 hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T
% 1.32/1.75 ) ), X ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.32/1.75 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ), U ) )
% 1.32/1.75 ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.32/1.75 ) ), Z ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.32/1.75 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) )
% 1.32/1.75 ), ~( hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), X ) ), Y ) ), U ) ) ) ),
% 1.32/1.75 ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), T ) ) ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Owellorder'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.32/1.75 'c_Orderings_Oord__class_OLeast'( Y, X ), X ), Z ) ), ~( hBOOL( hAPP( Y,
% 1.32/1.75 Z ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.75 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ) ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ),
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ),
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( Y, X, 'tc_nat' ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.75 X ), Y ), Z ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.32/1.75 ) ), Z ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 X ), Z ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.75 Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 1.32/1.75 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.75 'tc_nat' ) ) ), Y ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ) ), ~( hBOOL(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.32/1.75 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_in'( X ), Y ), T ) ) ), ~( =(
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( T, Z, 'tc_fun'( X,
% 1.32/1.75 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 1.32/1.75 ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( X, 'tc_bool' )
% 1.32/1.75 ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( X,
% 1.32/1.75 'tc_bool' ) ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( T, Z,
% 1.32/1.75 'tc_fun'( X, 'tc_bool' ) ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.75 'tc_fun'( X, 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.32/1.75 Y, Z, 'tc_fun'( X, 'tc_bool' ) ) ), T ) ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), Y ) ) ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Oorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), Y ) ) ) ],
% 1.32/1.75 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), X )
% 1.32/1.75 ) ) ],
% 1.32/1.75 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), X )
% 1.32/1.75 ) ) ],
% 1.32/1.75 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), X )
% 1.32/1.75 , X ) ) ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), Y ) ) ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.32/1.75 Z, X ), Y ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.32/1.75 [ ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), X ), Y ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.75 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.75 ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 X ), Y ), Z ) ), T ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 'tc_nat' ) ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( X, 'tc_nat' ), Z ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.32/1.75 Z ), 'tc_nat' ), Y ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ),
% 1.32/1.75 X ), 'tc_nat' ), Y ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( X, 'tc_nat' ), Z ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 1.32/1.75 'c_Finite__Set_Osetsum'( Y, Z, X ), 'c_Set_Oinsert'( T, U, Z ) ), hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( Y, T ) ), hAPP(
% 1.32/1.75 'c_Finite__Set_Osetsum'( Y, Z, X ), U ) ) ), hBOOL( hAPP( hAPP( 'c_in'( Z
% 1.32/1.75 ), T ), U ) ), ~( 'c_Finite__Set_Ofinite'( U, Z ) ) ],
% 1.32/1.75 [ =( 'c_Set_Oinsert'( X, 'c_Set_Oinsert'( Y, Z, T ), T ),
% 1.32/1.75 'c_Set_Oinsert'( Y, 'c_Set_Oinsert'( X, Z, T ), T ) ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.32/1.75 Y, X ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z
% 1.32/1.75 ), Y ) ) ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.32/1.75 Z, X ), Y ) ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.32/1.75 Y, X ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y
% 1.32/1.75 ), Y ) ) ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), Y ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.32/1.75 Y, X ), Y ) ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( Z, X ), Y ) ) ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y
% 1.32/1.75 , X ), Z ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), Y )
% 1.32/1.75 ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.32/1.75 Z, X ), Y ) ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.32/1.75 Y, X ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z
% 1.32/1.75 ), Y ) ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.75 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T
% 1.32/1.75 , X ) ), T, X ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.75 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.32/1.75 ), Z ), T, X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.32/1.75 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X )
% 1.32/1.75 , Z ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.32/1.75 Y ), Z ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ),
% 1.32/1.75 ~( hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ), X ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.75 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( X, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y
% 1.32/1.75 , 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), X )
% 1.32/1.75 ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.75 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( X, 'tc_nat' ), Z ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.75 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z )
% 1.32/1.75 , X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ), ~(
% 1.32/1.75 hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) )
% 1.32/1.75 ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.32/1.75 [ ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ),
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ), ~(
% 1.32/1.75 hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( Y, 'tc_nat' ), X ) ) ), =( X, Z ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ) ), =( Z, T ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( X ), T ), T ) ) ), =( Y, Z ) ],
% 1.32/1.75 [ =( 'c_Set_Oimage'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.32/1.75 'tc_bool' ) ), Y, Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.32/1.75 'tc_bool' ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), =( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.32/1.75 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 X ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.32/1.75 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP(
% 1.32/1.75 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.32/1.75 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), U ) ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ) ) ) ],
% 1.32/1.75 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.32/1.75 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.32/1.75 'class_OrderedGroup_Omonoid__mult'( X ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ), ~(
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.32/1.75 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Z ), ~( hBOOL(
% 1.32/1.75 hAPP( 'c_lessequals'( Z, X ), Y ) ) ) ],
% 1.32/1.75 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), ~( =(
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y ) ), hBOOL(
% 1.32/1.75 hAPP( 'c_lessequals'( Y, X ), Z ) ) ],
% 1.32/1.75 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y ), ~( hBOOL(
% 1.32/1.75 hAPP( 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.32/1.75 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Z, Y, X ) ) ],
% 1.32/1.75 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.32/1.75 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, X,
% 1.32/1.75 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.32/1.75 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Z, Y, X ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.32/1.75 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ) ) )
% 1.32/1.75 ],
% 1.32/1.75 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.75 'tc_nat' ), X ), Y ), 'tc_nat' ), X ) ) ],
% 1.32/1.75 [ ~( =( 'c_Set_Oinsert'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y
% 1.32/1.75 , 'tc_bool' ) ), Y ), 'c_Set_Oinsert'( Z, 'c_Orderings_Obot__class_Obot'(
% 1.32/1.75 'tc_fun'( Y, 'tc_bool' ) ), Y ) ) ), =( X, Z ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.32/1.75 ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 'tc_nat' ) ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.75 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.32/1.75 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ), Y ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y
% 1.32/1.75 , 'tc_nat' ), X ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( Y, 'tc_nat' ), X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.32/1.75 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.75 'tc_nat' ) ), 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X,
% 1.32/1.75 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.32/1.75 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ) ) ],
% 1.32/1.75 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.75 'tc_nat' ) ), 'tc_nat' ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_OrderedGroup_Omonoid__mult'( Z
% 1.32/1.75 , X, T ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_OrderedGroup_Omonoid__mult'( Y
% 1.32/1.75 , X, T ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.75 , 'tc_nat' ), 'tc_nat' ), hBOOL( hAPP( 'c_lessequals'( Z, X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP(
% 1.32/1.75 hAPP( 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.75 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), T ) ), ~( hBOOL( hAPP( Y, T )
% 1.32/1.75 ) ) ],
% 1.32/1.75 [ =( 'c_Set_Oinsert'( hAPP( X, Y ), 'c_Set_Oimage'( X, Z, T, U ), U ),
% 1.32/1.75 'c_Set_Oimage'( X, Z, T, U ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), Z
% 1.32/1.75 ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.32/1.75 'tc_nat' ), 'tc_nat' ), X ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), Z ) ) ), ~( hBOOL(
% 1.32/1.75 hAPP( 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.32/1.75 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Set_Oinsert'( X, Y
% 1.32/1.75 , Z ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 1.32/1.75 'tc_bool' ) ) ), hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), T ) ) ],
% 1.32/1.75 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, 'c_Set_Oinsert'( Y
% 1.32/1.75 , Z, T ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.32/1.75 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 1.32/1.75 'tc_bool' ) ) ), hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), X ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ),
% 1.32/1.75 'c_Int_OBit1'( X ) ), 'c_Int_OMin' ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), X ), 'c_Int_OMin' ) ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), X ),
% 1.32/1.75 'c_Int_OMin' ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'tc_Int_Oint' ), 'c_Int_OBit1'( X ) ), 'c_Int_OMin' ) ) ) ],
% 1.32/1.75 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), hBOOL( hAPP(
% 1.32/1.75 hAPP( U, T ), W ) ), ~( hBOOL( hAPP( hAPP( X, Z ), V0 ) ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, U, X, V4, V0, Y, V5,
% 1.32/1.75 V6 ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( X, U ), Z ) ) ), hBOOL( hAPP( hAPP( W, V0 ), T ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, W, X, V4, U, Y, V5,
% 1.32/1.75 V6 ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), hBOOL( hAPP(
% 1.32/1.75 hAPP( U, Y ), W ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), T ) ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, U, X, V4, V0, Z, V5,
% 1.32/1.75 V6 ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( X, T ), U ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Y ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, W, X, V4, U, Z, V5,
% 1.32/1.75 V6 ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), hBOOL( hAPP(
% 1.32/1.75 hAPP( U, Z ), W ) ), ~( hBOOL( hAPP( hAPP( X, T ), V0 ) ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, U, X, V4, V0, Y, V5,
% 1.32/1.75 V6 ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( X, U ), T ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Z ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, W, X, V4, U, Y, V5,
% 1.32/1.75 V6 ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), hBOOL( hAPP(
% 1.32/1.75 hAPP( U, Y ), W ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), T ) ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, U, X, V4, V0, Z, V5,
% 1.32/1.75 V6 ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( X, T ), U ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Y ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, W, X, V4, U, Z, V5,
% 1.32/1.75 V6 ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), hBOOL( hAPP(
% 1.32/1.75 hAPP( U, T ), W ) ), ~( hBOOL( hAPP( hAPP( X, Z ), V0 ) ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, U, V4, V0, Y, V5,
% 1.32/1.75 V6 ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( X, U ), Z ) ) ), hBOOL( hAPP( hAPP( W, V0 ), T ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, X, W, V4, U, Y, V5,
% 1.32/1.75 V6 ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), hBOOL( hAPP(
% 1.32/1.75 hAPP( U, Y ), W ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), T ) ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, U, V4, V0, Z, V5,
% 1.32/1.75 V6 ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( X, T ), U ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Y ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, X, W, V4, U, Z, V5,
% 1.32/1.75 V6 ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), hBOOL( hAPP(
% 1.32/1.75 hAPP( U, Z ), W ) ), ~( hBOOL( hAPP( hAPP( X, T ), V0 ) ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, U, V4, V0, Y, V5,
% 1.32/1.75 V6 ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( X, U ), T ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Z ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, X, W, V4, U, Y, V5,
% 1.32/1.75 V6 ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), hBOOL( hAPP(
% 1.32/1.75 hAPP( U, Y ), W ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), T ) ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, U, V4, V0, Z, V5,
% 1.32/1.75 V6 ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( X, T ), U ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Y ) ), ~(
% 1.32/1.75 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, X, W, V4, U, Z, V5,
% 1.32/1.75 V6 ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( Z, T ) ) ), ~( hBOOL( hAPP( hAPP( X,
% 1.32/1.75 Y ), T ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, Y, V0, V1, X
% 1.32/1.75 , V2, V3, V4, Z, V5 ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, Y ), hAPP(
% 1.32/1.75 T, Z ) ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, Y, V0, V1, X
% 1.32/1.75 , V2, V3, V4, T, V5 ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, hAPP( Y, Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( X,
% 1.32/1.75 Z ), T ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, T, V0, V1, X
% 1.32/1.75 , V2, V3, V4, Y, V5 ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, hAPP( T, Y
% 1.32/1.75 ) ), Z ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, Z, V0, V1, X
% 1.32/1.75 , V2, V3, V4, T, V5 ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ), =( Y, T ), ~( hBOOL(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL(
% 1.32/1.75 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.32/1.75 ,
% 1.32/1.75 [ ~( 'class_Orderings_Oorder'( X ) ), =( 'c_Orderings_Obot__class_Obot'(
% 1.32/1.75 'tc_fun'( X, 'tc_bool' ) ), hAPP(
% 1.32/1.75 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Oorder'( X ) ), ~( =(
% 1.32/1.75 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), hAPP(
% 1.32/1.75 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, X ), Z ) ) ), ~( hBOOL(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ],
% 1.32/1.75 [ =( 'c_Set_Oinsert'( X, Y, Z ),
% 1.32/1.75 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Oinsert'( X,
% 1.32/1.75 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ), Z ), Y,
% 1.32/1.75 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.32/1.75 [ =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.32/1.75 'c_Set_Oimage'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool'
% 1.32/1.75 ) ), Z, X ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), Y ),
% 1.32/1.75 ~( 'c_Groebner__Basis_Ogb__semiring'( Z, T, X, U, W, V0 ) ) ],
% 1.32/1.75 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.32/1.75 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.32/1.75 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.32/1.75 ), U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( X ), W ), T ), Z, X ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ),
% 1.32/1.75 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.32/1.75 Y, X ), Z ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), X ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.32/1.75 [ =( X, hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.75 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), ~( hBOOL(
% 1.32/1.75 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.32/1.75 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ) ) ],
% 1.32/1.75 [ =( hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' )
% 1.32/1.75 , X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), X ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 'tc_nat' ) ), X ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.32/1.75 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X
% 1.32/1.75 ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z )
% 1.32/1.75 ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.32/1.75 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y
% 1.32/1.75 , X ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.32/1.75 Z ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.32/1.75 [ 'c_Finite__Set_Ofinite'( 'c_Set_Oimage'( X, Y, Z, T ), T ), ~(
% 1.32/1.75 'c_Finite__Set_Ofinite'( Y, Z ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.32/1.75 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z )
% 1.32/1.75 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.32/1.75 'c_HOL_Oone__class_Oone'( X ) ), Y ) ) ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) )
% 1.32/1.75 ) ],
% 1.32/1.75 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.75 X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.75 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL(
% 1.32/1.75 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Z
% 1.32/1.75 ), Y ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.32/1.75 [ =( hAPP( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 't_a', 'tc_bool' )
% 1.32/1.75 ), 'v_x' ), hAPP( hAPP( 'c_in'( 't_a' ), 'v_x' ),
% 1.32/1.75 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 't_a', 'tc_bool' ) ) ) ) ],
% 1.32/1.75 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.75 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.32/1.75 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), hBOOL( hAPP(
% 1.32/1.75 'c_SEQ_OLIMSEQ'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL(
% 1.32/1.75 'c_Series_Osummable'( Y, X ) ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Y ), X ), ~( hBOOL(
% 1.32/1.75 hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), Y ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.32/1.75 [ ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ), =( Y, hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), X ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( Y, 'tc_nat' ), X ) ) ) ],
% 1.32/1.75 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ) ), ~( hBOOL( hAPP(
% 1.32/1.75 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.32/1.75 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.32/1.75 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ) ), X ) ), ~( hBOOL( hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.75 'tc_nat' ) ), X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.32/1.75 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), Y ) ) ) ],
% 1.32/1.75 [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.32/1.75 'c_Set_Oinsert'( Y, Z, X ) ) ) ],
% 1.32/1.75 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ),
% 1.32/1.75 'c_Int_OPls' ), 'c_Int_OMin' ) ) ) ],
% 1.32/1.75 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.32/1.75 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), hAPP( hAPP(
% 1.32/1.75 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), U ) ) ) ), =(
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ) ) )
% 1.32/1.76 , =( Z, T ) ],
% 1.32/1.76 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, 'c_Set_Oinsert'( Y
% 1.32/1.76 , Z, T ), 'tc_fun'( T, 'tc_bool' ) ), 'c_Set_Oinsert'( Y,
% 1.32/1.76 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 1.32/1.76 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), X ) ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Set_Oinsert'( X, Y
% 1.32/1.76 , Z ), T, 'tc_fun'( Z, 'tc_bool' ) ), 'c_Set_Oinsert'( X,
% 1.32/1.76 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 1.32/1.76 'tc_bool' ) ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), T ) ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.32/1.76 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.32/1.76 hBOOL( hAPP( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.32/1.76 X ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.32/1.76 ) ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.32/1.76 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.76 Y ) ) ), 'c_Parity_Oeven__odd__class_Oeven'(
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ],
% 1.32/1.76 [ =( 'c_Set_Oimage'( X, 'c_Set_Oinsert'( Y, Z, T ), T, U ),
% 1.32/1.76 'c_Set_Oinsert'( hAPP( X, Y ), 'c_Set_Oimage'( X, Z, T, U ), U ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( 'c_Set_Oinsert'( X, Y, Z ), X ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y
% 1.32/1.76 , 'tc_nat' ), X ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.32/1.76 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z
% 1.32/1.76 , 'tc_nat' ), X ) ) ) ],
% 1.32/1.76 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.32/1.76 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.32/1.76 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ),
% 1.32/1.76 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ],
% 1.32/1.76 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.32/1.76 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.32/1.76 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.32/1.76 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.32/1.76 'tc_bool' ) ) ) ],
% 1.32/1.76 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.32/1.76 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.32/1.76 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ),
% 1.32/1.76 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y
% 1.32/1.76 ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X
% 1.32/1.76 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.32/1.76 Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.32/1.76 [ 'c_Finite__Set_Ofinite'( 'c_List_Oset'( X, Y ), Y ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), T ), Y ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ), T ) ) )
% 1.32/1.76 ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ) ) )
% 1.32/1.76 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Z ), T ) )
% 1.32/1.76 ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), T ), Y ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ), T ) ) )
% 1.32/1.76 ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ) ) )
% 1.32/1.76 ],
% 1.32/1.76 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Y ) ) ) ],
% 1.32/1.76 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), X ) ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( X, 'tc_bool' )
% 1.32/1.76 ), 'c_List_Oset'( Y, X ) ), 'c_Set_Oinsert'( Z,
% 1.32/1.76 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ) ),
% 1.32/1.76 'c_List_Oset'( 'c_List_Ofilter'( hAPP( hAPP( 'c_COMBB'( 'tc_bool',
% 1.32/1.76 'tc_bool', X ), 'c_Not' ), hAPP( 'c_COMBC'( 'c_fequal'( X ), X, X,
% 1.32/1.76 'tc_bool' ), Z ) ), Y, X ), X ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ) ) ],
% 1.32/1.76 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, hAPP( V1
% 1.32/1.76 , V2 ), V3, V1, V4 ) ), hBOOL( hAPP( hAPP( W, Z ), V2 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( hAPP( X, W ), hAPP( hAPP( V0, W ), Z ) ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, X, T, V4, Y, V0, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( hAPP( X, U ), hAPP( hAPP( V0, U ), Y ) ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, T, V4, Z, V0, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( U, Y ), W ) ), hBOOL( hAPP( hAPP( U, W ), Y ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, X, U, V3, V4, Z, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( X, T ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, X, V3, V4, U, Z, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, W ), Y ) ), W ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, X, T, V4, Z, V0, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, U ), Z ) ), U ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, T, V4, Y, V0, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( U, Z ), W ) ), hBOOL( hAPP( hAPP( U, W ), Z ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, X, U, V3, V4, Y, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( X, U ), T ) ) ), ~( hBOOL( hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, X, V3, V4, U, Y, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( hAPP( X, W ), hAPP( hAPP( V0, Z ), W ) ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, X, T, V4, Y, V0, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( hAPP( X, U ), hAPP( hAPP( V0, Y ), U ) ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, T, V4, Z, V0, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( U, Y ), W ) ), hBOOL( hAPP( hAPP( U, W ), Y ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, X, U, V3, V4, Z, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( X, T ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, X, V3, V4, U, Z, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, Y ), W ) ), W ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, X, T, V4, Z, V0, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, Z ), U ) ), U ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, T, V4, Y, V0, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( U, T ), W ) ), hBOOL( hAPP( hAPP( U, W ), T ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, X, U, V3, V4, Y, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( X, U ), Z ) ) ), ~( hBOOL( hAPP( hAPP( X, Z ), U ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, X, V3, V4, U, Y, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( hAPP( X, W ), hAPP( hAPP( V0, W ), Z ) ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, T, X, V4, Y, V0, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( hAPP( X, U ), hAPP( hAPP( V0, U ), Y ) ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, T, X, V4, Z, V0, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( U, Y ), W ) ), hBOOL( hAPP( hAPP( U, W ), Y ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, U, X, V3, V4, Z, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( X, T ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, X, V4, U, Z, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, W ), Y ) ), W ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, T, X, V4, Z, V0, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, U ), Z ) ), U ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, T, X, V4, Y, V0, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( U, Z ), W ) ), hBOOL( hAPP( hAPP( U, W ), Z ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, U, X, V3, V4, Y, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( X, U ), T ) ) ), ~( hBOOL( hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, X, V4, U, Y, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( hAPP( X, W ), hAPP( hAPP( V0, Z ), W ) ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, T, X, V4, Y, V0, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( hAPP( X, U ), hAPP( hAPP( V0, Y ), U ) ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, T, X, V4, Z, V0, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( U, Y ), W ) ), hBOOL( hAPP( hAPP( U, W ), Y ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, U, X, V3, V4, Z, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( X, T ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, X, V4, U, Z, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, Y ), W ) ), W ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, T, X, V4, Z, V0, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, Z ), U ) ), U ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, T, X, V4, Y, V0, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( U, T ), W ) ), hBOOL( hAPP( hAPP( U, W ), T ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, U, X, V3, V4, Y, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( X, U ), Z ) ) ), ~( hBOOL( hAPP( hAPP( X, Z ), U ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, X, V4, U, Y, V5,
% 1.32/1.76 V6 ) ) ],
% 1.32/1.76 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ),
% 1.32/1.76 'c_Int_OMin' ), 'c_Int_OMin' ) ) ) ],
% 1.32/1.76 [ =( 'c_Set_Oinsert'( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.76 'tc_fun'( Y, 'tc_bool' ) ), Z ), 'c_Set_Oinsert'( X,
% 1.32/1.76 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), Y ) ), Y ), Z
% 1.32/1.76 ), ~( hBOOL( hAPP( hAPP( 'c_in'( Y ), X ), Z ) ) ) ],
% 1.32/1.76 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, X, 'tc_fun'( Y,
% 1.32/1.76 'tc_bool' ) ), X ) ],
% 1.32/1.76 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.32/1.76 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Y, X ), Y ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.32/1.76 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.32/1.76 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.32/1.76 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.32/1.76 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ],
% 1.32/1.76 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( Y, 'tc_bool' ) ), Z ), X ),
% 1.32/1.76 'tc_fun'( Y, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.32/1.76 'tc_bool' ) ) ) ],
% 1.32/1.76 [ ~( 'class_Finite__Set_Ofinite_Ofinite'( X ) ), 'c_Finite__Set_Ofinite'(
% 1.32/1.76 Y, X ) ],
% 1.32/1.76 [ ~( 'class_Orderings_Owellorder'( X ) ), hBOOL( hAPP( Y,
% 1.32/1.76 'c_Orderings_Oord__class_OLeast'( Y, X ) ) ), ~( hBOOL( hAPP( Y, Z ) ) )
% 1.32/1.76 ],
% 1.32/1.76 [ ~( 'class_Orderings_Owellorder'( X ) ), hBOOL( hAPP( Y,
% 1.32/1.76 'c_Orderings_Oord__class_OLeast'( Y, X ) ) ), ~( hBOOL( hAPP( Y, Z ) ) )
% 1.32/1.76 ],
% 1.32/1.76 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~( hBOOL(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.32/1.76 'c_Groebner__Basis_Ogb__semiring'( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( X, 'tc_bool' )
% 1.32/1.76 ), 'c_Set_Oinsert'( Y, Z, X ) ), T ), 'c_Set_Oinsert'( Y, hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( X, 'tc_bool' ) ), Z ), T ), X ) )
% 1.32/1.76 , hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.32/1.76 U ), hAPP( W, V0 ) ), V1 ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'(
% 1.32/1.76 V2, V3, Y, V4, X, V5, W, Z, T, V6, U ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 1.32/1.76 'c_Finite__Set_Osetsum'( Y, Z, X ), T ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), hAPP( Y, U ) ), hAPP(
% 1.32/1.76 'c_Finite__Set_Osetsum'( Y, Z, X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( Z, 'tc_bool' ) ), T ),
% 1.32/1.76 'c_Set_Oinsert'( U, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.32/1.76 'tc_bool' ) ), Z ) ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), U ), T ) )
% 1.32/1.76 ), ~( 'c_Finite__Set_Ofinite'( T, Z ) ) ],
% 1.32/1.76 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.76 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.32/1.76 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.32/1.76 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.76 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.32/1.76 , 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), Y, 'tc_nat' )
% 1.32/1.76 , 'c_Divides_Odiv__class_Omod'( Z, Y, 'tc_nat' ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( X, 'tc_bool' )
% 1.32/1.76 ), 'c_Set_Oinsert'( Y, Z, X ) ), 'c_Set_Oinsert'( Y,
% 1.32/1.76 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ) ), Z ),
% 1.32/1.76 hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.76 X ), Y ), Z ) ), Z ), Y ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), X ), Y ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Y ), X ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X )
% 1.32/1.76 ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.32/1.76 'c_HOL_Oone__class_Oone'( X ) ), Y ) ) ) ],
% 1.32/1.76 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.76 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.32/1.76 ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.32/1.76 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( Z, X ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.32/1.76 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), Z ), U ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.32/1.76 [ 'c_Finite__Set_Ofinite'( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.32/1.76 X, Y, 'tc_fun'( Z, 'tc_bool' ) ), Z ), ~( 'c_Finite__Set_Ofinite'( X, Z )
% 1.32/1.76 ) ],
% 1.32/1.76 [ 'c_Finite__Set_Ofinite'( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.32/1.76 X, Y, 'tc_fun'( Z, 'tc_bool' ) ), Z ), ~( 'c_Finite__Set_Ofinite'( Y, Z )
% 1.32/1.76 ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__vector'( 't_a' ) ), =(
% 1.32/1.76 'c_Series_Osums'( 'v_f', 't_a' ), 'c_SEQ_OLIMSEQ'( hAPP( hAPP( 'c_COMBB'(
% 1.32/1.76 'tc_fun'( 'tc_nat', 'tc_bool' ), 't_a', 'tc_nat' ),
% 1.32/1.76 'c_Finite__Set_Osetsum'( 'v_f', 'tc_nat', 't_a' ) ),
% 1.32/1.76 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 'tc_nat' ), 'tc_nat' ) ), 't_a' ) ) ],
% 1.32/1.76 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.32/1.76 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.76 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ),
% 1.32/1.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ),
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Odiv'( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ),
% 1.32/1.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ],
% 1.32/1.76 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.76 ) ],
% 1.32/1.76 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.32/1.76 ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 1.32/1.76 =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.32/1.76 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.32/1.76 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.32/1.76 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.76 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.76 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 X ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 X ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.32/1.76 , Y ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.32/1.76 X ) ), =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.32/1.76 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 1.32/1.76 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.32/1.76 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 X ) ) ), =( Y, Z ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 X ) ) ), =( Y, Z ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.32/1.76 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.76 Y ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.32/1.76 Y ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.76 Y ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.32/1.76 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.32/1.76 Y ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.32/1.76 Y ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.76 Y ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.32/1.76 Y ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.32/1.76 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( hAPP( hAPP(
% 1.32/1.76 'c_COMBB'( X, Y, X ), Z ), hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ) ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), hAPP( Z, T ), X, Y ), ~( 'c_Lim_OLIM'( Z
% 1.32/1.76 , T, hAPP( Z, T ), X, Y ) ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.32/1.76 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( Z, T, hAPP( Z, T
% 1.32/1.76 ), X, Y ), ~( 'c_Lim_OLIM'( hAPP( hAPP( 'c_COMBB'( X, Y, X ), Z ), hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), T ) ), 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.76 hAPP( Z, T ), X, Y ) ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Ometric__space'( X ) ), ~(
% 1.32/1.76 'class_RealVector_Oreal__normed__vector'( Y ) ), 'c_Lim_OLIM'( hAPP( hAPP(
% 1.32/1.76 'c_COMBB'( Y, X, Y ), Z ), hAPP( 'c_HOL_Oplus__class_Oplus'( Y ), T ) ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( Y ), U, Y, X ), ~( 'c_Lim_OLIM'( Z, T, U, Y,
% 1.32/1.76 X ) ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Ometric__space'( X ) ), ~(
% 1.32/1.76 'class_RealVector_Oreal__normed__vector'( Y ) ), 'c_Lim_OLIM'( Z, T, U, Y
% 1.32/1.76 , X ), ~( 'c_Lim_OLIM'( hAPP( hAPP( 'c_COMBB'( Y, X, Y ), Z ), hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( Y ), T ) ), 'c_HOL_Ozero__class_Ozero'( Y ),
% 1.32/1.76 U, Y, X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.32/1.76 , Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), U ) ) ), ~( hBOOL(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.76 ) ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z )
% 1.32/1.76 , U ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.76 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.76 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.32/1.76 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ),
% 1.32/1.76 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ) ), =( Z,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.76 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.76 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.32/1.76 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ),
% 1.32/1.76 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ) ), =( T,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.32/1.76 X ), Y ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ),
% 1.32/1.76 'c_HOL_Oone__class_Oone'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.32/1.76 X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.32/1.76 'c_HOL_Oone__class_Oone'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( hBOOL(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.76 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), ~(
% 1.32/1.76 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), U ) ) ), ~( hBOOL(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ), X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( hBOOL(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.32/1.76 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.32/1.76 ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.76 ) ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z )
% 1.32/1.76 , U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T )
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.32/1.76 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~(
% 1.32/1.76 hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.32/1.76 ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.32/1.76 ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.32/1.76 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~(
% 1.32/1.76 hBOOL( hAPP( 'c_lessequals'( T, X ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.32/1.76 ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), T ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.32/1.76 ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ) ), =( Z,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ) ), =( Y,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.32/1.76 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, 'tc_fun'( X,
% 1.32/1.76 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~(
% 1.32/1.76 hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.32/1.76 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, 'tc_fun'( X,
% 1.32/1.76 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~(
% 1.32/1.76 hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), =( Y, T ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( T, Z, X ) ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_in'( X ), Y ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( X,
% 1.32/1.76 'tc_bool' ) ), Z ), T ) ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_in'( X ), Y ), 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T,
% 1.32/1.76 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_in'( X ), Y ), 'c_Lattices_Olower__semilattice__class_Oinf'( T, Z,
% 1.32/1.76 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ],
% 1.32/1.76 [ ~( hBOOL( hAPP( X, Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), Y ),
% 1.32/1.76 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), 'c_Set_Oimage'( Y, T,
% 1.32/1.76 U, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), T ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), 'c_Set_Oimage'( Y, T,
% 1.32/1.76 U, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), T ) ) ) ],
% 1.32/1.76 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_in'( T ), hAPP( U, Y ) ), 'c_Set_Oimage'( U, Z, X, T ) ) ) ],
% 1.32/1.76 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_in'( T ), hAPP( U, Y ) ), 'c_Set_Oimage'( U, Z, X, T ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Z, T, X ) ) ),
% 1.32/1.76 ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Z, T, X ) ) ),
% 1.32/1.76 ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ],
% 1.32/1.76 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Orderings_Obot__class_Obot'(
% 1.32/1.76 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ],
% 1.32/1.76 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Orderings_Obot__class_Obot'(
% 1.32/1.76 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), Y ),
% 1.32/1.76 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ) ) ],
% 1.32/1.76 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Orderings_Obot__class_Obot'(
% 1.32/1.76 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.32/1.76 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.32/1.76 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.32/1.76 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP(
% 1.32/1.76 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( 't_a', X )
% 1.32/1.76 ), 'v_x' ), 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( Y, 'v_x'
% 1.32/1.76 ), hAPP( Z, 'v_x' ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y
% 1.32/1.76 , X ), Y ) ) ],
% 1.32/1.76 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X
% 1.32/1.76 ), Y ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), X ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X
% 1.32/1.76 , 'tc_nat' ), Z ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( T, X ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z )
% 1.32/1.76 , T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( U, X ), T ) ) ), ~( hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.32/1.76 , Z ), U ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y
% 1.32/1.76 , X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( T, X ), Z ) ) ), ~( hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z
% 1.32/1.76 ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( T, X ), Z ) ) ) ],
% 1.32/1.76 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( Y, X ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ) ],
% 1.32/1.76 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X
% 1.32/1.76 ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ), ~( hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( T, X ), Z ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( hBOOL(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL(
% 1.32/1.76 hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) )
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( X, 'tc_bool' ) ), hAPP(
% 1.32/1.76 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, X ), Z ) ), hAPP(
% 1.32/1.76 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, X ), T ) ), hAPP(
% 1.32/1.76 'c_SetInterval_Oord__class_OatLeastLessThan'( T, X ), Z ) ), ~( hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Y,
% 1.32/1.76 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ) ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.32/1.76 , X ), hAPP( 'c_Suc', Y ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y,
% 1.32/1.76 'tc_nat' ), X ) ) ) ],
% 1.32/1.76 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), X ) ), ~(
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ), ~(
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X )
% 1.32/1.76 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.76 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ), Y ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( X, 'tc_bool' )
% 1.32/1.76 ), Y ), 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, 'tc_fun'( X
% 1.32/1.76 , 'tc_bool' ) ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( X, 'tc_bool' ) ), Y ), Z )
% 1.32/1.76 , hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( X, 'tc_bool' ) ), Y
% 1.32/1.76 ), T ), 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.32/1.76 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ) ) ), =( Y,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), X ) ), ~( hBOOL(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 'tc_nat' ) ), Y ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ), ~( hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Z ), Y ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ),
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ),
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ),
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ) ],
% 1.32/1.76 [ =( hAPP( 'c_Collect'( X ), hAPP( 'c_fequal'( X ), Y ) ),
% 1.32/1.76 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.32/1.76 'tc_bool' ) ), X ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), Y ), hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), X ) ) ],
% 1.32/1.76 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X )
% 1.32/1.76 , 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ), 'tc_nat' ), Y ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ],
% 1.32/1.76 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ],
% 1.32/1.76 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y
% 1.32/1.76 , X ), Z ) ), hBOOL( hAPP( 'c_lessequals'( Z, X ), Y ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( Y, 'tc_nat' ), X ) ) ],
% 1.32/1.76 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ],
% 1.32/1.76 [ ~( 'class_Orderings_Oorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_SEQ_OLIMSEQ'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_SEQ_OLIMSEQ'( hAPP(
% 1.32/1.76 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'( X, X ), 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( X ) ), Y ), 'tc_nat', X, X ), T ), X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_SEQ_OLIMSEQ'( T
% 1.32/1.76 , X ), Z ) ) ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_SEQ_OLIMSEQ'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_SEQ_OLIMSEQ'( hAPP(
% 1.32/1.76 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'( X, X ), 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( X ) ), T ), 'tc_nat', X, X ), Y ), X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_SEQ_OLIMSEQ'( T
% 1.32/1.76 , X ), Z ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ),
% 1.32/1.76 'c_Int_OPls' ), X ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), 'c_Int_OPls' ), X ) ) )
% 1.32/1.76 ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.32/1.76 , hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ),
% 1.32/1.76 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ), X ), ~(
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ) ), hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( 'c_Suc',
% 1.32/1.76 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ) ) ) ) ],
% 1.32/1.76 [ =( hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.32/1.76 , hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.32/1.76 ) ), 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ), X ),
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( Y, hAPP( hAPP( Y, T ), T ) )
% 1.32/1.76 , T ) ), ~( 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 1.32/1.76 'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), hAPP(
% 1.32/1.76 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, 'tc_nat' ), hAPP(
% 1.32/1.76 'c_Suc', T ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'tc_nat' ), T ), Z ) ) ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_Series_Osums'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z
% 1.32/1.76 ), hAPP( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ), ~( hBOOL(
% 1.32/1.76 hAPP( 'c_Series_Osums'( hAPP( hAPP( 'c_COMBB'( 'tc_nat', X, 'tc_nat' ), Y
% 1.32/1.76 ), 'c_Suc' ), X ), Z ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.32/1.76 'c_List_Osko__List__Xex__nat__less__eq__1__2'( X, Y ) ), Y ) ), ~( hBOOL(
% 1.32/1.76 hAPP( X, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_nat' ), Z ), hAPP(
% 1.32/1.76 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 'tc_nat' ), 'tc_nat' ), Y ) ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_nat' ), Y ),
% 1.32/1.76 hAPP( 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Z ) ) ) ), hBOOL(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.32/1.76 'c_List_Osko__List__Xall__nat__less__eq__1__1'( X, Z ) ), Z ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.32/1.76 ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.32/1.76 ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( X
% 1.32/1.76 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 1.32/1.76 ) ), X ) ) ) ],
% 1.32/1.76 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.76 'tc_nat' ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.32/1.76 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Divides_Odiv__class_Omod'(
% 1.32/1.76 X, 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.76 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.32/1.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 'tc_nat' ) ), 'c_Divides_Odiv__class_Omod'( X,
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), ~(
% 1.32/1.76 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ), hAPP(
% 1.32/1.76 hAPP( 'c_Power_Opower__class_Opower'( X ), T ), hAPP( 'c_Suc', Z ) ) ),
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), hAPP(
% 1.32/1.76 'c_Finite__Set_Osetsum'( hAPP( 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( X,
% 1.32/1.76 'tc_fun'( X, X ), 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X ) ), hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ) ), 'tc_nat', X, X ), hAPP( hAPP(
% 1.32/1.76 'c_COMBB'( 'tc_nat', X, 'tc_nat' ), hAPP( 'c_Power_Opower__class_Opower'(
% 1.32/1.76 X ), T ) ), hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ) ) ),
% 1.32/1.76 'tc_nat', X ), hAPP( 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc', Z ) )
% 1.32/1.76 ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 X ), T ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y )
% 1.32/1.76 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.32/1.76 ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 X ), T ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.32/1.76 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.32/1.76 ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.32/1.76 ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.32/1.76 ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), Y ) ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.32/1.76 ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), T ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.32/1.76 ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.32/1.76 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.32/1.76 ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.76 ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~(
% 1.32/1.76 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.32/1.76 ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.76 ) ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.76 ) ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.76 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.76 ), Y ), Z ), Y, X ), Z ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.76 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.76 ), Y ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.76 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.76 ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z )
% 1.32/1.76 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.32/1.76 , Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ), ~( hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z )
% 1.32/1.76 , Y ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.32/1.76 , Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z )
% 1.32/1.76 , Y ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.32/1.76 ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.32/1.76 ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.32/1.76 ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.32/1.76 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~(
% 1.32/1.76 hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.32/1.76 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~(
% 1.32/1.76 hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.32/1.76 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~(
% 1.32/1.76 hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.32/1.76 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~(
% 1.32/1.76 hBOOL( hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( 'c_lessequals'( T, X ), Z ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.32/1.76 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~(
% 1.32/1.76 hBOOL( hAPP( 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( 'c_lessequals'( T, X ), Y ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.32/1.76 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ), =( T, U ), =( Z,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_in'( X ), Y ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( X,
% 1.32/1.76 'tc_bool' ) ), T ), Z ) ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Y, Z, X ) ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Y, Z, X ) ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Oinsert'( Y, Z, X ) ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( X, 'tc_bool' ) ), Z ), T ) ) ),
% 1.32/1.76 hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.32/1.76 X ), Y ), Z ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( X, 'tc_bool' ) ), Z ), T ) ) ),
% 1.32/1.76 hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.32/1.76 X ), Y ), Z ) ) ) ],
% 1.32/1.76 [ ~( =( 'c_Set_Oinsert'( X, Y, Z ), 'c_Set_Oinsert'( X, T, Z ) ) ),
% 1.32/1.76 hBOOL( hAPP( hAPP( 'c_in'( Z ), X ), T ) ), hBOOL( hAPP( hAPP( 'c_in'( Z
% 1.32/1.76 ), X ), Y ) ), =( Y, T ) ],
% 1.32/1.76 [ =( 'c_Set_Oinsert'( X, Y, Z ), Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z )
% 1.32/1.76 , X ), Y ) ) ) ],
% 1.32/1.76 [ =( 'c_Set_Oimage'( X, 'c_Set_Oimage'( Y, Z, T, U ), U, W ),
% 1.32/1.76 'c_Set_Oimage'( hAPP( hAPP( 'c_COMBB'( U, W, T ), X ), Y ), Z, T, W ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_RealVector_Ometric__space'( X ) ), ~(
% 1.32/1.76 'class_RealVector_Ometric__space'( Y ) ), ~(
% 1.32/1.76 'class_RealVector_Ometric__space'( Z ) ), 'c_Lim_OLIM'( hAPP( hAPP(
% 1.32/1.76 'c_COMBB'( X, Y, Z ), T ), U ), W, hAPP( T, V0 ), Z, Y ), ~( 'c_Lim_OLIM'(
% 1.32/1.76 U, W, V0, Z, X ) ), ~( 'c_Lim_OLIM'( T, V0, hAPP( T, V0 ), X, Y ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.76 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.32/1.76 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), Z ) ) ],
% 1.32/1.76 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.76 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.32/1.76 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( Z, T, X ) ) ) ],
% 1.32/1.76 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.32/1.76 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.76 ), U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), W ), T ), Z, X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.32/1.76 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.32/1.76 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.32/1.76 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.32/1.76 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.32/1.76 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.76 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.32/1.76 ) ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 X ), Z ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.32/1.76 ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 X ), T ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y )
% 1.32/1.76 ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.32/1.76 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.76 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.76 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.76 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.76 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_Lim_OLIM'(
% 1.32/1.76 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X, X ) ],
% 1.32/1.76 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.76 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.76 ), Y ), T ), Z, X ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.32/1.76 Y ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.32/1.76 Y ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.32/1.76 Y ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.32/1.76 Y ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.32/1.76 Y ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.32/1.76 Y ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.32/1.76 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.32/1.76 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), U )
% 1.32/1.76 ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.76 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z,
% 1.32/1.76 T, X ) ), T, X ) ) ],
% 1.32/1.76 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.76 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.32/1.76 ) ), Z ), T, X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 X ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.32/1.76 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.32/1.76 ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.32/1.76 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.32/1.76 hAPP( 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.76 ) ), Y ) ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 hAPP( 'c_Suc', T ) ), X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.32/1.76 ), Z ), hAPP( 'c_Suc', T ) ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.32/1.76 hAPP( 'c_Power_Opower__class_Opower'( X ), T ), hAPP( 'c_Suc', Z ) ) ) )
% 1.32/1.76 , =( Y, T ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 X ), X ), T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ), Y ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP(
% 1.32/1.76 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.32/1.76 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ) ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.32/1.76 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( hAPP( 'c_COMBS'(
% 1.32/1.76 hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'( X, X ), Y ),
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ) ), Z ), Y, X, X ), T ), U, hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), W ), V0 ), Y, X ), ~( 'c_Lim_OLIM'( T, U
% 1.32/1.76 , V0, Y, X ) ), ~( 'c_Lim_OLIM'( Z, U, W, Y, X ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 1.32/1.76 'c_Finite__Set_Osetsum'( hAPP( 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( X,
% 1.32/1.76 'tc_fun'( X, X ), Y ), 'c_HOL_Ominus__class_Ominus'( X ) ), Z ), Y, X, X
% 1.32/1.76 ), T ), Y, X ), U ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), hAPP(
% 1.32/1.76 'c_Finite__Set_Osetsum'( Z, Y, X ), U ) ), hAPP( 'c_Finite__Set_Osetsum'(
% 1.32/1.76 T, Y, X ), U ) ) ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.32/1.76 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( hAPP( 'c_COMBS'(
% 1.32/1.76 hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'( X, X ), Y ),
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( X ) ), Z ), Y, X, X ), T ), U, hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( X ), W ), V0 ), Y, X ), ~( 'c_Lim_OLIM'( T
% 1.32/1.76 , U, V0, Y, X ) ), ~( 'c_Lim_OLIM'( Z, U, W, Y, X ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 1.32/1.76 'c_Finite__Set_Osetsum'( hAPP( 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( X,
% 1.32/1.76 'tc_fun'( X, X ), Y ), 'c_HOL_Oplus__class_Oplus'( X ) ), Z ), Y, X, X )
% 1.32/1.76 , T ), Y, X ), U ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.32/1.76 'c_Finite__Set_Osetsum'( Z, Y, X ), U ) ), hAPP( 'c_Finite__Set_Osetsum'(
% 1.32/1.76 T, Y, X ), U ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.32/1.76 hAPP( 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.76 ) ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ) ) ) ), ~(
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.76 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.32/1.76 , 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.76 Z, 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.32/1.76 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.76 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X
% 1.32/1.76 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ),
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.32/1.76 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.32/1.76 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.76 , 'tc_nat' ), 'tc_nat' ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.32/1.76 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.76 , 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.32/1.76 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Omod'( Y,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.32/1.76 , Y ) ) ],
% 1.32/1.76 [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.32/1.76 'tc_nat' ) ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.32/1.76 [ hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.32/1.76 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.32/1.76 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 'tc_nat' ) ) ) ) ],
% 1.32/1.76 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.32/1.76 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.32/1.76 [ ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), hBOOL(
% 1.32/1.76 hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 'tc_nat' ), 'tc_nat' ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ), ~( hBOOL( hAPP( X
% 1.32/1.76 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ), =( X,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.76 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 'tc_nat' ), 'tc_nat' ) ],
% 1.32/1.76 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.32/1.76 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ),
% 1.32/1.76 ~( 'c_Groebner__Basis_Ogb__semiring'( T, U, X, W, Z, V0 ) ) ],
% 1.32/1.76 [ ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ],
% 1.32/1.76 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) )
% 1.32/1.76 ) ],
% 1.32/1.76 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.32/1.76 [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 1.32/1.76 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 1.32/1.76 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 'tc_nat' ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.32/1.76 'tc_nat' ), X ) ) ],
% 1.32/1.76 [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 1.32/1.76 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( Y ), X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.76 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.76 Y, X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.32/1.76 ), Z ) ), T ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP( 'c_Suc', Y ) ) ), X
% 1.32/1.76 ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ) ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc',
% 1.32/1.76 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.32/1.76 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ), ~(
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.32/1.76 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), ~(
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc',
% 1.32/1.76 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.32/1.76 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP(
% 1.32/1.76 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ),
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.32/1.76 [ =( hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' )
% 1.32/1.76 , X ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ),
% 1.32/1.76 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ), ~( hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ), ~( hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.32/1.76 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), ~(
% 1.32/1.76 hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.32/1.76 , T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), U ) ) ), ~( hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.32/1.76 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), ~(
% 1.32/1.76 hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) )
% 1.32/1.76 ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.32/1.76 , Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), U ) ) ), ~( hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.76 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.76 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.32/1.76 ), 'c_Divides_Odiv__class_Odiv'( Z, T, X ) ), =( Y,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.76 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.76 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.32/1.76 ), 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), =( Z,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.76 ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.32/1.76 ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.76 ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 X ), Z ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y )
% 1.32/1.76 ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( hBOOL(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 X ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.32/1.76 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.32/1.76 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.32/1.76 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.32/1.76 , Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.32/1.76 , Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.32/1.76 , Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.32/1.76 , Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.32/1.76 , Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.76 ), Y ), Z ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.32/1.76 ), Y ), Z ), Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.32/1.76 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.76 ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ),
% 1.32/1.76 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.32/1.76 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.76 ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ),
% 1.32/1.76 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), ~(
% 1.32/1.76 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( hAPP( hAPP(
% 1.32/1.76 'c_COMBB'( X, X, Y ), hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ) ), T )
% 1.32/1.76 , U, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), W ), Y, X ), ~(
% 1.32/1.76 'c_Lim_OLIM'( T, U, W, Y, X ) ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( 'c_Finite__Set_Osetsum'( Z
% 1.32/1.76 , T, X ), U ) ), hAPP( 'c_Finite__Set_Osetsum'( hAPP( hAPP( 'c_COMBB'( X
% 1.32/1.76 , X, T ), hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ) ), Z ), T, X ), U
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( 'c_Finite__Set_Osetsum'( Z
% 1.32/1.76 , T, X ), U ) ), hAPP( 'c_Finite__Set_Osetsum'( hAPP( hAPP( 'c_COMBB'( X
% 1.32/1.76 , X, T ), hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ) ), Z ), T, X ), U
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.32/1.76 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.32/1.76 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.32/1.76 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.32/1.76 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.32/1.76 ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.32/1.76 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.76 , X ) ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.32/1.76 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.76 , X ) ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.32/1.76 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.32/1.76 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.32/1.76 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.76 hAPP( 'c_Suc', Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_Lim_OLIM'(
% 1.32/1.76 hAPP( 'c_COMBC'( 'c_HOL_Otimes__class_Otimes'( X ), X, X, X ), Y ), Z,
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X, X ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_SEQ_OCauchy'(
% 1.32/1.76 hAPP( hAPP( 'c_COMBB'( X, X, 'tc_nat' ), hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ) ), Z ), X ), ~( 'c_SEQ_OCauchy'( Z
% 1.32/1.76 , X ) ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_SEQ_OLIMSEQ'( hAPP( hAPP( 'c_COMBB'( X, X, 'tc_nat' ), hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ) ), Z ), X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_SEQ_OLIMSEQ'( Z, X ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_SEQ_OZseq'(
% 1.32/1.76 hAPP( hAPP( 'c_COMBB'( X, X, 'tc_nat' ), hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ) ), Z ), X ), ~( 'c_SEQ_OZseq'( Z,
% 1.32/1.76 X ) ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_SEQ_OZseq'(
% 1.32/1.76 hAPP( hAPP( 'c_COMBB'( X, X, 'tc_nat' ), hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ) ), Z ), X ), ~( 'c_SEQ_OZseq'( Z,
% 1.32/1.76 X ) ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), hBOOL(
% 1.32/1.76 'c_Series_Osummable'( hAPP( hAPP( 'c_COMBB'( X, X, 'tc_nat' ), hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ) ), Z ), X ) ), ~( hBOOL(
% 1.32/1.76 'c_Series_Osummable'( Z, X ) ) ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), hBOOL(
% 1.32/1.76 'c_Series_Osummable'( hAPP( hAPP( 'c_COMBB'( X, X, 'tc_nat' ), hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ) ), Z ), X ) ), ~( hBOOL(
% 1.32/1.76 'c_Series_Osummable'( Z, X ) ) ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_Series_Osums'( hAPP( hAPP( 'c_COMBB'( X, X, 'tc_nat' ), hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ) ), Z ), X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_Series_Osums'( Z, X ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_Series_Osums'( hAPP( hAPP( 'c_COMBB'( X, X, 'tc_nat' ), hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ) ), Z ), X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_Series_Osums'( Z, X ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.32/1.76 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.32/1.76 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.32/1.76 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ) ],
% 1.32/1.76 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.76 'c_Int_OPls', X ) ), Y ) ],
% 1.32/1.76 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.76 'c_Int_OPls', X ) ), Y ), Y ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.32/1.76 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), Y ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_in'( X ), Y ), 'c_Lattices_Olower__semilattice__class_Oinf'( Z, hAPP(
% 1.32/1.76 'c_Collect'( X ), T ), 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), Y ),
% 1.32/1.76 'c_Lattices_Olower__semilattice__class_Oinf'( T, hAPP( 'c_Collect'( Z ),
% 1.32/1.76 X ), 'tc_fun'( Z, 'tc_bool' ) ) ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.32/1.76 'c_Lattices_Olower__semilattice__class_Oinf'( Z, hAPP( 'c_Collect'( X ),
% 1.32/1.76 T ), 'tc_fun'( X, 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( T, Y ) ) ), ~( hBOOL(
% 1.32/1.76 hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ],
% 1.32/1.76 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.32/1.76 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.32/1.76 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.32/1.76 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP( 'c_Suc',
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.32/1.76 [ ~( =( hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) )
% 1.32/1.76 , Y ) ), =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat'
% 1.32/1.76 ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( 'c_Suc', X ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( 'c_Suc', X ) ) ) ],
% 1.32/1.76 [ =( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X
% 1.32/1.76 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP( 'c_Suc', hAPP( 'c_Suc'
% 1.32/1.76 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ) ],
% 1.32/1.76 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP( 'c_Suc',
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 'tc_nat' ) ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.32/1.76 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.32/1.76 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.32/1.76 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, hAPP( 'c_Suc'
% 1.32/1.76 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc',
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ) ],
% 1.32/1.76 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, hAPP(
% 1.32/1.76 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP( 'c_Suc',
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.32/1.76 [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 'tc_nat' ) ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) )
% 1.32/1.76 ],
% 1.32/1.76 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( 'c_Suc',
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.32/1.76 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, hAPP(
% 1.32/1.76 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, hAPP( 'c_Suc'
% 1.32/1.76 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc',
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.76 [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 'tc_nat' ) ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( 'c_Suc',
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.32/1.76 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.76 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.76 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ) ), Z ) ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.32/1.76 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.76 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ) ],
% 1.32/1.76 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), X ),
% 1.32/1.76 'c_Int_OPls' ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'tc_Int_Oint' ), 'c_Int_OBit1'( X ) ), 'c_Int_OPls' ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ),
% 1.32/1.76 'c_Int_OBit1'( X ) ), 'c_Int_OPls' ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), X ), 'c_Int_OPls' ) ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), X ), Y
% 1.32/1.76 ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ),
% 1.32/1.76 'c_Int_OBit1'( X ) ), 'c_Int_OBit0'( Y ) ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ),
% 1.32/1.76 'c_Int_OBit1'( X ) ), 'c_Int_OBit0'( Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), X ), Y ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), X ), Y
% 1.32/1.76 ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ),
% 1.32/1.76 'c_Int_OBit1'( X ) ), 'c_Int_OBit0'( Y ) ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ),
% 1.32/1.76 'c_Int_OBit1'( X ) ), 'c_Int_OBit0'( Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), X ), Y ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), X ),
% 1.32/1.76 'c_Int_OPls' ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'tc_Int_Oint' ), 'c_Int_OBit0'( X ) ), 'c_Int_OPls' ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ),
% 1.32/1.76 'c_Int_OBit0'( X ) ), 'c_Int_OPls' ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), X ), 'c_Int_OPls' ) ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ),
% 1.32/1.76 'c_Int_OPls' ), X ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'tc_Int_Oint' ), 'c_Int_OPls' ), 'c_Int_OBit0'( X ) ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ),
% 1.32/1.76 'c_Int_OPls' ), 'c_Int_OBit0'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), 'c_Int_OPls' ), X ) ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.76 'class_Int_Onumber__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.32/1.76 ) ), 'c_HOL_Oone__class_Oone'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), Y ), 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.76 'class_Int_Onumber__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), Y ), 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X )
% 1.32/1.76 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.76 X ) ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.76 'class_Int_Onumber__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), 'c_Int_OBit1'( 'c_Int_OPls' )
% 1.32/1.76 ), Y ) ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.76 'class_Int_Onumber__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), 'c_Int_OBit1'( 'c_Int_OPls' )
% 1.32/1.76 ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.32/1.76 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.32/1.76 ) ) ) ) ],
% 1.32/1.76 [ =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.32/1.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ) ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( hAPP( 'c_Suc', X ), 'tc_nat' ), hAPP( 'c_Suc', Y ) ) ) )
% 1.32/1.76 ],
% 1.32/1.76 [ hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_Suc', X ), 'tc_nat' ), hAPP(
% 1.32/1.76 'c_Suc', Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) )
% 1.32/1.76 ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.32/1.76 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'(
% 1.32/1.76 X, Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_Suc', X ), 'tc_nat' ), X ) )
% 1.32/1.76 ) ],
% 1.32/1.76 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( hAPP( 'c_Suc', X ), 'tc_nat' ), Y ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( 'c_Suc', Y ) ) ),
% 1.32/1.76 ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.32/1.76 [ =( X, Y ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X
% 1.32/1.76 ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X
% 1.32/1.76 ), hAPP( 'c_Suc', Y ) ) ) ) ],
% 1.32/1.76 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.32/1.76 , Y ), hAPP( 'c_Suc', X ) ) ) ), hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), X ) ) ],
% 1.32/1.76 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.32/1.76 , X ), hAPP( 'c_Suc', Y ) ) ) ), hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.32/1.76 , X ) ), hAPP( 'c_Suc', Y ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.32/1.76 'tc_nat' ), X ), Y ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( 'c_Suc'
% 1.32/1.76 , U ) ), hAPP( hAPP( Y, T ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z
% 1.32/1.76 ), T ), U ) ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.32/1.76 'c_Suc', Y ) ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.76 'tc_nat' ), X ), Y ) ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.32/1.76 X ) ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.76 'tc_nat' ), X ), Y ) ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.32/1.76 X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.32/1.76 'c_Suc', Y ) ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y ) ),
% 1.32/1.76 hAPP( 'c_Suc', Z ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.32/1.76 ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z )
% 1.32/1.76 ) ],
% 1.32/1.76 [ =( X, hAPP( 'c_Suc', Y ) ), hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' )
% 1.32/1.76 , Y ) ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( 'c_Suc', Y
% 1.32/1.76 ) ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP(
% 1.32/1.76 'c_Suc', Y ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat'
% 1.32/1.76 ), Y ), X ) ) ],
% 1.32/1.76 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y )
% 1.32/1.76 ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ),
% 1.32/1.76 hAPP( 'c_Suc', X ) ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), X ) ),
% 1.32/1.76 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP(
% 1.32/1.76 'c_Suc', X ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.32/1.76 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP(
% 1.32/1.76 'c_Suc', X ) ), Y ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP(
% 1.32/1.76 'c_Suc', Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'tc_nat' ), X ), Y ) ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', Z ) ), hAPP( hAPP( T, Y ), hAPP(
% 1.32/1.76 hAPP( X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W,
% 1.32/1.76 V0, V1 ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', Z ) ), hAPP( hAPP( T, Y ), hAPP(
% 1.32/1.76 hAPP( X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W,
% 1.32/1.76 V0, V1 ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ), hAPP( hAPP( Y, Z ),
% 1.32/1.76 hAPP( 'c_Suc', T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Y, W
% 1.32/1.76 , V0, V1 ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ), hAPP( hAPP( Z, Y ),
% 1.32/1.76 hAPP( 'c_Suc', T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Z, W
% 1.32/1.76 , V0, V1 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP(
% 1.32/1.76 'c_Suc', X ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP(
% 1.32/1.76 'c_Suc', X ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP(
% 1.32/1.76 'c_Suc', X ) ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'tc_nat' ), X ), Z ) ) ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.32/1.76 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =(
% 1.32/1.76 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP(
% 1.32/1.76 'c_Suc', X ) ), Y ) ), =( hAPP( 'c_Suc', X ), Y ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_Suc', X ), 'tc_nat' ), Y ) ),
% 1.32/1.76 hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) ) ],
% 1.32/1.76 [ ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( hAPP( 'c_Suc', Y ), 'tc_nat' ), X ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_Suc', X ), 'tc_nat' ), hAPP(
% 1.32/1.76 'c_Suc', X ) ) ) ],
% 1.32/1.76 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', X ), 'tc_nat' ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', X ), 'tc_nat' ),
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP(
% 1.32/1.76 'c_Suc', X ) ), hAPP( 'c_Suc', Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.32/1.76 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP(
% 1.32/1.76 'c_Suc', X ) ), hAPP( 'c_Suc', Y ) ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP(
% 1.32/1.76 'c_Suc', X ) ), hAPP( 'c_Suc', Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.32/1.76 [ =( 'c_Int_OBit1'( 'c_Int_OMin' ), 'c_Int_OMin' ) ],
% 1.32/1.76 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OMin' ) ), =( X, 'c_Int_OMin' ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( =( 'c_Int_OMin', 'c_Int_OBit1'( X ) ) ), =( 'c_Int_OMin', X ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ),
% 1.32/1.76 'c_Int_OBit1'( X ) ), 'c_Int_OBit1'( Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), X ), Y ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), X ), Y
% 1.32/1.76 ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ),
% 1.32/1.76 'c_Int_OBit1'( X ) ), 'c_Int_OBit1'( Y ) ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ),
% 1.32/1.76 'c_Int_OBit1'( X ) ), 'c_Int_OBit1'( Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), X ), Y ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), X ), Y
% 1.32/1.76 ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ),
% 1.32/1.76 'c_Int_OBit1'( X ) ), 'c_Int_OBit1'( Y ) ) ) ) ],
% 1.32/1.76 [ =( 'c_Int_OMin', 'c_Int_OBit1'( 'c_Int_OMin' ) ) ],
% 1.32/1.76 [ ~( =( 'c_Int_OPls', 'c_Int_OMin' ) ) ],
% 1.32/1.76 [ ~( =( 'c_Int_OMin', 'c_Int_OPls' ) ) ],
% 1.32/1.76 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ),
% 1.32/1.76 'c_Int_OPls' ), 'c_Int_OPls' ) ) ) ],
% 1.32/1.76 [ ~( =( 'c_Int_OMin', 'c_Int_OBit0'( X ) ) ) ],
% 1.32/1.76 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OMin' ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ),
% 1.32/1.76 'c_Int_OBit0'( X ) ), 'c_Int_OBit0'( Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), X ), Y ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), X ), Y
% 1.32/1.76 ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ),
% 1.32/1.76 'c_Int_OBit0'( X ) ), 'c_Int_OBit0'( Y ) ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ),
% 1.32/1.76 'c_Int_OBit0'( X ) ), 'c_Int_OBit0'( Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), X ), Y ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), X ), Y
% 1.32/1.76 ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ),
% 1.32/1.76 'c_Int_OBit0'( X ) ), 'c_Int_OBit0'( Y ) ) ) ) ],
% 1.32/1.76 [ =( X, 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), hAPP( 'c_Suc', X ) ) ) ) )
% 1.32/1.76 , ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), 'tc_nat' ), Y ) ) ),
% 1.32/1.76 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ) ) ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.76 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.32/1.76 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.76 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.32/1.76 , ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ), Y ),
% 1.32/1.76 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ) ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ), X ),
% 1.32/1.76 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y ) ) ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.32/1.76 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 'tc_nat' ) ), X ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 'tc_nat' ) ), X ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 'tc_nat' ) ), Y ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 'tc_nat' ) ), X ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z )
% 1.32/1.76 , X ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.76 Z ), Y ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat'
% 1.32/1.76 ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 'tc_nat' ) ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), 'tc_nat' ), hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 'tc_nat' ) ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ), hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), Y ), 'c_Int_OPls' ) ) ),
% 1.32/1.76 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), X ),
% 1.32/1.76 'c_Int_OPls' ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), Y ), 'c_Int_OPls' ) ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), X ), 'c_Int_OPls' ) ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), X ), Y ) ) ), ~( hBOOL(
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), 'c_Int_OPls' ), Y
% 1.32/1.76 ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ),
% 1.32/1.76 'c_Int_OPls' ), X ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'tc_Int_Oint' ), Y ), X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.76 Y, 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ) ) )
% 1.32/1.76 ],
% 1.32/1.76 [ =( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( 'c_COMBC'(
% 1.32/1.76 'c_in'( 't_a' ), 't_a', 'tc_fun'( 't_a', 'tc_bool' ), 'tc_bool' ), X ),
% 1.32/1.76 hAPP( 'c_COMBC'( 'c_in'( 't_a' ), 't_a', 'tc_fun'( 't_a', 'tc_bool' ),
% 1.32/1.76 'tc_bool' ), Y ), 'tc_fun'( 't_a', 'tc_bool' ) ), 'v_x' ), hAPP( hAPP(
% 1.32/1.76 'c_in'( 't_a' ), 'v_x' ), 'c_Lattices_Olower__semilattice__class_Oinf'( X
% 1.32/1.76 , Y, 'tc_fun'( 't_a', 'tc_bool' ) ) ) ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ) ), Y, 'tc_nat'
% 1.32/1.76 ), 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', Z ), Y, 'tc_nat' ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_Series_Osums'( hAPP( 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'( X
% 1.32/1.76 , X ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X ) ), Y ), 'tc_nat', X, X
% 1.32/1.76 ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ),
% 1.32/1.76 ~( hBOOL( hAPP( 'c_Series_Osums'( Z, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_Series_Osums'( Y, X ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_SEQ_OLIMSEQ'( hAPP( 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'( X,
% 1.32/1.76 X ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X ) ), Y ), 'tc_nat', X, X
% 1.32/1.76 ), Z ), X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) )
% 1.32/1.76 , ~( hBOOL( hAPP( 'c_SEQ_OLIMSEQ'( Z, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_SEQ_OLIMSEQ'( Y, X ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), hBOOL(
% 1.32/1.76 'c_Series_Osummable'( hAPP( 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'(
% 1.32/1.76 X, X ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X ) ), Y ), 'tc_nat', X,
% 1.32/1.76 X ), Z ), X ) ), ~( hBOOL( 'c_Series_Osummable'( Z, X ) ) ), ~( hBOOL(
% 1.32/1.76 'c_Series_Osummable'( Y, X ) ) ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_SEQ_OLIMSEQ'( hAPP( 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'( X,
% 1.32/1.76 X ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X ) ), Y ), 'tc_nat', X, X )
% 1.32/1.76 , Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ),
% 1.32/1.76 ~( hBOOL( hAPP( 'c_SEQ_OLIMSEQ'( Z, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_SEQ_OLIMSEQ'( Y, X ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), hBOOL(
% 1.32/1.76 'c_Series_Osummable'( hAPP( 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'(
% 1.32/1.76 X, X ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X ) ), Y ), 'tc_nat', X
% 1.32/1.76 , X ), Z ), X ) ), ~( hBOOL( 'c_Series_Osummable'( Z, X ) ) ), ~( hBOOL(
% 1.32/1.76 'c_Series_Osummable'( Y, X ) ) ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_SEQ_OZseq'(
% 1.32/1.76 hAPP( 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'( X, X ), 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ominus__class_Ominus'( X ) ), Y ), 'tc_nat', X, X ), Z ), X ), ~(
% 1.32/1.76 'c_SEQ_OZseq'( Z, X ) ), ~( 'c_SEQ_OZseq'( Y, X ) ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_Series_Osums'( hAPP( 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'( X
% 1.32/1.76 , X ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X ) ), Y ), 'tc_nat', X
% 1.32/1.76 , X ), Z ), X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), T ), U )
% 1.32/1.76 ) ), ~( hBOOL( hAPP( 'c_Series_Osums'( Z, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_Series_Osums'( Y, X ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_SEQ_OZseq'(
% 1.32/1.76 hAPP( 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'( X, X ), 'tc_nat' ),
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ) ), Y ), 'tc_nat', X, X ), Z ), X ), ~(
% 1.32/1.76 'c_SEQ_OZseq'( Z, X ) ), ~( 'c_SEQ_OZseq'( Y, X ) ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_SEQ_OLIMSEQ'( hAPP( 'c_COMBC'( hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'( X,
% 1.32/1.76 X ), 'tc_nat' ), 'c_HOL_Oplus__class_Oplus'( X ) ), Y ), 'tc_nat', X, X )
% 1.32/1.76 , Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ),
% 1.32/1.76 ~( hBOOL( hAPP( 'c_SEQ_OLIMSEQ'( Y, X ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_SEQ_OLIMSEQ'( hAPP( 'c_COMBC'( hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'( X,
% 1.32/1.76 X ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X ) ), Y ), 'tc_nat', X, X
% 1.32/1.76 ), Z ), X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), T ), Z ) ) )
% 1.32/1.76 , ~( hBOOL( hAPP( 'c_SEQ_OLIMSEQ'( Y, X ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.32/1.76 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Y ), ~( hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( Z, X ), Y ) ) ) ],
% 1.32/1.76 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), ~( =(
% 1.32/1.76 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Z ) ), hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( Y, X ), Z ) ) ],
% 1.32/1.76 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.32/1.76 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Z ), ~( hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.32/1.76 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.32/1.76 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.32/1.76 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ), Y ) ],
% 1.32/1.76 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.32/1.76 X ), T ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ), ~( hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.32/1.76 X ), T ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ), ~( hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( Y, X ), 'c_Lattices_Oupper__semilattice__class_Osup'( Z,
% 1.32/1.76 Y, X ) ) ) ],
% 1.32/1.76 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( Y, X ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.32/1.76 Z, X ) ) ) ],
% 1.32/1.76 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.32/1.76 X ), T ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ), ~( hBOOL(
% 1.32/1.76 hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.32/1.76 [ ~( 'class_Lattices_Olattice'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X
% 1.32/1.76 ), 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ) ) ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.32/1.76 'c_Suc', X ) ) ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.32/1.76 'c_Suc', Y ) ) ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.32/1.76 'c_Suc', X ) ) ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.32/1.76 'c_Suc', Y ) ) ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.32/1.76 'c_Suc', X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.32/1.76 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.76 Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.32/1.76 'c_Suc', X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.32/1.76 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.76 Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.32/1.76 , X ) ), Y ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ),
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.32/1.76 'tc_nat' ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' )
% 1.32/1.76 ), Y ) ) ) ],
% 1.32/1.76 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.76 'c_Int_OMin', X ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.32/1.76 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ), 'c_HOL_Oone__class_Oone'( X ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.32/1.76 V3, V4 ) ), =( hAPP( hAPP( 'c_Power_Opower_Opower'( V1, V2, V4 ), Z ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ],
% 1.32/1.76 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( Z, hAPP( hAPP( T, hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( U, W, V0 ), X ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( U
% 1.32/1.76 , W, V0 ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), Y ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, T, Z, V4, V5, U, W, V6,
% 1.32/1.76 V0 ) ) ],
% 1.32/1.76 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( Z, hAPP( hAPP( T, hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( U, W, V0 ), V1 ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( U
% 1.32/1.76 , W, V0 ), X ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), Y ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, T, Z, V4, V5, U, W, V6,
% 1.32/1.76 V0 ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, U ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y
% 1.32/1.76 , Z ), U ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Ocomm__ring__1'( X, Y, W, T, V0, V1, Z ) ) ],
% 1.32/1.76 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ),
% 1.32/1.76 ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.32/1.76 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.32/1.76 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, hAPP( hAPP( Z, hAPP(
% 1.32/1.76 hAPP( 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.32/1.76 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), Z, V2, V3, V4, T, U, V5
% 1.32/1.76 , W ) ), =( V0, hAPP( hAPP( Z, hAPP( hAPP( 'c_Power_Opower_Opower'( T, U
% 1.32/1.76 , W ), V0 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( T, U, W ), V1 ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.32/1.76 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, hAPP( hAPP( Z, hAPP(
% 1.32/1.76 hAPP( 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.32/1.76 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), Z, V2, V3, V4, T, U, V5
% 1.32/1.76 , W ) ), =( V1, hAPP( hAPP( Z, hAPP( hAPP( 'c_Power_Opower_Opower'( T, U
% 1.32/1.76 , W ), V0 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( T, U, W ), V1 ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.32/1.76 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, Z, X, V4, V5, T, U, V6, W
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.32/1.76 V3, V4 ) ), hBOOL( hAPP( hAPP( U, hAPP( hAPP( T, hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( V1, V2, V4 ), Z ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( V1
% 1.32/1.76 , V2, V4 ), Z ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), Z ) ) ],
% 1.32/1.76 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.32/1.76 U ), W ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V0, V1, Y, V2, X, V3, V4, Z, T, V5,
% 1.32/1.76 U ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( Y, T ), T ) ), ~(
% 1.32/1.76 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.32/1.76 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( Z, T, U ), W ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), V0, V1, V2, V3, Z, T, V4, U ) ), =( W,
% 1.32/1.76 hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T, U ), W ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.32/1.76 [ =( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), U ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y
% 1.32/1.76 , Z, T ), U ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, V4, X, Y, Z, V5,
% 1.32/1.76 T ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, U ) ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y
% 1.32/1.76 , Z ), U ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, V4, T, X, Y, V5,
% 1.32/1.76 Z ) ) ],
% 1.32/1.76 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.32/1.76 V3, V4 ) ), =( hAPP( hAPP( T, hAPP( hAPP( 'c_Power_Opower_Opower'( V1, V2
% 1.32/1.76 , V4 ), Z ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( V1, V2, V4 ), Z ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), Z ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.76 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T
% 1.32/1.76 ), U ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), W ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, V3, X, V4, Y, Z, V5,
% 1.32/1.76 T ) ) ],
% 1.32/1.76 [ ~( hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z,
% 1.32/1.76 T, U ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( W, V0, Y, V1, V2, X, V3, Z, T, V4, U
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( Z, T, U ), W ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z
% 1.32/1.76 , T, U ), V0 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), V1 ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V2, V3, V1, Y, V4, X, V5, Z, T, V6,
% 1.32/1.76 U ) ) ],
% 1.32/1.76 [ ~( hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( T, U, W ), Y ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.32/1.76 , U, W ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ) ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V0, V1, Y, Z, V2, X, V3, T, U, V4, W
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.32/1.76 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), =( V0, Y ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, Z, V4, X, V5, T, U, V6, W
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP(
% 1.32/1.76 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.32/1.76 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), =( V1, Y ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, Z, V4, X, V5, T, U, V6, W
% 1.32/1.76 ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.32/1.76 U ), W ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), =( W, Y ), ~(
% 1.32/1.76 'c_Ring__and__Field_Oordered__idom'( V0, V1, Y, V2, V3, X, V4, Z, T, V5,
% 1.32/1.76 U ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 'tc_nat' ) ), Y ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 'tc_nat' ) ), X ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 'tc_nat' ) ), X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'tc_nat' ), Y ), Z ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 'tc_nat' ) ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'tc_nat' ), X ), Z ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.32/1.76 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 'tc_nat' ) ), Z ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 'tc_nat' ) ), X ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ),
% 1.32/1.76 X ) ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.32/1.76 Y ) ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ) ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) ) ],
% 1.32/1.76 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~(
% 1.32/1.76 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ) ), =( Y, Z ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 'tc_nat' ) ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.32/1.76 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ) ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 'tc_nat' ) ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y ), 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ) ) ), =( Z, T ), =( Y
% 1.32/1.76 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.32/1.76 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), =( X,
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( =( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.32/1.76 ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.32/1.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.32/1.76 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ),
% 1.32/1.76 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.76 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 1.32/1.76 'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), hAPP(
% 1.32/1.76 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.76 'tc_nat' ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.76 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ) ) ), hAPP(
% 1.32/1.76 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.76 X ), hAPP( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( Y,
% 1.32/1.76 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), hAPP( Y,
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( Y,
% 1.32/1.76 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.32/1.76 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.76 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Z ) ) ),
% 1.32/1.76 ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.32/1.76 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.76 hAPP( 'c_Suc', Z ) ), X ), 'tc_nat' ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), Y ) ) ) )
% 1.32/1.76 ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y ) ),
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', X )
% 1.32/1.76 ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.32/1.76 , Y ), Z ) ) ) ],
% 1.32/1.76 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.32/1.76 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.76 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), X ) ),
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', Z )
% 1.32/1.76 ), Y ) ) ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.32/1.76 , X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ),
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.32/1.76 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.32/1.76 'c_Suc', Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.32/1.76 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.32/1.76 [ ~( 'class_RealVector_Ometric__space'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_SEQ_OLIMSEQ'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_SEQ_OLIMSEQ'( hAPP(
% 1.32/1.76 hAPP( 'c_COMBB'( 'tc_nat', X, 'tc_nat' ), Y ), 'c_Suc' ), X ), Z ) ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_RealVector_Ometric__space'( X ) ), hBOOL( hAPP(
% 1.32/1.76 'c_SEQ_OLIMSEQ'( hAPP( hAPP( 'c_COMBB'( 'tc_nat', X, 'tc_nat' ), Y ),
% 1.32/1.76 'c_Suc' ), X ), Z ) ), ~( hBOOL( hAPP( 'c_SEQ_OLIMSEQ'( Y, X ), Z ) ) ) ]
% 1.32/1.76 ,
% 1.32/1.76 [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP(
% 1.32/1.76 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( 't_a', X )
% 1.32/1.76 ), 'v_x' ), 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( Y, 'v_x'
% 1.32/1.76 ), hAPP( Z, 'v_x' ), X ) ) ],
% 1.32/1.77 [ =( hAPP( 'c_Collect'( X ), hAPP( 'c_COMBS'( hAPP( hAPP( 'c_COMBB'(
% 1.32/1.77 'tc_bool', 'tc_fun'( 'tc_bool', 'tc_bool' ), X ), 'c_and' ), hAPP(
% 1.32/1.77 'c_fequal'( X ), Y ) ), X, 'tc_bool', 'tc_bool' ), Z ) ), 'c_Set_Oinsert'(
% 1.32/1.77 Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), X ) ), ~(
% 1.32/1.77 hBOOL( hAPP( Z, Y ) ) ) ],
% 1.32/1.77 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP(
% 1.32/1.77 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, X ), Z ), hAPP(
% 1.32/1.77 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, X ), T ), 'tc_fun'( X,
% 1.32/1.77 'tc_bool' ) ), hAPP( 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, X )
% 1.32/1.77 , T ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.32/1.77 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), ~(
% 1.32/1.77 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP(
% 1.32/1.77 'c_Finite__Set_Osetsum'( hAPP( 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( X,
% 1.32/1.77 'tc_fun'( X, X ), 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X ) ), hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), Y ) ), 'tc_nat', X, X ), hAPP( hAPP(
% 1.32/1.77 'c_COMBB'( 'tc_nat', X, 'tc_nat' ), hAPP( 'c_Power_Opower__class_Opower'(
% 1.32/1.77 X ), Z ) ), hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.32/1.77 , T ) ) ) ), 'tc_nat', X ), hAPP(
% 1.32/1.77 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.77 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc', T ) ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( 'c_Finite__Set_Osetsum'(
% 1.32/1.77 hAPP( 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'( X, X ), 'tc_nat' ),
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ) ), hAPP( 'c_Power_Opower__class_Opower'(
% 1.32/1.77 X ), Y ) ), 'tc_nat', X, X ), hAPP( hAPP( 'c_COMBB'( 'tc_nat', X,
% 1.32/1.77 'tc_nat' ), hAPP( 'c_Power_Opower__class_Opower'( X ), Z ) ), hAPP(
% 1.32/1.77 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ) ) ), 'tc_nat', X ), hAPP(
% 1.32/1.77 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.77 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc', T ) ) ) ) ) ],
% 1.32/1.77 [ ~( 'class_Power_Opower'( X ) ), ~(
% 1.32/1.77 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 1.32/1.77 'c_Finite__Set_Osetsum'( hAPP( 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( X,
% 1.32/1.77 'tc_fun'( X, X ), 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X ) ), hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), Y ) ), 'tc_nat', X, X ), hAPP( hAPP(
% 1.32/1.77 'c_COMBB'( 'tc_nat', X, 'tc_nat' ), hAPP( 'c_Power_Opower__class_Opower'(
% 1.32/1.77 X ), Z ) ), hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ) ) ),
% 1.32/1.77 'tc_nat', X ), hAPP( 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc', T ) )
% 1.32/1.77 ), hAPP( 'c_Finite__Set_Osetsum'( hAPP( 'c_COMBS'( hAPP( hAPP( 'c_COMBB'(
% 1.32/1.77 X, 'tc_fun'( X, X ), 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X ) ),
% 1.32/1.77 hAPP( hAPP( 'c_COMBB'( 'tc_nat', X, 'tc_nat' ), hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), Y ) ), hAPP(
% 1.32/1.77 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ) ) ), 'tc_nat', X, X ), hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), Z ) ), 'tc_nat', X ), hAPP(
% 1.32/1.77 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.77 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc', T ) ) ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.32/1.77 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.77 ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.32/1.77 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.32/1.77 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.77 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.32/1.77 ), Y ), Y ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.32/1.77 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.32/1.77 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.32/1.77 =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.32/1.77 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.77 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( hBOOL( hAPP(
% 1.32/1.77 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.77 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.77 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( hBOOL( hAPP(
% 1.32/1.77 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.77 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.32/1.77 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.32/1.77 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.77 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.32/1.77 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.77 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.32/1.77 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.77 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.32/1.77 ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), =(
% 1.32/1.77 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.77 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.32/1.77 ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.77 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), U ) ), hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.32/1.77 X, Y, Z ), T ), U ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.77 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~(
% 1.32/1.77 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.32/1.77 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.32/1.77 U ), W ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), V0 ) ) ) ), ~(
% 1.32/1.77 'c_Ring__and__Field_Oordered__idom'( V1, V2, Y, V3, X, V4, V5, Z, T, V6,
% 1.32/1.77 U ) ) ],
% 1.32/1.77 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, U ) ),
% 1.32/1.77 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), W ) ), hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower_Opower'( X, Y, Z ), U ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), W ) ) ), ~(
% 1.32/1.77 'c_Ring__and__Field_Ocomm__ring__1'( X, Y, V0, T, V1, V2, Z ) ) ],
% 1.32/1.77 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, X ) ),
% 1.32/1.77 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), U ) ), X ), ~(
% 1.32/1.77 'c_Ring__and__Field_Ocomm__ring__1'( X, Y, W, T, V0, V1, Z ) ) ],
% 1.32/1.77 [ ~( 'class_Orderings_Odense__linear__order'( X ) ), =( hAPP(
% 1.32/1.77 'c_Collect'( X ), hAPP( 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( 'tc_bool',
% 1.32/1.77 'tc_fun'( 'tc_bool', 'tc_bool' ), X ), 'c_and' ), hAPP(
% 1.32/1.77 'c_HOL_Oord__class_Oless'( X ), Y ) ), X, 'tc_bool', 'tc_bool' ), hAPP(
% 1.32/1.77 'c_COMBC'( 'c_HOL_Oord__class_Oless'( X ), X, X, 'tc_bool' ), Z ) ) ),
% 1.32/1.77 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), hBOOL( hAPP(
% 1.32/1.77 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ],
% 1.32/1.77 [ ~( 'class_Orderings_Odense__linear__order'( X ) ), ~( =( hAPP(
% 1.32/1.77 'c_Collect'( X ), hAPP( 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( 'tc_bool',
% 1.32/1.77 'tc_fun'( 'tc_bool', 'tc_bool' ), X ), 'c_and' ), hAPP(
% 1.32/1.77 'c_HOL_Oord__class_Oless'( X ), Y ) ), X, 'tc_bool', 'tc_bool' ), hAPP(
% 1.32/1.77 'c_COMBC'( 'c_HOL_Oord__class_Oless'( X ), X, X, 'tc_bool' ), Z ) ) ),
% 1.32/1.77 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ), ~( hBOOL(
% 1.32/1.77 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ],
% 1.32/1.77 [ =( hAPP( 'c_Collect'( X ), hAPP( 'c_COMBS'( hAPP( hAPP( 'c_COMBB'(
% 1.32/1.77 'tc_bool', 'tc_fun'( 'tc_bool', 'tc_bool' ), X ), 'c_and' ), hAPP(
% 1.32/1.77 'c_COMBC'( 'c_fequal'( X ), X, X, 'tc_bool' ), Y ) ), X, 'tc_bool',
% 1.32/1.77 'tc_bool' ), Z ) ), 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'(
% 1.32/1.77 'tc_fun'( X, 'tc_bool' ) ), X ) ), ~( hBOOL( hAPP( Z, Y ) ) ) ],
% 1.32/1.77 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), ~(
% 1.32/1.77 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( hAPP( hAPP(
% 1.32/1.77 'c_COMBB'( X, X, Y ), hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ) ), T )
% 1.32/1.77 , U, 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_Lim_OLIM'( T, U,
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.77 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), ~(
% 1.32/1.77 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( hAPP( hAPP(
% 1.32/1.77 'c_COMBB'( X, X, Y ), hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ) ), T )
% 1.32/1.77 , U, 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_Lim_OLIM'( T, U,
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.77 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), ~(
% 1.32/1.77 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( hAPP( 'c_COMBC'(
% 1.32/1.77 hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'( X, X ), Y ),
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ) ), Z ), Y, X, X ), T ), U, hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), W ), T ), Y, X ), ~( 'c_Lim_OLIM'( Z,
% 1.32/1.77 U, W, Y, X ) ) ],
% 1.32/1.77 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_Finite__Set_Osetsum'( Y, Z, X
% 1.32/1.77 ), T ) ), U ), hAPP( 'c_Finite__Set_Osetsum'( hAPP( 'c_COMBC'( hAPP(
% 1.32/1.77 hAPP( 'c_COMBB'( X, 'tc_fun'( X, X ), Z ), 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.77 X ) ), Y ), Z, X, X ), U ), Z, X ), T ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_Finite__Set_Osetsum'( Y, Z, X
% 1.32/1.77 ), T ) ), U ), hAPP( 'c_Finite__Set_Osetsum'( hAPP( 'c_COMBC'( hAPP(
% 1.32/1.77 hAPP( 'c_COMBB'( X, 'tc_fun'( X, X ), Z ), 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.77 X ) ), Y ), Z, X, X ), U ), Z, X ), T ) ) ],
% 1.32/1.77 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.77 X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.32/1.77 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), ~(
% 1.32/1.77 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( hAPP( 'c_COMBS'(
% 1.32/1.77 hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'( X, X ), Y ),
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ) ), Z ), Y, X, X ), T ), U, hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), W ), V0 ), Y, X ), ~( 'c_Lim_OLIM'( T
% 1.32/1.77 , U, V0, Y, X ) ), ~( 'c_Lim_OLIM'( Z, U, W, Y, X ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.32/1.77 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.32/1.77 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.32/1.77 ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =( hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.32/1.77 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.77 Y, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.32/1.77 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.32/1.77 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.32/1.77 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.77 , 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ), =(
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.77 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oone__class_Oone'( X )
% 1.32/1.77 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X )
% 1.32/1.77 ) ],
% 1.32/1.77 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ),
% 1.32/1.77 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.32/1.77 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.32/1.77 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.77 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ) ), Z ) ) ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( X ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP(
% 1.32/1.77 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.77 ) ) ) ) ],
% 1.32/1.77 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.77 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.77 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.32/1.77 ), Z ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.77 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.32/1.77 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ) ) ],
% 1.32/1.77 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_SEQ_OZseq'(
% 1.32/1.77 hAPP( 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'( X, X ), 'tc_nat' ),
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ) ), Y ), 'tc_nat', X, X ), Z ), X ), ~(
% 1.32/1.77 'c_SEQ_OZseq'( Z, X ) ), ~( 'c_SEQ_OZseq'( Y, X ) ) ],
% 1.32/1.77 [ ~( 'class_Lattices_Olattice'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X
% 1.32/1.77 ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ) ) ],
% 1.32/1.77 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ) ) ), ~( hBOOL(
% 1.32/1.77 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.32/1.77 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ) ) ), ~( hBOOL(
% 1.32/1.77 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ],
% 1.32/1.77 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP(
% 1.32/1.77 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( T, Y, X ), X ), Z ) ) ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP(
% 1.32/1.77 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ), Z ) ) ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP(
% 1.32/1.77 'c_lessequals'( Y, X ), 'c_Lattices_Oupper__semilattice__class_Osup'( Z,
% 1.32/1.77 T, X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.32/1.77 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP(
% 1.32/1.77 'c_lessequals'( Y, X ), 'c_Lattices_Oupper__semilattice__class_Osup'( Z,
% 1.32/1.77 T, X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.32/1.77 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP(
% 1.32/1.77 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( T, Y, X ), X ), Z ) ) ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP(
% 1.32/1.77 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ), Z ) ) ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.32/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 1.32/1.77 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ),
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ],
% 1.32/1.77 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.32/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.32/1.77 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ],
% 1.32/1.77 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.32/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ), Y ) ],
% 1.32/1.77 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.32/1.77 'c_Orderings_Obot__class_Obot'( X ), X ), Y ) ],
% 1.32/1.77 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.32/1.77 'c_Orderings_Obot__class_Obot'( X ), Y, X ), Y ) ],
% 1.32/1.77 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 1.32/1.77 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.32/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ),
% 1.32/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ],
% 1.32/1.77 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 1.32/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.32/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.32/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ],
% 1.32/1.77 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__join'( X ) ), =(
% 1.32/1.77 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ), T ),
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.32/1.77 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__join'( X ) ), =(
% 1.32/1.77 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ) ),
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ],
% 1.32/1.77 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.32/1.77 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ) ),
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ],
% 1.32/1.77 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.32/1.77 hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ), T ),
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.32/1.77 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =(
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.32/1.77 'c_Orderings_Obot__class_Obot'( X ) ) ), =( Z,
% 1.32/1.77 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.32/1.77 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =(
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.32/1.77 'c_Orderings_Obot__class_Obot'( X ) ) ), =( Y,
% 1.32/1.77 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.32/1.77 [ =( hAPP( 'c_Collect'( X ), hAPP( 'c_COMBC'( 'c_fequal'( X ), X, X,
% 1.32/1.77 'tc_bool' ), Y ) ), 'c_Set_Oinsert'( Y, 'c_Orderings_Obot__class_Obot'(
% 1.32/1.77 'tc_fun'( X, 'tc_bool' ) ), X ) ) ],
% 1.32/1.77 [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), hAPP(
% 1.32/1.77 'c_Collect'( X ), Y ) ) ), ~( hBOOL( hAPP( Y, Z ) ) ) ],
% 1.32/1.77 [ ~( =( hAPP( 'c_Collect'( X ), Y ), 'c_Orderings_Obot__class_Obot'(
% 1.32/1.77 'tc_fun'( X, 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( Y, Z ) ) ) ],
% 1.32/1.77 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.32/1.77 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.32/1.77 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( Y,
% 1.32/1.77 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.32/1.77 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ) ) ],
% 1.32/1.77 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.32/1.77 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.32/1.77 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.32/1.77 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ),
% 1.32/1.77 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.32/1.77 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.32/1.77 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.32/1.77 , Z ) ],
% 1.32/1.77 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.32/1.77 , Z ) ],
% 1.32/1.77 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.32/1.77 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.32/1.77 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.32/1.77 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.32/1.77 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.32/1.77 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.32/1.77 'c_Groebner__Basis_Ogb__semiring'( U, W, X, V0, V1, V2 ) ) ],
% 1.32/1.77 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), X ) ) ) ) ],
% 1.32/1.77 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.77 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.32/1.77 'c_lessequals'( Y, 'tc_nat' ), T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X
% 1.32/1.77 , 'tc_nat' ), Z ) ) ) ],
% 1.32/1.77 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.32/1.77 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.32/1.77 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.32/1.77 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.77 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.32/1.77 'c_lessequals'( X, 'tc_nat' ), Z ) ) ) ],
% 1.32/1.77 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.77 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.77 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ) ],
% 1.32/1.77 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.77 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.32/1.77 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ) ],
% 1.32/1.77 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.77 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.32/1.77 'c_lessequals'( X, 'tc_nat' ), Z ) ) ) ],
% 1.32/1.77 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.32/1.77 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ) ],
% 1.32/1.77 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.32/1.77 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ) ],
% 1.32/1.77 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.77 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.32/1.77 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.77 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ), X ) ],
% 1.32/1.77 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.32/1.77 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ],
% 1.32/1.77 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.32/1.77 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.32/1.77 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.32/1.77 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 1.32/1.77 'tc_nat' ) ) ],
% 1.32/1.77 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.32/1.77 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 1.32/1.77 'tc_nat' ) ) ],
% 1.32/1.77 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ), T ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), T ) ) ],
% 1.32/1.77 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.32/1.77 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.32/1.77 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.32/1.77 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), X ) ) ) ],
% 1.32/1.77 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.77 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.77 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.32/1.77 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.77 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Z ),
% 1.32/1.77 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.77 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.32/1.77 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.32/1.77 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.32/1.77 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ),
% 1.32/1.77 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.77 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.32/1.77 ), X ), Z ), 'tc_nat' ) ) ],
% 1.32/1.77 [ =( 'c_Set_Oimage'( X, 'c_Lattices_Oupper__semilattice__class_Osup'( Y
% 1.32/1.77 , Z, 'tc_fun'( T, 'tc_bool' ) ), T, U ),
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Oimage'( X, Y, T, U
% 1.32/1.77 ), 'c_Set_Oimage'( X, Z, T, U ), 'tc_fun'( U, 'tc_bool' ) ) ) ],
% 1.32/1.77 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Oinsert'( X, Y
% 1.32/1.77 , Z ), T, 'tc_fun'( Z, 'tc_bool' ) ), 'c_Set_Oinsert'( X,
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, 'tc_fun'( Z,
% 1.32/1.77 'tc_bool' ) ), Z ) ) ],
% 1.32/1.77 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, 'c_Set_Oinsert'( Y
% 1.32/1.77 , Z, T ), 'tc_fun'( T, 'tc_bool' ) ), 'c_Set_Oinsert'( Y,
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( T,
% 1.32/1.77 'tc_bool' ) ), T ) ) ],
% 1.32/1.77 [ =( 'c_Relation_OImage'( X,
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 1.32/1.77 'tc_bool' ) ), T, U ), 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.32/1.77 'c_Relation_OImage'( X, Y, T, U ), 'c_Relation_OImage'( X, Z, T, U ),
% 1.32/1.77 'tc_fun'( U, 'tc_bool' ) ) ) ],
% 1.32/1.77 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, hAPP( hAPP(
% 1.32/1.77 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( Y, 'tc_bool' ) ), Z ), X ),
% 1.32/1.77 'tc_fun'( Y, 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.32/1.77 X, Z, 'tc_fun'( Y, 'tc_bool' ) ) ) ],
% 1.32/1.77 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ), Z,
% 1.32/1.77 'tc_fun'( X, 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.32/1.77 Y, Z, 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.32/1.77 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( X, 'tc_bool' )
% 1.32/1.77 ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( X,
% 1.32/1.77 'tc_bool' ) ) ), T ), 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP(
% 1.32/1.77 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( X, 'tc_bool' ) ), Y ), T )
% 1.32/1.77 , hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( X, 'tc_bool' ) ), Z
% 1.32/1.77 ), T ), 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.32/1.77 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.32/1.77 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.32/1.77 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), 'tc_fun'( X,
% 1.32/1.77 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 1.32/1.77 ) ],
% 1.32/1.77 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.32/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 1.32/1.77 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.32/1.77 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( T,
% 1.32/1.77 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z,
% 1.32/1.77 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.32/1.77 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.32/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.32/1.77 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.32/1.77 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( X, T, 'tc_fun'( Z,
% 1.32/1.77 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T,
% 1.32/1.77 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.32/1.77 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.32/1.77 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 1.32/1.77 X, 'tc_bool' ) ), Y ) ],
% 1.32/1.77 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.32/1.77 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 1.32/1.77 'tc_bool' ) ), X ) ],
% 1.32/1.77 [ 'c_Finite__Set_Ofinite'( X, Y ), ~( 'c_Finite__Set_Ofinite'(
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( Y,
% 1.32/1.77 'tc_bool' ) ), Y ) ) ],
% 1.32/1.77 [ 'c_Finite__Set_Ofinite'( X, Y ), ~( 'c_Finite__Set_Ofinite'(
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Z, X, 'tc_fun'( Y,
% 1.32/1.77 'tc_bool' ) ), Y ) ) ],
% 1.32/1.77 [ 'c_Finite__Set_Ofinite'( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.32/1.77 X, Y, 'tc_fun'( Z, 'tc_bool' ) ), Z ), ~( 'c_Finite__Set_Ofinite'( Y, Z )
% 1.32/1.77 ), ~( 'c_Finite__Set_Ofinite'( X, Z ) ) ],
% 1.32/1.77 [ 'c_Finite__Set_Ofinite'( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.32/1.77 X, Y, 'tc_fun'( Z, 'tc_bool' ) ), Z ), ~( 'c_Finite__Set_Ofinite'( Y, Z )
% 1.32/1.77 ), ~( 'c_Finite__Set_Ofinite'( X, Z ) ) ],
% 1.32/1.77 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 1.32/1.77 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.32/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( T,
% 1.32/1.77 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z,
% 1.32/1.77 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.32/1.77 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.32/1.77 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.32/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( X, T, 'tc_fun'( Z,
% 1.32/1.77 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T,
% 1.32/1.77 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.32/1.77 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.32/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.32/1.77 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T,
% 1.32/1.77 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.32/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( T, X, 'tc_fun'( Z,
% 1.32/1.77 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.32/1.77 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.32/1.77 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.32/1.77 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T,
% 1.32/1.77 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( T, X, 'tc_fun'( Z,
% 1.32/1.77 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.32/1.77 [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z
% 1.32/1.77 , 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' )
% 1.32/1.77 ) ) ), =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.32/1.77 ) ],
% 1.32/1.77 [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z
% 1.32/1.77 , 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' )
% 1.32/1.77 ) ) ), =( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.32/1.77 ) ],
% 1.32/1.77 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), hBOOL( hAPP(
% 1.32/1.77 'c_SEQ_OLIMSEQ'( hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 'tc_nat', 'tc_bool' ),
% 1.32/1.77 X, 'tc_nat' ), 'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ) ),
% 1.32/1.77 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.77 'tc_nat' ), 'tc_nat' ) ), X ), Z ) ), ~( hBOOL( hAPP( 'c_Series_Osums'( Y
% 1.32/1.77 , X ), Z ) ) ) ],
% 1.32/1.77 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), hBOOL( hAPP(
% 1.32/1.77 'c_Series_Osums'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_SEQ_OLIMSEQ'( hAPP(
% 1.32/1.77 hAPP( 'c_COMBB'( 'tc_fun'( 'tc_nat', 'tc_bool' ), X, 'tc_nat' ),
% 1.32/1.77 'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ) ),
% 1.32/1.77 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.77 'tc_nat' ), 'tc_nat' ) ), X ), Z ) ) ) ],
% 1.32/1.77 [ =( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'v_n' ),
% 1.32/1.77 'c_lessequals'( hAPP( 'c_Suc', 'v_n' ), 'tc_nat' ) ) ],
% 1.32/1.77 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'(
% 1.32/1.77 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.32/1.77 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.77 'tc_nat' ) ), X ) ) ) ],
% 1.32/1.77 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.32/1.77 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.77 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.32/1.77 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.77 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.32/1.77 ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.32/1.77 [ =( hAPP( 'c_SetInterval_Oord__class_OatLeastLessThan'( X, 'tc_nat' ),
% 1.32/1.77 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ),
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP(
% 1.32/1.77 'c_SetInterval_Oord__class_OatLeastLessThan'( X, 'tc_nat' ), Y ), hAPP(
% 1.32/1.77 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, 'tc_nat' ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), 'tc_fun'( 'tc_nat',
% 1.32/1.77 'tc_bool' ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), ~(
% 1.32/1.77 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP(
% 1.32/1.77 'c_Finite__Set_Osetsum'( hAPP( 'c_COMBC'( hAPP( hAPP( 'c_COMBB'( X,
% 1.32/1.77 'tc_fun'( X, X ), 'tc_nat' ), 'c_HOL_Ominus__class_Ominus'( X ) ), hAPP(
% 1.32/1.77 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'( X, X ), 'tc_nat' ),
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ) ), hAPP( hAPP( 'c_COMBB'( 'tc_nat', X,
% 1.32/1.77 'tc_nat' ), hAPP( 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), hAPP(
% 1.32/1.77 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ) ) ), 'tc_nat', X, X ), hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), Y ) ) ), 'tc_nat', X, X ), hAPP(
% 1.32/1.77 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), 'tc_nat', X ),
% 1.32/1.77 hAPP( 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), T ) ), hAPP(
% 1.32/1.77 'c_Finite__Set_Osetsum'( hAPP( 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( X,
% 1.32/1.77 'tc_fun'( X, X ), 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X ) ), hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), Y ) ), 'tc_nat', X, X ), hAPP(
% 1.32/1.77 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'( X, X ), 'tc_nat' ),
% 1.32/1.77 'c_HOL_Ominus__class_Ominus'( X ) ), hAPP( hAPP( 'c_COMBB'( 'tc_nat', X,
% 1.32/1.77 'tc_nat' ), hAPP( 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), hAPP(
% 1.32/1.77 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ) ) ), 'tc_nat', X, X ), hAPP(
% 1.32/1.77 hAPP( 'c_COMBB'( 'tc_nat', X, 'tc_nat' ), hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), Y ) ), hAPP(
% 1.32/1.77 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ) ) ) ), 'tc_nat', X ), hAPP(
% 1.32/1.77 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.77 'tc_nat' ), 'tc_nat' ), T ) ) ) ],
% 1.32/1.77 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.32/1.77 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( hAPP( 'c_COMBC'(
% 1.32/1.77 hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'( X, X ), Y ),
% 1.32/1.77 'c_HOL_Ominus__class_Ominus'( X ) ), Z ), Y, X, X ), T ), U,
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_Lim_OLIM'( Z, U, T, Y, X )
% 1.32/1.77 ) ],
% 1.32/1.77 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.32/1.77 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( Z, T, U, Y, X ),
% 1.32/1.77 ~( 'c_Lim_OLIM'( hAPP( 'c_COMBC'( hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'( X,
% 1.32/1.77 X ), Y ), 'c_HOL_Ominus__class_Ominus'( X ) ), Z ), Y, X, X ), U ), T,
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.77 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.32/1.77 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( hAPP( 'c_COMBS'(
% 1.32/1.77 hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'( X, X ), Y ),
% 1.32/1.77 'c_HOL_Oplus__class_Oplus'( X ) ), Z ), Y, X, X ), T ), U,
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_Lim_OLIM'( T, U,
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_Lim_OLIM'( Z, U,
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.77 'class_Int_Onumber__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oord__class_Oless'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.32/1.77 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), Y ), 'c_Int_OPls' ) ) ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.77 'class_Int_Onumber__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), Y ), 'c_Int_OPls' ) ), ~(
% 1.32/1.77 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.77 X ) ) ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.77 'class_Int_Onumber__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), 'c_Int_OPls' ), Y ) ) ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.32/1.77 'class_Int_Onumber__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), 'c_Int_OPls' ), Y ) ), ~(
% 1.32/1.77 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.77 , X ) ) ) ) ],
% 1.32/1.77 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.77 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.32/1.77 hAPP( 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.77 ) ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ) ) ) ), hBOOL(
% 1.32/1.77 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.77 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hBOOL( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.32/1.77 hAPP( 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ) ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.32/1.77 'class_Power_Opower'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.32/1.77 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.32/1.77 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( hBOOL( hAPP(
% 1.32/1.77 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ),
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.32/1.77 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), hBOOL( hAPP(
% 1.32/1.77 'c_SEQ_OLIMSEQ'( hAPP( 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'( X,
% 1.32/1.77 X ), 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X ) ), Y ), 'tc_nat', X, X
% 1.32/1.77 ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) )
% 1.32/1.77 , ~( hBOOL( hAPP( 'c_SEQ_OLIMSEQ'( Z, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.32/1.77 'c_SEQ_OLIMSEQ'( Y, X ), T ) ) ) ],
% 1.32/1.77 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_SEQ_OZseq'(
% 1.32/1.77 hAPP( 'c_COMBC'( hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'( X, X ), 'tc_nat' ),
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ) ), Y ), 'tc_nat', X, X ), Z ), X ), ~(
% 1.32/1.77 'c_SEQ_OZseq'( Y, X ) ) ],
% 1.32/1.77 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_SEQ_OZseq'(
% 1.32/1.77 hAPP( 'c_COMBC'( hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'( X, X ), 'tc_nat' ),
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ) ), Y ), 'tc_nat', X, X ), Z ), X ), ~(
% 1.32/1.77 'c_SEQ_OZseq'( Y, X ) ) ],
% 1.32/1.77 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), hBOOL( hAPP(
% 1.32/1.77 'c_SEQ_OLIMSEQ'( hAPP( 'c_COMBC'( hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'( X,
% 1.32/1.77 X ), 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X ) ), Y ), 'tc_nat', X, X
% 1.32/1.77 ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) )
% 1.32/1.77 , ~( hBOOL( hAPP( 'c_SEQ_OLIMSEQ'( Y, X ), T ) ) ) ],
% 1.32/1.77 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_SEQ_OCauchy'(
% 1.32/1.77 hAPP( 'c_COMBC'( hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'( X, X ), 'tc_nat' ),
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ) ), Y ), 'tc_nat', X, X ), Z ), X ), ~(
% 1.32/1.77 'c_SEQ_OCauchy'( Y, X ) ) ],
% 1.32/1.77 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), hBOOL(
% 1.32/1.77 'c_Series_Osummable'( hAPP( 'c_COMBC'( hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'(
% 1.32/1.77 X, X ), 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X ) ), Y ), 'tc_nat', X
% 1.32/1.77 , X ), Z ), X ) ), ~( hBOOL( 'c_Series_Osummable'( Y, X ) ) ) ],
% 1.32/1.77 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), hBOOL(
% 1.32/1.77 'c_Series_Osummable'( hAPP( 'c_COMBC'( hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'(
% 1.32/1.77 X, X ), 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X ) ), Y ), 'tc_nat', X
% 1.32/1.77 , X ), Z ), X ) ), ~( hBOOL( 'c_Series_Osummable'( Y, X ) ) ) ],
% 1.32/1.77 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), hBOOL( hAPP(
% 1.32/1.77 'c_Series_Osums'( hAPP( 'c_COMBC'( hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'( X
% 1.32/1.77 , X ), 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X ) ), Y ), 'tc_nat', X
% 1.32/1.77 , X ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.32/1.77 ) ), ~( hBOOL( hAPP( 'c_Series_Osums'( Y, X ), T ) ) ) ],
% 1.32/1.77 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), hBOOL( hAPP(
% 1.32/1.77 'c_Series_Osums'( hAPP( 'c_COMBC'( hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'( X
% 1.32/1.77 , X ), 'tc_nat' ), 'c_HOL_Otimes__class_Otimes'( X ) ), Y ), 'tc_nat', X
% 1.32/1.77 , X ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.32/1.77 ) ), ~( hBOOL( hAPP( 'c_Series_Osums'( Y, X ), T ) ) ) ],
% 1.32/1.77 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ) ), 'tc_nat' ) ) ],
% 1.32/1.77 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ), 'tc_nat' ) ],
% 1.32/1.77 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP(
% 1.32/1.77 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.32/1.77 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), Y ) ) ) ],
% 1.32/1.77 [ hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.77 'tc_nat' ) ), 'tc_nat' ), X ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP(
% 1.32/1.77 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ) ) ],
% 1.32/1.77 [ hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.77 'tc_nat' ) ), 'tc_nat' ), X ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP(
% 1.32/1.77 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ) ],
% 1.32/1.77 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP(
% 1.32/1.77 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), ~( hBOOL(
% 1.32/1.77 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X ) ) ) ],
% 1.32/1.77 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP(
% 1.32/1.77 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ), ~( hBOOL(
% 1.32/1.77 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X ) ) ) ],
% 1.32/1.77 [ hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.77 'tc_nat' ) ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.77 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_Suc',
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), Y ) ) ), ~( hBOOL(
% 1.32/1.77 hAPP( 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.32/1.77 ) ), 'tc_nat' ), X ) ) ) ],
% 1.32/1.77 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.32/1.77 'tc_nat' ) ) ],
% 1.32/1.77 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.32/1.77 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.32/1.77 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, X ) ),
% 1.32/1.77 hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), U ) ) ), hAPP( T, X ) ), ~(
% 1.32/1.77 'c_Ring__and__Field_Ocomm__ring__1'( X, Y, W, T, V0, V1, Z ) ) ],
% 1.32/1.77 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( 'c_Suc'
% 1.32/1.77 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), U ) ) ), hAPP( hAPP( Y, T ), hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.32/1.77 X, Y, Z ), T ), U ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.77 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), ~(
% 1.32/1.77 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.32/1.77 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ),
% 1.32/1.77 U ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.32/1.77 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), W ) ) ) ), V0 ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.77 X, U ), V0 ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3
% 1.32/1.77 , V4, X, V5, Y, Z, V6, T ) ) ],
% 1.32/1.77 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, Y ), hAPP(
% 1.32/1.77 hAPP( 'c_Power_Opower_Opower'( T, U, W ), Z ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), V0 ) ) ) ) ) ), ~(
% 1.32/1.77 'c_Ring__and__Field_Oordered__idom'( V1, V2, Y, V3, X, V4, V5, T, U, V6,
% 1.32/1.77 W ) ) ],
% 1.32/1.77 [ =( X, hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.77 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.77 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ),
% 1.32/1.77 'c_Parity_Osko__Parity__Xodd__Suc__mult__two__ex__1__1'( X ) ) ) ),
% 1.32/1.77 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.32/1.77 [ =( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( 'c_COMBC'(
% 1.32/1.77 'c_in'( 't_a' ), 't_a', 'tc_fun'( 't_a', 'tc_bool' ), 'tc_bool' ), X ),
% 1.32/1.77 hAPP( 'c_COMBC'( 'c_in'( 't_a' ), 't_a', 'tc_fun'( 't_a', 'tc_bool' ),
% 1.32/1.77 'tc_bool' ), Y ), 'tc_fun'( 't_a', 'tc_bool' ) ), 'v_x' ), hAPP( hAPP(
% 1.32/1.77 'c_in'( 't_a' ), 'v_x' ), 'c_Lattices_Oupper__semilattice__class_Osup'( X
% 1.32/1.77 , Y, 'tc_fun'( 't_a', 'tc_bool' ) ) ) ) ],
% 1.32/1.77 [ =( 'c_List_Oset'( 'c_List_Ofilter'( X, Y, Z ), Z ), hAPP( 'c_Collect'(
% 1.32/1.77 Z ), hAPP( 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'(
% 1.32/1.77 'tc_bool', 'tc_bool' ), Z ), 'c_and' ), hAPP( 'c_COMBC'( 'c_in'( Z ), Z,
% 1.32/1.77 'tc_fun'( Z, 'tc_bool' ), 'tc_bool' ), 'c_List_Oset'( Y, Z ) ) ), Z,
% 1.32/1.77 'tc_bool', 'tc_bool' ), X ) ) ) ],
% 1.32/1.77 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_fun'( X, 'tc_bool' )
% 1.32/1.77 ), Y ), Z ), hAPP( 'c_Collect'( X ), hAPP( 'c_COMBS'( hAPP( hAPP(
% 1.32/1.77 'c_COMBB'( 'tc_bool', 'tc_fun'( 'tc_bool', 'tc_bool' ), X ), 'c_and' ),
% 1.32/1.77 hAPP( 'c_COMBC'( 'c_in'( X ), X, 'tc_fun'( X, 'tc_bool' ), 'tc_bool' ), Y
% 1.32/1.77 ) ), X, 'tc_bool', 'tc_bool' ), hAPP( hAPP( 'c_COMBB'( 'tc_bool',
% 1.32/1.77 'tc_bool', X ), 'c_Not' ), hAPP( 'c_COMBC'( 'c_in'( X ), X, 'tc_fun'( X,
% 1.32/1.77 'tc_bool' ), 'tc_bool' ), Z ) ) ) ) ) ],
% 1.32/1.77 [ =( 'c_Set_Oinsert'( X, Y, Z ),
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( 'c_Collect'( Z ),
% 1.32/1.77 hAPP( 'c_COMBC'( 'c_fequal'( Z ), Z, Z, 'tc_bool' ), X ) ), Y, 'tc_fun'(
% 1.32/1.77 Z, 'tc_bool' ) ) ) ],
% 1.32/1.77 [ 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( X ), Y ), X ), ~(
% 1.32/1.77 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( X ), hAPP( 'c_COMBS'( hAPP(
% 1.32/1.77 hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'( 'tc_bool', 'tc_bool' ), X ), 'c_or'
% 1.32/1.77 ), Y ), X, 'tc_bool', 'tc_bool' ), Z ) ), X ) ) ],
% 1.32/1.77 [ 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( X ), Y ), X ), ~(
% 1.32/1.77 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( X ), hAPP( 'c_COMBS'( hAPP(
% 1.32/1.77 hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'( 'tc_bool', 'tc_bool' ), X ), 'c_or'
% 1.32/1.77 ), Z ), X, 'tc_bool', 'tc_bool' ), Y ) ), X ) ) ],
% 1.32/1.77 [ 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( X ), hAPP( 'c_COMBS'( hAPP(
% 1.32/1.77 hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'( 'tc_bool', 'tc_bool' ), X ), 'c_or'
% 1.32/1.77 ), Y ), X, 'tc_bool', 'tc_bool' ), Z ) ), X ), ~(
% 1.32/1.77 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( X ), Z ), X ) ), ~(
% 1.32/1.77 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( X ), Y ), X ) ) ],
% 1.32/1.77 [ 'c_Limits_Oeventually'( hAPP( 'c_COMBS'( hAPP( hAPP( 'c_COMBB'(
% 1.32/1.77 'tc_bool', 'tc_fun'( 'tc_bool', 'tc_bool' ), X ), 'c_and' ), Y ), X,
% 1.32/1.77 'tc_bool', 'tc_bool' ), Z ), T, X ), ~( 'c_Limits_Oeventually'( Z, T, X )
% 1.32/1.77 ), ~( 'c_Limits_Oeventually'( Y, T, X ) ) ],
% 1.32/1.77 [ 'c_Limits_Oeventually'( hAPP( 'c_COMBS'( hAPP( hAPP( 'c_COMBB'(
% 1.32/1.77 'tc_bool', 'tc_fun'( 'tc_bool', 'tc_bool' ), X ), 'c_and' ), Y ), X,
% 1.32/1.77 'tc_bool', 'tc_bool' ), Z ), T, X ), ~( 'c_Limits_Oeventually'( Z, T, X )
% 1.32/1.77 ), ~( 'c_Limits_Oeventually'( Y, T, X ) ) ],
% 1.32/1.77 [ 'c_Limits_Oeventually'( X, Y, Z ), ~( 'c_Limits_Oeventually'( hAPP(
% 1.32/1.77 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'( 'tc_bool',
% 1.32/1.77 'tc_bool' ), Z ), 'c_and' ), T ), Z, 'tc_bool', 'tc_bool' ), X ), Y, Z )
% 1.32/1.77 ) ],
% 1.32/1.77 [ 'c_Limits_Oeventually'( X, Y, Z ), ~( 'c_Limits_Oeventually'( hAPP(
% 1.32/1.77 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'( 'tc_bool',
% 1.32/1.77 'tc_bool' ), Z ), 'c_and' ), X ), Z, 'tc_bool', 'tc_bool' ), T ), Y, Z )
% 1.32/1.77 ) ],
% 1.32/1.77 [ =( 'c_List_Ofilter'( X, 'c_List_Ofilter'( Y, Z, T ), T ),
% 1.32/1.77 'c_List_Ofilter'( hAPP( 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( 'tc_bool',
% 1.32/1.77 'tc_fun'( 'tc_bool', 'tc_bool' ), T ), 'c_and' ), Y ), T, 'tc_bool',
% 1.32/1.77 'tc_bool' ), X ), Z, T ) ) ],
% 1.32/1.77 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 1.32/1.77 'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), hAPP(
% 1.32/1.77 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( 'c_Suc', Z ),
% 1.32/1.77 'tc_nat' ), hAPP( 'c_Suc', T ) ) ), hAPP( 'c_Finite__Set_Osetsum'( hAPP(
% 1.32/1.77 hAPP( 'c_COMBB'( 'tc_nat', X, 'tc_nat' ), Y ), 'c_Suc' ), 'tc_nat', X ),
% 1.32/1.77 hAPP( 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, 'tc_nat' ), T ) )
% 1.32/1.77 ) ],
% 1.32/1.77 [ hBOOL( hAPP( X, 'c_List_Osko__List__Xex__nat__less__eq__1__2'( X, Y )
% 1.32/1.77 ) ), ~( hBOOL( hAPP( X, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_nat'
% 1.32/1.77 ), Z ), hAPP( 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Y ) ) ) ) ],
% 1.32/1.77 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_nat' ), Y ),
% 1.32/1.77 hAPP( 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Z ) ) ) ), ~( hBOOL(
% 1.32/1.77 hAPP( X, 'c_List_Osko__List__Xall__nat__less__eq__1__1'( X, Z ) ) ) ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP(
% 1.32/1.77 'c_Finite__Set_Osetsum'( Y, Z, X ), T ), hAPP( 'c_Finite__Set_Osetsum'(
% 1.32/1.77 hAPP( hAPP( 'c_COMBB'( 'tc_fun'( Z, 'tc_bool' ), X, U ),
% 1.32/1.77 'c_Finite__Set_Osetsum'( Y, Z, X ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( Z
% 1.32/1.77 , 'tc_bool' ), 'tc_fun'( Z, 'tc_bool' ), U ), 'c_Collect'( Z ) ), hAPP(
% 1.32/1.77 hAPP( 'c_COMBB'( 'tc_fun'( Z, 'tc_bool' ), 'tc_fun'( Z, 'tc_bool' ), U )
% 1.32/1.77 , 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'( 'tc_bool',
% 1.32/1.77 'tc_bool' ), Z ), 'c_and' ), hAPP( 'c_COMBC'( 'c_in'( Z ), Z, 'tc_fun'( Z
% 1.32/1.77 , 'tc_bool' ), 'tc_bool' ), T ) ), Z, 'tc_bool', 'tc_bool' ) ), 'c_COMBC'(
% 1.32/1.77 hAPP( hAPP( 'c_COMBB'( U, 'tc_fun'( U, 'tc_bool' ), Z ), 'c_fequal'( U )
% 1.32/1.77 ), W ), Z, U, 'tc_bool' ) ) ) ), U, X ), 'c_Set_Oimage'( W, T, Z, U ) )
% 1.32/1.77 ), ~( 'c_Finite__Set_Ofinite'( T, Z ) ) ],
% 1.32/1.77 [ =( 'c_Relation_OImage'( hAPP( 'c_Collect'( 'tc_prod'( X, Y ) ),
% 1.32/1.77 'c_split'( Z, X, Y, 'tc_bool' ) ), T, X, Y ), hAPP( 'c_Collect'( Y ),
% 1.32/1.77 hAPP( hAPP( 'c_COMBB'( 'tc_fun'( X, 'tc_bool' ), 'tc_bool', Y ), 'c_Ex'(
% 1.32/1.77 X ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( X, 'tc_bool' ), 'tc_fun'( X,
% 1.32/1.77 'tc_bool' ), Y ), 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'(
% 1.32/1.77 'tc_bool', 'tc_bool' ), X ), 'c_and' ), hAPP( 'c_COMBC'( 'c_in'( X ), X,
% 1.32/1.77 'tc_fun'( X, 'tc_bool' ), 'tc_bool' ), T ) ), X, 'tc_bool', 'tc_bool' ) )
% 1.32/1.77 , 'c_COMBC'( Z, X, Y, 'tc_bool' ) ) ) ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.32/1.77 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.32/1.77 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ) ) ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ) ), 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.77 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.32/1.77 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.77 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ),
% 1.32/1.77 hAPP( hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.32/1.77 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.32/1.77 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.77 'c_Int_OMin', X ) ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ) ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ) ],
% 1.32/1.77 [ =( hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' )
% 1.32/1.77 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 1.32/1.77 ) ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.77 'tc_nat' ) ) ],
% 1.32/1.77 [ 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( X ), hAPP( hAPP( 'c_COMBB'(
% 1.32/1.77 'tc_fun'( Y, 'tc_bool' ), 'tc_bool', X ), 'c_Ex'( Y ) ), hAPP( hAPP(
% 1.32/1.77 'c_COMBB'( 'tc_fun'( Y, 'tc_bool' ), 'tc_fun'( Y, 'tc_bool' ), X ),
% 1.32/1.77 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'( 'tc_bool',
% 1.32/1.77 'tc_bool' ), Y ), 'c_and' ), Z ), Y, 'tc_bool', 'tc_bool' ) ), T ) ) ), X
% 1.32/1.77 ), hBOOL( hAPP( Z,
% 1.32/1.77 'c_ATP__Linkup_Osko__Finite__Set__Xfinite__Collect__bounded__ex__1__1'( Z
% 1.32/1.77 , T, Y, X ) ) ), ~( 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( Y ), Z )
% 1.32/1.77 , Y ) ) ],
% 1.32/1.77 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), ~(
% 1.32/1.77 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( hAPP( 'c_COMBC'(
% 1.32/1.77 hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'( X, X ), Y ),
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ) ), Z ), Y, X, X ), T ), U,
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_Lim_OLIM'( Z, U,
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.77 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), ~(
% 1.32/1.77 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( hAPP( 'c_COMBC'(
% 1.32/1.77 hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'( X, X ), Y ),
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ) ), Z ), Y, X, X ), T ), U,
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_Lim_OLIM'( Z, U,
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.77 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), ~(
% 1.32/1.77 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( hAPP( 'c_COMBS'(
% 1.32/1.77 hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'( X, X ), Y ),
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ) ), Z ), Y, X, X ), T ), U,
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_Lim_OLIM'( T, U,
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_Lim_OLIM'( Z, U,
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.32/1.77 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.77 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), Y ) ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~( =( hAPP( Y,
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.77 ) ), hBOOL( hAPP( 'c_Series_Osums'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.32/1.77 'c_Series_Osums'( hAPP( hAPP( 'c_COMBB'( 'tc_nat', X, 'tc_nat' ), Y ),
% 1.32/1.77 'c_Suc' ), X ), Z ) ) ) ],
% 1.32/1.77 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), ~( =( hAPP( Y,
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.77 ) ), =( hAPP( 'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), hAPP(
% 1.32/1.77 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( 'c_Suc',
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), Z ) ), hAPP(
% 1.32/1.77 'c_Finite__Set_Osetsum'( Y, 'tc_nat', X ), hAPP(
% 1.32/1.77 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.77 'tc_nat' ), 'tc_nat' ), Z ) ) ) ],
% 1.32/1.77 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.32/1.77 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, Y ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( T
% 1.32/1.77 , X, Z, U, W, V0 ) ) ],
% 1.32/1.77 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), Z ) ),
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), X ), 'c_Int_OPls' ) ) ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oord__class_Oless'( 'tc_Int_Oint' ), X ), 'c_Int_OPls' ) ) ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ 'c_Lattices_Oboolean__algebra'( hAPP( 'c_COMBC'( hAPP( hAPP( 'c_COMBB'(
% 1.32/1.77 'tc_fun'( X, X ), 'tc_fun'( 'tc_fun'( X, X ), 'tc_fun'( X, X ) ), X ),
% 1.32/1.77 'c_COMBB'( X, X, X ) ), Y ), X, 'tc_fun'( X, X ), 'tc_fun'( X, X ) ), Z )
% 1.32/1.77 , Z, 'c_COMBC'( T, X, X, 'tc_bool' ), 'c_COMBC'( U, X, X, 'tc_bool' ), Y
% 1.32/1.77 , W, V0, V1, X ), ~( 'c_Lattices_Oboolean__algebra'( V2, Z, T, U, W, Y,
% 1.32/1.77 V1, V0, X ) ) ],
% 1.32/1.77 [ =( hAPP( 'c_Collect'( X ), hAPP( 'c_COMBS'( hAPP( hAPP( 'c_COMBB'(
% 1.32/1.77 'tc_bool', 'tc_fun'( 'tc_bool', 'tc_bool' ), X ), 'c_and' ), Y ), X,
% 1.32/1.77 'tc_bool', 'tc_bool' ), Z ) ),
% 1.32/1.77 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( 'c_Collect'( X ), Y )
% 1.32/1.77 , hAPP( 'c_Collect'( X ), Z ), 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.32/1.77 [ 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( X ), hAPP( 'c_COMBS'( hAPP(
% 1.32/1.77 hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'( 'tc_bool', 'tc_bool' ), X ),
% 1.32/1.77 'c_and' ), Y ), X, 'tc_bool', 'tc_bool' ), Z ) ), X ), ~(
% 1.32/1.77 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( X ), Y ), X ) ) ],
% 1.32/1.77 [ 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( X ), hAPP( 'c_COMBS'( hAPP(
% 1.32/1.77 hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'( 'tc_bool', 'tc_bool' ), X ),
% 1.32/1.77 'c_and' ), Y ), X, 'tc_bool', 'tc_bool' ), Z ) ), X ), ~(
% 1.32/1.77 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( X ), Z ), X ) ) ],
% 1.32/1.77 [ =( hAPP( 'c_Collect'( X ), hAPP( 'c_COMBS'( hAPP( hAPP( 'c_COMBB'(
% 1.32/1.77 'tc_bool', 'tc_fun'( 'tc_bool', 'tc_bool' ), X ), 'c_and' ), hAPP(
% 1.32/1.77 'c_fequal'( X ), Y ) ), X, 'tc_bool', 'tc_bool' ), Z ) ),
% 1.32/1.77 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), hBOOL( hAPP(
% 1.32/1.77 Z, Y ) ) ],
% 1.32/1.77 [ =( 'c_Orderings_Oord__class_OLeast'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.32/1.77 'c_Orderings_Oord__class_OLeast'( hAPP( hAPP( 'c_COMBB'( 'tc_nat',
% 1.32/1.77 'tc_bool', 'tc_nat' ), X ), 'c_Suc' ), 'tc_nat' ) ) ), hBOOL( hAPP( X,
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( hBOOL( hAPP( X, Y ) ) ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ =( 'c_Set_Oimage'( 'v_f', 'v_A', 't_a', 't_b' ), hAPP( 'c_Collect'(
% 1.32/1.77 't_b' ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 't_a', 'tc_bool' ), 'tc_bool',
% 1.32/1.77 't_b' ), 'c_Ex'( 't_a' ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 't_a',
% 1.32/1.77 'tc_bool' ), 'tc_fun'( 't_a', 'tc_bool' ), 't_b' ), 'c_COMBS'( hAPP( hAPP(
% 1.32/1.77 'c_COMBB'( 'tc_bool', 'tc_fun'( 'tc_bool', 'tc_bool' ), 't_a' ), 'c_and'
% 1.32/1.77 ), hAPP( 'c_COMBC'( 'c_in'( 't_a' ), 't_a', 'tc_fun'( 't_a', 'tc_bool' )
% 1.32/1.77 , 'tc_bool' ), 'v_A' ) ), 't_a', 'tc_bool', 'tc_bool' ) ), hAPP(
% 1.32/1.77 'c_COMBC'( hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 't_b', 'tc_bool' ), 'tc_fun'(
% 1.32/1.77 'tc_fun'( 't_a', 't_b' ), 'tc_fun'( 't_a', 'tc_bool' ) ), 't_b' ),
% 1.32/1.77 'c_COMBB'( 't_b', 'tc_bool', 't_a' ) ), 'c_fequal'( 't_b' ) ), 't_b',
% 1.32/1.77 'tc_fun'( 't_a', 't_b' ), 'tc_fun'( 't_a', 'tc_bool' ) ), 'v_f' ) ) ) ) )
% 1.32/1.77 ],
% 1.32/1.77 [ 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( X ), hAPP( hAPP( 'c_COMBB'(
% 1.32/1.77 'tc_fun'( Y, 'tc_bool' ), 'tc_bool', X ), 'c_Ex'( Y ) ), hAPP( hAPP(
% 1.32/1.77 'c_COMBB'( 'tc_fun'( Y, 'tc_bool' ), 'tc_fun'( Y, 'tc_bool' ), X ),
% 1.32/1.77 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'( 'tc_bool',
% 1.32/1.77 'tc_bool' ), Y ), 'c_and' ), Z ), Y, 'tc_bool', 'tc_bool' ) ), T ) ) ), X
% 1.32/1.77 ), ~( 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( X ), hAPP( 'c_COMBC'(
% 1.32/1.77 T, X, Y, 'tc_bool' ),
% 1.32/1.77 'c_ATP__Linkup_Osko__Finite__Set__Xfinite__Collect__bounded__ex__1__1'( Z
% 1.32/1.77 , T, Y, X ) ) ), X ) ), ~( 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( Y
% 1.32/1.77 ), Z ), Y ) ) ],
% 1.32/1.77 [ 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( X ), hAPP( hAPP( 'c_COMBB'(
% 1.32/1.77 'tc_fun'( Y, 'tc_bool' ), 'tc_bool', X ), 'c_Ex'( Y ) ), hAPP( hAPP(
% 1.32/1.77 'c_COMBB'( 'tc_fun'( Y, 'tc_bool' ), 'tc_fun'( Y, 'tc_bool' ), X ),
% 1.32/1.77 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'( 'tc_bool',
% 1.32/1.77 'tc_bool' ), Y ), 'c_and' ), hAPP( 'c_COMBC'( 'c_in'( Y ), Y, 'tc_fun'( Y
% 1.32/1.77 , 'tc_bool' ), 'tc_bool' ), Z ) ), Y, 'tc_bool', 'tc_bool' ) ), T ) ) ),
% 1.32/1.77 X ), hBOOL( hAPP( hAPP( 'c_in'( Y ),
% 1.32/1.77 'c_ATP__Linkup_Osko__Finite__Set__Xfinite__Collect__bex__1__1'( Z, T, Y,
% 1.32/1.77 X ) ), Z ) ), ~( 'c_Finite__Set_Ofinite'( Z, Y ) ) ],
% 1.32/1.77 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y )
% 1.32/1.77 , Y ) ) ],
% 1.32/1.77 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.77 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y
% 1.32/1.77 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.77 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.77 X ), Y ), Y ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.32/1.77 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.32/1.77 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X
% 1.32/1.77 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.32/1.77 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ) ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( 'c_Suc', hAPP( 'c_Suc', X ) )
% 1.32/1.77 ) ],
% 1.32/1.77 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.32/1.77 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.77 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.32/1.77 ) ],
% 1.32/1.77 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ) ) ],
% 1.32/1.77 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.32/1.77 'tc_nat' ), X ), X ) ) ],
% 1.32/1.77 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'tc_nat' ) ],
% 1.32/1.77 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.32/1.77 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.77 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.32/1.77 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP( T, hAPP(
% 1.32/1.77 hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ), ~(
% 1.32/1.77 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.32/1.77 [ =( hAPP( 'c_Collect'( X ), hAPP( 'c_COMBS'( hAPP( hAPP( 'c_COMBB'(
% 1.32/1.77 'tc_bool', 'tc_fun'( 'tc_bool', 'tc_bool' ), X ), 'c_and' ), hAPP(
% 1.32/1.77 'c_COMBC'( 'c_fequal'( X ), X, X, 'tc_bool' ), Y ) ), X, 'tc_bool',
% 1.32/1.77 'tc_bool' ), Z ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.32/1.77 'tc_bool' ) ) ), hBOOL( hAPP( Z, Y ) ) ],
% 1.32/1.77 [ 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( X ), hAPP( hAPP( 'c_COMBB'(
% 1.32/1.77 'tc_fun'( Y, 'tc_bool' ), 'tc_bool', X ), 'c_Ex'( Y ) ), hAPP( hAPP(
% 1.32/1.77 'c_COMBB'( 'tc_fun'( Y, 'tc_bool' ), 'tc_fun'( Y, 'tc_bool' ), X ),
% 1.32/1.77 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'( 'tc_bool',
% 1.32/1.77 'tc_bool' ), Y ), 'c_and' ), hAPP( 'c_COMBC'( 'c_in'( Y ), Y, 'tc_fun'( Y
% 1.32/1.77 , 'tc_bool' ), 'tc_bool' ), Z ) ), Y, 'tc_bool', 'tc_bool' ) ), T ) ) ),
% 1.32/1.77 X ), ~( 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( X ), hAPP( 'c_COMBC'(
% 1.32/1.77 T, X, Y, 'tc_bool' ),
% 1.32/1.77 'c_ATP__Linkup_Osko__Finite__Set__Xfinite__Collect__bex__1__1'( Z, T, Y,
% 1.32/1.77 X ) ) ), X ) ), ~( 'c_Finite__Set_Ofinite'( Z, Y ) ) ],
% 1.32/1.77 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), ~( 'class_Int_Onumber'(
% 1.32/1.77 X ) ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.32/1.77 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.32/1.77 [ =( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X
% 1.32/1.77 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.32/1.77 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.32/1.77 T, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ) ), ~(
% 1.32/1.77 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.32/1.77 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), 'tc_nat' ) ) ],
% 1.32/1.77 [ =( 'c_Set_Oinsert'( X, Y, Z ), hAPP( 'c_Collect'( Z ), hAPP( 'c_COMBS'(
% 1.32/1.77 hAPP( hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'( 'tc_bool', 'tc_bool' ), Z ),
% 1.32/1.77 'c_or' ), hAPP( 'c_COMBC'( 'c_fequal'( Z ), Z, Z, 'tc_bool' ), X ) ), Z,
% 1.32/1.77 'tc_bool', 'tc_bool' ), hAPP( 'c_COMBC'( 'c_in'( Z ), Z, 'tc_fun'( Z,
% 1.32/1.77 'tc_bool' ), 'tc_bool' ), Y ) ) ) ) ],
% 1.32/1.77 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.32/1.77 'tc_bool' ) ), hAPP( 'c_Collect'( Z ), hAPP( 'c_COMBS'( hAPP( hAPP(
% 1.32/1.77 'c_COMBB'( 'tc_bool', 'tc_fun'( 'tc_bool', 'tc_bool' ), Z ), 'c_and' ),
% 1.32/1.77 hAPP( 'c_COMBC'( 'c_in'( Z ), Z, 'tc_fun'( Z, 'tc_bool' ), 'tc_bool' ), X
% 1.32/1.77 ) ), Z, 'tc_bool', 'tc_bool' ), hAPP( 'c_COMBC'( 'c_in'( Z ), Z,
% 1.32/1.77 'tc_fun'( Z, 'tc_bool' ), 'tc_bool' ), Y ) ) ) ) ],
% 1.32/1.77 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.77 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ) ],
% 1.32/1.77 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( hAPP(
% 1.32/1.77 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.32/1.77 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ) ), X ) ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.32/1.77 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ) ), X ) ), =( X,
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.77 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( hAPP(
% 1.32/1.77 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.77 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP(
% 1.32/1.77 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.77 'tc_nat' ) ) ],
% 1.32/1.77 [ 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( X ), hAPP( 'c_COMBC'( Y, X
% 1.32/1.77 , Z, 'tc_bool' ), T ) ), X ), ~( hBOOL( hAPP( U, T ) ) ), ~(
% 1.32/1.77 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( X ), hAPP( hAPP( 'c_COMBB'(
% 1.32/1.77 'tc_fun'( Z, 'tc_bool' ), 'tc_bool', X ), 'c_Ex'( Z ) ), hAPP( hAPP(
% 1.32/1.77 'c_COMBB'( 'tc_fun'( Z, 'tc_bool' ), 'tc_fun'( Z, 'tc_bool' ), X ),
% 1.32/1.77 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'( 'tc_bool',
% 1.32/1.77 'tc_bool' ), Z ), 'c_and' ), U ), Z, 'tc_bool', 'tc_bool' ) ), Y ) ) ), X
% 1.32/1.77 ) ), ~( 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( Z ), U ), Z ) ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( X ), hAPP( 'c_COMBC'( Y, X
% 1.32/1.77 , Z, 'tc_bool' ), T ) ), X ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), T ), U )
% 1.32/1.77 ) ), ~( 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( X ), hAPP( hAPP(
% 1.32/1.77 'c_COMBB'( 'tc_fun'( Z, 'tc_bool' ), 'tc_bool', X ), 'c_Ex'( Z ) ), hAPP(
% 1.32/1.77 hAPP( 'c_COMBB'( 'tc_fun'( Z, 'tc_bool' ), 'tc_fun'( Z, 'tc_bool' ), X )
% 1.32/1.77 , 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'( 'tc_bool',
% 1.32/1.77 'tc_bool' ), Z ), 'c_and' ), hAPP( 'c_COMBC'( 'c_in'( Z ), Z, 'tc_fun'( Z
% 1.32/1.77 , 'tc_bool' ), 'tc_bool' ), U ) ), Z, 'tc_bool', 'tc_bool' ) ), Y ) ) ),
% 1.32/1.77 X ) ), ~( 'c_Finite__Set_Ofinite'( U, Z ) ) ],
% 1.32/1.77 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.77 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ) ) ],
% 1.32/1.77 [ =( hAPP( 'c_Collect'( X ), hAPP( 'c_COMBC'( 'c_in'( X ), X, 'tc_fun'(
% 1.32/1.77 X, 'tc_bool' ), 'tc_bool' ), Y ) ), Y ) ],
% 1.32/1.77 [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ) ) ],
% 1.32/1.77 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.32/1.77 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.32/1.77 'tc_bool' ) ), hAPP( 'c_Collect'( Z ), hAPP( 'c_COMBS'( hAPP( hAPP(
% 1.32/1.77 'c_COMBB'( 'tc_bool', 'tc_fun'( 'tc_bool', 'tc_bool' ), Z ), 'c_or' ),
% 1.32/1.77 hAPP( 'c_COMBC'( 'c_in'( Z ), Z, 'tc_fun'( Z, 'tc_bool' ), 'tc_bool' ), X
% 1.32/1.77 ) ), Z, 'tc_bool', 'tc_bool' ), hAPP( 'c_COMBC'( 'c_in'( Z ), Z,
% 1.32/1.77 'tc_fun'( Z, 'tc_bool' ), 'tc_bool' ), Y ) ) ) ) ],
% 1.32/1.77 [ =( 'c_Int_OBit0'( 'c_Int_OPls' ), 'c_Int_OPls' ) ],
% 1.32/1.77 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.32/1.77 'tc_nat' ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ ~( =( hAPP( 'c_Suc', X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ ~( =( hAPP( 'c_Suc', X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ),
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.77 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ),
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.32/1.77 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.77 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.32/1.77 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.32/1.77 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.32/1.77 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.32/1.77 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.32/1.77 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.77 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.32/1.77 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.77 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.32/1.77 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.77 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.77 'tc_nat' ) ) ],
% 1.32/1.77 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.77 'tc_nat' ) ) ],
% 1.32/1.77 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.32/1.77 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.77 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.32/1.77 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.32/1.77 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.32/1.77 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.77 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.32/1.77 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.32/1.77 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP( 'c_in'(
% 1.32/1.77 X ), Y ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( T, Z, 'tc_fun'( X,
% 1.32/1.77 'tc_bool' ) ) ) ) ) ],
% 1.32/1.77 [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X, Y ) ],
% 1.32/1.77 [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X, Y ) ],
% 1.32/1.77 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.32/1.77 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( Y
% 1.32/1.77 , Z ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.77 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.32/1.77 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( X
% 1.32/1.77 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 1.32/1.77 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.32/1.77 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), =( Y
% 1.32/1.77 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 1.32/1.77 [ ~( =( 'c_Int_OPls', 'c_Int_OBit1'( X ) ) ) ],
% 1.32/1.77 [ =( hAPP( 'c_Collect'( X ), Y ), Y ) ],
% 1.32/1.77 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OPls' ) ) ],
% 1.32/1.77 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OPls' ) ), =( X, 'c_Int_OPls' ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ) ) ), =( X, Y ) ],
% 1.32/1.77 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), Y ), X ) ) )
% 1.32/1.77 ],
% 1.32/1.77 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( Z, Y ) ) )
% 1.32/1.77 ],
% 1.32/1.77 [ =( hAPP( 'c_Collect'( X ), hAPP( 'c_COMBS'( hAPP( hAPP( 'c_COMBB'(
% 1.32/1.77 'tc_bool', 'tc_fun'( 'tc_bool', 'tc_bool' ), X ), 'c_or' ), Y ), X,
% 1.32/1.77 'tc_bool', 'tc_bool' ), Z ) ),
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( 'c_Collect'( X ), Y )
% 1.32/1.77 , hAPP( 'c_Collect'( X ), Z ), 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.32/1.77 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ) ) ) ],
% 1.32/1.77 [ =( 'c_Int_OPls', 'c_Int_OBit0'( 'c_Int_OPls' ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.32/1.77 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.32/1.77 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.32/1.77 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP(
% 1.32/1.77 'c_Suc', X ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.32/1.77 , hAPP( 'c_Suc', X ) ), Z ) ) ), =( Y, Z ) ],
% 1.32/1.77 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( 'c_Suc'
% 1.32/1.77 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ],
% 1.32/1.77 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.32/1.77 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), Y ) ],
% 1.32/1.77 [ ~( =( hAPP( 'c_Suc', X ), X ) ) ],
% 1.32/1.77 [ ~( =( X, hAPP( 'c_Suc', X ) ) ) ],
% 1.32/1.77 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, 'tc_fun'( X,
% 1.32/1.77 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ],
% 1.32/1.77 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, 'tc_fun'( X,
% 1.32/1.77 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ],
% 1.32/1.77 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.77 'tc_nat' ) ), Y ) ) ],
% 1.32/1.77 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.77 'tc_nat' ) ) ) ],
% 1.32/1.77 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.32/1.77 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), U ) ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.32/1.77 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( Z, Y ) ), ~( hBOOL( hAPP(
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Z, X, 'tc_fun'( T,
% 1.32/1.77 'tc_bool' ) ), Y ) ) ) ],
% 1.32/1.77 [ hBOOL( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 1.32/1.77 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( Y, T ) ) ) ],
% 1.32/1.77 [ hBOOL( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 1.32/1.77 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( X, T ) ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.32/1.77 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.77 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.32/1.77 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.77 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.32/1.77 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.32/1.77 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.32/1.77 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.32/1.77 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.32/1.77 'c_Int_OBit1'( 'c_Int_OPls' ), X ) ), Y ), Y ) ],
% 1.32/1.77 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ) )
% 1.32/1.77 , Y ) ],
% 1.32/1.77 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.32/1.77 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, hAPP(
% 1.32/1.77 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.32/1.77 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.32/1.77 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.32/1.77 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.32/1.77 [ ~( =( 'c_Int_OPls', 'c_Int_OBit0'( X ) ) ), =( 'c_Int_OPls', X ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ) ) ), =( X, Y ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.32/1.77 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.32/1.77 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ],
% 1.32/1.77 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.32/1.77 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Y, X ), Y ) ],
% 1.32/1.77 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, X, 'tc_fun'( Y,
% 1.32/1.77 'tc_bool' ) ), X ) ],
% 1.32/1.77 [ =( hAPP( hAPP( hAPP( 'c_COMBB'( X, Y, Z ), T ), U ), W ), hAPP( T,
% 1.32/1.77 hAPP( U, W ) ) ) ],
% 1.32/1.77 [ =( hAPP( hAPP( 'c_COMBC'( X, Y, Z, T ), U ), W ), hAPP( hAPP( X, W ),
% 1.32/1.77 U ) ) ],
% 1.32/1.77 [ =( hAPP( hAPP( 'c_COMBS'( X, Y, Z, T ), U ), W ), hAPP( hAPP( X, W ),
% 1.32/1.77 hAPP( U, W ) ) ) ],
% 1.32/1.77 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.32/1.77 ) ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.32/1.77 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.32/1.77 ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =( Y, Z ) ],
% 1.32/1.77 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Z,
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ],
% 1.32/1.77 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ],
% 1.32/1.77 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.32/1.77 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, 'tc_fun'( Z,
% 1.32/1.77 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.32/1.77 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 1.32/1.77 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( T,
% 1.32/1.77 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.32/1.77 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Z,
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ],
% 1.32/1.77 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ],
% 1.32/1.77 [ ~( =( hAPP( 'c_COMBC'( 'c_in'( X ), X, 'tc_fun'( X, 'tc_bool' ),
% 1.32/1.77 'tc_bool' ), Y ), hAPP( 'c_COMBC'( 'c_in'( X ), X, 'tc_fun'( X, 'tc_bool'
% 1.32/1.77 ), 'tc_bool' ), Z ) ) ), =( Y, Z ) ],
% 1.32/1.77 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), Y ), hAPP(
% 1.32/1.77 'c_Collect'( Z ), X ) ) ) ) ],
% 1.32/1.77 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( 'c_Collect'( X ), Z ) ) ),
% 1.32/1.77 ~( hBOOL( hAPP( Z, Y ) ) ) ],
% 1.32/1.77 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ) ) ],
% 1.32/1.77 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.32/1.77 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y, X,
% 1.32/1.77 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.32/1.77 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ) ) ],
% 1.32/1.77 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ),
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ) ],
% 1.32/1.77 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.32/1.77 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.32/1.77 'tc_bool' ) ) ) ],
% 1.32/1.77 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ),
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ) ],
% 1.32/1.77 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ) ) ) ],
% 1.32/1.77 [ ~( =( hAPP( 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.32/1.77 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), hAPP( hAPP(
% 1.32/1.77 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_n' ) ),
% 1.32/1.77 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( 'c_Collect'( 'tc_nat'
% 1.32/1.77 ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 'tc_nat', 'tc_bool' ), 'tc_bool',
% 1.32/1.77 'tc_nat' ), 'c_Ex'( 'tc_nat' ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'(
% 1.32/1.77 'tc_nat', 'tc_bool' ), 'tc_fun'( 'tc_nat', 'tc_bool' ), 'tc_nat' ),
% 1.32/1.77 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'( 'tc_bool',
% 1.32/1.77 'tc_bool' ), 'tc_nat' ), 'c_and' ), hAPP( 'c_COMBC'( 'c_in'( 'tc_nat' ),
% 1.32/1.77 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ), 'tc_bool' ), hAPP(
% 1.32/1.77 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.77 'tc_nat' ), 'tc_nat' ), 'v_n' ) ) ), 'tc_nat', 'tc_bool', 'tc_bool' ) ),
% 1.32/1.77 hAPP( 'c_COMBC'( hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 'tc_nat', 'tc_bool' ),
% 1.32/1.77 'tc_fun'( 'tc_fun'( 'tc_nat', 'tc_nat' ), 'tc_fun'( 'tc_nat', 'tc_bool' )
% 1.32/1.77 ), 'tc_nat' ), 'c_COMBB'( 'tc_nat', 'tc_bool', 'tc_nat' ) ), 'c_fequal'(
% 1.32/1.77 'tc_nat' ) ), 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_nat' ), 'tc_fun'(
% 1.32/1.77 'tc_nat', 'tc_bool' ) ), hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ) ), hAPP( 'c_Collect'( 'tc_nat' ),
% 1.32/1.77 hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 'tc_nat', 'tc_bool' ), 'tc_bool',
% 1.32/1.77 'tc_nat' ), 'c_Ex'( 'tc_nat' ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'(
% 1.32/1.77 'tc_nat', 'tc_bool' ), 'tc_fun'( 'tc_nat', 'tc_bool' ), 'tc_nat' ),
% 1.32/1.77 'c_COMBS'( hAPP( hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'( 'tc_bool',
% 1.32/1.77 'tc_bool' ), 'tc_nat' ), 'c_and' ), hAPP( 'c_COMBC'( 'c_in'( 'tc_nat' ),
% 1.32/1.77 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ), 'tc_bool' ), hAPP(
% 1.32/1.77 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.32/1.77 'tc_nat' ), 'tc_nat' ), 'v_n' ) ) ), 'tc_nat', 'tc_bool', 'tc_bool' ) ),
% 1.32/1.77 hAPP( 'c_COMBC'( hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 'tc_nat', 'tc_bool' ),
% 1.32/1.77 'tc_fun'( 'tc_fun'( 'tc_nat', 'tc_nat' ), 'tc_fun'( 'tc_nat', 'tc_bool' )
% 1.32/1.77 ), 'tc_nat' ), 'c_COMBB'( 'tc_nat', 'tc_bool', 'tc_nat' ) ), 'c_fequal'(
% 1.32/1.77 'tc_nat' ) ), 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_nat' ), 'tc_fun'(
% 1.32/1.77 'tc_nat', 'tc_bool' ) ), hAPP( hAPP( 'c_COMBB'( 'tc_nat', 'tc_nat',
% 1.32/1.77 'tc_nat' ), 'c_Suc' ), hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.32/1.77 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.32/1.77 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ) ) ), 'tc_fun'( 'tc_nat', 'tc_bool' )
% 1.32/1.77 ) ) ) ],
% 1.32/1.77 [ 'class_Finite__Set_Ofinite_Ofinite'( 'tc_prod'( X, Y ) ), ~(
% 1.32/1.77 'class_Finite__Set_Ofinite_Ofinite'( Y ) ), ~(
% 1.32/1.77 'class_Finite__Set_Ofinite_Ofinite'( X ) ) ],
% 1.32/1.77 [ 'class_Lattices_Oupper__semilattice'( 'tc_fun'( X, Y ) ), ~(
% 1.32/1.77 'class_Lattices_Olattice'( Y ) ) ],
% 1.32/1.77 [ 'class_Lattices_Olower__semilattice'( 'tc_fun'( X, Y ) ), ~(
% 1.32/1.77 'class_Lattices_Olattice'( Y ) ) ],
% 1.32/1.77 [ 'class_Lattices_Odistrib__lattice'( 'tc_fun'( X, Y ) ), ~(
% 1.32/1.77 'class_Lattices_Odistrib__lattice'( Y ) ) ],
% 1.32/1.77 [ 'class_Lattices_Obounded__lattice'( 'tc_fun'( X, Y ) ), ~(
% 1.32/1.77 'class_Lattices_Obounded__lattice'( Y ) ) ],
% 1.32/1.77 [ 'class_Finite__Set_Ofinite_Ofinite'( 'tc_fun'( X, Y ) ), ~(
% 1.32/1.77 'class_Finite__Set_Ofinite_Ofinite'( Y ) ), ~(
% 1.32/1.77 'class_Finite__Set_Ofinite_Ofinite'( X ) ) ],
% 1.32/1.77 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 1.32/1.77 'class_Orderings_Opreorder'( Y ) ) ],
% 1.32/1.77 [ 'class_Lattices_Olattice'( 'tc_fun'( X, Y ) ), ~(
% 1.32/1.77 'class_Lattices_Olattice'( Y ) ) ],
% 1.32/1.77 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 1.32/1.77 'class_Orderings_Oorder'( Y ) ) ],
% 1.32/1.77 [ 'class_Orderings_Obot'( 'tc_fun'( X, Y ) ), ~( 'class_Orderings_Obot'(
% 1.32/1.77 Y ) ) ],
% 1.32/1.77 [ 'class_HOL_Ominus'( 'tc_fun'( X, Y ) ), ~( 'class_HOL_Ominus'( Y ) ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.32/1.77 ],
% 1.32/1.77 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.32/1.77 ) ],
% 1.32/1.77 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.32/1.77 ],
% 1.32/1.77 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 1.32/1.77 ,
% 1.32/1.77 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.32/1.77 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 1.44/1.78 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.44/1.78 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.44/1.78 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.44/1.78 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 1.44/1.78 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 1.44/1.78 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.44/1.78 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.44/1.78 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.44/1.78 [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_nat' ) ],
% 1.44/1.78 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.44/1.78 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.44/1.78 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.44/1.78 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.44/1.78 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.44/1.78 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.44/1.78 [ 'class_Lattices_Oupper__semilattice'( 'tc_nat' ) ],
% 1.44/1.78 [ 'class_Lattices_Olower__semilattice'( 'tc_nat' ) ],
% 1.44/1.78 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.44/1.78 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.44/1.78 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.44/1.78 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.44/1.78 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.44/1.78 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.44/1.78 [ 'class_Lattices_Odistrib__lattice'( 'tc_nat' ) ],
% 1.44/1.78 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.44/1.78 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.44/1.78 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 1.44/1.78 [ 'class_Orderings_Owellorder'( 'tc_nat' ) ],
% 1.44/1.78 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.44/1.78 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.44/1.78 [ 'class_Lattices_Olattice'( 'tc_nat' ) ],
% 1.44/1.78 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.44/1.78 [ 'class_Orderings_Obot'( 'tc_nat' ) ],
% 1.44/1.78 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 1.44/1.78 [ 'class_Int_Onumber'( 'tc_nat' ) ],
% 1.44/1.78 [ 'class_HOL_Ominus'( 'tc_nat' ) ],
% 1.44/1.78 [ 'class_Lattices_Oupper__semilattice'( 'tc_bool' ) ],
% 1.44/1.78 [ 'class_Lattices_Olower__semilattice'( 'tc_bool' ) ],
% 1.44/1.78 [ 'class_Lattices_Odistrib__lattice'( 'tc_bool' ) ],
% 1.44/1.78 [ 'class_Lattices_Obounded__lattice'( 'tc_bool' ) ],
% 1.44/1.78 [ 'class_Finite__Set_Ofinite_Ofinite'( 'tc_bool' ) ],
% 1.44/1.78 [ 'class_Orderings_Opreorder'( 'tc_bool' ) ],
% 1.44/1.78 [ 'class_Lattices_Olattice'( 'tc_bool' ) ],
% 1.44/1.78 [ 'class_Orderings_Oorder'( 'tc_bool' ) ],
% 1.44/1.78 [ 'class_Orderings_Obot'( 'tc_bool' ) ],
% 1.44/1.78 [ 'class_HOL_Ominus'( 'tc_bool' ) ],
% 1.44/1.78 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.44/1.78 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.44/1.78 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.44/1.78 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_Int_Oint' )
% 1.44/1.78 ],
% 1.44/1.78 [ 'class_OrderedGroup_Olordered__ab__group__add__meet'( 'tc_Int_Oint' )
% 1.44/1.78 ],
% 1.44/1.78 [ 'class_OrderedGroup_Olordered__ab__group__add__join'( 'tc_Int_Oint' )
% 1.44/1.78 ],
% 1.44/1.78 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'( 'tc_Int_Oint' )
% 1.44/1.78 ],
% 1.44/1.78 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_Int_Oint' ) ]
% 1.44/1.78 ,
% 1.44/1.78 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.44/1.78 ,
% 1.44/1.78 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_Int_Oint' ) ]
% 1.44/1.78 ,
% 1.44/1.78 [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_Int_Oint' ) ]
% 1.44/1.78 ,
% 1.44/1.78 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.44/1.78 ,
% 1.44/1.78 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_Int_Oint' ) ]
% 1.44/1.78 ,
% 1.44/1.78 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_Lattices_Oupper__semilattice'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_Lattices_Olower__semilattice'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_Ring__and__Field_Omult__mono'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_Lattices_Odistrib__lattice'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_Ring__and__Field_Osemiring'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_Divides_Osemiring__div'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_Ring__and__Field_Oring'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_Ring__and__Field_Oidom'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_Orderings_Opreorder'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_Orderings_Olinorder'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_Lattices_Olattice'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_Divides_Oring__div'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_Orderings_Oorder'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_Int_Oring__char__0'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_Int_Onumber__ring'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_Power_Opower'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_Int_Onumber'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ 'class_HOL_Ominus'( 'tc_Int_Oint' ) ],
% 1.44/1.78 [ =( hAPP( hAPP( 'c_COMBS'( X, Y, Z, T ), U ), W ), hAPP( hAPP( X, W ),
% 1.44/1.78 hAPP( U, W ) ) ) ],
% 1.44/1.78 [ =( hAPP( hAPP( 'c_COMBC'( X, Y, Z, T ), U ), W ), hAPP( hAPP( X, W ),
% 1.44/1.78 U ) ) ],
% 1.44/1.78 [ =( hAPP( hAPP( hAPP( 'c_COMBB'( X, Y, Z ), T ), U ), W ), hAPP( T,
% 1.44/1.78 hAPP( U, W ) ) ) ],
% 1.44/1.78 [ hBOOL( hAPP( hAPP( 'c_fequal'( X ), Y ), Y ) ) ],
% 1.44/1.78 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_fequal'( Z ), X ), Y ) ) ) ]
% 1.44/1.78 ] .
% 1.44/1.78
% 1.44/1.78
% 1.44/1.78 percentage equality = 0.258688, percentage horn = 0.885410
% 1.44/1.78 This is a problem with some equality
% 1.44/1.78
% 1.44/1.78
% 1.44/1.78
% 1.44/1.78 Options Used:
% 1.44/1.78
% 1.44/1.78 useres = 1
% 1.44/1.78 useparamod = 1
% 1.44/1.78 useeqrefl = 1
% 1.44/1.78 useeqfact = 1
% 1.44/1.78 usefactor = 1
% 1.44/1.78 usesimpsplitting = 0
% 1.44/1.78 usesimpdemod = 5
% 1.44/1.78 usesimpres = 3
% 1.44/1.78
% 1.44/1.78 resimpinuse = 1000
% 1.44/1.78 resimpclauses = 20000
% 1.44/1.78 substype = eqrewr
% 1.44/1.78 backwardsubs = 1
% 1.44/1.78 selectoldest = 5
% 1.44/1.78
% 1.44/1.78 litorderings [0] = split
% 1.44/1.78 litorderings [1] = extend the termordering, first sorting on arguments
% 1.44/1.78
% 1.44/1.78 termordering = kbo
% 1.44/1.78
% 1.44/1.78 litapriori = 0
% 1.44/1.78 termapriori = 1
% 1.44/1.78 litaposteriori = 0
% 1.44/1.78 termaposteriori = 0
% 1.44/1.78 demodaposteriori = 0
% 1.44/1.78 ordereqreflfact = 0
% 1.44/1.78
% 1.44/1.78 litselect = negord
% 1.44/1.78
% 1.44/1.78 maxweight = 15
% 1.44/1.78 maxdepth = 30000
% 1.44/1.78 maxlength = 115
% 1.44/1.78 maxnrvars = 195
% 1.44/1.78 excuselevel = 1
% 1.44/1.78 increasemaxweight = 1
% 1.44/1.78
% 1.44/1.78 maxselected = 10000000
% 1.44/1.78 maxnrclauses = 10000000
% 1.44/1.78
% 1.44/1.78 showgenerated = 0
% 1.44/1.78 showkept = 0
% 1.44/1.78 showselected = 0
% 1.44/1.78 showdeleted = 0
% 1.44/1.78 showresimp = 1
% 1.44/1.78 showstatus = 2000
% 1.44/1.78
% 1.44/1.78 prologoutput = 1
% 1.44/1.78 nrgoals = 5000000
% 1.44/1.78 totalproof = 1
% 1.44/1.78
% 1.44/1.78 Symbols occurring in the translation:
% 1.44/1.78
% 1.44/1.78 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.44/1.78 . [1, 2] (w:1, o:193, a:1, s:1, b:0),
% 1.44/1.78 ! [4, 1] (w:0, o:105, a:1, s:1, b:0),
% 1.44/1.78 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.44/1.78 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.44/1.78 'class_Orderings_Oorder' [40, 1] (w:1, o:110, a:1, s:1, b:0),
% 1.44/1.78 'c_SetInterval_Oord__class_OatLeastLessThan' [42, 2] (w:1, o:218, a:1
% 1.44/1.78 , s:1, b:0),
% 1.44/1.78 hAPP [44, 2] (w:1, o:219, a:1, s:1, b:0),
% 1.44/1.78 'tc_bool' [45, 0] (w:1, o:15, a:1, s:1, b:0),
% 1.44/1.78 'tc_fun' [46, 2] (w:1, o:220, a:1, s:1, b:0),
% 1.44/1.78 'c_Orderings_Obot__class_Obot' [47, 1] (w:1, o:111, a:1, s:1, b:0),
% 1.44/1.78 'c_HOL_Oord__class_Oless' [48, 1] (w:1, o:112, a:1, s:1, b:0),
% 1.44/1.78 hBOOL [49, 1] (w:1, o:113, a:1, s:1, b:0),
% 1.44/1.78 'c_Power_Opower_Opower' [52, 3] (w:1, o:236, a:1, s:1, b:0),
% 1.44/1.78 'tc_nat' [53, 0] (w:1, o:39, a:1, s:1, b:0),
% 1.44/1.78 'c_HOL_Oplus__class_Oplus' [54, 1] (w:1, o:115, a:1, s:1, b:0),
% 1.44/1.78 'c_OrderedGroup_Omonoid__mult' [57, 3] (w:1, o:235, a:1, s:1, b:0),
% 1.44/1.78 'c_Set_Oimage' [61, 4] (w:1, o:247, a:1, s:1, b:0),
% 1.44/1.78 'c_HOL_Ominus__class_Ominus' [62, 1] (w:1, o:116, a:1, s:1, b:0),
% 1.44/1.78 'c_Lattices_Oupper__semilattice__class_Osup' [65, 3] (w:1, o:237, a:1
% 1.44/1.78 , s:1, b:0),
% 1.44/1.78 'c_Lattices_Olower__semilattice__class_Oinf' [66, 3] (w:1, o:238, a:1
% 1.44/1.78 , s:1, b:0),
% 1.44/1.78 'class_OrderedGroup_Ocomm__monoid__add' [67, 1] (w:1, o:117, a:1, s:1
% 1.44/1.78 , b:0),
% 1.44/1.78 'c_Finite__Set_Osetsum' [68, 3] (w:1, o:239, a:1, s:1, b:0),
% 1.44/1.78 'c_Suc' [69, 0] (w:1, o:48, a:1, s:1, b:0),
% 1.44/1.78 'c_lessequals' [71, 2] (w:1, o:221, a:1, s:1, b:0),
% 1.44/1.78 'class_Int_Onumber__ring' [72, 1] (w:1, o:119, a:1, s:1, b:0),
% 1.44/1.78 'c_Power_Opower__class_Opower' [73, 1] (w:1, o:120, a:1, s:1, b:0),
% 1.44/1.78 'c_Int_OMin' [74, 0] (w:1, o:50, a:1, s:1, b:0),
% 1.44/1.78 'c_Int_Onumber__class_Onumber__of' [75, 2] (w:1, o:222, a:1, s:1, b:0
% 1.44/1.78 ),
% 1.44/1.78 'c_HOL_Oone__class_Oone' [77, 1] (w:1, o:114, a:1, s:1, b:0),
% 1.44/1.78 'c_Parity_Oeven__odd__class_Oeven' [78, 2] (w:1, o:224, a:1, s:1, b:0
% 1.44/1.78 ),
% 1.44/1.78 'class_Ring__and__Field_Oordered__idom' [79, 1] (w:1, o:125, a:1, s:1
% 1.44/1.78 , b:0),
% 1.44/1.78 'c_HOL_Ozero__class_Ozero' [80, 1] (w:1, o:126, a:1, s:1, b:0),
% 1.44/1.78 'class_OrderedGroup_Opordered__ab__group__add' [82, 1] (w:1, o:127
% 1.44/1.78 , a:1, s:1, b:0),
% 1.44/1.78 'class_Divides_Osemiring__div' [85, 1] (w:1, o:129, a:1, s:1, b:0),
% 1.44/1.78 'c_Divides_Odiv__class_Omod' [87, 3] (w:1, o:241, a:1, s:1, b:0),
% 1.44/1.78 'c_HOL_Otimes__class_Otimes' [88, 1] (w:1, o:130, a:1, s:1, b:0),
% 1.44/1.78 'c_Divides_Odiv__class_Odiv' [89, 3] (w:1, o:242, a:1, s:1, b:0),
% 1.44/1.78 'class_Orderings_Olinorder' [90, 1] (w:1, o:131, a:1, s:1, b:0),
% 1.44/1.78 'class_OrderedGroup_Olordered__ab__group__add' [92, 1] (w:1, o:132
% 1.44/1.78 , a:1, s:1, b:0),
% 1.44/1.78 'class_Ring__and__Field_Oordered__semidom' [97, 1] (w:1, o:134, a:1
% 1.44/1.78 , s:1, b:0),
% 1.44/1.78 'c_Lattices_Oboolean__algebra' [106, 9] (w:1, o:256, a:1, s:1, b:0),
% 1.44/1.78
% 1.44/1.78 'c_Ring__and__Field_Oordered__idom' [113, 11] (w:1, o:257, a:1, s:1
% 1.44/1.78 , b:0),
% 1.44/1.78 'c_Set_Oinsert' [114, 3] (w:1, o:243, a:1, s:1, b:0),
% 1.44/1.78 'c_Finite__Set_Ofinite' [115, 2] (w:1, o:225, a:1, s:1, b:0),
% 1.44/1.78 'class_Lattices_Olower__semilattice' [116, 1] (w:1, o:135, a:1, s:1
% 1.44/1.78 , b:0),
% 1.44/1.78 'class_Lattices_Olattice' [118, 1] (w:1, o:136, a:1, s:1, b:0),
% 1.44/1.78 'class_Ring__and__Field_Ocomm__semiring__1' [119, 1] (w:1, o:139, a:1
% 1.44/1.78 , s:1, b:0),
% 1.44/1.78 'class_Power_Opower' [120, 1] (w:1, o:160, a:1, s:1, b:0),
% 1.44/1.78 'class_OrderedGroup_Omonoid__mult' [121, 1] (w:1, o:142, a:1, s:1, b:
% 1.44/1.78 0),
% 1.44/1.78 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [122, 1]
% 1.44/1.78 (w:1, o:143, a:1, s:1, b:0),
% 1.44/1.78 'class_OrderedGroup_Opordered__ab__semigroup__add' [123, 1] (w:1, o:
% 1.44/1.78 144, a:1, s:1, b:0),
% 1.44/1.78 'class_OrderedGroup_Oab__group__add' [125, 1] (w:1, o:145, a:1, s:1
% 1.44/1.78 , b:0),
% 1.44/1.78 'class_RealVector_Ometric__space' [126, 1] (w:1, o:161, a:1, s:1, b:0
% 1.44/1.78 ),
% 1.44/1.78 'class_RealVector_Oreal__normed__algebra__1' [127, 1] (w:1, o:162, a:
% 1.44/1.78 1, s:1, b:0),
% 1.44/1.78 'c_Lim_OLIM' [130, 5] (w:1, o:253, a:1, s:1, b:0),
% 1.44/1.78 'tc_Int_Oint' [131, 0] (w:1, o:82, a:1, s:1, b:0),
% 1.44/1.78 'c_SEQ_OLIMSEQ' [133, 2] (w:1, o:226, a:1, s:1, b:0),
% 1.44/1.78 'class_RealVector_Oreal__normed__vector' [134, 1] (w:1, o:163, a:1
% 1.44/1.78 , s:1, b:0),
% 1.44/1.78 'c_COMBB' [135, 3] (w:1, o:240, a:1, s:1, b:0),
% 1.44/1.78 'c_COMBC' [136, 4] (w:1, o:248, a:1, s:1, b:0),
% 1.44/1.78 'class_OrderedGroup_Opordered__comm__monoid__add' [137, 1] (w:1, o:
% 2.78/3.17 146, a:1, s:1, b:0),
% 2.78/3.17 't_a' [138, 0] (w:1, o:84, a:1, s:1, b:0),
% 2.78/3.17 'v_f' [139, 0] (w:1, o:85, a:1, s:1, b:0),
% 2.78/3.17 'c_Series_Osummable' [140, 2] (w:1, o:227, a:1, s:1, b:0),
% 2.78/3.17 'c_Ex' [141, 1] (w:1, o:164, a:1, s:1, b:0),
% 2.78/3.17 'c_Series_Osums' [142, 2] (w:1, o:228, a:1, s:1, b:0),
% 2.78/3.17 'class_HOL_Ominus' [145, 1] (w:1, o:118, a:1, s:1, b:0),
% 2.78/3.17 'v_x' [146, 0] (w:1, o:86, a:1, s:1, b:0),
% 2.78/3.17 'c_Groebner__Basis_Ogb__semiring' [152, 6] (w:1, o:254, a:1, s:1, b:0
% 2.78/3.17 ),
% 2.78/3.17 'class_Divides_Oring__div' [157, 1] (w:1, o:128, a:1, s:1, b:0),
% 2.78/3.17 'class_Ring__and__Field_Oidom' [158, 1] (w:1, o:165, a:1, s:1, b:0),
% 2.78/3.17
% 2.78/3.17 'class_OrderedGroup_Ocancel__ab__semigroup__add' [159, 1] (w:1, o:147
% 2.78/3.17 , a:1, s:1, b:0),
% 2.78/3.17 'class_OrderedGroup_Ocancel__semigroup__add' [160, 1] (w:1, o:148, a:
% 2.78/3.17 1, s:1, b:0),
% 2.78/3.17 'c_in' [162, 1] (w:1, o:166, a:1, s:1, b:0),
% 2.78/3.17 'class_OrderedGroup_Olordered__ab__group__add__meet' [164, 1] (w:1
% 2.78/3.17 , o:140, a:1, s:1, b:0),
% 2.78/3.17 'class_Lattices_Obounded__lattice' [167, 1] (w:1, o:167, a:1, s:1, b:
% 2.78/3.17 0),
% 2.78/3.17 'class_Ring__and__Field_Oring' [168, 1] (w:1, o:168, a:1, s:1, b:0),
% 2.78/3.17
% 2.78/3.17 'class_Ring__and__Field_Opordered__ring' [169, 1] (w:1, o:172, a:1
% 2.78/3.17 , s:1, b:0),
% 2.78/3.17 'c_Relation_OImage' [172, 4] (w:1, o:246, a:1, s:1, b:0),
% 2.78/3.17 'class_Orderings_Obot' [173, 1] (w:1, o:149, a:1, s:1, b:0),
% 2.78/3.17 'c_Int_OPls' [174, 0] (w:1, o:90, a:1, s:1, b:0),
% 2.78/3.17 'c_SEQ_OCauchy' [175, 2] (w:1, o:229, a:1, s:1, b:0),
% 2.78/3.17 'c_List_Ofilter' [177, 3] (w:1, o:244, a:1, s:1, b:0),
% 2.78/3.17 'c_List_Oset' [178, 2] (w:1, o:230, a:1, s:1, b:0),
% 2.78/3.17 'class_OrderedGroup_Ogroup__add' [179, 1] (w:1, o:150, a:1, s:1, b:0)
% 2.78/3.17 ,
% 2.78/3.17 'c_SEQ_OZseq' [180, 2] (w:1, o:231, a:1, s:1, b:0),
% 2.78/3.17 'class_Orderings_Opreorder' [181, 1] (w:1, o:151, a:1, s:1, b:0),
% 2.78/3.17 'class_OrderedGroup_Oab__semigroup__add' [182, 1] (w:1, o:152, a:1
% 2.78/3.17 , s:1, b:0),
% 2.78/3.17 'c_Int_OBit0' [184, 1] (w:1, o:173, a:1, s:1, b:0),
% 2.78/3.17 'c_Int_OBit1' [185, 1] (w:1, o:174, a:1, s:1, b:0),
% 2.78/3.17 'class_Orderings_Owellorder' [186, 1] (w:1, o:153, a:1, s:1, b:0),
% 2.78/3.17 'c_Orderings_Oord__class_OLeast' [187, 2] (w:1, o:223, a:1, s:1, b:0)
% 2.78/3.17 ,
% 2.78/3.17 'class_RealVector_Oreal__normed__algebra' [191, 1] (w:1, o:175, a:1
% 2.78/3.17 , s:1, b:0),
% 2.78/3.17 'class_Ring__and__Field_Oordered__ring__strict' [192, 1] (w:1, o:133
% 2.78/3.17 , a:1, s:1, b:0),
% 2.78/3.17 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [193, 1]
% 2.78/3.17 (w:1, o:154, a:1, s:1, b:0),
% 2.78/3.17 'class_Int_Onumber' [196, 1] (w:1, o:176, a:1, s:1, b:0),
% 2.78/3.17 'c_Not' [197, 0] (w:1, o:93, a:1, s:1, b:0),
% 2.78/3.17 'c_fequal' [198, 1] (w:1, o:177, a:1, s:1, b:0),
% 2.78/3.17 'class_Finite__Set_Ofinite_Ofinite' [199, 1] (w:1, o:178, a:1, s:1
% 2.78/3.17 , b:0),
% 2.78/3.17 'class_Ring__and__Field_Ozero__neq__one' [201, 1] (w:1, o:179, a:1
% 2.78/3.17 , s:1, b:0),
% 2.78/3.17 'class_Ring__and__Field_Oring__1__no__zero__divisors' [202, 1] (w:1
% 2.78/3.17 , o:180, a:1, s:1, b:0),
% 2.78/3.17 'class_Ring__and__Field_Ono__zero__divisors' [203, 1] (w:1, o:124, a:
% 2.78/3.17 1, s:1, b:0),
% 2.78/3.17 'class_Ring__and__Field_Omult__zero' [204, 1] (w:1, o:121, a:1, s:1
% 2.78/3.17 , b:0),
% 2.78/3.17 'class_OrderedGroup_Omonoid__add' [205, 1] (w:1, o:155, a:1, s:1, b:0
% 2.78/3.17 ),
% 2.78/3.17 'class_Ring__and__Field_Oordered__semiring__strict' [206, 1] (w:1, o:
% 2.78/3.17 169, a:1, s:1, b:0),
% 2.78/3.17 'class_Ring__and__Field_Oordered__semiring' [207, 1] (w:1, o:170, a:1
% 2.78/3.17 , s:1, b:0),
% 2.78/3.17 'c_Collect' [209, 1] (w:1, o:181, a:1, s:1, b:0),
% 2.78/3.17 'c_COMBS' [210, 4] (w:1, o:249, a:1, s:1, b:0),
% 2.78/3.17 'c_List_Osko__List__Xex__nat__less__eq__1__2' [211, 2] (w:1, o:232
% 2.78/3.17 , a:1, s:1, b:0),
% 2.78/3.17 'c_List_Osko__List__Xall__nat__less__eq__1__1' [212, 2] (w:1, o:233
% 2.78/3.17 , a:1, s:1, b:0),
% 2.78/3.17 'class_Ring__and__Field_Ocomm__ring' [213, 1] (w:1, o:137, a:1, s:1
% 2.78/3.17 , b:0),
% 2.78/3.17 'class_Ring__and__Field_Oordered__comm__semiring__strict' [214, 1]
% 2.78/3.17 (w:1, o:171, a:1, s:1, b:0),
% 2.78/3.17 'class_Ring__and__Field_Omult__mono1' [215, 1] (w:1, o:122, a:1, s:1
% 2.78/3.17 , b:0),
% 2.78/3.17 'class_Ring__and__Field_Omult__mono' [216, 1] (w:1, o:123, a:1, s:1
% 2.78/3.17 , b:0),
% 2.78/3.17 'class_Ring__and__Field_Ocomm__semiring' [218, 1] (w:1, o:182, a:1
% 13.31/13.70 , s:1, b:0),
% 13.31/13.70 'class_OrderedGroup_Ocomm__monoid__mult' [220, 1] (w:1, o:156, a:1
% 13.31/13.70 , s:1, b:0),
% 13.31/13.70 'class_Ring__and__Field_Osemiring' [221, 1] (w:1, o:184, a:1, s:1, b:
% 13.31/13.70 0),
% 13.31/13.70 'class_Ring__and__Field_Osemiring__0' [222, 1] (w:1, o:185, a:1, s:1
% 13.31/13.70 , b:0),
% 13.31/13.70 'class_Ring__and__Field_Opordered__cancel__semiring' [223, 1] (w:1
% 13.31/13.70 , o:186, a:1, s:1, b:0),
% 13.31/13.70 'class_Ring__and__Field_Opordered__semiring' [224, 1] (w:1, o:187, a:
% 13.31/13.70 1, s:1, b:0),
% 13.31/13.70 'class_Lattices_Oupper__semilattice' [229, 1] (w:1, o:188, a:1, s:1
% 13.31/13.70 , b:0),
% 13.31/13.70 'c_Ring__and__Field_Ocomm__ring__1' [230, 7] (w:1, o:255, a:1, s:1
% 13.31/13.70 , b:0),
% 13.31/13.70 'class_Ring__and__Field_Osemiring__1' [231, 1] (w:1, o:189, a:1, s:1
% 13.31/13.70 , b:0),
% 13.31/13.70 'c_and' [232, 0] (w:1, o:98, a:1, s:1, b:0),
% 13.31/13.70 'class_Ring__and__Field_Ocomm__semiring__0' [233, 1] (w:1, o:138, a:1
% 13.31/13.70 , s:1, b:0),
% 13.31/13.70 'class_Orderings_Odense__linear__order' [234, 1] (w:1, o:157, a:1, s:
% 13.31/13.70 1, b:0),
% 13.31/13.70 'class_Lattices_Odistrib__lattice' [235, 1] (w:1, o:190, a:1, s:1, b:
% 13.31/13.70 0),
% 13.31/13.70 'class_OrderedGroup_Olordered__ab__group__add__join' [236, 1] (w:1
% 13.31/13.70 , o:141, a:1, s:1, b:0),
% 13.31/13.70 'v_n' [238, 0] (w:1, o:99, a:1, s:1, b:0),
% 13.31/13.70 'c_Parity_Osko__Parity__Xodd__Suc__mult__two__ex__1__1' [239, 1] (w:1
% 13.31/13.70 , o:191, a:1, s:1, b:0),
% 13.31/13.70 'c_or' [240, 0] (w:1, o:100, a:1, s:1, b:0),
% 13.31/13.70 'c_Limits_Oeventually' [243, 3] (w:1, o:245, a:1, s:1, b:0),
% 13.31/13.70 'tc_prod' [244, 2] (w:1, o:234, a:1, s:1, b:0),
% 13.31/13.70 'c_split' [245, 4] (w:1, o:250, a:1, s:1, b:0),
% 13.31/13.70 'c_ATP__Linkup_Osko__Finite__Set__Xfinite__Collect__bounded__ex__1__1' [
% 13.31/13.70 246, 4] (w:1, o:251, a:1, s:1, b:0),
% 13.31/13.70 'v_A' [247, 0] (w:1, o:101, a:1, s:1, b:0),
% 13.31/13.70 't_b' [248, 0] (w:1, o:102, a:1, s:1, b:0),
% 13.31/13.70 'c_ATP__Linkup_Osko__Finite__Set__Xfinite__Collect__bex__1__1' [249, 4
% 13.31/13.70 ] (w:1, o:252, a:1, s:1, b:0),
% 13.31/13.70 'class_Ring__and__Field_Oring__no__zero__divisors' [251, 1] (w:1, o:
% 13.31/13.70 183, a:1, s:1, b:0),
% 13.31/13.70 'class_OrderedGroup_Oab__semigroup__mult' [253, 1] (w:1, o:158, a:1
% 13.31/13.70 , s:1, b:0),
% 13.31/13.70 'class_OrderedGroup_Oab__semigroup__idem__mult' [254, 1] (w:1, o:159
% 13.31/13.70 , a:1, s:1, b:0),
% 13.31/13.70 'class_Int_Oring__char__0' [255, 1] (w:1, o:192, a:1, s:1, b:0).
% 13.31/13.70
% 13.31/13.70
% 13.31/13.70 Starting Search:
% 13.31/13.70
% 13.31/13.70 Resimplifying inuse:
% 13.31/13.70 Done
% 13.31/13.70
% 13.31/13.70
% 13.31/13.70 Intermediate Status:
% 13.31/13.70 Generated: 2928
% 13.31/13.70 Kept: 2000
% 13.31/13.70 Inuse: 77
% 13.31/13.70 Deleted: 1
% 13.31/13.70 Deletedinuse: 0
% 13.31/13.70
% 13.31/13.70 Resimplifying inuse:
% 13.31/13.70 Done
% 13.31/13.70
% 13.31/13.70 Resimplifying inuse:
% 13.31/13.70 Done
% 13.31/13.70
% 13.31/13.70
% 13.31/13.70 Intermediate Status:
% 13.31/13.70 Generated: 6313
% 13.31/13.70 Kept: 4172
% 13.31/13.70 Inuse: 124
% 13.31/13.70 Deleted: 2
% 13.31/13.70 Deletedinuse: 0
% 13.31/13.70
% 13.31/13.70 Resimplifying inuse:
% 13.31/13.70 Done
% 13.31/13.70
% 13.31/13.70 Resimplifying inuse:
% 13.31/13.70 Done
% 13.31/13.70
% 13.31/13.70
% 13.31/13.70 Intermediate Status:
% 13.31/13.70 Generated: 12061
% 13.31/13.70 Kept: 6452
% 13.31/13.70 Inuse: 172
% 13.31/13.70 Deleted: 4
% 13.31/13.70 Deletedinuse: 0
% 13.31/13.70
% 13.31/13.70 Resimplifying inuse:
% 13.31/13.70 Done
% 13.31/13.70
% 13.31/13.70
% 13.31/13.70 Intermediate Status:
% 13.31/13.70 Generated: 16862
% 13.31/13.70 Kept: 8580
% 13.31/13.70 Inuse: 232
% 13.31/13.70 Deleted: 4
% 13.31/13.70 Deletedinuse: 0
% 13.31/13.70
% 13.31/13.70 Resimplifying inuse:
% 13.31/13.70 Done
% 13.31/13.70
% 13.31/13.70 Resimplifying inuse:
% 13.31/13.70 Done
% 13.31/13.70
% 13.31/13.70
% 13.31/13.70 Intermediate Status:
% 13.31/13.70 Generated: 20804
% 13.31/13.70 Kept: 10668
% 13.31/13.70 Inuse: 252
% 13.31/13.70 Deleted: 4
% 13.31/13.70 Deletedinuse: 0
% 13.31/13.70
% 13.31/13.70 Resimplifying inuse:
% 13.31/13.70 Done
% 13.31/13.70
% 13.31/13.70 Resimplifying inuse:
% 13.31/13.70 Done
% 13.31/13.70
% 13.31/13.70
% 13.31/13.70 Intermediate Status:
% 13.31/13.70 Generated: 25012
% 13.31/13.70 Kept: 12955
% 13.31/13.70 Inuse: 272
% 13.31/13.70 Deleted: 4
% 13.31/13.70 Deletedinuse: 0
% 13.31/13.70
% 13.31/13.70 Resimplifying inuse:
% 13.31/13.70 Done
% 13.31/13.70
% 13.31/13.70 Resimplifying inuse:
% 13.31/13.70 Done
% 13.31/13.70
% 13.31/13.70
% 13.31/13.70 Intermediate Status:
% 13.31/13.70 Generated: 29795
% 13.31/13.70 Kept: 15146
% 13.31/13.70 Inuse: 306
% 13.31/13.70 Deleted: 5
% 13.31/13.70 Deletedinuse: 0
% 13.31/13.70
% 13.31/13.70 Resimplifying inuse:
% 13.31/13.70 Done
% 13.31/13.70
% 13.31/13.70 Resimplifying inuse:
% 13.31/13.70 Done
% 13.31/13.70
% 13.31/13.70
% 13.31/13.70 Intermediate Status:
% 13.31/13.70 Generated: 35111
% 13.31/13.70 Kept: 17264
% 13.31/13.70 Inuse: 359
% 13.31/13.70 Deleted: 7
% 13.31/13.70 Deletedinuse: 0
% 13.31/13.70
% 13.31/13.70 Resimplifying inuse:
% 13.31/13.70 Done
% 13.31/13.70
% 13.31/13.70 Resimplifying inuse:
% 13.31/13.70 Done
% 13.31/13.70
% 13.31/13.70
% 13.31/13.70 Intermediate Status:
% 13.31/13.70 Generated: 40969
% 13.31/13.70 Kept: 19389
% 13.31/13.70 Inuse: 423
% 13.31/13.70 Deleted: 8
% 13.31/13.70 Deletedinuse: 0
% 13.31/13.70
% 13.31/13.70 Resimplifying inuse:
% 13.31/13.70 Done
% 13.31/13.70
% 13.31/13.70 Resimplifying clauses:
% 13.31/13.70 Done
% 13.31/13.70
% 13.31/13.70
% 13.31/13.70 Intermediate Status:
% 13.31/13.70 Generated: 46104
% 13.31/13.70 Kept: 21928
% 13.31/13.70 Inuse: 449
% 13.31/13.70 Deleted: 280
% 13.31/13.70 Deletedinuse: 0
% 13.31/13.70
% 13.31/13.70 Resimplifying inuse:
% 13.31/13.70 Done
% 13.31/13.70
% 13.31/13.70 Resimplifying inuse:
% 13.31/13.70 Done
% 13.31/13.70
% 13.31/13.70
% 13.31/13.70 Intermediate Status:
% 13.31/13.70 Generated: 55067
% 13.31/13.70 Kept: 24316
% 13.31/13.70 Inuse: 483
% 13.31/13.70 Deleted: 280
% 13.31/13.70 Deletedinuse: 0
% 13.31/13.70
% 13.31/13.70 Resimplifying inuse:
% 13.31/13.70 Done
% 13.31/13.70
% 13.31/13.70 Resimplifying inuse:
% 13.31/13.70 Done
% 43.23/43.59
% 43.23/43.59
% 43.23/43.59 Intermediate Status:
% 43.23/43.59 Generated: 68896
% 43.23/43.59 Kept: 26836
% 43.23/43.59 Inuse: 498
% 43.23/43.59 Deleted: 281
% 43.23/43.59 Deletedinuse: 1
% 43.23/43.59
% 43.23/43.59 Resimplifying inuse:
% 43.23/43.59 Done
% 43.23/43.59
% 43.23/43.59
% 43.23/43.59 Intermediate Status:
% 43.23/43.59 Generated: 84291
% 43.23/43.59 Kept: 29548
% 43.23/43.59 Inuse: 513
% 43.23/43.59 Deleted: 281
% 43.23/43.59 Deletedinuse: 1
% 43.23/43.59
% 43.23/43.59 Resimplifying inuse:
% 43.23/43.59 Done
% 43.23/43.59
% 43.23/43.59 Resimplifying inuse:
% 43.23/43.59 Done
% 43.23/43.59
% 43.23/43.59
% 43.23/43.59 Intermediate Status:
% 43.23/43.59 Generated: 94024
% 43.23/43.59 Kept: 31741
% 43.23/43.59 Inuse: 543
% 43.23/43.59 Deleted: 281
% 43.23/43.59 Deletedinuse: 1
% 43.23/43.59
% 43.23/43.59 Resimplifying inuse:
% 43.23/43.59 Done
% 43.23/43.59
% 43.23/43.59 Resimplifying inuse:
% 43.23/43.59 Done
% 43.23/43.59
% 43.23/43.59
% 43.23/43.59 Intermediate Status:
% 43.23/43.59 Generated: 102645
% 43.23/43.59 Kept: 33955
% 43.23/43.59 Inuse: 583
% 43.23/43.59 Deleted: 281
% 43.23/43.59 Deletedinuse: 1
% 43.23/43.59
% 43.23/43.59 Resimplifying inuse:
% 43.23/43.59 Done
% 43.23/43.59
% 43.23/43.59 Resimplifying inuse:
% 43.23/43.59 Done
% 43.23/43.59
% 43.23/43.59
% 43.23/43.59 Intermediate Status:
% 43.23/43.59 Generated: 115683
% 43.23/43.59 Kept: 36890
% 43.23/43.59 Inuse: 617
% 43.23/43.59 Deleted: 282
% 43.23/43.59 Deletedinuse: 1
% 43.23/43.59
% 43.23/43.59 Resimplifying inuse:
% 43.23/43.59 Done
% 43.23/43.59
% 43.23/43.59 Resimplifying inuse:
% 43.23/43.59 Done
% 43.23/43.59
% 43.23/43.59
% 43.23/43.59 Intermediate Status:
% 43.23/43.59 Generated: 123167
% 43.23/43.59 Kept: 39146
% 43.23/43.59 Inuse: 647
% 43.23/43.59 Deleted: 282
% 43.23/43.59 Deletedinuse: 1
% 43.23/43.59
% 43.23/43.59 Resimplifying inuse:
% 43.23/43.59 Done
% 43.23/43.59
% 43.23/43.59 Resimplifying inuse:
% 43.23/43.59 Done
% 43.23/43.59
% 43.23/43.59 Resimplifying clauses:
% 43.23/43.59 Done
% 43.23/43.59
% 43.23/43.59
% 43.23/43.59 Intermediate Status:
% 43.23/43.60 Generated: 131920
% 43.23/43.60 Kept: 41995
% 43.23/43.60 Inuse: 687
% 43.23/43.60 Deleted: 502
% 43.23/43.60 Deletedinuse: 1
% 43.23/43.60
% 43.23/43.60 Resimplifying inuse:
% 43.23/43.60 Done
% 43.23/43.60
% 43.23/43.60 Resimplifying inuse:
% 43.23/43.60 Done
% 43.23/43.60
% 43.23/43.60
% 43.23/43.60 Intermediate Status:
% 43.23/43.60 Generated: 136341
% 43.23/43.60 Kept: 44059
% 43.23/43.60 Inuse: 702
% 43.23/43.60 Deleted: 502
% 43.23/43.60 Deletedinuse: 1
% 43.23/43.60
% 43.23/43.60 Resimplifying inuse:
% 43.23/43.60 Done
% 43.23/43.60
% 43.23/43.60 Resimplifying inuse:
% 43.23/43.60 Done
% 43.23/43.60
% 43.23/43.60
% 43.23/43.60 Intermediate Status:
% 43.23/43.60 Generated: 143178
% 43.23/43.60 Kept: 46215
% 43.23/43.60 Inuse: 732
% 43.23/43.60 Deleted: 502
% 43.23/43.60 Deletedinuse: 1
% 43.23/43.60
% 43.23/43.60 Resimplifying inuse:
% 43.23/43.60 Done
% 43.23/43.60
% 43.23/43.60 Resimplifying inuse:
% 43.23/43.60 Done
% 43.23/43.60
% 43.23/43.60
% 43.23/43.60 Intermediate Status:
% 43.23/43.60 Generated: 150624
% 43.23/43.60 Kept: 48420
% 43.23/43.60 Inuse: 752
% 43.23/43.60 Deleted: 502
% 43.23/43.60 Deletedinuse: 1
% 43.23/43.60
% 43.23/43.60 Resimplifying inuse:
% 43.23/43.60 Done
% 43.23/43.60
% 43.23/43.60
% 43.23/43.60 Intermediate Status:
% 43.23/43.60 Generated: 159139
% 43.23/43.60 Kept: 50650
% 43.23/43.60 Inuse: 772
% 43.23/43.60 Deleted: 502
% 43.23/43.60 Deletedinuse: 1
% 43.23/43.60
% 43.23/43.60 Resimplifying inuse:
% 43.23/43.60 Done
% 43.23/43.60
% 43.23/43.60 Resimplifying inuse:
% 43.23/43.60 Done
% 43.23/43.60
% 43.23/43.60
% 43.23/43.60 Intermediate Status:
% 43.23/43.60 Generated: 172797
% 43.23/43.60 Kept: 53731
% 43.23/43.60 Inuse: 792
% 43.23/43.60 Deleted: 502
% 43.23/43.60 Deletedinuse: 1
% 43.23/43.60
% 43.23/43.60 Resimplifying inuse:
% 43.23/43.60 Done
% 43.23/43.60
% 43.23/43.60 Resimplifying inuse:
% 43.23/43.60 Done
% 43.23/43.60
% 43.23/43.60
% 43.23/43.60 Intermediate Status:
% 43.23/43.60 Generated: 189162
% 43.23/43.60 Kept: 56302
% 43.23/43.60 Inuse: 802
% 43.23/43.60 Deleted: 502
% 43.23/43.60 Deletedinuse: 1
% 43.23/43.60
% 43.23/43.60 Resimplifying inuse:
% 43.23/43.60 Done
% 43.23/43.60
% 43.23/43.60 Resimplifying inuse:
% 43.23/43.60 Done
% 43.23/43.60
% 43.23/43.60
% 43.23/43.60 Intermediate Status:
% 43.23/43.60 Generated: 205866
% 43.23/43.60 Kept: 58870
% 43.23/43.60 Inuse: 812
% 43.23/43.60 Deleted: 502
% 43.23/43.60 Deletedinuse: 1
% 43.23/43.60
% 43.23/43.60 Resimplifying inuse:
% 43.23/43.60 Done
% 43.23/43.60
% 43.23/43.60 Resimplifying inuse:
% 43.23/43.60 Done
% 43.23/43.60
% 43.23/43.60 Resimplifying clauses:
% 43.23/43.60 Done
% 43.23/43.60
% 43.23/43.60
% 43.23/43.60 Intermediate Status:
% 43.23/43.60 Generated: 218726
% 43.23/43.60 Kept: 61249
% 43.23/43.60 Inuse: 827
% 43.23/43.60 Deleted: 937
% 43.23/43.60 Deletedinuse: 1
% 43.23/43.60
% 43.23/43.60 Resimplifying inuse:
% 43.23/43.60 Done
% 43.23/43.60
% 43.23/43.60 Resimplifying inuse:
% 43.23/43.60 Done
% 43.23/43.60
% 43.23/43.60
% 43.23/43.60 Intermediate Status:
% 43.23/43.60 Generated: 233286
% 43.23/43.60 Kept: 65882
% 43.23/43.60 Inuse: 842
% 43.23/43.60 Deleted: 937
% 43.23/43.60 Deletedinuse: 1
% 43.23/43.60
% 43.23/43.60 Resimplifying inuse:
% 43.23/43.60 Done
% 43.23/43.60
% 43.23/43.60 Resimplifying inuse:
% 43.23/43.60 Done
% 43.23/43.60
% 43.23/43.60
% 43.23/43.60 Intermediate Status:
% 43.23/43.60 Generated: 242357
% 43.23/43.60 Kept: 67935
% 43.23/43.60 Inuse: 867
% 43.23/43.60 Deleted: 937
% 43.23/43.60 Deletedinuse: 1
% 43.23/43.60
% 43.23/43.60 Resimplifying inuse:
% 43.23/43.60 Done
% 43.23/43.60
% 43.23/43.60 Resimplifying inuse:
% 43.23/43.60 Done
% 43.23/43.60
% 43.23/43.60
% 43.23/43.60 Intermediate Status:
% 43.23/43.60 Generated: 256826
% 43.23/43.60 Kept: 71349
% 43.23/43.60 Inuse: 897
% 43.23/43.60 Deleted: 937
% 43.23/43.60 Deletedinuse: 1
% 43.23/43.60
% 43.23/43.60 Resimplifying inuse:
% 43.23/43.60 Done
% 43.23/43.60
% 43.23/43.60 Resimplifying inuse:
% 43.23/43.60 Done
% 43.23/43.60
% 43.23/43.60
% 43.23/43.60 Intermediate Status:
% 43.23/43.60 Generated: 265735
% 43.23/43.60 Kept: 73607
% 43.23/43.60 Inuse: 917
% 43.23/43.60 Deleted: 937
% 43.23/43.60 Deletedinuse: 1
% 43.23/43.60
% 43.23/43.60 Resimplifying inuse:
% 43.23/43.60 Done
% 43.23/43.60
% 43.23/43.60 Resimplifying inuse:
% 43.23/43.60 Done
% 43.23/43.60
% 43.23/43.60
% 43.23/43.60 Intermediate Status:
% 43.23/43.60 Generated: 276330
% 43.23/43.60 Kept: 76145
% 43.23/43.60 Inuse: 942
% 43.23/43.60 Deleted: 937
% 43.23/43.60 Deletedinuse: 1
% 43.23/43.60
% 43.23/43.60 Resimplifying inuse:
% 43.23/43.60 Done
% 43.23/43.60
% 43.23/43.60 Resimplifying inuse:
% 43.23/43.60 Done
% 43.23/43.60
% 43.23/43.60
% 43.23/43.60 Intermediate Status:
% 43.23/43.60 Generated: 283038
% 43.23/43.60 Kept: 78209
% 43.23/43.60 Inuse: 957
% 43.23/43.60 Deleted: 937
% 43.23/43.60 Deletedinuse: 1
% 43.23/43.60
% 43.23/43.60 Resimplifying inuse:
% 43.23/43.60 Done
% 43.23/43.60
% 43.23/43.60
% 43.23/43.60 Intermediate Status:
% 43.23/43.60 Generated: 288987
% 43.23/43.60 Kept: 80262
% 43.23/43.60 Inuse: 972
% 43.23/43.60 Deleted: 937
% 43.23/43.60 Deletedinuse: 1
% 43.23/43.60
% 43.23/43.60 Resimplifying inuse:
% 43.23/43.60 Done
% 43.23/43.60
% 43.23/43.60 Resimplifying clauses:
% 43.23/43.60 Done
% 43.23/43.60
% 43.23/43.60
% 43.23/43.60 Intermediate Status:
% 43.23/43.60 Generated: 294238
% 43.23/43.60 Kept: 82453
% 43.23/43.60 Inuse: 982
% 43.23/43.60 Deleted: 1073
% 43.23/43.60 Deletedinuse: 1
% 43.23/43.60
% 43.23/43.60 Resimplifying inuse:
% 43.23/43.60 Done
% 43.23/43.60
% 43.23/43.60
% 43.23/43.60 Intermediate Status:
% 43.23/43.60 Generated: 301826
% 43.23/43.60 Kept: 84806
% 43.23/43.60 Inuse: 992
% 43.23/43.60 Deleted: 1073
% 43.23/43.60 Deletedinuse: 1
% 43.23/43.60
% 43.23/43.60 Resimplifying inuse:
% 43.23/43.60 Done
% 43.23/43.60
% 43.23/43.60 Resimplifying inuse:
% 43.23/43.60 Done
% 43.23/43.60
% 43.23/43.60
% 43.23/43.60 Intermediate Status:
% 43.23/43.60 Generated: 310437
% 43.23/43.60 Kept: 87272
% 104.87/105.23 Inuse: 1012
% 104.87/105.23 Deleted: 1073
% 104.87/105.23 Deletedinuse: 1
% 104.87/105.23
% 104.87/105.23 Resimplifying inuse:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23
% 104.87/105.23 Intermediate Status:
% 104.87/105.23 Generated: 323460
% 104.87/105.23 Kept: 90667
% 104.87/105.23 Inuse: 1022
% 104.87/105.23 Deleted: 1073
% 104.87/105.23 Deletedinuse: 1
% 104.87/105.23
% 104.87/105.23 Resimplifying inuse:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23 Resimplifying inuse:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23
% 104.87/105.23 Intermediate Status:
% 104.87/105.23 Generated: 334320
% 104.87/105.23 Kept: 93709
% 104.87/105.23 Inuse: 1032
% 104.87/105.23 Deleted: 1073
% 104.87/105.23 Deletedinuse: 1
% 104.87/105.23
% 104.87/105.23 Resimplifying inuse:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23
% 104.87/105.23 Intermediate Status:
% 104.87/105.23 Generated: 343613
% 104.87/105.23 Kept: 96148
% 104.87/105.23 Inuse: 1037
% 104.87/105.23 Deleted: 1073
% 104.87/105.23 Deletedinuse: 1
% 104.87/105.23
% 104.87/105.23 Resimplifying inuse:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23 Resimplifying inuse:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23
% 104.87/105.23 Intermediate Status:
% 104.87/105.23 Generated: 352860
% 104.87/105.23 Kept: 98433
% 104.87/105.23 Inuse: 1057
% 104.87/105.23 Deleted: 1073
% 104.87/105.23 Deletedinuse: 1
% 104.87/105.23
% 104.87/105.23 Resimplifying inuse:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23 Resimplifying inuse:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23
% 104.87/105.23 Intermediate Status:
% 104.87/105.23 Generated: 361502
% 104.87/105.23 Kept: 100703
% 104.87/105.23 Inuse: 1077
% 104.87/105.23 Deleted: 1073
% 104.87/105.23 Deletedinuse: 1
% 104.87/105.23
% 104.87/105.23 Resimplifying inuse:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23 Resimplifying clauses:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23
% 104.87/105.23 Intermediate Status:
% 104.87/105.23 Generated: 370545
% 104.87/105.23 Kept: 103140
% 104.87/105.23 Inuse: 1107
% 104.87/105.23 Deleted: 1409
% 104.87/105.23 Deletedinuse: 1
% 104.87/105.23
% 104.87/105.23 Resimplifying inuse:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23 Resimplifying inuse:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23
% 104.87/105.23 Intermediate Status:
% 104.87/105.23 Generated: 376972
% 104.87/105.23 Kept: 106044
% 104.87/105.23 Inuse: 1117
% 104.87/105.23 Deleted: 1409
% 104.87/105.23 Deletedinuse: 1
% 104.87/105.23
% 104.87/105.23 Resimplifying inuse:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23 Resimplifying inuse:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23
% 104.87/105.23 Intermediate Status:
% 104.87/105.23 Generated: 383519
% 104.87/105.23 Kept: 108474
% 104.87/105.23 Inuse: 1132
% 104.87/105.23 Deleted: 1409
% 104.87/105.23 Deletedinuse: 1
% 104.87/105.23
% 104.87/105.23 Resimplifying inuse:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23 Resimplifying inuse:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23
% 104.87/105.23 Intermediate Status:
% 104.87/105.23 Generated: 390194
% 104.87/105.23 Kept: 110482
% 104.87/105.23 Inuse: 1152
% 104.87/105.23 Deleted: 1415
% 104.87/105.23 Deletedinuse: 7
% 104.87/105.23
% 104.87/105.23 Resimplifying inuse:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23 Resimplifying inuse:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23
% 104.87/105.23 Intermediate Status:
% 104.87/105.23 Generated: 398543
% 104.87/105.23 Kept: 112519
% 104.87/105.23 Inuse: 1177
% 104.87/105.23 Deleted: 1415
% 104.87/105.23 Deletedinuse: 7
% 104.87/105.23
% 104.87/105.23 Resimplifying inuse:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23
% 104.87/105.23 Intermediate Status:
% 104.87/105.23 Generated: 406953
% 104.87/105.23 Kept: 114953
% 104.87/105.23 Inuse: 1197
% 104.87/105.23 Deleted: 1415
% 104.87/105.23 Deletedinuse: 7
% 104.87/105.23
% 104.87/105.23 Resimplifying inuse:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23
% 104.87/105.23 Intermediate Status:
% 104.87/105.23 Generated: 412971
% 104.87/105.23 Kept: 117145
% 104.87/105.23 Inuse: 1207
% 104.87/105.23 Deleted: 1415
% 104.87/105.23 Deletedinuse: 7
% 104.87/105.23
% 104.87/105.23 Resimplifying inuse:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23
% 104.87/105.23 Intermediate Status:
% 104.87/105.23 Generated: 427695
% 104.87/105.23 Kept: 121230
% 104.87/105.23 Inuse: 1208
% 104.87/105.23 Deleted: 1415
% 104.87/105.23 Deletedinuse: 7
% 104.87/105.23
% 104.87/105.23 Resimplifying inuse:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23 Resimplifying clauses:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23 Resimplifying inuse:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23
% 104.87/105.23 Intermediate Status:
% 104.87/105.23 Generated: 437242
% 104.87/105.23 Kept: 124609
% 104.87/105.23 Inuse: 1217
% 104.87/105.23 Deleted: 1943
% 104.87/105.23 Deletedinuse: 7
% 104.87/105.23
% 104.87/105.23 Resimplifying inuse:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23 Resimplifying inuse:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23
% 104.87/105.23 Intermediate Status:
% 104.87/105.23 Generated: 444007
% 104.87/105.23 Kept: 126827
% 104.87/105.23 Inuse: 1227
% 104.87/105.23 Deleted: 1943
% 104.87/105.23 Deletedinuse: 7
% 104.87/105.23
% 104.87/105.23 Resimplifying inuse:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23
% 104.87/105.23 Intermediate Status:
% 104.87/105.23 Generated: 451626
% 104.87/105.23 Kept: 128836
% 104.87/105.23 Inuse: 1249
% 104.87/105.23 Deleted: 1943
% 104.87/105.23 Deletedinuse: 7
% 104.87/105.23
% 104.87/105.23 Resimplifying inuse:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23 Resimplifying inuse:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23
% 104.87/105.23 Intermediate Status:
% 104.87/105.23 Generated: 459336
% 104.87/105.23 Kept: 130911
% 104.87/105.23 Inuse: 1272
% 104.87/105.23 Deleted: 1943
% 104.87/105.23 Deletedinuse: 7
% 104.87/105.23
% 104.87/105.23 Resimplifying inuse:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23 Resimplifying inuse:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23
% 104.87/105.23 Intermediate Status:
% 104.87/105.23 Generated: 467594
% 104.87/105.23 Kept: 133054
% 104.87/105.23 Inuse: 1292
% 104.87/105.23 Deleted: 1943
% 104.87/105.23 Deletedinuse: 7
% 104.87/105.23
% 104.87/105.23 Resimplifying inuse:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23
% 104.87/105.23 Intermediate Status:
% 104.87/105.23 Generated: 483973
% 104.87/105.23 Kept: 135675
% 104.87/105.23 Inuse: 1302
% 104.87/105.23 Deleted: 1943
% 104.87/105.23 Deletedinuse: 7
% 104.87/105.23
% 104.87/105.23 Resimplifying inuse:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23 Resimplifying inuse:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23
% 104.87/105.23 Intermediate Status:
% 104.87/105.23 Generated: 496564
% 104.87/105.23 Kept: 137682
% 104.87/105.23 Inuse: 1330
% 104.87/105.23 Deleted: 1945
% 104.87/105.23 Deletedinuse: 9
% 104.87/105.23
% 104.87/105.23 Resimplifying inuse:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23 Resimplifying inuse:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23
% 104.87/105.23 Intermediate Status:
% 104.87/105.23 Generated: 505329
% 104.87/105.23 Kept: 140070
% 104.87/105.23 Inuse: 1352
% 104.87/105.23 Deleted: 1945
% 104.87/105.23 Deletedinuse: 9
% 104.87/105.23
% 104.87/105.23 Resimplifying inuse:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23
% 104.87/105.23 Intermediate Status:
% 104.87/105.23 Generated: 523810
% 104.87/105.23 Kept: 144941
% 104.87/105.23 Inuse: 1359
% 104.87/105.23 Deleted: 1945
% 104.87/105.23 Deletedinuse: 9
% 104.87/105.23
% 104.87/105.23 Resimplifying inuse:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23 Resimplifying clauses:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23
% 104.87/105.23 Intermediate Status:
% 104.87/105.23 Generated: 530875
% 104.87/105.23 Kept: 147202
% 104.87/105.23 Inuse: 1362
% 104.87/105.23 Deleted: 3599
% 104.87/105.23 Deletedinuse: 9
% 104.87/105.23
% 104.87/105.23 Resimplifying inuse:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23 Resimplifying inuse:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23
% 104.87/105.23 Intermediate Status:
% 104.87/105.23 Generated: 544249
% 104.87/105.23 Kept: 151408
% 104.87/105.23 Inuse: 1387
% 104.87/105.23 Deleted: 3600
% 104.87/105.23 Deletedinuse: 10
% 104.87/105.23
% 104.87/105.23 Resimplifying inuse:
% 104.87/105.23 Done
% 104.87/105.23
% 104.87/105.23
% 104.87/105.23 Intermediate Status:
% 104.87/105.23 Generated: 554661
% 104.87/105.23 Kept: 154852
% 197.98/198.40 Inuse: 1392
% 197.98/198.40 Deleted: 3600
% 197.98/198.40 Deletedinuse: 10
% 197.98/198.40
% 197.98/198.40 Resimplifying inuse:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40 Resimplifying inuse:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40
% 197.98/198.40 Intermediate Status:
% 197.98/198.40 Generated: 563533
% 197.98/198.40 Kept: 157254
% 197.98/198.40 Inuse: 1412
% 197.98/198.40 Deleted: 3600
% 197.98/198.40 Deletedinuse: 10
% 197.98/198.40
% 197.98/198.40 Resimplifying inuse:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40 Resimplifying inuse:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40
% 197.98/198.40 Intermediate Status:
% 197.98/198.40 Generated: 572389
% 197.98/198.40 Kept: 159449
% 197.98/198.40 Inuse: 1432
% 197.98/198.40 Deleted: 3600
% 197.98/198.40 Deletedinuse: 10
% 197.98/198.40
% 197.98/198.40
% 197.98/198.40 Intermediate Status:
% 197.98/198.40 Generated: 585744
% 197.98/198.40 Kept: 163056
% 197.98/198.40 Inuse: 1437
% 197.98/198.40 Deleted: 3600
% 197.98/198.40 Deletedinuse: 10
% 197.98/198.40
% 197.98/198.40 Resimplifying inuse:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40 Resimplifying inuse:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40 Resimplifying clauses:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40
% 197.98/198.40 Intermediate Status:
% 197.98/198.40 Generated: 600377
% 197.98/198.40 Kept: 166281
% 197.98/198.40 Inuse: 1462
% 197.98/198.40 Deleted: 3916
% 197.98/198.40 Deletedinuse: 10
% 197.98/198.40
% 197.98/198.40 Resimplifying inuse:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40 Resimplifying inuse:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40
% 197.98/198.40 Intermediate Status:
% 197.98/198.40 Generated: 612342
% 197.98/198.40 Kept: 168765
% 197.98/198.40 Inuse: 1487
% 197.98/198.40 Deleted: 3916
% 197.98/198.40 Deletedinuse: 10
% 197.98/198.40
% 197.98/198.40 Resimplifying inuse:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40
% 197.98/198.40 Intermediate Status:
% 197.98/198.40 Generated: 628417
% 197.98/198.40 Kept: 173475
% 197.98/198.40 Inuse: 1492
% 197.98/198.40 Deleted: 3916
% 197.98/198.40 Deletedinuse: 10
% 197.98/198.40
% 197.98/198.40 Resimplifying inuse:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40 Resimplifying inuse:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40
% 197.98/198.40 Intermediate Status:
% 197.98/198.40 Generated: 637931
% 197.98/198.40 Kept: 175628
% 197.98/198.40 Inuse: 1507
% 197.98/198.40 Deleted: 3916
% 197.98/198.40 Deletedinuse: 10
% 197.98/198.40
% 197.98/198.40 Resimplifying inuse:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40 Resimplifying inuse:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40
% 197.98/198.40 Intermediate Status:
% 197.98/198.40 Generated: 648109
% 197.98/198.40 Kept: 177635
% 197.98/198.40 Inuse: 1525
% 197.98/198.40 Deleted: 3916
% 197.98/198.40 Deletedinuse: 10
% 197.98/198.40
% 197.98/198.40 Resimplifying inuse:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40 Resimplifying inuse:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40
% 197.98/198.40 Intermediate Status:
% 197.98/198.40 Generated: 657838
% 197.98/198.40 Kept: 179890
% 197.98/198.40 Inuse: 1547
% 197.98/198.40 Deleted: 3917
% 197.98/198.40 Deletedinuse: 11
% 197.98/198.40
% 197.98/198.40 Resimplifying inuse:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40 Resimplifying inuse:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40
% 197.98/198.40 Intermediate Status:
% 197.98/198.40 Generated: 668122
% 197.98/198.40 Kept: 183468
% 197.98/198.40 Inuse: 1562
% 197.98/198.40 Deleted: 3917
% 197.98/198.40 Deletedinuse: 11
% 197.98/198.40
% 197.98/198.40 Resimplifying inuse:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40 Resimplifying inuse:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40 Resimplifying clauses:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40
% 197.98/198.40 Intermediate Status:
% 197.98/198.40 Generated: 674235
% 197.98/198.40 Kept: 185488
% 197.98/198.40 Inuse: 1570
% 197.98/198.40 Deleted: 4356
% 197.98/198.40 Deletedinuse: 11
% 197.98/198.40
% 197.98/198.40 Resimplifying inuse:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40
% 197.98/198.40 Intermediate Status:
% 197.98/198.40 Generated: 682551
% 197.98/198.40 Kept: 189227
% 197.98/198.40 Inuse: 1577
% 197.98/198.40 Deleted: 4356
% 197.98/198.40 Deletedinuse: 11
% 197.98/198.40
% 197.98/198.40 Resimplifying inuse:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40 Resimplifying inuse:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40
% 197.98/198.40 Intermediate Status:
% 197.98/198.40 Generated: 693895
% 197.98/198.40 Kept: 191333
% 197.98/198.40 Inuse: 1597
% 197.98/198.40 Deleted: 4356
% 197.98/198.40 Deletedinuse: 11
% 197.98/198.40
% 197.98/198.40 Resimplifying inuse:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40 Resimplifying inuse:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40
% 197.98/198.40 Intermediate Status:
% 197.98/198.40 Generated: 700488
% 197.98/198.40 Kept: 193456
% 197.98/198.40 Inuse: 1609
% 197.98/198.40 Deleted: 4356
% 197.98/198.40 Deletedinuse: 11
% 197.98/198.40
% 197.98/198.40 Resimplifying inuse:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40
% 197.98/198.40 Intermediate Status:
% 197.98/198.40 Generated: 716310
% 197.98/198.40 Kept: 197743
% 197.98/198.40 Inuse: 1617
% 197.98/198.40 Deleted: 4356
% 197.98/198.40 Deletedinuse: 11
% 197.98/198.40
% 197.98/198.40 Resimplifying inuse:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40
% 197.98/198.40 Intermediate Status:
% 197.98/198.40 Generated: 724449
% 197.98/198.40 Kept: 200215
% 197.98/198.40 Inuse: 1627
% 197.98/198.40 Deleted: 4356
% 197.98/198.40 Deletedinuse: 11
% 197.98/198.40
% 197.98/198.40 Resimplifying inuse:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40 Resimplifying inuse:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40
% 197.98/198.40 Intermediate Status:
% 197.98/198.40 Generated: 731450
% 197.98/198.40 Kept: 202225
% 197.98/198.40 Inuse: 1635
% 197.98/198.40 Deleted: 4356
% 197.98/198.40 Deletedinuse: 11
% 197.98/198.40
% 197.98/198.40 Resimplifying inuse:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40
% 197.98/198.40 Intermediate Status:
% 197.98/198.40 Generated: 742512
% 197.98/198.40 Kept: 205982
% 197.98/198.40 Inuse: 1642
% 197.98/198.40 Deleted: 4356
% 197.98/198.40 Deletedinuse: 11
% 197.98/198.40
% 197.98/198.40 Resimplifying inuse:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40 Resimplifying clauses:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40 Resimplifying inuse:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40
% 197.98/198.40 Intermediate Status:
% 197.98/198.40 Generated: 749789
% 197.98/198.40 Kept: 208214
% 197.98/198.40 Inuse: 1657
% 197.98/198.40 Deleted: 4847
% 197.98/198.40 Deletedinuse: 11
% 197.98/198.40
% 197.98/198.40 Resimplifying inuse:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40 Resimplifying inuse:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40
% 197.98/198.40 Intermediate Status:
% 197.98/198.40 Generated: 756446
% 197.98/198.40 Kept: 210456
% 197.98/198.40 Inuse: 1667
% 197.98/198.40 Deleted: 4847
% 197.98/198.40 Deletedinuse: 11
% 197.98/198.40
% 197.98/198.40 Resimplifying inuse:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40 Resimplifying inuse:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40
% 197.98/198.40 Intermediate Status:
% 197.98/198.40 Generated: 762814
% 197.98/198.40 Kept: 212531
% 197.98/198.40 Inuse: 1677
% 197.98/198.40 Deleted: 4847
% 197.98/198.40 Deletedinuse: 11
% 197.98/198.40
% 197.98/198.40 Resimplifying inuse:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40 Resimplifying inuse:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40
% 197.98/198.40 Intermediate Status:
% 197.98/198.40 Generated: 772182
% 197.98/198.40 Kept: 214564
% 197.98/198.40 Inuse: 1697
% 197.98/198.40 Deleted: 4847
% 197.98/198.40 Deletedinuse: 11
% 197.98/198.40
% 197.98/198.40 Resimplifying inuse:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40 Resimplifying inuse:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40
% 197.98/198.40 Intermediate Status:
% 197.98/198.40 Generated: 783904
% 197.98/198.40 Kept: 217242
% 197.98/198.40 Inuse: 1725
% 197.98/198.40 Deleted: 4851
% 197.98/198.40 Deletedinuse: 13
% 197.98/198.40
% 197.98/198.40 Resimplifying inuse:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40 Resimplifying inuse:
% 197.98/198.40 Done
% 197.98/198.40
% 197.98/198.40
% 197.98/198.40 Intermediate Status:
% 197.98/198.40 Generated: 797119
% 197.98/198.40 Kept: 219735
% 197.98/198.40 InuseCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------