TSTP Solution File: SWV653-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV653-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 16:27:30 EDT 2022
% Result : Timeout 300.03s 300.50s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV653-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Wed Jun 15 18:54:54 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.41/1.80 *** allocated 10000 integers for termspace/termends
% 1.41/1.80 *** allocated 10000 integers for clauses
% 1.41/1.80 *** allocated 10000 integers for justifications
% 1.41/1.80 *** allocated 15000 integers for termspace/termends
% 1.41/1.80 *** allocated 22500 integers for termspace/termends
% 1.41/1.80 *** allocated 33750 integers for termspace/termends
% 1.41/1.80 *** allocated 50625 integers for termspace/termends
% 1.41/1.80 *** allocated 75937 integers for termspace/termends
% 1.41/1.80 Bliksem 1.12
% 1.41/1.80
% 1.41/1.80
% 1.41/1.80 Automatic Strategy Selection
% 1.41/1.80
% 1.41/1.80 Clauses:
% 1.41/1.80 [
% 1.41/1.80 [ =( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), hAPP( U, W
% 1.41/1.80 ) ), V0 ) ), hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), W
% 1.41/1.80 ), V0 ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( V1, U, V2, V3, V4,
% 1.41/1.80 V5, X, Y, Z, V6, T ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.41/1.80 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.41/1.80 ,
% 1.41/1.80 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP(
% 1.41/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), hAPP(
% 1.41/1.80 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ),
% 1.41/1.80 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.41/1.80 'tc_nat' ), Z, 'tc_nat' ) ) ), 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.41/1.80 'tc_nat' ) ) ) ],
% 1.41/1.80 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.41/1.80 V3, V4 ) ), hBOOL( hAPP( hAPP( W, Z ), hAPP( hAPP(
% 1.41/1.80 'c_Power_Opower_Opower'( V1, V2, V4 ), hAPP( V0, V5 ) ),
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.41/1.80 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.80 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.41/1.80 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ) ), T ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( T, X, 'tc_nat' ) ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.41/1.80 'tc_nat' ) ) ],
% 1.41/1.80 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.41/1.80 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.41/1.80 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y,
% 1.41/1.80 'tc_nat' ) ],
% 1.41/1.80 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.41/1.80 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, hAPP(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), Y ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.41/1.80 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), hAPP( 'c_Suc',
% 1.41/1.80 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.41/1.80 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ), ~( 'c_lessequals'( Y, X,
% 1.41/1.80 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.80 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.41/1.80 X ), ~( 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.41/1.80 T, X ), Z, X ) ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.41/1.80 X ), ~( 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( T,
% 1.41/1.80 Y, X ), Z, X ) ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ), ~(
% 1.41/1.80 'c_lessequals'( Y, Z, X ) ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ), ~(
% 1.41/1.80 'c_lessequals'( Y, T, X ) ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.41/1.80 X ), ~( 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.41/1.80 T, X ), Z, X ) ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.41/1.80 X ), ~( 'c_lessequals'( 'c_Lattices_Oupper__semilattice__class_Osup'( T,
% 1.41/1.80 Y, X ), Z, X ) ) ],
% 1.41/1.80 [ ~( 'class_Orderings_Oorder'( X ) ), ~( =(
% 1.41/1.80 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ),
% 1.41/1.80 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.41/1.80 [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.41/1.80 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ),
% 1.41/1.80 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.41/1.80 [ 'c_lessequals'( 'c_Int_OMin', 'c_Int_OMin', 'tc_Int_Oint' ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.41/1.80 'class_Int_Onumber__ring'( X ) ), =( hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.41/1.80 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ),
% 1.41/1.80 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), U ), W ) ), hAPP( hAPP( Y, hAPP(
% 1.41/1.80 hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), U ) ), hAPP( hAPP(
% 1.41/1.80 'c_Power_Opower_Opower'( X, Y, Z ), T ), W ) ) ), ~(
% 1.41/1.80 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.41/1.80 [ ~( =( 'c_Set_Oimage'( X, Y, Z, T ), 'c_Orderings_Obot__class_Obot'(
% 1.41/1.80 'tc_fun'( T, 'tc_bool' ) ) ) ), =( Y, 'c_Orderings_Obot__class_Obot'(
% 1.41/1.80 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.41/1.80 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.41/1.80 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( Z, T, U, Y, X ),
% 1.41/1.80 ~( 'c_Lim_OLIM'( 'c_COMBC'( 'c_COMBB'( 'c_HOL_Ominus__class_Ominus'( X )
% 1.41/1.80 , Z, X, 'tc_fun'( X, X ), Y ), U, Y, X, X ), T,
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.80 [ =( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), U ), W ) )
% 1.41/1.80 , hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), hAPP( X, U ) ), W ) ),
% 1.41/1.80 ~( 'c_Ring__and__Field_Oordered__idom'( V0, V1, V2, V3, V4, V5, X, Y, Z,
% 1.41/1.80 V6, T ) ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ),
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ],
% 1.41/1.80 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 1.41/1.80 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( T,
% 1.41/1.80 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z,
% 1.41/1.80 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.41/1.80 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.41/1.80 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( X, T, 'tc_fun'( Z,
% 1.41/1.80 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T,
% 1.41/1.80 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.41/1.80 ), Y ) ), Z ) ), Z ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.41/1.80 ), Z ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.41/1.80 hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.41/1.80 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ),
% 1.41/1.80 ~( 'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ), Z, X ) ) ]
% 1.41/1.80 ,
% 1.41/1.80 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.41/1.80 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.41/1.80 , Y ), Z ), Z, X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.41/1.80 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.41/1.80 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.41/1.80 , Y ), Z ), Y, X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ), Z, X
% 1.41/1.80 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.41/1.80 ), Y ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), U ), W ) ), hAPP( hAPP(
% 1.41/1.80 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.41/1.80 X, Y, Z ), T ), U ) ), W ) ), ~( 'c_OrderedGroup_Omonoid__mult'( X, Y, Z
% 1.41/1.80 ) ) ],
% 1.41/1.80 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), ~(
% 1.41/1.80 'class_Power_Opower'( X ) ), 'c_SEQ_OLIMSEQ'( 'c_COMBC'( 'c_COMBB'(
% 1.41/1.80 'c_Power_Opower__class_Opower'( X ), Y, X, 'tc_fun'( 'tc_nat', X ),
% 1.41/1.80 'tc_nat' ), Z, 'tc_nat', 'tc_nat', X ), hAPP( hAPP(
% 1.41/1.80 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_SEQ_OLIMSEQ'( Y
% 1.41/1.80 , T, X ) ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ), ~(
% 1.41/1.80 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ), ~(
% 1.41/1.80 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ), ~(
% 1.41/1.80 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'(
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Z, X ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'(
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y, X ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Z, X ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y, X ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.80 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.41/1.80 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~( 'c_lessequals'( Y,
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.80 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.80 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.80 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.80 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.80 X ), X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.41/1.80 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.41/1.80 ), X ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), T ),
% 1.41/1.80 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.80 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.41/1.80 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~( 'c_lessequals'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.80 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.80 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.80 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.80 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.80 ), Y, X ), 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'(
% 1.41/1.80 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.41/1.80 ), X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.41/1.80 X ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.41/1.80 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ),
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.41/1.80 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.41/1.80 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ),
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.80 'class_Int_Onumber'( X ) ), 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.80 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.41/1.80 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z
% 1.41/1.80 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.80 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.41/1.80 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.41/1.80 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.41/1.80 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X )
% 1.41/1.80 ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.41/1.80 , Y ), 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.41/1.80 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastAtMost'(
% 1.41/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), U ), T ), 'tc_nat' ), 'tc_nat', X
% 1.41/1.80 ), 'c_Finite__Set_Osetsum'( 'c_COMBB'( Y, 'c_COMBC'(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T, 'tc_nat', 'tc_nat', 'tc_nat' )
% 1.41/1.80 , 'tc_nat', X, 'tc_nat' ), 'c_SetInterval_Oord__class_OatLeastAtMost'( Z
% 1.41/1.80 , U, 'tc_nat' ), 'tc_nat', X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.41/1.80 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ),
% 1.41/1.80 ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z )
% 1.41/1.80 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.41/1.80 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, hAPP(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ],
% 1.41/1.80 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.41/1.80 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.41/1.80 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.41/1.80 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.80 'tc_nat' ), X ), 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z,
% 1.41/1.80 'tc_nat' ) ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), X ), T ), X ), ~(
% 1.41/1.80 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.41/1.80 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.41/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.41/1.80 'c_lessequals'( Y, T, X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.41/1.80 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.41/1.80 , 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.41/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.41/1.80 'c_lessequals'( Z, T, X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.41/1.80 , 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.41/1.80 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.41/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.41/1.80 'c_lessequals'( Y, T, X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.41/1.80 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.41/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.41/1.80 'c_lessequals'( Z, T, X ) ) ],
% 1.41/1.80 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.41/1.80 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ),
% 1.41/1.80 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.41/1.80 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ) ],
% 1.41/1.80 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.41/1.80 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ),
% 1.41/1.80 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP(
% 1.41/1.80 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) )
% 1.41/1.80 ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), hAPP( 'c_Suc', Y ) )
% 1.41/1.80 ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.41/1.80 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.80 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.41/1.80 hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ), hAPP( 'c_HOL_Oabs__class_Oabs'(
% 1.41/1.80 X ), T ), X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ]
% 1.41/1.80 ,
% 1.41/1.80 [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.41/1.80 Y, Z, X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Olower__semilattice'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.41/1.80 Y, Z, X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ), Y ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.41/1.80 'c_HOL_Oabs__class_Oabs'( X ), Y ), Y ), ~( 'c_lessequals'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.41/1.80 ), =( Z, Y ) ],
% 1.41/1.80 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Z, Y, X ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.41/1.80 ) ],
% 1.41/1.80 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.41/1.80 ) ],
% 1.41/1.80 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.41/1.80 , X ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.41/1.80 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y, Z
% 1.41/1.80 , X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.41/1.80 [ ~( 'class_RealVector_Ometric__space'( X ) ), ~(
% 1.41/1.80 'class_RealVector_Oreal__normed__algebra__1'( Y ) ), =( Z, T ), ~(
% 1.41/1.80 'c_Lim_OLIM'( U, W, T, Y, X ) ), ~( 'c_Lim_OLIM'( U, W, Z, Y, X ) ) ]
% 1.41/1.80 ,
% 1.41/1.80 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 1.41/1.80 , Y, 'tc_nat' ) ) ],
% 1.41/1.80 [ =( X, Y ), ~( 'c_lessequals'( Y, X, 'tc_Int_Oint' ) ), ~(
% 1.41/1.80 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.41/1.80 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.80 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.41/1.80 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), =( Y, X ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Y, X, 'tc_Int_Oint' ) ],
% 1.41/1.80 [ ~( 'class_RealVector_Ometric__space'( X ) ), =( Y, Z ), ~(
% 1.41/1.80 'c_SEQ_OLIMSEQ'( T, Z, X ) ), ~( 'c_SEQ_OLIMSEQ'( T, Y, X ) ) ],
% 1.41/1.80 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 1.41/1.80 'tc_nat' ), =( Z, Y ), 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ],
% 1.41/1.80 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.80 Y, X, 'tc_nat' ), =( Y, X ) ],
% 1.41/1.80 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.41/1.80 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.41/1.80 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.41/1.80 , X ), 'c_HOL_Oord__class_Oless'( Z, Y, X ), =( Z, Y ) ],
% 1.41/1.80 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Z, Y
% 1.41/1.80 , X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =( hAPP(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), =( Y, Z ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), =( Y, Z ) ],
% 1.41/1.80 [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.41/1.80 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Z, X ),
% 1.41/1.80 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ),
% 1.41/1.80 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP(
% 1.41/1.80 'c_HOL_Oabs__class_Oabs'( X ), T ) ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), Z, X ) ) ],
% 1.41/1.80 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.41/1.80 [ ~( 'class_RealVector_Ometric__space'( X ) ), ~(
% 1.41/1.80 'class_RealVector_Oreal__normed__vector'( Y ) ), 'c_Lim_OLIM'( 'c_COMBB'(
% 1.41/1.80 Z, 'c_COMBC'( 'c_HOL_Oplus__class_Oplus'( Y ), T, Y, Y, Y ), Y, X, Y ),
% 1.41/1.80 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( Y ), U ), T ), W, Y, X ), ~(
% 1.41/1.80 'c_Lim_OLIM'( Z, U, W, Y, X ) ) ],
% 1.41/1.80 [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.41/1.80 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ),
% 1.41/1.80 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ), ~(
% 1.41/1.80 'c_lessequals'( Z, Y, X ) ) ],
% 1.41/1.80 [ =( 'c_Set_Oimage'( 'c_Suc', 'c_SetInterval_Oord__class_OatLeastAtMost'(
% 1.41/1.80 X, Y, 'tc_nat' ), 'tc_nat', 'tc_nat' ),
% 1.41/1.80 'c_SetInterval_Oord__class_OatLeastAtMost'( hAPP( 'c_Suc', X ), hAPP(
% 1.41/1.80 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.41/1.80 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X )
% 1.41/1.80 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.41/1.80 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ), X ) ],
% 1.41/1.80 [ 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.41/1.80 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.41/1.80 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.41/1.80 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( Y, Z, 'tc_Int_Oint' ),
% 1.41/1.80 ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.41/1.80 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.41/1.80 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'(
% 1.41/1.80 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.41/1.80 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~( 'c_lessequals'( Y, Z
% 1.41/1.80 , 'tc_Int_Oint' ) ) ],
% 1.41/1.80 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_SEQ_OLIMSEQ'(
% 1.41/1.80 'c_COMBC'( 'c_COMBB'( 'c_HOL_Ominus__class_Ominus'( X ), Y, X, 'tc_fun'(
% 1.41/1.80 X, X ), 'tc_nat' ), Z, 'tc_nat', X, X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( X ), T ), Z ), X ), ~( 'c_SEQ_OLIMSEQ'( Y,
% 1.41/1.80 T, X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( Y,
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP(
% 1.41/1.80 'c_HOL_Oabs__class_Oabs'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.41/1.80 ) ],
% 1.41/1.80 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_SEQ_OZseq'(
% 1.41/1.80 'c_COMBB'( 'c_HOL_Ouminus__class_Ouminus'( X ), Y, X, X, 'tc_nat' ), X )
% 1.41/1.80 , ~( 'c_SEQ_OZseq'( Y, X ) ) ],
% 1.41/1.80 [ ~( hBOOL( hAPP( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.41/1.80 ) ), Y ) ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.41/1.80 'c_HOL_Oabs__class_Oabs'( X ), Y ),
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, hAPP(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =(
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, hAPP(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.80 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.80 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.41/1.80 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ),
% 1.41/1.80 'c_SetInterval_Oord__class_OatLeastAtMost'( Z, T, X ), 'tc_fun'( X,
% 1.41/1.80 'tc_bool' ) ), 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, T, X ) ),
% 1.41/1.80 ~( 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ), ~( 'c_lessequals'(
% 1.41/1.80 Z, Y, 'tc_nat' ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ), Y ) ), ~(
% 1.41/1.80 'c_lessequals'( Z, X, 'tc_nat' ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.41/1.80 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.41/1.80 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.41/1.80 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.41/1.80 , hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), hAPP(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.41/1.80 'c_Orderings_Obot__class_Obot'( X ), X ), Y ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.41/1.80 'c_Orderings_Obot__class_Obot'( X ), Y, X ), Y ) ],
% 1.41/1.80 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.41/1.80 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 1.41/1.80 X, 'tc_bool' ) ), Y ) ],
% 1.41/1.80 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.41/1.80 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 1.41/1.80 'tc_bool' ) ), X ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.41/1.80 , Y ) ), Z ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.41/1.80 ,
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.41/1.80 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.41/1.80 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.41/1.80 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.41/1.80 ), Y ), T ), Z, X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.41/1.80 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.41/1.80 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.41/1.80 Y, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.80 X ), T ), Z ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.41/1.80 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ),
% 1.41/1.80 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, X ), 'tc_fun'( X,
% 1.41/1.80 'tc_bool' ) ), 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, T, X ) )
% 1.41/1.80 , ~( 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.41/1.80 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.41/1.80 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBC'(
% 1.41/1.80 'c_COMBB'( 'c_HOL_Ominus__class_Ominus'( X ), Z, X, 'tc_fun'( X, X ), Y )
% 1.41/1.80 , T, Y, X, X ), U, 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.41/1.80 'c_Lim_OLIM'( Z, U, T, Y, X ) ) ],
% 1.41/1.80 [ ~( 'class_Orderings_Oorder'( X ) ), ~( =(
% 1.41/1.80 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Z, X ),
% 1.41/1.80 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ), ~(
% 1.41/1.80 'c_lessequals'( Y, Z, X ) ) ],
% 1.41/1.80 [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.41/1.80 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Z, X ),
% 1.41/1.80 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.41/1.80 'c_lessequals'( Y, Z, X ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.41/1.80 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.41/1.80 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.41/1.80 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.41/1.80 'c_Int_OMin', X ) ), Y ), 'c_HOL_Oone__class_Oone'( X ) ), ~(
% 1.41/1.80 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.41/1.80 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.80 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'( Y
% 1.41/1.80 , T, X ) ), 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.41/1.80 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.41/1.80 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat'
% 1.41/1.80 ), ~( 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ) ],
% 1.41/1.80 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP(
% 1.41/1.80 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ]
% 1.41/1.80 ,
% 1.41/1.80 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_SEQ_OLIMSEQ'(
% 1.41/1.80 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'( X ), Y, X, 'tc_fun'( X
% 1.41/1.80 , X ), 'tc_nat' ), Z, 'tc_nat', X, X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~( 'c_SEQ_OLIMSEQ'( Y, T
% 1.41/1.80 , X ) ) ],
% 1.41/1.80 [ hBOOL( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y,
% 1.41/1.80 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( Y, T ) ) ), ~( hBOOL(
% 1.41/1.80 hAPP( X, T ) ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.41/1.80 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( T, U
% 1.41/1.80 , X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.41/1.80 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( T, U, X ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.41/1.80 , X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.41/1.80 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), 'c_lessequals'( Z, Y, X
% 1.41/1.80 ), ~( 'c_lessequals'( U, T, X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.41/1.80 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), 'c_lessequals'( U, T, X
% 1.41/1.80 ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.41/1.80 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.41/1.80 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.41/1.80 , Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ),
% 1.41/1.80 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.41/1.80 , Y ), Z ), T, X ) ) ],
% 1.41/1.80 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.41/1.80 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.41/1.80 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.41/1.80 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.41/1.80 , Y ), T ), Z, X ) ) ],
% 1.41/1.80 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.41/1.80 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.41/1.80 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), 'tc_fun'( X,
% 1.41/1.80 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 1.41/1.80 ) ],
% 1.41/1.80 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( Y, hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.80 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.41/1.80 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ) ],
% 1.41/1.80 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.80 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.41/1.80 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), Y ) ],
% 1.41/1.80 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.80 X ), Y ), 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ),
% 1.41/1.80 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ), Z ) ],
% 1.41/1.80 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.41/1.80 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.41/1.80 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.41/1.80 ,
% 1.41/1.80 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 1.41/1.80 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.41/1.80 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.41/1.80 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.41/1.80 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), =( X, Y ), ~(
% 1.41/1.80 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.41/1.80 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), =( X, Y ), ~(
% 1.41/1.80 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.41/1.80 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.41/1.80 ), =( Y, Z ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.41/1.80 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.41/1.80 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Y, Z ) ],
% 1.41/1.80 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( 'c_lessequals'( Y
% 1.41/1.80 , Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.41/1.80 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.41/1.80 ,
% 1.41/1.80 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.41/1.80 ), ~( 'c_lessequals'( Y, Z, X ) ), =( Z, Y ) ],
% 1.41/1.80 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.41/1.80 ), =( Z, Y ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.41/1.80 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.41/1.80 ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.41/1.80 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ), ~( 'c_lessequals'( Z
% 1.41/1.80 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) )
% 1.41/1.80 ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), 'c_HOL_Oone__class_Oone'(
% 1.41/1.80 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ],
% 1.41/1.80 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.41/1.80 X ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.41/1.80 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), hAPP(
% 1.41/1.80 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.41/1.80 , Z ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), X ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.41/1.80 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), U )
% 1.41/1.80 , X ), ~( 'c_lessequals'( U, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.80 Y, T, X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.41/1.80 ],
% 1.41/1.80 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.41/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.41/1.80 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y
% 1.41/1.80 , 'tc_nat' ) ) ],
% 1.41/1.80 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.41/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' )
% 1.41/1.80 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X
% 1.41/1.80 , 'tc_nat' ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.41/1.80 ,
% 1.41/1.80 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Y,
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Y,
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.41/1.80 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.41/1.80 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.80 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.41/1.80 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.41/1.80 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.41/1.80 X ), Y ), Z ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( X ), Z ), Y ) ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), hAPP(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), Z ) ) ],
% 1.41/1.80 [ ~( 'c_lessequals'( 'c_Int_OPls', 'c_Int_OMin', 'tc_Int_Oint' ) ) ]
% 1.41/1.80 ,
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.41/1.80 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.80 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.41/1.80 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.41/1.80 Y, Z, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.80 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.41/1.80 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.41/1.80 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.80 'c_Power_Opower__class_Opower'( X ), Y ), T ), X ), ~( 'c_lessequals'( Z
% 1.41/1.80 , T, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.41/1.80 X ), Y, X ) ) ],
% 1.41/1.80 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Oone__class_Oone'(
% 1.41/1.80 'tc_nat' ), 'tc_nat' ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( 'c_Suc'
% 1.41/1.80 , U ) ), hAPP( hAPP( Y, hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T
% 1.41/1.80 ), U ) ), T ) ), ~( 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.41/1.80 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.41/1.80 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.41/1.80 , Y ), Z ), Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.41/1.80 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.41/1.80 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.80 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.41/1.80 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.41/1.80 , Y ), Z ), Z, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.41/1.80 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), 'c_HOL_Oone__class_Oone'( X )
% 1.41/1.80 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP(
% 1.41/1.80 'c_HOL_Oabs__class_Oabs'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.41/1.80 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.41/1.80 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP(
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Z, X, 'tc_fun'( T,
% 1.41/1.80 'tc_bool' ) ), Y ) ) ) ],
% 1.41/1.80 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP(
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 1.41/1.80 'tc_bool' ) ), Y ) ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.41/1.80 'c_HOL_Oone__class_Oone'( X ) ), X ) ],
% 1.41/1.80 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.41/1.80 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 1.41/1.80 Z, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.41/1.80 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.80 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Z, 'tc_nat' ) ),
% 1.41/1.80 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z, 'tc_nat' ) ) ) ]
% 1.41/1.80 ,
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.41/1.80 ), T ), Z ), Y, X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.41/1.80 ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.41/1.80 X ), T ), Z ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.41/1.80 X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.41/1.80 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.41/1.80 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.41/1.80 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.41/1.80 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.41/1.80 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.41/1.80 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.41/1.80 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.41/1.80 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.41/1.80 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.41/1.80 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.41/1.80 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.41/1.80 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.41/1.80 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.41/1.80 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.41/1.80 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.41/1.80 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.41/1.80 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.41/1.80 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.41/1.80 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.41/1.80 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.41/1.80 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.41/1.80 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.41/1.80 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.41/1.80 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.41/1.80 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ),
% 1.41/1.80 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.41/1.80 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.41/1.80 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ), ~(
% 1.41/1.80 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.41/1.80 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.41/1.80 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.41/1.80 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.41/1.80 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ],
% 1.41/1.80 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.41/1.80 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ),
% 1.41/1.80 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ],
% 1.41/1.80 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP(
% 1.41/1.80 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Y ), ~(
% 1.41/1.80 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.41/1.80 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.41/1.80 hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ),
% 1.41/1.80 'c_Divides_Odiv__class_Omod'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.41/1.80 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), Z, X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.41/1.80 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( X ), Y, X, 'tc_fun'( X, X ), 'tc_nat' ),
% 1.41/1.80 'c_COMBB'( Y, 'c_COMBC'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.41/1.80 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat', 'tc_nat', 'tc_nat' ),
% 1.41/1.80 'tc_nat', X, 'tc_nat' ), 'tc_nat', X, X ),
% 1.41/1.80 'c_SetInterval_Oord__class_OatLeastAtMost'( Z, T, 'tc_nat' ), 'tc_nat', X
% 1.41/1.80 ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), hAPP( Y, Z ) ), hAPP(
% 1.41/1.80 Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ),
% 1.41/1.80 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ) ), ~( 'c_lessequals'( Z, T,
% 1.41/1.80 'tc_nat' ) ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =( hAPP(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ),
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ),
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.41/1.80 ,
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.41/1.80 ,
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.41/1.80 ,
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.41/1.80 ,
% 1.41/1.80 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.41/1.80 , hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ],
% 1.41/1.80 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Series_Osums'(
% 1.41/1.80 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Y, X,
% 1.41/1.80 'tc_fun'( X, X ), 'tc_nat' ), Z, 'tc_nat', X, X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ), ~( 'c_Series_Osums'(
% 1.41/1.80 Y, T, X ) ) ],
% 1.41/1.80 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Series_Osums'(
% 1.41/1.80 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Y, X,
% 1.41/1.80 'tc_fun'( X, X ), 'tc_nat' ), Z, 'tc_nat', X, X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ), ~( 'c_Series_Osums'(
% 1.41/1.80 Y, T, X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.41/1.80 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.41/1.80 'c_HOL_Oone__class_Oone'( X ) ) ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.80 Y, Z, X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.41/1.80 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.41/1.80 'c_HOL_Oone__class_Oone'( X ) ) ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.41/1.80 Z, X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.80 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.41/1.80 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 1.41/1.80 [ 'c_lessequals'( X, 'c_Int_OMin', 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.41/1.80 'c_Int_OBit1'( X ), 'c_Int_OMin', 'tc_Int_Oint' ) ) ],
% 1.41/1.80 [ 'c_lessequals'( 'c_Int_OBit1'( X ), 'c_Int_OMin', 'tc_Int_Oint' ), ~(
% 1.41/1.80 'c_lessequals'( X, 'c_Int_OMin', 'tc_Int_Oint' ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP(
% 1.41/1.80 'c_Suc', Y ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.41/1.80 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ),
% 1.41/1.80 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), Y ) ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ],
% 1.41/1.80 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.41/1.80 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 1.41/1.80 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.41/1.80 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 1.41/1.80 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 1.41/1.80 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.41/1.80 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oabs__class_Oabs'( X
% 1.41/1.80 ), Y ), Z, X ) ) ],
% 1.41/1.80 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP( X, Z ), Y ) ),
% 1.41/1.80 =( Z, Y ), ~( 'c_Ring__and__Field_Oordered__idom'( T, U, W, V0, V1, X, V2
% 1.41/1.80 , V3, V4, V5, V6 ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( X, hAPP( Y, Z ) ), hAPP( Y, Z ) ), hAPP( hAPP( X, Z ),
% 1.41/1.80 Z ) ), ~( 'c_Ring__and__Field_Oordered__idom'( T, U, W, V0, V1, V2, Y, V3
% 1.41/1.80 , X, V4, V5 ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( X, hAPP( Y, Z ) ), hAPP( T, Z ) ), Z ), ~(
% 1.41/1.80 'c_Ring__and__Field_Oordered__idom'( U, W, V0, V1, V2, V3, T, V4, X, Y,
% 1.41/1.80 V5 ) ) ],
% 1.41/1.80 [ =( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, hAPP( X, Z ) ),
% 1.41/1.80 hAPP( X, T ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, V0, V1,
% 1.41/1.80 V2, V3, V4, V5, Y, X, V6 ) ) ],
% 1.41/1.80 [ =( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, hAPP( X, Z ) ),
% 1.41/1.80 hAPP( X, T ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, V0, V1,
% 1.41/1.80 V2, V3, X, V4, Y, V5, V6 ) ) ],
% 1.41/1.80 [ =( hAPP( X, hAPP( X, Y ) ), hAPP( X, Y ) ), ~(
% 1.41/1.80 'c_Ring__and__Field_Oordered__idom'( Z, T, U, W, V0, V1, V2, V3, V4, X,
% 1.41/1.80 V5 ) ) ],
% 1.41/1.80 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.41/1.80 V3, V4 ) ), =( hAPP( V3, Z ), Z ) ],
% 1.41/1.80 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, hAPP( Z, T ), U, W, V0,
% 1.41/1.80 V1, V2, V3, Z, V4 ) ), =( T, hAPP( Z, T ) ) ],
% 1.41/1.80 [ =( hAPP( X, Y ), hAPP( hAPP( Z, Y ), hAPP( T, Y ) ) ), ~(
% 1.41/1.80 'c_Ring__and__Field_Oordered__idom'( U, W, V0, V1, V2, V3, X, V4, Z, T,
% 1.41/1.80 V5 ) ) ],
% 1.41/1.80 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( Z, Y ) ), ~( hBOOL( hAPP(
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Z, X, 'tc_fun'( T,
% 1.41/1.80 'tc_bool' ) ), Y ) ) ) ],
% 1.41/1.80 [ hBOOL( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 1.41/1.80 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( Y, T ) ) ) ],
% 1.41/1.80 [ hBOOL( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y,
% 1.41/1.80 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( X, T ) ) ) ],
% 1.41/1.80 [ ~( hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z,
% 1.41/1.80 T, U ), hAPP( W, Y ) ), V0 ) ) ) ), ~(
% 1.41/1.80 'c_Ring__and__Field_Oordered__idom'( V1, V2, Y, V3, V4, X, W, Z, T, V5, U
% 1.41/1.80 ) ), =( V0, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.41/1.80 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.41/1.80 ,
% 1.41/1.80 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.41/1.80 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.41/1.80 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.41/1.80 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.41/1.80 ,
% 1.41/1.80 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ) ), ~(
% 1.41/1.80 'c_lessequals'( X, T, 'tc_nat' ) ), =( Z, hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), X ) ), Y ) ), U ) ) ],
% 1.41/1.80 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ) ), ~(
% 1.41/1.80 'c_lessequals'( T, X, 'tc_nat' ) ), =( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), T ) ), Y ) ), Z ), U ) ]
% 1.41/1.80 ,
% 1.41/1.80 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.41/1.80 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.41/1.80 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat'
% 1.41/1.80 ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ) ],
% 1.41/1.80 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.41/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Z,
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.41/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( 'c_lessequals'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), =( Y,
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.80 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), hAPP( 'c_Suc',
% 1.41/1.80 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.41/1.80 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'( X, Y
% 1.41/1.80 , 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.80 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.41/1.80 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), Z ) ), T ) ) ) ]
% 1.41/1.80 ,
% 1.41/1.80 [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.41/1.80 ~( hBOOL( hAPP( X, T ) ) ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.41/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), hAPP( 'c_Suc', T ) ),
% 1.41/1.80 'tc_nat' ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.80 'tc_nat' ), Z ), T ), Y, 'tc_nat' ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.41/1.80 'c_HOL_Oabs__class_Oabs'( X ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.41/1.80 X ), Y ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.80 X ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =( hAPP(
% 1.41/1.80 'c_HOL_Oabs__class_Oabs'( X ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.41/1.80 X ), Y ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.80 X ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.41/1.80 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.41/1.80 'c_HOL_Oabs__class_Oabs'( X ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.41/1.80 X ), Y ) ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.80 X ), X ) ) ],
% 1.41/1.80 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.41/1.80 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'( Y
% 1.41/1.80 , hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.41/1.80 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ),
% 1.41/1.80 Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.80 T, X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.41/1.80 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.41/1.80 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.41/1.80 ), X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.41/1.80 , Z, X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.41/1.80 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.41/1.80 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ),
% 1.41/1.80 Z, X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.41/1.80 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.41/1.80 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T )
% 1.41/1.80 , Z ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.41/1.80 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.41/1.80 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.41/1.80 ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.41/1.80 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.41/1.80 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T
% 1.41/1.80 ), Z, X ) ) ],
% 1.41/1.80 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_Lim_OLIM'(
% 1.41/1.80 'c_COMBC'( 'c_HOL_Otimes__class_Otimes'( X ), Y, X, X, X ), Z, hAPP( hAPP(
% 1.41/1.80 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X, X ) ],
% 1.41/1.80 [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), Y,
% 1.41/1.80 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.80 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.41/1.80 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastAtMost'( Z
% 1.41/1.80 , hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'( Y,
% 1.41/1.80 'c_SetInterval_Oord__class_OatLeastAtMost'( Z, T, 'tc_nat' ), 'tc_nat', X
% 1.41/1.80 ) ), hAPP( Y, hAPP( 'c_Suc', T ) ) ) ), 'c_HOL_Oord__class_Oless'( hAPP(
% 1.41/1.80 'c_Suc', T ), Z, 'tc_nat' ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.41/1.80 'c_Orderings_Obot__class_Obot'( X ), X ), 'c_Orderings_Obot__class_Obot'(
% 1.41/1.80 X ) ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.41/1.80 'c_Orderings_Obot__class_Obot'( X ), Y, X ),
% 1.41/1.80 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.41/1.80 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.41/1.80 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 1.41/1.80 X, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.41/1.80 ) ) ) ],
% 1.41/1.80 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.41/1.80 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 1.41/1.80 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.41/1.80 ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.41/1.80 ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.41/1.80 ,
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.41/1.80 ), X ) ) ],
% 1.41/1.80 [ ~( =( 'c_Set_Oimage'( X, Y, Z, T ), 'c_Set_Oimage'( X, U, Z, T ) ) ),
% 1.41/1.80 ~( 'c_Fun_Oinj__on'( X, 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.41/1.80 U, 'tc_fun'( Z, 'tc_bool' ) ), Z, T ) ), =( Y, U ) ],
% 1.41/1.80 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.41/1.80 , X ) ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.41/1.80 'tc_nat' ), X ), Y ) ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.41/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.80 X ), U ), Z ) ), W ), X ), ~( 'c_lessequals'( T, hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.80 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W
% 1.41/1.80 ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'( Y
% 1.41/1.80 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), U ) ), W ), X ), ~(
% 1.41/1.80 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), Y ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.80 X ), Z ), U ) ), W ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.41/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.80 X ), U ), Z ) ), W ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.80 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T
% 1.41/1.80 ), W, X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.41/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ) ), U ), W, X ), ~(
% 1.41/1.80 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), U ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.80 X ), Z ), T ) ), W ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.41/1.80 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.41/1.80 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.41/1.80 , X ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ],
% 1.41/1.80 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.80 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.41/1.80 'tc_nat' ) ) ],
% 1.41/1.80 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.80 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.41/1.80 'tc_nat' ) ) ],
% 1.41/1.80 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.80 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.41/1.80 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.80 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.41/1.80 'tc_nat' ) ) ],
% 1.41/1.80 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.80 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.41/1.80 'tc_nat' ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.41/1.80 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ),
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ),
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ) ],
% 1.41/1.80 [ 'c_lessequals'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.41/1.80 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP(
% 1.41/1.80 'c_Suc', X ), Y, 'tc_nat' ) ) ],
% 1.41/1.80 [ 'c_lessequals'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.41/1.80 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP(
% 1.41/1.80 'c_Suc', X ), Y, 'tc_nat' ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.41/1.80 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.41/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.41/1.80 'c_lessequals'( Y, Z, X ) ), ~( 'c_lessequals'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.41/1.80 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), 'c_lessequals'( Y,
% 1.41/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ), ~(
% 1.41/1.80 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.41/1.80 [ =( 'c_SetInterval_Oord__class_OatLeastLessThan'( X, hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ),
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.41/1.80 'c_SetInterval_Oord__class_OatLeastLessThan'( X, Y, 'tc_nat' ),
% 1.41/1.80 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), 'tc_fun'(
% 1.41/1.80 'tc_nat', 'tc_bool' ) ) ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.41/1.80 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP(
% 1.41/1.80 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.41/1.80 ) ],
% 1.41/1.80 [ 'c_lessequals'( 'c_Int_OMin', 'c_Int_OBit0'( X ), 'tc_Int_Oint' ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', X, 'tc_Int_Oint' ) ) ],
% 1.41/1.80 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', X, 'tc_Int_Oint' ), ~(
% 1.41/1.80 'c_lessequals'( 'c_Int_OMin', 'c_Int_OBit0'( X ), 'tc_Int_Oint' ) ) ]
% 1.41/1.80 ,
% 1.41/1.80 [ ~( 'class_Orderings_Obot'( X ) ), 'c_lessequals'(
% 1.41/1.80 'c_Orderings_Obot__class_Obot'( X ), Y, X ) ],
% 1.41/1.80 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.41/1.80 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ),
% 1.41/1.80 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.41/1.80 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.41/1.80 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.41/1.80 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.41/1.80 ), Y ), Z, 'tc_nat' ), ~( 'c_lessequals'( X, hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ), ~(
% 1.41/1.80 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.41/1.80 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.41/1.80 ), Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ), ~(
% 1.41/1.80 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.41/1.80 [ 'c_lessequals'( 'c_Int_OMin', 'c_Int_OBit1'( X ), 'tc_Int_Oint' ), ~(
% 1.41/1.80 'c_lessequals'( 'c_Int_OMin', X, 'tc_Int_Oint' ) ) ],
% 1.41/1.80 [ 'c_lessequals'( 'c_Int_OMin', X, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.41/1.80 'c_Int_OMin', 'c_Int_OBit1'( X ), 'tc_Int_Oint' ) ) ],
% 1.41/1.80 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.41/1.80 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), 'tc_nat' ) ],
% 1.41/1.80 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), 'tc_nat' ) ],
% 1.41/1.80 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.80 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.41/1.80 ) ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.41/1.80 ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.80 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP(
% 1.41/1.80 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), X ) ), Y ) ), U ),
% 1.41/1.80 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.41/1.80 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.80 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP(
% 1.41/1.80 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), T ) ), U ),
% 1.41/1.80 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ), U ), 'tc_nat' ) ),
% 1.41/1.80 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.41/1.80 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.80 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.41/1.80 ) ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.41/1.80 ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.80 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP(
% 1.41/1.80 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), T ) ), Y ) ), Z ), U
% 1.41/1.80 , 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.41/1.80 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.80 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP(
% 1.41/1.80 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ) ), T ), U
% 1.41/1.80 , 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), T ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), U ), 'tc_nat' ) ),
% 1.41/1.80 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.80 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( X ), T ), Y ) ), Z ) ), U ) ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.80 X ), T ), Z ) ), U ) ) ],
% 1.41/1.80 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.41/1.80 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBB'(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ), Z, X, X, Y ), T, hAPP(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ), U ), Y, X ), ~( 'c_Lim_OLIM'( Z, T,
% 1.41/1.80 U, Y, X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.41/1.80 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), hAPP(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.41/1.80 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ), ~( 'c_lessequals'( Z, Y, X
% 1.41/1.80 ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Olordered__ring'( X ) ), 'c_lessequals'(
% 1.41/1.80 hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y
% 1.41/1.80 ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Z ) ), X ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.41/1.80 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP(
% 1.41/1.80 'c_HOL_Oabs__class_Oabs'( X ), Y ), Z, X ) ) ],
% 1.41/1.80 [ ~( =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.41/1.80 'c_Set_Oimage'( Y, Z, T, X ) ) ), =( Z, 'c_Orderings_Obot__class_Obot'(
% 1.41/1.80 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.80 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.41/1.80 'tc_nat' ) ), Y ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.41/1.80 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), X ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 'c_lessequals'( Y
% 1.41/1.80 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.41/1.80 ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.41/1.80 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.80 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.41/1.80 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_Int_Oint' ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.41/1.80 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z,
% 1.41/1.80 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.80 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.41/1.80 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.41/1.80 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.41/1.80 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' )
% 1.41/1.80 ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.41/1.80 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), hAPP(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), hAPP(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), =( Z,
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.80 [ 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.41/1.80 'c_Divides_Odiv__class_Odiv'( Z, Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.41/1.80 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.41/1.80 X ), ~( 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.41/1.80 Z, T, X ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.41/1.80 X ), ~( 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.41/1.80 T, Z, X ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'(
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ), ~(
% 1.41/1.80 'c_lessequals'( Y, T, X ) ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'(
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ), ~(
% 1.41/1.80 'c_lessequals'( Z, T, X ) ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.41/1.80 X ), ~( 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.41/1.80 Z, T, X ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), 'c_lessequals'( Y, Z,
% 1.41/1.80 X ), ~( 'c_lessequals'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.41/1.80 T, Z, X ), X ) ) ],
% 1.41/1.80 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_SEQ_OZseq'(
% 1.41/1.80 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Y, X,
% 1.41/1.80 'tc_fun'( X, X ), 'tc_nat' ), Z, 'tc_nat', X, X ), X ), ~( 'c_SEQ_OZseq'(
% 1.41/1.80 Y, X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.41/1.80 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z )
% 1.41/1.80 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.41/1.80 X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.41/1.80 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z )
% 1.41/1.80 , X ), ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.80 X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), T ) )
% 1.41/1.80 , hAPP( hAPP( Y, hAPP( hAPP( X, Z ), U ) ), T ) ), ~(
% 1.41/1.80 'c_Groebner__Basis_Ogb__semiring'( X, Y, W, V0, V1, V2 ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ), hAPP( hAPP( Y, hAPP(
% 1.41/1.80 hAPP( X, Z ), U ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Y, W
% 1.41/1.80 , V0, U, V1 ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ), hAPP( hAPP( Z, hAPP(
% 1.41/1.80 hAPP( X, T ), U ) ), Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, W
% 1.41/1.80 , V0, U, V1 ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, hAPP( hAPP( X, T ), T ) ),
% 1.41/1.80 Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, U, W, T, V0 ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.41/1.80 X, T, U, Y, W, V0 ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.41/1.80 X, T, U, Z, W, V0 ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.41/1.80 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.41/1.80 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.41/1.80 'c_Groebner__Basis_Ogb__semiring'( Y, X, W, V0, V1, V2 ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.41/1.80 T, X, U, Y, W, V0 ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.41/1.80 T, X, U, Z, W, V0 ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.41/1.80 T, X, U, W, Y, V0 ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.41/1.80 T, X, U, W, Z, V0 ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.41/1.80 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.41/1.80 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.41/1.80 , hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), hAPP( hAPP( X, T ), U ) ) ) ),
% 1.41/1.80 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.41/1.80 , hAPP( hAPP( X, T ), hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), U ) ) ),
% 1.41/1.80 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.41/1.80 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.41/1.80 , V0, V1, V2 ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.41/1.80 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.41/1.80 W, V0, V1, V2 ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.41/1.80 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.41/1.80 , V0, V1, V2 ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.41/1.80 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.41/1.80 W, V0, V1, V2 ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.41/1.80 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.41/1.80 ~( 'c_Groebner__Basis_Ogb__semiring'( X, W, V0, V1, V2, V3 ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.41/1.80 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.41/1.80 W, V0, V1, V2 ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.41/1.80 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.41/1.80 W, V0, V1, V2 ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.41/1.80 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.41/1.80 , V0, V1, V2 ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.41/1.80 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.41/1.80 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.41/1.80 , V0, V1, V2 ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.41/1.80 X, T, U, Y, W, V0 ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.41/1.80 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.41/1.80 , V0, V1, V2 ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.41/1.80 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.41/1.80 T, X, U, Y, W, V0 ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.41/1.80 T, X, U, W, Y, V0 ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.41/1.80 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.41/1.80 , V0, V1, V2 ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.41/1.80 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 1.41/1.80 hAPP( X, Y ), T ) ), hAPP( hAPP( X, Y ), U ) ) ), ~(
% 1.41/1.80 'c_Groebner__Basis_Ogb__semiring'( Z, X, W, V0, V1, V2 ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.41/1.80 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.41/1.80 'c_Groebner__Basis_Ogb__semiring'( W, Y, X, V0, V1, V2 ) ) ],
% 1.41/1.80 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.41/1.80 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), T, X ),
% 1.41/1.80 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.41/1.80 ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ),
% 1.41/1.80 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.41/1.80 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.41/1.80 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.80 [ =( 'c_Set_Oimage'( 'c_COMBC'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.41/1.80 X, 'tc_nat', 'tc_nat', 'tc_nat' ),
% 1.41/1.80 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Z, 'tc_nat' ), 'tc_nat',
% 1.41/1.80 'tc_nat' ), 'c_SetInterval_Oord__class_OatLeastAtMost'( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ), 'tc_nat' ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.41/1.80 ), Y ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.41/1.80 'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ), Z, X ), ~(
% 1.41/1.80 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ) )
% 1.41/1.80 , ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.41/1.80 'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ), Z, X ), ~(
% 1.41/1.80 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ) )
% 1.41/1.80 , ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.41/1.80 'c_HOL_Oabs__class_Oabs'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X )
% 1.41/1.80 , Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ) ) ],
% 1.41/1.80 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.41/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 1.41/1.80 ) ],
% 1.41/1.80 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.41/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.41/1.80 ) ],
% 1.41/1.80 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.41/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.41/1.80 ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.41/1.80 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 1.41/1.80 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 1.41/1.80 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.41/1.80 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.41/1.80 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 1.41/1.80 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_SEQ_OLIMSEQ'(
% 1.41/1.80 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Y, X,
% 1.41/1.80 'tc_fun'( X, X ), 'tc_nat' ), Z, 'tc_nat', X, X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ), ~( 'c_SEQ_OLIMSEQ'(
% 1.41/1.80 Y, T, X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.80 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.41/1.80 X ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ), 'c_HOL_Oone__class_Oone'( X
% 1.41/1.80 ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.41/1.80 'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ),
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ]
% 1.41/1.80 ,
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.41/1.80 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'(
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ),
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ), X ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( Y,
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Olattice'( X ) ), 'c_lessequals'( Y,
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ), X ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'(
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ), ~(
% 1.41/1.80 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'( Y,
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ), X ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'(
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ), ~(
% 1.41/1.80 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), 'c_lessequals'(
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ), ~(
% 1.41/1.80 'c_lessequals'( Z, T, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ],
% 1.41/1.80 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.41/1.80 U ), hAPP( W, V0 ) ), V1 ) ) ), =( V0, Y ), ~(
% 1.41/1.80 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, V4, V5, X, W, Z, T, V6, U
% 1.41/1.80 ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.41/1.80 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.41/1.80 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.41/1.80 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.41/1.80 Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.41/1.80 X ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.41/1.80 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.41/1.80 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.41/1.80 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.41/1.80 ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.41/1.80 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.41/1.80 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.41/1.80 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.41/1.80 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.41/1.80 , X ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.41/1.80 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.41/1.80 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.41/1.80 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ),
% 1.41/1.80 Z, X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.41/1.80 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.80 'c_Power_Opower__class_Opower'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.41/1.80 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T,
% 1.41/1.80 'tc_nat' ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.41/1.80 hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ), T ),
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.41/1.80 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ) ),
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__meet'( X ) ), =(
% 1.41/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ) ),
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__meet'( X ) ), =(
% 1.41/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ), T ),
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.41/1.80 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.41/1.80 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.41/1.80 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), ~( 'c_lessequals'( Y,
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.80 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.41/1.80 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), =( hAPP(
% 1.41/1.80 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.41/1.80 , Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Z ) ) ), =( Z,
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.80 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.41/1.80 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), T, X ),
% 1.41/1.80 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.41/1.80 ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), Z ), T, X ) ) ],
% 1.41/1.80 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.41/1.80 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), T, X ),
% 1.41/1.80 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.41/1.80 ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 1.41/1.80 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.41/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.41/1.80 'tc_nat' ) ) ), Y ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 1.41/1.80 ,
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.41/1.80 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), X ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~( 'c_lessequals'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z, X ) )
% 1.41/1.80 ],
% 1.41/1.80 [ =( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, X, Z ), T )
% 1.41/1.80 , U ) ), T ), hAPP( hAPP( X, T ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y
% 1.41/1.80 , X, Z ), T ), U ) ) ), ~( 'c_OrderedGroup_Omonoid__mult'( Y, X, Z ) ) ]
% 1.41/1.80 ,
% 1.41/1.80 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.41/1.80 , hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ) ), Z )
% 1.41/1.80 , hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc', X
% 1.41/1.80 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ),
% 1.41/1.80 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.41/1.80 [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OMin', 'tc_Int_Oint' ), ~(
% 1.41/1.80 'c_lessequals'( X, 'c_Int_OMin', 'tc_Int_Oint' ) ) ],
% 1.41/1.80 [ 'c_lessequals'( X, 'c_Int_OMin', 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.41/1.80 'c_Int_OBit0'( X ), 'c_Int_OMin', 'tc_Int_Oint' ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.41/1.80 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), U )
% 1.41/1.80 , X ), ~( 'c_HOL_Oord__class_Oless'( U, Z, X ) ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), U, X ) ), ~(
% 1.41/1.80 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.41/1.80 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.80 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.41/1.80 ) ), Z ) ) ],
% 1.41/1.80 [ =( hAPP( 'c_Suc', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.80 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ) ],
% 1.41/1.80 [ =( hAPP( 'c_Suc', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.80 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), Y ), hAPP(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), =( Z,
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.41/1.80 'class_Int_Onumber__ring'( X ) ), =( hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.41/1.80 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), hAPP(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.41/1.80 Y, X ) ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.80 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.80 ), X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.41/1.80 , 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.41/1.80 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.80 [ 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ), X,
% 1.41/1.80 'tc_nat' ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.41/1.80 'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y
% 1.41/1.80 ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Z ) ) ), hAPP(
% 1.41/1.80 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.41/1.80 X ), Y ), Z ) ), X ) ],
% 1.41/1.80 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.41/1.80 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), T ), ~(
% 1.41/1.80 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.41/1.80 , hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP(
% 1.41/1.80 'c_HOL_Oabs__class_Oabs'( X ), Z ) ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Z ), U, X
% 1.41/1.80 ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ),
% 1.41/1.80 Y ), T, X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.41/1.80 X ), Y ), Z ) ), Z ), Y ) ],
% 1.41/1.80 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_SEQ_OZseq'(
% 1.41/1.80 'c_COMBC'( 'c_COMBB'( 'c_HOL_Ominus__class_Ominus'( X ), Y, X, 'tc_fun'(
% 1.41/1.80 X, X ), 'tc_nat' ), Z, 'tc_nat', X, X ), X ), ~( 'c_SEQ_OLIMSEQ'( Y, Z, X
% 1.41/1.80 ) ) ],
% 1.41/1.80 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_SEQ_OLIMSEQ'( Y
% 1.41/1.80 , Z, X ), ~( 'c_SEQ_OZseq'( 'c_COMBC'( 'c_COMBB'(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( X ), Y, X, 'tc_fun'( X, X ), 'tc_nat' ), Z
% 1.41/1.80 , 'tc_nat', X, X ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ),
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Odistrib__lattice'( X ) ), =(
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ],
% 1.41/1.80 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 1.41/1.80 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( T,
% 1.41/1.80 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z,
% 1.41/1.80 'tc_fun'( T, 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.41/1.80 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.41/1.80 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( X, T, 'tc_fun'( Z,
% 1.41/1.80 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T,
% 1.41/1.80 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.41/1.80 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Lim_OLIM'(
% 1.41/1.80 'c_COMBC'( 'c_HOL_Oinverse__class_Odivide'( X ), Y, X, X, X ), Z, hAPP(
% 1.41/1.80 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ), X, X ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~(
% 1.41/1.80 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.41/1.80 =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.80 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.41/1.80 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.41/1.80 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.41/1.80 ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__join'( X ) ), =(
% 1.41/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ), T ),
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__join'( X ) ), =(
% 1.41/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ) ),
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.41/1.80 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ) ),
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.41/1.80 hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ), T ),
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Y, X ), Y ) ],
% 1.41/1.80 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, X, 'tc_fun'( Y,
% 1.41/1.80 'tc_bool' ) ), X ) ],
% 1.41/1.80 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.41/1.80 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.41/1.80 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.41/1.80 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~(
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.80 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.41/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.80 X ), Y ), Z ) ), T ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.80 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.41/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.80 X ), Y ), Z ) ), T ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.80 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.41/1.80 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.80 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.41/1.80 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.41/1.80 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.41/1.80 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.80 'tc_nat' ), Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.41/1.80 'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y )
% 1.41/1.80 ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Z ) ), X ) ],
% 1.41/1.80 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.41/1.80 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.41/1.80 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.41/1.80 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.41/1.80 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ],
% 1.41/1.80 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ), Y, 'tc_nat' ) ) ],
% 1.41/1.80 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.41/1.80 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.41/1.80 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.41/1.80 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.41/1.80 [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), Y ) ) ]
% 1.41/1.80 ,
% 1.41/1.80 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.41/1.80 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.41/1.80 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.41/1.80 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.41/1.80 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Y, X ) )
% 1.41/1.80 , ~( 'c_HOL_Oord__class_Oless'( Y, Y, X ) ) ],
% 1.41/1.80 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Y
% 1.41/1.80 , X ), 'c_lessequals'( Y, Y, X ) ],
% 1.41/1.80 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.41/1.80 , Z, X ) ), ~( 'c_lessequals'( Z, Y, X ) ) ],
% 1.41/1.80 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Z, Y, X ) ],
% 1.41/1.80 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.41/1.80 , X ), 'c_lessequals'( Z, Y, X ) ],
% 1.41/1.80 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_lessequals'( Y, Z, X ) )
% 1.41/1.80 , ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ) ), =( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.41/1.80 X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.41/1.80 X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.41/1.80 X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.80 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.41/1.80 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.41/1.80 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T
% 1.41/1.80 , X ) ), T, X ) ) ],
% 1.41/1.80 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.41/1.80 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.41/1.80 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.41/1.80 ), Z ), T, X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ) ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.41/1.80 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.41/1.80 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.41/1.80 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~(
% 1.41/1.80 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.41/1.80 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ), 'tc_nat' ) ), ~(
% 1.41/1.80 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_lessequals'( Z, X, 'tc_nat' ) )
% 1.41/1.80 ],
% 1.41/1.80 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.41/1.80 X ), Y ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y )
% 1.41/1.80 , 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y
% 1.41/1.80 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.41/1.80 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.41/1.80 X ), Y ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y )
% 1.41/1.80 , 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.41/1.80 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.41/1.80 X ), Y ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z )
% 1.41/1.80 , 'tc_nat' ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP(
% 1.41/1.80 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ),
% 1.41/1.80 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.41/1.80 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.41/1.80 [ ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ),
% 1.41/1.80 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ), ~(
% 1.41/1.80 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) )
% 1.41/1.80 , =( X, Z ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ) ), =( Z, T ) ],
% 1.41/1.80 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( X ), T ), T ) ) ), =( Y, Z ) ],
% 1.41/1.80 [ =( 'c_Set_Oimage'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.41/1.80 'tc_bool' ) ), Y, Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.41/1.80 'tc_bool' ) ) ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ),
% 1.41/1.80 'c_Lattices_Olower__semilattice__class_Oinf'( Y, hAPP(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ],
% 1.41/1.80 [ 'c_Fun_Oinj__on'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.41/1.80 'tc_bool' ) ), Y, Z ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Z,
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ],
% 1.41/1.80 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.41/1.80 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, 'tc_fun'( Z,
% 1.41/1.80 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.41/1.80 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, 'tc_fun'( T,
% 1.41/1.80 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( X, Z, 'tc_fun'( T,
% 1.41/1.80 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ),
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Z,
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T, X ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), T, X ),
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.41/1.80 'c_Lattices_Oupper__semilattice__class_Osup'( Z, T, X ), X ) ) ],
% 1.41/1.80 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.80 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), hAPP(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), hAPP(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ],
% 1.41/1.80 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), hAPP(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), Z ), hAPP(
% 1.41/1.80 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ) ],
% 1.41/1.80 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.80 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ) ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), U ) ) ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.41/1.80 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ) ) ) ],
% 1.41/1.81 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ),
% 1.41/1.81 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.41/1.81 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.41/1.81 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.41/1.81 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.41/1.81 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.41/1.81 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.41/1.81 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Z ), ~(
% 1.41/1.81 'c_lessequals'( Z, Y, X ) ) ],
% 1.41/1.81 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), ~( =(
% 1.41/1.81 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y ) ),
% 1.41/1.81 'c_lessequals'( Y, Z, X ) ],
% 1.41/1.81 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.41/1.81 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), Y ), ~(
% 1.41/1.81 'c_lessequals'( Y, Z, X ) ) ],
% 1.41/1.81 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.41/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.81 [ =( 'c_Set_Oimage'( 'c_COMBC'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.41/1.81 X, 'tc_nat', 'tc_nat', 'tc_nat' ),
% 1.41/1.81 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, 'tc_nat' ), 'tc_nat'
% 1.41/1.81 , 'tc_nat' ), 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ), 'tc_nat' ) ) ],
% 1.41/1.81 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.41/1.81 'tc_nat' ), X ), Y ), hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.41/1.81 ), Z ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.41/1.81 ), T ) ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.41/1.81 ), T ) ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Z
% 1.41/1.81 ), T ) ) ) ],
% 1.41/1.81 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ), ~(
% 1.41/1.81 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.41/1.81 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.41/1.81 hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.41/1.81 [ ~( 'c_lessequals'( X, X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X,
% 1.41/1.81 hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.41/1.81 [ ~( 'class_RealVector_Ometric__space'( X ) ), 'c_SEQ_OLIMSEQ'( Y, Z, X
% 1.41/1.81 ), ~( 'c_SEQ_OLIMSEQ'( 'c_COMBB'( Y, 'c_COMBC'(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T, 'tc_nat', 'tc_nat', 'tc_nat' )
% 1.41/1.81 , 'tc_nat', X, 'tc_nat' ), Z, X ) ) ],
% 1.41/1.81 [ ~( 'class_RealVector_Ometric__space'( X ) ), 'c_SEQ_OLIMSEQ'(
% 1.41/1.81 'c_COMBB'( Y, 'c_COMBC'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z,
% 1.41/1.81 'tc_nat', 'tc_nat', 'tc_nat' ), 'tc_nat', X, 'tc_nat' ), T, X ), ~(
% 1.41/1.81 'c_SEQ_OLIMSEQ'( Y, T, X ) ) ],
% 1.41/1.81 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.41/1.81 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ),
% 1.41/1.81 'tc_nat' ), ~( 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 1.41/1.81 Z, 'tc_nat' ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ),
% 1.41/1.81 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.41/1.81 'c_lessequals'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.41/1.81 [ ~( hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.41/1.81 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), Y ) )
% 1.41/1.81 ) ), hBOOL( hAPP( X, Z ) ) ],
% 1.41/1.81 [ ~( hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.41/1.81 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), Y ) )
% 1.41/1.81 ) ), hBOOL( hAPP( X, Z ) ) ],
% 1.41/1.81 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), T ) ), Y ) ), Z ) ), U ) )
% 1.41/1.81 , ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.41/1.81 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), X ) ), Y ) ), U ) ) ), ~(
% 1.41/1.81 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.41/1.81 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.41/1.81 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 1.41/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( Y, hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.81 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 1.41/1.81 Y, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc',
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ) ),
% 1.41/1.81 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.81 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ),
% 1.41/1.81 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.81 'tc_nat' ) ), Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =(
% 1.41/1.81 'c_Lattices_Olower__semilattice__class_Oinf'( Y, hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.81 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.81 [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.41/1.81 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.41/1.81 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ),
% 1.41/1.81 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, X ), 'tc_fun'( X,
% 1.41/1.81 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 1.41/1.81 ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.41/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.41/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.41/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ), ~( 'c_lessequals'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.41/1.81 ), 'c_HOL_Oone__class_Oone'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.41/1.81 , X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.41/1.81 ), 'c_HOL_Oone__class_Oone'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.41/1.81 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.81 X ) ) ],
% 1.41/1.81 [ ~( 'class_RealVector_Oreal__field'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), W ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.81 X ), Y ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ), W ) ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), W ) ), U ) ) ) ],
% 1.41/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.41/1.81 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.41/1.81 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.41/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.41/1.81 'c_Divides_Odiv__class_Odiv'( Y, Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.41/1.81 , =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.81 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OPls', 'tc_Int_Oint' )
% 1.41/1.81 ],
% 1.41/1.81 [ 'c_lessequals'( X, 'c_Int_OMin', 'tc_Int_Oint' ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OMin',
% 1.41/1.81 'tc_Int_Oint' ) ) ],
% 1.41/1.81 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OMin',
% 1.41/1.81 'tc_Int_Oint' ), ~( 'c_lessequals'( X, 'c_Int_OMin', 'tc_Int_Oint' ) ) ]
% 1.41/1.81 ,
% 1.41/1.81 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.41/1.81 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.41/1.81 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls',
% 1.41/1.81 'tc_Int_Oint' ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.41/1.81 'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.81 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.41/1.81 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.41/1.81 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.41/1.81 X ), Y ), T ) ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ) ), X ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.41/1.81 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.41/1.81 , Z ), T ), X ), ~( 'c_lessequals'( Y, T, X ) ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.41/1.81 ,
% 1.41/1.81 [ =( hAPP( X, Y ), hAPP( Z, T ) ), ~( hBOOL( hAPP( hAPP( U, Y ), W ) ) )
% 1.41/1.81 , ~( 'c_Ring__and__Field_Oordered__idom'( V0, Z, W, V1, V2, U, V3, T, V4
% 1.41/1.81 , X, V5 ) ) ],
% 1.41/1.81 [ =( hAPP( X, Y ), Z ), ~( hBOOL( hAPP( hAPP( T, U ), Y ) ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( W, V0, U, V1, V2, T, V3, Z, V4, X,
% 1.41/1.81 V5 ) ) ],
% 1.41/1.81 [ ~( =( hAPP( X, Y ), hAPP( Z, T ) ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( U, Z, W, V0, V1, V2, V3, T, V4, X,
% 1.41/1.81 V5 ) ), hBOOL( hAPP( hAPP( V2, Y ), W ) ) ],
% 1.41/1.81 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X, Y,
% 1.41/1.81 'tc_nat' ) ) ],
% 1.41/1.81 [ ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X, Y,
% 1.41/1.81 'tc_nat' ) ],
% 1.41/1.81 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 1.41/1.81 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ),
% 1.41/1.81 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.41/1.81 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 1.41/1.81 'c_Lattices_Olower__semilattice__class_Oinf'( Y, hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ),
% 1.41/1.81 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.41/1.81 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.41/1.81 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) )
% 1.41/1.81 ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.41/1.81 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ),
% 1.41/1.81 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.41/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.41/1.81 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ) )
% 1.41/1.81 ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.41/1.81 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ),
% 1.41/1.81 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.41/1.81 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.41/1.81 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) )
% 1.41/1.81 ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.41/1.81 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ),
% 1.41/1.81 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.41/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.41/1.81 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ) )
% 1.41/1.81 ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ),
% 1.41/1.81 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ),
% 1.41/1.81 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.81 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.41/1.81 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.81 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T
% 1.41/1.81 ) ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.41/1.81 X ), Y ) ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z
% 1.41/1.81 ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.41/1.81 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), ~(
% 1.41/1.81 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBC'(
% 1.41/1.81 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Z, X, 'tc_fun'( X, X ),
% 1.41/1.81 Y ), T, Y, X, X ), U, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), W
% 1.41/1.81 ), T ), Y, X ), ~( 'c_Lim_OLIM'( Z, U, W, Y, X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.41/1.81 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.41/1.81 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), Y,
% 1.41/1.81 X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.41/1.81 'c_HOL_Oabs__class_Oabs'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ) )
% 1.41/1.81 , hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.81 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.41/1.81 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( hAPP(
% 1.41/1.81 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T ), W ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.81 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.41/1.81 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( T, hAPP(
% 1.41/1.81 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W ) ) ],
% 1.41/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.81 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.41/1.81 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.41/1.81 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ), T ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ],
% 1.41/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.81 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.41/1.81 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ), 'c_Divides_Odiv__class_Omod'(
% 1.41/1.81 Z, Y, X ) ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.41/1.81 ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.41/1.81 'c_HOL_Oabs__class_Oabs'( X ), Y ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.81 X ) ) ],
% 1.41/1.81 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', X, 'tc_Int_Oint' ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OBit0'( X ),
% 1.41/1.81 'tc_Int_Oint' ) ) ],
% 1.41/1.81 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OBit0'( X ),
% 1.41/1.81 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', X,
% 1.41/1.81 'tc_Int_Oint' ) ) ],
% 1.41/1.81 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', X, 'tc_Int_Oint' ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OBit1'( X ),
% 1.41/1.81 'tc_Int_Oint' ) ) ],
% 1.41/1.81 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OBit1'( X ),
% 1.41/1.81 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', X,
% 1.41/1.81 'tc_Int_Oint' ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.41/1.81 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.41/1.81 X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X )
% 1.41/1.81 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.41/1.81 ), ~( 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ) ],
% 1.41/1.81 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ), hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ]
% 1.41/1.81 ,
% 1.41/1.81 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X
% 1.41/1.81 , Y, 'tc_nat' ) ), Y ) ) ) ],
% 1.41/1.81 [ 'c_Fun_Oinj__on'( 'c_COMBC'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X
% 1.41/1.81 , 'tc_nat', 'tc_nat', 'tc_nat' ), Y, 'tc_nat', 'tc_nat' ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.41/1.81 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.81 'c_Power_Opower__class_Opower'( X ), Y ), T ), X ), ~( 'c_lessequals'( Y
% 1.41/1.81 , 'c_HOL_Oone__class_Oone'( X ), X ) ), ~( 'c_lessequals'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( T, Z,
% 1.41/1.81 'tc_nat' ) ) ],
% 1.41/1.81 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), X, 'tc_nat' ),
% 1.41/1.81 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 'c_HOL_Oone__class_Oone'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.41/1.81 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 X, T, 'tc_nat' ) ],
% 1.41/1.81 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 1.41/1.81 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'( Z,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'( Y,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.81 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.41/1.81 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.41/1.81 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Z, X, 'tc_nat' )
% 1.41/1.81 ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ) ],
% 1.41/1.81 [ 'c_lessequals'( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.41/1.81 'c_Divides_Odiv__class_Odiv'( X, Z, 'tc_nat' ), 'tc_nat' ), ~(
% 1.41/1.81 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.41/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.41/1.81 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.41/1.81 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.81 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.41/1.81 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.41/1.81 , Z, X ) ) ), =( 'c_Divides_Odiv__class_Omod'( hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ),
% 1.41/1.81 'c_Divides_Odiv__class_Omod'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.41/1.81 T ), Z, X ) ) ],
% 1.41/1.81 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, Z ), U ) )
% 1.41/1.81 , hAPP( hAPP( Y, Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.41/1.81 , T ), U ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, Y, V0, V1, V2
% 1.41/1.81 ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.81 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.41/1.81 Y ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.41/1.81 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.41/1.81 'c_HOL_Oabs__class_Oabs'( X ), Y ), X ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.41/1.81 'c_lessequals'( Y, hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ), X ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ) ), U ), W, X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), U ), hAPP(
% 1.41/1.81 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), W ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP(
% 1.41/1.81 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T ), W, X ) ) ]
% 1.41/1.81 ,
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.41/1.81 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), U ) ), W ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), Y ), hAPP(
% 1.41/1.81 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ), W ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP(
% 1.41/1.81 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.41/1.81 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W ), X ) ) ],
% 1.41/1.81 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), Z ) ), T ) ), hAPP(
% 1.41/1.81 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), T ) ) ],
% 1.41/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.41/1.81 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.41/1.81 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.41/1.81 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.41/1.81 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.41/1.81 , U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), W ), T ), Z, X ) ) ],
% 1.41/1.81 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.41/1.81 X ), Y ), Z, 'tc_nat' ), ~( 'c_lessequals'( X, hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ) ],
% 1.41/1.81 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.41/1.81 , Y ), Z ), 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ]
% 1.41/1.81 ,
% 1.41/1.81 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), =( Y,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.41/1.81 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.81 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.41/1.81 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, T ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.81 ) ) ), =( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.81 ) ) ), =( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.41/1.81 'c_HOL_Oabs__class_Oabs'( X ), Y ), Z, X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.41/1.81 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastAtMost'( Z
% 1.41/1.81 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), U ), 'tc_nat'
% 1.41/1.81 ), 'tc_nat', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.41/1.81 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastAtMost'( Z
% 1.41/1.81 , T, 'tc_nat' ), 'tc_nat', X ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.41/1.81 'c_SetInterval_Oord__class_OatLeastAtMost'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), 'c_HOL_Oone__class_Oone'(
% 1.41/1.81 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), U
% 1.41/1.81 ), 'tc_nat' ), 'tc_nat', X ) ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), 'c_HOL_Oone__class_Oone'(
% 1.41/1.81 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.41/1.81 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ) ), T ), U,
% 1.41/1.81 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.81 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z
% 1.41/1.81 ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), U ), 'tc_nat' ) ),
% 1.41/1.81 ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.41/1.81 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.41/1.81 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.41/1.81 'c_Lattices_Olower__semilattice__class_Oinf'( Z, Y, X ) ) ],
% 1.41/1.81 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.41/1.81 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, X,
% 1.41/1.81 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.41/1.81 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.41/1.81 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.41/1.81 'c_Lattices_Olower__semilattice__class_Oinf'( Z, Y, X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.41/1.81 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.41/1.81 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.41/1.81 , Y, X ) ) ],
% 1.41/1.81 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.41/1.81 X ), Y ), X, 'tc_nat' ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.41/1.81 ), Y ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.41/1.81 ), Y ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.81 ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.41/1.81 ), Y ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.81 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.41/1.81 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.41/1.81 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.41/1.81 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T,
% 1.41/1.81 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.41/1.81 'c_Lattices_Olower__semilattice__class_Oinf'( T, X, 'tc_fun'( Z,
% 1.41/1.81 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.41/1.81 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.41/1.81 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.41/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.41/1.81 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y, T,
% 1.41/1.81 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.41/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( T, X, 'tc_fun'( Z,
% 1.41/1.81 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.41/1.81 ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.41/1.81 ,
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.41/1.81 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.81 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~( 'c_lessequals'( T,
% 1.41/1.81 Z, 'tc_nat' ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.81 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.41/1.81 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ) ) ],
% 1.41/1.81 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ), Y ) ) ],
% 1.41/1.81 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ), ~( 'c_lessequals'(
% 1.41/1.81 Y, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.41/1.81 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.41/1.81 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.41/1.81 ), Z ), Y ), 'tc_nat' ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.41/1.81 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.41/1.81 'tc_nat' ) ), 'tc_nat' ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( X,
% 1.41/1.81 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.81 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.41/1.81 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.41/1.81 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.41/1.81 'tc_nat' ) ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.41/1.81 , Y ) ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) )
% 1.41/1.81 , ~( 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.41/1.81 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.41/1.81 'tc_nat' ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.41/1.81 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_OrderedGroup_Omonoid__mult'( Z
% 1.41/1.81 , X, T ) ) ],
% 1.41/1.81 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_OrderedGroup_Omonoid__mult'( Y
% 1.41/1.81 , X, T ) ) ],
% 1.41/1.81 [ 'c_lessequals'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X,
% 1.41/1.81 'tc_nat' ) ],
% 1.41/1.81 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.41/1.81 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), Z ),
% 1.41/1.81 'tc_nat' ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X )
% 1.41/1.81 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.41/1.81 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.41/1.81 X ), T ), Y ) ), Z, X ) ) ],
% 1.41/1.81 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =(
% 1.41/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.41/1.81 'c_Orderings_Obot__class_Obot'( X ) ) ), =( Z,
% 1.41/1.81 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.41/1.81 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =(
% 1.41/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.41/1.81 'c_Orderings_Obot__class_Obot'( X ) ) ), =( Y,
% 1.41/1.81 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.41/1.81 [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z
% 1.41/1.81 , 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' )
% 1.41/1.81 ) ) ), =( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.41/1.81 ) ],
% 1.41/1.81 [ ~( =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z
% 1.41/1.81 , 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' )
% 1.41/1.81 ) ) ), =( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.41/1.81 ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP(
% 1.41/1.81 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.41/1.81 , Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Z ) ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.41/1.81 'c_HOL_Oabs__class_Oabs'( X ), Y ), Y ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.81 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OMin',
% 1.41/1.81 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OMin',
% 1.41/1.81 'tc_Int_Oint' ) ) ],
% 1.41/1.81 [ 'c_HOL_Oord__class_Oless'( X, 'c_Int_OMin', 'tc_Int_Oint' ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OMin',
% 1.41/1.81 'tc_Int_Oint' ) ) ],
% 1.41/1.81 [ 'c_lessequals'( 'c_Int_OMin', 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.41/1.81 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.41/1.81 , Y, 'tc_nat' ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), hBOOL( hAPP(
% 1.41/1.81 hAPP( U, T ), W ) ), ~( hBOOL( hAPP( hAPP( X, Z ), V0 ) ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, U, X, V4, V0, Y, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), ~( hBOOL( hAPP(
% 1.41/1.81 hAPP( X, U ), Z ) ) ), hBOOL( hAPP( hAPP( W, V0 ), T ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, W, X, V4, U, Y, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), hBOOL( hAPP(
% 1.41/1.81 hAPP( U, Y ), W ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), T ) ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, U, X, V4, V0, Z, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), ~( hBOOL( hAPP(
% 1.41/1.81 hAPP( X, T ), U ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Y ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, W, X, V4, U, Z, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), hBOOL( hAPP(
% 1.41/1.81 hAPP( U, Z ), W ) ), ~( hBOOL( hAPP( hAPP( X, T ), V0 ) ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, U, X, V4, V0, Y, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), ~( hBOOL( hAPP(
% 1.41/1.81 hAPP( X, U ), T ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Z ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, W, X, V4, U, Y, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), hBOOL( hAPP(
% 1.41/1.81 hAPP( U, Y ), W ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), T ) ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, U, X, V4, V0, Z, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.41/1.81 hAPP( X, T ), U ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Y ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, W, X, V4, U, Z, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), hBOOL( hAPP(
% 1.41/1.81 hAPP( U, T ), W ) ), ~( hBOOL( hAPP( hAPP( X, Z ), V0 ) ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, U, V4, V0, Y, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), ~( hBOOL( hAPP(
% 1.41/1.81 hAPP( X, U ), Z ) ) ), hBOOL( hAPP( hAPP( W, V0 ), T ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, X, W, V4, U, Y, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), hBOOL( hAPP(
% 1.41/1.81 hAPP( U, Y ), W ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), T ) ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, U, V4, V0, Z, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), ~( hBOOL( hAPP(
% 1.41/1.81 hAPP( X, T ), U ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Y ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, X, W, V4, U, Z, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), hBOOL( hAPP(
% 1.41/1.81 hAPP( U, Z ), W ) ), ~( hBOOL( hAPP( hAPP( X, T ), V0 ) ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, U, V4, V0, Y, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), ~( hBOOL( hAPP(
% 1.41/1.81 hAPP( X, U ), T ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Z ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, X, W, V4, U, Y, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), hBOOL( hAPP(
% 1.41/1.81 hAPP( U, Y ), W ) ), ~( hBOOL( hAPP( hAPP( X, V0 ), T ) ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, U, V4, V0, Z, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.41/1.81 hAPP( X, T ), U ) ) ), hBOOL( hAPP( hAPP( W, V0 ), Y ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3, X, W, V4, U, Z, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( Z, T ) ) ), ~( hBOOL( hAPP( hAPP( X,
% 1.41/1.81 Y ), T ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, Y, V0, V1, X
% 1.41/1.81 , V2, V3, V4, Z, V5 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, Y ), hAPP(
% 1.41/1.81 T, Z ) ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, Y, V0, V1, X
% 1.41/1.81 , V2, V3, V4, T, V5 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, hAPP( Y, Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( X,
% 1.41/1.81 Z ), T ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, T, V0, V1, X
% 1.41/1.81 , V2, V3, V4, Y, V5 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, hAPP( T, Y
% 1.41/1.81 ) ), Z ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( U, W, Z, V0, V1, X
% 1.41/1.81 , V2, V3, V4, T, V5 ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 1.41/1.81 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.41/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ) ],
% 1.41/1.81 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.41/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.41/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ) ) ],
% 1.41/1.81 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.41/1.81 'tc_bool' ) ), 'c_Lattices_Oupper__semilattice__class_Osup'( Y, X,
% 1.41/1.81 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.41/1.81 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.41/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ),
% 1.41/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( Z, Y, X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.41/1.81 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ),
% 1.41/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =( hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.41/1.81 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ),
% 1.41/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.41/1.81 ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.41/1.81 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.41/1.81 ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.41/1.81 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Orderings_Oorder'( X ) ), =( 'c_Orderings_Obot__class_Obot'(
% 1.41/1.81 'tc_fun'( X, 'tc_bool' ) ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.41/1.81 Y, Z, X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X ) ],
% 1.41/1.81 [ ~( 'class_Orderings_Oorder'( X ) ), ~( =(
% 1.41/1.81 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.41/1.81 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ) ) ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), Z ) ), =( Y, hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), T ) ) ],
% 1.41/1.81 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.41/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.41/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ),
% 1.41/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ) ],
% 1.41/1.81 [ =( 'c_Lattices_Oupper__semilattice__class_Osup'( X,
% 1.41/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.41/1.81 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.41/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( X, Y, 'tc_fun'( Z,
% 1.41/1.81 'tc_bool' ) ) ) ],
% 1.41/1.81 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.41/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.41/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), X ),
% 1.41/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ) ) ],
% 1.41/1.81 [ =( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.41/1.81 'c_Set_Oimage'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool'
% 1.41/1.81 ) ), Z, X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber__ring'( X ) ), =( hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.41/1.81 , hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ), Y ) ),
% 1.41/1.81 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.41/1.81 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.41/1.81 'c_HOL_Oabs__class_Oabs'( X ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.41/1.81 X ), Y ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.41/1.81 ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.41/1.81 U ), hAPP( W, V0 ) ), V1 ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'(
% 1.41/1.81 V2, V3, Y, V4, X, V5, W, Z, T, V6, U ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), Y ), hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ],
% 1.41/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.41/1.81 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.41/1.81 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.41/1.81 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.41/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.41/1.81 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.41/1.81 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.41/1.81 , 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 1.41/1.81 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), Y, 'tc_nat' )
% 1.41/1.81 , 'c_Divides_Odiv__class_Omod'( Z, Y, 'tc_nat' ) ) ],
% 1.41/1.81 [ 'c_Fun_Oinj__on'( X, Y, Z, T ), ~( 'c_Fun_Oinj__on'( X,
% 1.41/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( Y, U, 'tc_fun'( Z,
% 1.41/1.81 'tc_bool' ) ), Z, T ) ) ],
% 1.41/1.81 [ 'c_Fun_Oinj__on'( X, Y, Z, T ), ~( 'c_Fun_Oinj__on'( X,
% 1.41/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( U, Y, 'tc_fun'( Z,
% 1.41/1.81 'tc_bool' ) ), Z, T ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.41/1.81 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.41/1.81 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.41/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'( Z,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), Y, X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.41/1.81 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastAtMost'( Z
% 1.41/1.81 , T, 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.41/1.81 ), hAPP( Y, Z ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.41/1.81 'c_SetInterval_Oord__class_OatLeastAtMost'( hAPP( 'c_Suc', Z ), T,
% 1.41/1.81 'tc_nat' ), 'tc_nat', X ) ) ), ~( 'c_lessequals'( Z, T, 'tc_nat' ) ) ]
% 1.41/1.81 ,
% 1.41/1.81 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.81 X ), Y ), Z ) ), Z ), Y ) ],
% 1.41/1.81 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), X ), Y ) ],
% 1.41/1.81 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Y ), X ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ) ],
% 1.41/1.81 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP(
% 1.41/1.81 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T, X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.41/1.81 , Z ), T ), X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ), Y, X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Z, X ) ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.41/1.81 X ), Y ) ), Y ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y, hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.41/1.81 X ), Y ) ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y, hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.41/1.81 X ), Y ) ) ) ],
% 1.41/1.81 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =( hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.41/1.81 X ), Y ) ), Y ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.41/1.81 X ), Y ) ), Y ) ],
% 1.41/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.41/1.81 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.41/1.81 ],
% 1.41/1.81 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ),
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.41/1.81 ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), T ) ), Y ) ), Z ), U,
% 1.41/1.81 'tc_nat' ) ), ~( 'c_lessequals'( T, X, 'tc_nat' ) ) ],
% 1.41/1.81 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.41/1.81 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), T ) ), U ),
% 1.41/1.81 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.81 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T
% 1.41/1.81 ) ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ), U ), 'tc_nat' ) ),
% 1.41/1.81 ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.41/1.81 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ),
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ), 'tc_nat' ),
% 1.41/1.81 ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.41/1.81 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), X ) ), Y ) ), U ),
% 1.41/1.81 'tc_nat' ) ), ~( 'c_lessequals'( X, T, 'tc_nat' ) ) ],
% 1.41/1.81 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), ~(
% 1.41/1.81 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBC'(
% 1.41/1.81 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Z, X, 'tc_fun'( X, X ),
% 1.41/1.81 Y ), T, Y, X, X ), U, 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.41/1.81 'c_Lim_OLIM'( Z, U, 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.41/1.81 ,
% 1.41/1.81 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.81 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ) ), Y ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ),
% 1.41/1.81 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ) ],
% 1.41/1.81 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.41/1.81 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ),
% 1.41/1.81 'c_Divides_Odiv__class_Omod'( Y, X, 'tc_nat' ) ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP(
% 1.41/1.81 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.41/1.81 X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), Z ) ), hAPP(
% 1.41/1.81 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.41/1.81 X ), Y ), Z ) ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.81 X ), Y ), Z ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.41/1.81 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.41/1.81 ) ), Z ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.81 X ), Z ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 1.41/1.81 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP(
% 1.41/1.81 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), ~(
% 1.41/1.81 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.41/1.81 Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.81 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 1.41/1.81 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.41/1.81 'tc_nat' ) ) ), Y ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 1.41/1.81 ,
% 1.41/1.81 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.41/1.81 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z,
% 1.41/1.81 'tc_nat' ) ) ],
% 1.41/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.41/1.81 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.81 [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.41/1.81 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.41/1.81 'c_SetInterval_Oord__class_OatLeastLessThan'( Y, Z, X ),
% 1.41/1.81 'c_SetInterval_Oord__class_OatLeastAtMost'( Z, T, X ), 'tc_fun'( X,
% 1.41/1.81 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 1.41/1.81 ) ],
% 1.41/1.81 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Y
% 1.41/1.81 , X ) ) ],
% 1.41/1.81 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.41/1.81 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ) ) ],
% 1.41/1.81 [ ~( 'c_HOL_Oord__class_Oless'( X, X, 'tc_Int_Oint' ) ) ],
% 1.41/1.81 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.41/1.81 , Y, X ) ) ],
% 1.41/1.81 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.41/1.81 , Y, X ) ) ],
% 1.41/1.81 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.41/1.81 , X ), 'c_lessequals'( Z, Y, X ), ~( 'c_lessequals'( Y, Z, X ) ) ],
% 1.41/1.81 [ ~( 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 1.41/1.81 ), Y ), X ), 'tc_nat' ) ), =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.41/1.81 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X )
% 1.41/1.81 ), X ), Y ) ],
% 1.41/1.81 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.41/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( Y,
% 1.41/1.81 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ), Y ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.41/1.81 ,
% 1.41/1.81 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.41/1.81 , X ), Y ), 'tc_nat' ) ],
% 1.41/1.81 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.41/1.81 , X ), Y ), 'tc_nat' ) ],
% 1.41/1.81 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.41/1.81 , Y ), X ), 'tc_nat' ) ],
% 1.41/1.81 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.41/1.81 , X ), Y ), 'tc_nat' ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~(
% 1.41/1.81 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.81 X ), X ) ) ],
% 1.41/1.81 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), Y ),
% 1.41/1.81 ~( 'c_Groebner__Basis_Ogb__semiring'( Z, T, X, U, W, V0 ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ), hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ],
% 1.41/1.81 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), ~(
% 1.41/1.81 'class_Power_Opower'( X ) ), ~( 'class_RealVector_Ometric__space'( Y ) )
% 1.41/1.81 , 'c_Lim_OLIM'( 'c_COMBC'( 'c_COMBB'( 'c_Power_Opower__class_Opower'( X )
% 1.41/1.81 , Z, X, 'tc_fun'( 'tc_nat', X ), Y ), T, Y, 'tc_nat', X ), U, hAPP( hAPP(
% 1.41/1.81 'c_Power_Opower__class_Opower'( X ), W ), T ), Y, X ), ~( 'c_Lim_OLIM'( Z
% 1.41/1.81 , U, W, Y, X ) ) ],
% 1.41/1.81 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.41/1.81 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.41/1.81 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.41/1.81 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.41/1.81 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.41/1.81 ), U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), W ), T ), Z, X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.41/1.81 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y, Z, X ) ) ]
% 1.41/1.81 ,
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.41/1.81 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.81 X ), X ) ) ],
% 1.41/1.81 [ =( X, hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.41/1.81 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.41/1.81 'tc_nat' ) ) ],
% 1.41/1.81 [ =( hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' )
% 1.41/1.81 , X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.41/1.81 'tc_nat' ) ) ],
% 1.41/1.81 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.81 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.41/1.81 , Z ), T ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, T, 'tc_nat' ) )
% 1.41/1.81 , ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.41/1.81 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.41/1.81 T, X ) ) ],
% 1.41/1.81 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.41/1.81 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.41/1.81 'tc_nat' ) ) ],
% 1.41/1.81 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.41/1.81 , Y, 'tc_Int_Oint' ) ) ],
% 1.41/1.81 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.41/1.81 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y,
% 1.41/1.81 'tc_nat' ) ) ],
% 1.41/1.81 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.41/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Z ), ~(
% 1.41/1.81 'c_lessequals'( Y, Z, X ) ) ],
% 1.41/1.81 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), ~( =(
% 1.41/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Z ) ),
% 1.41/1.81 'c_lessequals'( Y, Z, X ) ],
% 1.41/1.81 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.41/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), Y ), ~(
% 1.41/1.81 'c_lessequals'( Z, Y, X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.41/1.81 ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ), Z ) ]
% 1.41/1.81 ,
% 1.41/1.81 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.41/1.81 ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), Z ) ]
% 1.41/1.81 ,
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ), ~( 'c_lessequals'( Z
% 1.41/1.81 , 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), 'c_lessequals'(
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ), X ), ~( 'c_lessequals'( U
% 1.41/1.81 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.41/1.81 , U, X ) ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X )
% 1.41/1.81 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.41/1.81 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.81 'c_HOL_Oone__class_Oone'( X ), X ) ],
% 1.41/1.81 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Y ), X ), ~(
% 1.41/1.81 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.41/1.81 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), Y ), ~(
% 1.41/1.81 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.41/1.81 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), =( Y, hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), X ) ) ],
% 1.41/1.81 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =( Y,
% 1.41/1.81 'c_Series_Osuminf'( Z, X ) ), ~( 'c_Series_Osums'( Z, Y, X ) ) ],
% 1.41/1.81 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), =(
% 1.41/1.81 'c_Series_Osuminf'( Y, X ), Z ), ~( 'c_Series_Osums'( Y, Z, X ) ) ],
% 1.41/1.81 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), ~(
% 1.41/1.81 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.41/1.81 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ) ), ~(
% 1.41/1.81 'c_lessequals'( Z, Y, 'tc_nat' ) ) ],
% 1.41/1.81 [ 'c_HOL_Oord__class_Oless'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.41/1.81 'tc_nat' ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), Y,
% 1.41/1.81 'tc_nat' ) ) ],
% 1.41/1.81 [ ~( 'class_Orderings_Oorder'( X ) ), ~( =(
% 1.41/1.81 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.41/1.81 'c_SetInterval_Oord__class_OatLeastAtMost'( Y, Z, X ) ) ), ~(
% 1.41/1.81 'c_lessequals'( Y, Z, X ) ) ],
% 1.41/1.81 [ ~( 'class_Orderings_Oorder'( X ) ), =( 'c_Orderings_Obot__class_Obot'(
% 1.41/1.81 'tc_fun'( X, 'tc_bool' ) ), 'c_SetInterval_Oord__class_OatLeastAtMost'( Y
% 1.41/1.81 , Z, X ) ), 'c_lessequals'( Y, Z, X ) ],
% 1.41/1.81 [ ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OMin',
% 1.41/1.81 'tc_Int_Oint' ) ) ],
% 1.41/1.81 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.41/1.81 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), U ) ) ) ), =(
% 1.41/1.81 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.41/1.81 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.41/1.81 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.81 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ), =( Z
% 1.41/1.81 , T ) ],
% 1.41/1.81 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.41/1.81 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.41/1.81 , 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'(
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Int_Onumber'( X ) ),
% 1.41/1.81 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.41/1.81 'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y )
% 1.41/1.81 ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Z ) ), X ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.41/1.81 X ), Y ) ), Z ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.41/1.81 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ),
% 1.41/1.81 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.41/1.81 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_Series_Osums'(
% 1.41/1.81 'c_COMBB'( 'c_HOL_Ouminus__class_Ouminus'( X ), Y, X, X, 'tc_nat' ), hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ), ~( 'c_Series_Osums'( Y, Z
% 1.41/1.81 , X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.41/1.81 X ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ), hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.41/1.81 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ],
% 1.41/1.81 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_SEQ_OLIMSEQ'( Y
% 1.41/1.81 , Z, X ), ~( 'c_SEQ_OLIMSEQ'( 'c_COMBB'( 'c_HOL_Ouminus__class_Ouminus'(
% 1.41/1.81 X ), Y, X, X, 'tc_nat' ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z )
% 1.41/1.81 , X ) ) ],
% 1.41/1.81 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_SEQ_OLIMSEQ'(
% 1.41/1.81 'c_COMBB'( 'c_HOL_Ouminus__class_Ouminus'( X ), Y, X, X, 'tc_nat' ), hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ), ~( 'c_SEQ_OLIMSEQ'( Y, Z,
% 1.41/1.81 X ) ) ],
% 1.41/1.81 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.41/1.81 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.41/1.81 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 1.41/1.81 ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~( 'c_lessequals'( Y, X,
% 1.41/1.81 'tc_nat' ) ) ],
% 1.41/1.81 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.41/1.81 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.41/1.81 ), Y ), Z ), 'tc_nat' ) ), ~( 'c_lessequals'( Z, Y, 'tc_nat' ) ), ~(
% 1.41/1.81 'c_lessequals'( Z, X, 'tc_nat' ) ) ],
% 1.41/1.81 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.41/1.81 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.41/1.81 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ),
% 1.41/1.81 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ],
% 1.41/1.81 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.41/1.81 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.41/1.81 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.41/1.81 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.41/1.81 'tc_bool' ) ) ) ],
% 1.41/1.81 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.41/1.81 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.41/1.81 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ),
% 1.41/1.81 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ],
% 1.41/1.81 [ ~( =( 'c_Complex_Oii', 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.81 'tc_Complex_Ocomplex' ) ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.41/1.81 ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.41/1.81 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.41/1.81 , X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.41/1.81 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.41/1.81 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ),
% 1.41/1.81 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.41/1.81 'class_OrderedGroup_Olordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.41/1.81 'c_HOL_Oabs__class_Oabs'( X ), Y ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oabs__if'( X ) ), =( hAPP(
% 1.41/1.81 'c_HOL_Oabs__class_Oabs'( X ), Y ), Y ), 'c_HOL_Oord__class_Oless'( Y,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.41/1.81 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.41/1.81 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.41/1.81 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X )
% 1.41/1.81 ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), hAPP( hAPP(
% 1.41/1.81 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ) ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), T, X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.41/1.81 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ),
% 1.41/1.81 X ), ~( 'c_HOL_Oord__class_Oless'( Z, T, 'tc_nat' ) ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 'c_lessequals'(
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.81 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.41/1.81 , X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.41/1.81 ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.81 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.41/1.81 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.41/1.81 ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ) ) ],
% 1.41/1.81 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.81 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ) ],
% 1.41/1.81 [ ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.81 'tc_nat' ), X ), Y ), X, 'tc_nat' ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.41/1.81 X ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), Z ), Y ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.41/1.81 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.41/1.81 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.41/1.81 ,
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.41/1.81 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.41/1.81 ,
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.41/1.81 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), Y, X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.41/1.81 , Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), Y, X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.41/1.81 Z ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.41/1.81 Z ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.41/1.81 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ),
% 1.41/1.81 ~( 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), Y, X )
% 1.41/1.81 ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.41/1.81 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ),
% 1.41/1.81 ~( 'c_lessequals'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), Y, X )
% 1.41/1.81 ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.41/1.81 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ),
% 1.41/1.81 ~( 'c_lessequals'( Z, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X )
% 1.41/1.81 ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.41/1.81 'c_lessequals'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ),
% 1.41/1.81 ~( 'c_lessequals'( Z, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X )
% 1.41/1.81 ) ],
% 1.41/1.81 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.41/1.81 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.41/1.81 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.41/1.81 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.41/1.81 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.81 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.41/1.81 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.41/1.81 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ),
% 1.41/1.81 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ),
% 1.41/1.81 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Odiv'( hAPP(
% 1.41/1.81 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ),
% 1.41/1.81 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.81 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.41/1.81 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), Y, X, 'tc_fun'( X, X ), 'tc_nat' ),
% 1.41/1.81 'c_COMBB'( Y, 'c_COMBC'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.41/1.81 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat', 'tc_nat', 'tc_nat' ),
% 1.41/1.81 'tc_nat', X, 'tc_nat' ), 'tc_nat', X, X ),
% 1.41/1.81 'c_SetInterval_Oord__class_OatLeastAtMost'( Z, T, 'tc_nat' ), 'tc_nat', X
% 1.41/1.81 ), 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Z, T, 'tc_nat' ) ]
% 1.41/1.81 ,
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.81 ) ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~( =(
% 1.41/1.81 hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.41/1.81 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), =( hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.41/1.81 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.41/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.41/1.81 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.41/1.81 ) ],
% 1.41/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.41/1.81 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.41/1.81 ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.41/1.81 ,
% 1.41/1.81 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y ) ), =( Y,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.41/1.81 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.41/1.81 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.41/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.41/1.81 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.41/1.81 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.41/1.81 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.81 ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.81 X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.81 X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.41/1.81 , Y ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.81 X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.41/1.81 X ) ), =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.41/1.81 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 1.41/1.81 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.41/1.81 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.41/1.81 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.41/1.81 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.41/1.81 ,
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.41/1.81 'c_HOL_Oabs__class_Oabs'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.41/1.81 ), Y ) ) ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.81 X ) ) ), =( Y, Z ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.81 X ) ) ), =( Y, Z ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.41/1.81 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.41/1.81 Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.81 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.81 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.81 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.41/1.81 Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.41/1.81 Y ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.41/1.81 Y ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.41/1.81 Y ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.41/1.81 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.41/1.81 Y ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.41/1.81 Y ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.41/1.81 Y ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.41/1.81 Y ) ],
% 1.41/1.81 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.41/1.81 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBB'( Z,
% 1.41/1.81 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), X, Y, X ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), hAPP( Z, T ), X, Y ), ~( 'c_Lim_OLIM'( Z
% 1.41/1.81 , T, hAPP( Z, T ), X, Y ) ) ],
% 1.41/1.81 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.41/1.81 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( Z, T, hAPP( Z, T
% 1.41/1.81 ), X, Y ), ~( 'c_Lim_OLIM'( 'c_COMBB'( Z, hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), T ), X, Y, X ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), hAPP( Z, T ), X, Y ) ) ],
% 1.41/1.81 [ ~( 'class_RealVector_Ometric__space'( X ) ), ~(
% 1.41/1.81 'class_RealVector_Oreal__normed__vector'( Y ) ), 'c_Lim_OLIM'( 'c_COMBB'(
% 1.41/1.81 Z, hAPP( 'c_HOL_Oplus__class_Oplus'( Y ), T ), Y, X, Y ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( Y ), U, Y, X ), ~( 'c_Lim_OLIM'( Z, T, U, Y,
% 1.41/1.81 X ) ) ],
% 1.41/1.81 [ ~( 'class_RealVector_Ometric__space'( X ) ), ~(
% 1.41/1.81 'class_RealVector_Oreal__normed__vector'( Y ) ), 'c_Lim_OLIM'( Z, T, U, Y
% 1.41/1.81 , X ), ~( 'c_Lim_OLIM'( 'c_COMBB'( Z, hAPP( 'c_HOL_Oplus__class_Oplus'( Y
% 1.41/1.81 ), T ), Y, X, Y ), 'c_HOL_Ozero__class_Ozero'( Y ), U, Y, X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.41/1.81 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.41/1.81 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.41/1.81 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.41/1.81 'c_lessequals'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ]
% 1.41/1.81 ,
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.41/1.81 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.41/1.81 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ]
% 1.41/1.81 ,
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.41/1.81 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T )
% 1.41/1.81 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.41/1.81 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T )
% 1.41/1.81 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y
% 1.41/1.81 ) ), Z ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( 'c_lessequals'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.81 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.41/1.81 ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ), =( U,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.41/1.81 ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.41/1.81 X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.41/1.81 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.41/1.81 X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.41/1.81 X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.41/1.81 ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z
% 1.41/1.81 , hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), X ) ) ]
% 1.41/1.81 ,
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.41/1.81 ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'( Z,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.41/1.81 ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.41/1.81 ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.41/1.81 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), Y, X ) ) ]
% 1.41/1.81 ,
% 1.41/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.41/1.81 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.41/1.81 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.41/1.81 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ),
% 1.41/1.81 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ) ), =( Z,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.41/1.81 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.41/1.81 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.41/1.81 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ),
% 1.41/1.81 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ) ), =( T,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Y, X ), ~(
% 1.41/1.81 'c_lessequals'( Z, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.41/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.41/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), Z, X ), ~(
% 1.41/1.81 'c_lessequals'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.41/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.41/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), T ) ), =( T,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), Z ) ), =( Z,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.41/1.81 X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.41/1.81 , Y ), T ), Z, X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.41/1.81 X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.41/1.81 , Y ), T ), Z, X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.41/1.81 ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.41/1.81 ), T ), Z ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.41/1.81 ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), Y, X ) ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.41/1.81 ), T ), Z ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ), =( U,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.41/1.81 ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.81 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.41/1.81 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), X
% 1.41/1.81 ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.41/1.81 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.41/1.81 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.41/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.41/1.81 T, X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.41/1.81 X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.41/1.81 ,
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.41/1.81 ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.41/1.81 ,
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.41/1.81 X ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), Z, X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.41/1.81 , Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ) ) ]
% 1.41/1.81 ,
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.41/1.81 ), Y ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.41/1.81 ), Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), Z, X ) ) ]
% 1.41/1.81 ,
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =( hAPP(
% 1.41/1.81 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.81 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.41/1.81 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.41/1.81 , Z ) ) ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.41/1.81 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =( hAPP(
% 1.41/1.81 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.81 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.41/1.81 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.41/1.81 , Z ) ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.41/1.81 ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =( hAPP(
% 1.41/1.81 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.81 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.41/1.81 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.41/1.81 , Z ) ) ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.41/1.81 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Opordered__ring__abs'( X ) ), =( hAPP(
% 1.41/1.81 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.81 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.41/1.81 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.41/1.81 , Z ) ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.41/1.81 ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.41/1.81 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.41/1.81 ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.81 X ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.41/1.81 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.41/1.81 ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP(
% 1.41/1.81 'c_HOL_Oabs__class_Oabs'( X ), Z ) ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y )
% 1.41/1.81 ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Z ) ) ) ],
% 1.41/1.81 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.41/1.81 'tc_nat' ), Y ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.41/1.81 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ), Y, 'tc_nat' ) ) ]
% 1.41/1.81 ,
% 1.41/1.81 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.81 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X,
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ), 'tc_nat'
% 1.41/1.81 ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.41/1.81 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), T, X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~(
% 1.41/1.81 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z
% 1.41/1.81 ), Y, X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.41/1.81 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.41/1.81 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.41/1.81 Y, X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z,
% 1.41/1.81 X ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~(
% 1.41/1.81 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y )
% 1.41/1.81 , T ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.41/1.81 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.41/1.81 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T
% 1.41/1.81 , X ) ],
% 1.41/1.81 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, hAPP( V1
% 1.41/1.81 , V2 ), V3, V1, V4 ) ), hBOOL( hAPP( hAPP( W, Z ), V2 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.41/1.81 ), ~( hBOOL( hAPP( hAPP( X, W ), hAPP( hAPP( V0, W ), Z ) ) ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, X, T, V4, Y, V0, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.41/1.81 ), ~( hBOOL( hAPP( hAPP( X, U ), hAPP( hAPP( V0, U ), Y ) ) ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, T, V4, Z, V0, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), hBOOL( hAPP(
% 1.41/1.81 hAPP( U, Y ), W ) ), hBOOL( hAPP( hAPP( U, W ), Y ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, X, U, V3, V4, Z, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.41/1.81 hAPP( X, T ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, X, V3, V4, U, Z, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.41/1.81 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, W ), Y ) ), W ) ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, X, T, V4, Z, V0, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.41/1.81 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, U ), Z ) ), U ) ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, T, V4, Y, V0, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), hBOOL( hAPP(
% 1.41/1.81 hAPP( U, Z ), W ) ), hBOOL( hAPP( hAPP( U, W ), Z ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, X, U, V3, V4, Y, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), ~( hBOOL( hAPP(
% 1.41/1.81 hAPP( X, U ), T ) ) ), ~( hBOOL( hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, X, V3, V4, U, Y, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.41/1.81 ), ~( hBOOL( hAPP( hAPP( X, W ), hAPP( hAPP( V0, Z ), W ) ) ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, X, T, V4, Y, V0, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.41/1.81 ), ~( hBOOL( hAPP( hAPP( X, U ), hAPP( hAPP( V0, Y ), U ) ) ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, T, V4, Z, V0, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), hBOOL( hAPP(
% 1.41/1.81 hAPP( U, Y ), W ) ), hBOOL( hAPP( hAPP( U, W ), Y ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, X, U, V3, V4, Z, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), ~( hBOOL( hAPP(
% 1.41/1.81 hAPP( X, T ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, X, V3, V4, U, Z, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.41/1.81 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, Y ), W ) ), W ) ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, X, T, V4, Z, V0, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.41/1.81 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, Z ), U ) ), U ) ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, X, T, V4, Y, V0, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), hBOOL( hAPP(
% 1.41/1.81 hAPP( U, T ), W ) ), hBOOL( hAPP( hAPP( U, W ), T ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, X, U, V3, V4, Y, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), ~( hBOOL( hAPP(
% 1.41/1.81 hAPP( X, U ), Z ) ) ), ~( hBOOL( hAPP( hAPP( X, Z ), U ) ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, X, V3, V4, U, Y, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.41/1.81 ), ~( hBOOL( hAPP( hAPP( X, W ), hAPP( hAPP( V0, W ), Z ) ) ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, T, X, V4, Y, V0, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.41/1.81 ), ~( hBOOL( hAPP( hAPP( X, U ), hAPP( hAPP( V0, U ), Y ) ) ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, T, X, V4, Z, V0, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), hBOOL( hAPP(
% 1.41/1.81 hAPP( U, Y ), W ) ), hBOOL( hAPP( hAPP( U, W ), Y ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, U, X, V3, V4, Z, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.41/1.81 hAPP( X, T ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, X, V4, U, Z, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.41/1.81 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, W ), Y ) ), W ) ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, T, X, V4, Z, V0, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.41/1.81 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, U ), Z ) ), U ) ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, T, X, V4, Y, V0, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), hBOOL( hAPP(
% 1.41/1.81 hAPP( U, Z ), W ) ), hBOOL( hAPP( hAPP( U, W ), Z ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, U, X, V3, V4, Y, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ) ), ~( hBOOL( hAPP(
% 1.41/1.81 hAPP( X, U ), T ) ) ), ~( hBOOL( hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, X, V4, U, Y, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.41/1.81 ), ~( hBOOL( hAPP( hAPP( X, W ), hAPP( hAPP( V0, Z ), W ) ) ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, T, X, V4, Y, V0, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.41/1.81 ), ~( hBOOL( hAPP( hAPP( X, U ), hAPP( hAPP( V0, Y ), U ) ) ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, T, X, V4, Z, V0, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), hBOOL( hAPP(
% 1.41/1.81 hAPP( U, Y ), W ) ), hBOOL( hAPP( hAPP( U, W ), Y ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, U, X, V3, V4, Z, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ) ), ~( hBOOL( hAPP(
% 1.41/1.81 hAPP( X, T ), U ) ) ), ~( hBOOL( hAPP( hAPP( X, U ), T ) ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, X, V4, U, Z, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.41/1.81 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, Y ), W ) ), W ) ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, U, V3, T, X, V4, Z, V0, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, U ), W ) )
% 1.41/1.81 ), ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( V0, Z ), U ) ), U ) ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( V1, V2, W, V3, T, X, V4, Y, V0, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), hBOOL( hAPP(
% 1.41/1.81 hAPP( U, T ), W ) ), hBOOL( hAPP( hAPP( U, W ), T ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, U, X, V3, V4, Y, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ) ), ~( hBOOL( hAPP(
% 1.41/1.81 hAPP( X, U ), Z ) ) ), ~( hBOOL( hAPP( hAPP( X, Z ), U ) ) ), ~(
% 1.41/1.81 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, X, V4, U, Y, V5,
% 1.41/1.81 V6 ) ) ],
% 1.41/1.81 [ ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OMin', 'c_Int_OMin',
% 1.41/1.81 'tc_Int_Oint' ) ) ],
% 1.41/1.81 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, X, 'tc_fun'( Y,
% 1.41/1.81 'tc_bool' ) ), X ) ],
% 1.41/1.81 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.41/1.81 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Y, X ), Y ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.41/1.81 'c_HOL_Oabs__class_Oabs'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), X ) ) ]
% 1.41/1.81 ,
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.41/1.81 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.41/1.81 ,
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.41/1.81 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.41/1.81 ,
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.41/1.81 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.41/1.81 ,
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.41/1.81 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.41/1.81 ,
% 1.41/1.81 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.81 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.41/1.81 , Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) )
% 1.41/1.81 ],
% 1.41/1.81 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.81 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.41/1.81 , Z ), Y ), 'tc_nat' ) ) ],
% 1.41/1.81 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.81 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.41/1.81 , X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) )
% 1.41/1.81 ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.41/1.81 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.41/1.81 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.41/1.81 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ),
% 1.41/1.81 ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.41/1.81 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.41/1.81 , 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.41/1.81 , 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.41/1.81 , Y ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ),
% 1.41/1.81 ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.41/1.81 ), Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.41/1.81 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Y, X ) ]
% 1.41/1.81 ,
% 1.41/1.81 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Y, X ) ],
% 1.41/1.81 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 1.41/1.81 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'( Z, Y,
% 1.41/1.81 'tc_Int_Oint' ) ), ~( 'c_lessequals'( X, Z, 'tc_Int_Oint' ) ) ],
% 1.41/1.81 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( Z, Y, 'tc_nat' )
% 1.41/1.81 ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.41/1.81 [ 'c_lessequals'( X, X, 'tc_Int_Oint' ) ],
% 1.41/1.81 [ 'c_lessequals'( X, X, 'tc_nat' ) ],
% 1.41/1.81 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.41/1.81 , X ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_lessequals'( Y, T
% 1.41/1.81 , X ) ) ],
% 1.41/1.81 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z
% 1.41/1.81 , X ), ~( 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T
% 1.41/1.81 , X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.41/1.81 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.41/1.81 , X ), ~( 'c_lessequals'( U, T, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Orderings_Opreorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.41/1.81 'c_lessequals'( T, Z, X ) ), ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ),
% 1.41/1.81 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.41/1.81 ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X
% 1.41/1.81 ) ) ],
% 1.41/1.81 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_HOL_Oord__class_Oless'( Y, Z, X
% 1.41/1.81 ), ~( 'c_lessequals'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z, X
% 1.41/1.81 ) ) ],
% 1.41/1.81 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_lessequals'( Y, Z, X ), ~(
% 1.41/1.81 'c_lessequals'( Y, T, X ) ), ~( 'c_lessequals'( T, Z, X ) ) ],
% 1.41/1.81 [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ), ~( hBOOL( hAPP( X, hAPP(
% 1.41/1.81 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ) ) ],
% 1.41/1.81 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ),
% 1.41/1.81 'tc_nat' ) ), ~( 'c_lessequals'( Y, X, 'tc_nat' ) ) ],
% 1.41/1.81 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.41/1.81 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ), ~(
% 1.41/1.81 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.41/1.81 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ),
% 1.41/1.81 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.41/1.81 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.41/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X )
% 1.41/1.81 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.41/1.81 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ), Y ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.41/1.81 'c_Int_OMin', X ) ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP(
% 1.41/1.81 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X )
% 1.41/1.81 ), Y ) ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.41/1.81 , Z ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.41/1.81 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.41/1.81 X ), Y ), Z ) ), T, X ) ) ],
% 1.41/1.81 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.41/1.81 'tc_nat' ), X ), Y ), X, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.41/1.81 'tc_nat' ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =(
% 1.41/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( Y, Z, X ), hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.41/1.81 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), Z ), X ) ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.41/1.81 ,
% 1.41/1.81 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), Y ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.41/1.81 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.41/1.81 X, 'tc_nat' ) ), 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.81 'tc_nat' ), X ), 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ), Y,
% 1.41/1.81 'tc_nat' ) ],
% 1.41/1.81 [ =( 'c_Set_Oimage'( X, 'c_Lattices_Oupper__semilattice__class_Osup'( Y
% 1.41/1.81 , Z, 'tc_fun'( T, 'tc_bool' ) ), T, U ),
% 1.41/1.81 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Oimage'( X, Y, T, U
% 1.41/1.81 ), 'c_Set_Oimage'( X, Z, T, U ), 'tc_fun'( U, 'tc_bool' ) ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.41/1.81 Y ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.41/1.81 Y ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.81 ), X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.41/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.41/1.81 'c_HOL_Oabs__class_Oabs'( X ), Y ), X ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.41/1.81 ), Z ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.41/1.81 ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.41/1.81 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.41/1.81 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.41/1.81 [ ~( 'class_Orderings_Olinorder'( X ) ), 'c_lessequals'( Y, Z, X ),
% 1.41/1.81 'c_lessequals'( Z, Y, X ) ],
% 1.41/1.81 [ 'c_lessequals'( X, Y, 'tc_nat' ), 'c_lessequals'( Y, X, 'tc_nat' ) ]
% 1.41/1.81 ,
% 1.41/1.81 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), 'c_lessequals'( Y, X,
% 1.41/1.81 'tc_Int_Oint' ) ],
% 1.41/1.81 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.41/1.81 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.41/1.81 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y
% 1.41/1.81 , Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.41/1.81 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, Z
% 1.41/1.81 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Z, Y, X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.41/1.81 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.41/1.81 , 'tc_nat' ), 'tc_nat' ), 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.81 X ), X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.41/1.81 X ), Z ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.41/1.81 ), Y ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.41/1.81 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.41/1.81 , 'tc_nat' ), 'tc_nat' ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.41/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.81 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.41/1.81 ), X ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.41/1.81 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X )
% 1.41/1.81 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Z, U, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.41/1.81 T, X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.41/1.81 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.41/1.81 'c_lessequals'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.41/1.81 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.41/1.81 'c_lessequals'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.41/1.81 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.41/1.81 ,
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.41/1.81 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~(
% 1.41/1.81 'c_lessequals'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.41/1.81 'c_lessequals'( Y, Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.41/1.81 ,
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.81 X ), Z ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y )
% 1.41/1.81 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.81 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.41/1.81 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.81 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.41/1.81 ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.81 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.41/1.81 ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( Y,
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.41/1.81 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.41/1.81 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.41/1.81 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.41/1.81 ), Y ), T ), Z, X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), 'c_lessequals'( hAPP(
% 1.41/1.81 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), T, X ), ~(
% 1.41/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.41/1.81 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.41/1.81 Y, X ) ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.81 X ), T ), Z ), X ) ) ],
% 1.41/1.81 [ =( 'c_Set_Oimage'( X, 'c_Set_Oimage'( Y, Z, T, U ), U, W ),
% 1.41/1.81 'c_Set_Oimage'( 'c_COMBB'( X, Y, U, W, T ), Z, T, W ) ) ],
% 1.41/1.81 [ ~( 'class_RealVector_Ometric__space'( X ) ), ~(
% 1.41/1.81 'class_RealVector_Ometric__space'( Y ) ), ~(
% 1.41/1.81 'class_RealVector_Ometric__space'( Z ) ), 'c_Lim_OLIM'( 'c_COMBB'( T, U,
% 1.41/1.81 X, Y, Z ), W, hAPP( T, V0 ), Z, Y ), ~( 'c_Lim_OLIM'( U, W, V0, Z, X ) )
% 1.41/1.81 , ~( 'c_Lim_OLIM'( T, V0, hAPP( T, V0 ), X, Y ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber__ring'( X ) ), =( hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.41/1.81 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.81 ), X ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.81 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.41/1.81 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.41/1.81 ~( 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.41/1.81 , hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ) ) ]
% 1.41/1.81 ,
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.41/1.81 ), X ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.41/1.81 ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ),
% 1.41/1.81 ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.41/1.81 X ), T ), Z ), 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.41/1.81 ), X ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.81 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.41/1.81 X ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.41/1.81 ), X ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.81 ), X ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.41/1.81 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.41/1.81 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.41/1.81 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.41/1.81 ), X ) ), 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.41/1.81 , X ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.41/1.81 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~( 'c_lessequals'( Y,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~( 'c_lessequals'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.41/1.81 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_lessequals'(
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.41/1.81 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.41/1.81 ), X ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.41/1.81 ), X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.41/1.81 X ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.41/1.81 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.41/1.81 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~( 'c_lessequals'(
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~( 'c_lessequals'(
% 1.41/1.81 Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.41/1.81 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.41/1.81 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~( 'c_lessequals'( Y,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.81 ), X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.41/1.81 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~( 'c_lessequals'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.81 ), X ), ~( 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.81 X ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 'c_lessequals'(
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.81 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.81 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 'c_lessequals'(
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.81 ), X ) ), 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X )
% 1.41/1.81 , X ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.41/1.81 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.41/1.81 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.41/1.81 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.41/1.81 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.41/1.81 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.41/1.81 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'( Y,
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~( 'c_lessequals'( Y,
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~( 'c_lessequals'(
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.41/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.41/1.81 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.41/1.81 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.41/1.81 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.41/1.81 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), Z ) ) ],
% 1.41/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.41/1.81 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.41/1.81 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.41/1.81 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.41/1.81 'c_Divides_Odiv__class_Omod'( Z, T, X ) ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.41/1.81 X ), Y ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.41/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.41/1.81 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.41/1.81 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.41/1.81 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.41/1.81 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.41/1.81 ), U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), W ), T ), Z, X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y
% 1.41/1.81 ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.41/1.81 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.81 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.41/1.81 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.41/1.81 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.81 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.41/1.81 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.41/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.41/1.81 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.41/1.81 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.41/1.81 ) ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.41/1.81 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'( Z, Y, X
% 1.41/1.81 ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.41/1.81 X ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.41/1.81 X ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ],
% 1.41/1.81 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ],
% 1.41/1.81 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ],
% 1.41/1.81 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.41/1.81 X ), Y ) ), Z ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ],
% 1.41/1.81 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.41/1.81 X ), Y ) ), Z ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.81 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.41/1.81 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.81 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.41/1.81 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.81 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.41/1.81 ) ) ],
% 1.41/1.81 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.81 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.41/1.81 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.41/1.81 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.81 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.41/1.81 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.41/1.81 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.81 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.41/1.81 ) ) ],
% 1.41/1.81 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.81 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.41/1.81 ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.81 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.41/1.81 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.41/1.81 X ), Y ) ), Z ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP(
% 1.41/1.81 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.81 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.41/1.81 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.41/1.81 , Z ) ) ) ],
% 1.41/1.81 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_Lim_OLIM'(
% 1.41/1.81 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X, X ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ), =( Y, hAPP(
% 1.41/1.81 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), =( Y, Z ) ],
% 1.41/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.41/1.81 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.41/1.81 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.41/1.81 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.41/1.81 ), Y ), T ), Z, X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.41/1.81 Y ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.41/1.81 Y ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.41/1.81 Y ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.41/1.81 Y ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.41/1.81 Y ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.41/1.81 Y ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.41/1.81 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.81 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.41/1.81 ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.41/1.81 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.81 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.41/1.81 ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.81 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.81 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), U )
% 1.41/1.81 ) ],
% 1.41/1.81 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.41/1.81 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.41/1.81 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.41/1.81 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.41/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.41/1.81 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.41/1.81 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z,
% 1.41/1.81 T, X ) ), T, X ) ) ],
% 1.41/1.81 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.41/1.81 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.41/1.81 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.41/1.81 ) ), Z ), T, X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.41/1.81 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.41/1.81 , 'tc_nat' ), 'tc_nat' ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.81 X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.81 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.41/1.81 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.41/1.81 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.41/1.81 , 'tc_nat' ), 'tc_nat' ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.41/1.81 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.41/1.81 , 'tc_nat' ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.41/1.81 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.81 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.41/1.81 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.41/1.81 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ), ~(
% 1.41/1.81 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.81 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.41/1.81 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.41/1.81 , 'tc_nat' ), 'tc_nat' ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.81 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ), =( Y,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.41/1.81 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), T ) ),
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.81 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), T ) ) ), Y ) ), ~(
% 1.41/1.81 'c_lessequals'( T, Z, 'tc_nat' ) ) ],
% 1.41/1.81 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_SEQ_OLIMSEQ'( Y
% 1.41/1.81 , Z, X ), ~( 'c_SEQ_OLIMSEQ'( 'c_COMBS'( 'c_COMBB'(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), Y, X, 'tc_fun'( X, X ), 'tc_nat' ), T
% 1.41/1.81 , 'tc_nat', X, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.41/1.81 'c_SEQ_OLIMSEQ'( T, Z, X ) ) ],
% 1.41/1.81 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_SEQ_OLIMSEQ'( Y
% 1.41/1.81 , Z, X ), ~( 'c_SEQ_OLIMSEQ'( 'c_COMBS'( 'c_COMBB'(
% 1.41/1.81 'c_HOL_Ominus__class_Ominus'( X ), T, X, 'tc_fun'( X, X ), 'tc_nat' ), Y
% 1.41/1.81 , 'tc_nat', X, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.41/1.81 'c_SEQ_OLIMSEQ'( T, Z, X ) ) ],
% 1.41/1.81 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_SEQ_OLIMSEQ'(
% 1.41/1.81 'c_COMBS'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Y, X,
% 1.41/1.81 'tc_fun'( X, X ), 'tc_nat' ), Z, 'tc_nat', X, X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ), X ), =( U,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_SEQ_OLIMSEQ'( Z, U, X ) ), ~(
% 1.41/1.81 'c_SEQ_OLIMSEQ'( Y, T, X ) ) ],
% 1.41/1.81 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.41/1.81 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ), ~(
% 1.41/1.81 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ) ) ],
% 1.41/1.81 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.41/1.81 , hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ),
% 1.41/1.81 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ), X ), ~(
% 1.41/1.81 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.41/1.81 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.41/1.81 X, 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( 'c_Suc',
% 1.41/1.81 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ) ), 'tc_nat' ) ],
% 1.41/1.81 [ =( hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.41/1.81 , hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.41/1.81 ) ), 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ), X ),
% 1.41/1.81 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.41/1.81 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.41/1.81 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( Y, hAPP( hAPP( Y, T ), T ) )
% 1.41/1.81 , T ) ), ~( 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.41/1.81 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastAtMost'( Z
% 1.41/1.81 , hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ),
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.41/1.81 'c_Suc', T ), Z, 'tc_nat' ) ) ],
% 1.41/1.81 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_Series_Osums'(
% 1.41/1.81 Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( Y,
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X ), ~( 'c_Series_Osums'(
% 1.41/1.81 'c_COMBB'( Y, 'c_Suc', 'tc_nat', X, 'tc_nat' ), Z, X ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.41/1.81 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.41/1.81 Z, hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'( Y,
% 1.41/1.81 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ), 'tc_nat'
% 1.41/1.81 , X ) ), hAPP( Y, T ) ) ), 'c_HOL_Oord__class_Oless'( T, Z, 'tc_nat' ) ]
% 1.41/1.81 ,
% 1.41/1.81 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.41/1.81 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.41/1.81 Z, T, 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.81 X ), hAPP( Y, Z ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.41/1.81 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( 'c_Suc', Z ), T,
% 1.41/1.81 'tc_nat' ), 'tc_nat', X ) ) ), ~( 'c_HOL_Oord__class_Oless'( Z, T,
% 1.41/1.81 'tc_nat' ) ) ],
% 1.41/1.81 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.41/1.81 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.41/1.81 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), U ), T ), 'tc_nat' ), 'tc_nat', X
% 1.41/1.81 ), 'c_Finite__Set_Osetsum'( 'c_COMBB'( Y, 'c_COMBC'(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T, 'tc_nat', 'tc_nat', 'tc_nat' )
% 1.41/1.81 , 'tc_nat', X, 'tc_nat' ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.41/1.81 Z, U, 'tc_nat' ), 'tc_nat', X ) ) ],
% 1.41/1.81 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.81 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.81 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.81 'c_Int_OPls' ) ), X ) ), X ) ],
% 1.41/1.81 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.41/1.81 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.41/1.81 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.41/1.81 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.41/1.81 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.41/1.81 [ ~( =( 'c_Divides_Odiv__class_Omod'( X,
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.81 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.41/1.81 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.81 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.81 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ],
% 1.41/1.81 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.41/1.81 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.41/1.81 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.81 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X,
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.81 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.41/1.81 [ =( 'c_FFT__Mirabelle_ODFT'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.81 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.41/1.81 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, Z ), hAPP( hAPP(
% 1.41/1.81 'c_HOL_Oplus__class_Oplus'( 'tc_Complex_Ocomplex' ),
% 1.41/1.81 'c_FFT__Mirabelle_ODFT'( X, 'c_COMBB'( Y, hAPP(
% 1.41/1.81 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.81 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.81 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat'
% 1.41/1.81 ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.81 'tc_Complex_Ocomplex' ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.41/1.82 'tc_Complex_Ocomplex' ), 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ), Z ) ), 'c_FFT__Mirabelle_ODFT'(
% 1.41/1.82 X, 'c_COMBB'( Y, 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.82 'tc_nat' ), hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_nat' )
% 1.41/1.82 , 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat', 'tc_nat',
% 1.41/1.82 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ), Z ) ) ) ) ],
% 1.41/1.82 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.41/1.82 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ), 'tc_nat' ), 'tc_nat', X ), hAPP(
% 1.41/1.82 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'( 'c_COMBB'(
% 1.41/1.82 Y, hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', X, 'tc_nat' ),
% 1.41/1.82 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ) ), 'c_Finite__Set_Osetsum'(
% 1.41/1.82 'c_COMBB'( Y, 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 1.41/1.82 ), hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_nat' )
% 1.41/1.82 , 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat', 'tc_nat',
% 1.41/1.82 'tc_nat' ), 'tc_nat', X, 'tc_nat' ),
% 1.41/1.82 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ) ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.41/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.41/1.82 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.41/1.82 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.41/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.41/1.82 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.41/1.82 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.41/1.82 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.41/1.82 , ~( 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.41/1.82 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.41/1.82 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.41/1.82 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.41/1.82 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.41/1.82 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.41/1.82 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.41/1.82 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.41/1.82 , ~( 'c_HOL_Oord__class_Oless'( T, Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.41/1.82 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.41/1.82 , ~( 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.41/1.82 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.41/1.82 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.41/1.82 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) )
% 1.41/1.82 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.41/1.82 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.41/1.82 , ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.41/1.82 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X )
% 1.41/1.82 , ~( 'c_HOL_Oord__class_Oless'( T, Y, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.41/1.82 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.41/1.82 , ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) )
% 1.41/1.82 , ~( 'c_HOL_Oord__class_Oless'( Z, T, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ), =( Y,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), =( Z,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.41/1.82 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.41/1.82 ), Y ), Z ), Y, X ), Z ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.82 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.41/1.82 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.41/1.82 ), Y ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), Z ), Y ), =( Z,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), Z ) ), =( Z,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), Y ), Z ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), Y ) ) ],
% 1.41/1.82 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.41/1.82 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.41/1.82 ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z )
% 1.41/1.82 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.41/1.82 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 X ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.41/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 X ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.41/1.82 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.41/1.82 Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 X ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.41/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_lessequals'(
% 1.41/1.82 Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 X ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.41/1.82 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.41/1.82 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.41/1.82 , Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), 'c_lessequals'( hAPP(
% 1.41/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.41/1.82 ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.41/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, T, X ) )
% 1.41/1.82 ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), 'c_lessequals'( hAPP(
% 1.41/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.41/1.82 ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.41/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), ~( 'c_lessequals'( Y,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Z, X ) ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.41/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( T, Y, X ) ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.41/1.82 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ), =( T, U ), =( Z,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.41/1.82 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.41/1.82 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.82 X ), Y ), Z ), X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z
% 1.41/1.82 , X ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.82 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.41/1.82 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.82 X ), Y ), Z ), X ), ~( 'c_lessequals'( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.41/1.82 , X ) ), ~( 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.41/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), X ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.41/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.41/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'( Z,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Y,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.41/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.41/1.82 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.82 X ), Y ), Z ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.41/1.82 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.82 X ), Z ), Y ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.41/1.82 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.82 X ), Y ), Z ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.41/1.82 'c_lessequals'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.82 X ), Z ), Y ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.41/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.41/1.82 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), 'c_lessequals'(
% 1.41/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Z, U, X ) )
% 1.41/1.82 , ~( 'c_lessequals'( Y, T, X ) ) ],
% 1.41/1.82 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.41/1.82 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.41/1.82 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.41/1.82 ), 'c_Divides_Odiv__class_Odiv'( Z, T, X ) ), =( Y,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.82 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.41/1.82 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.41/1.82 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.41/1.82 ), 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), =( Z,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.41/1.82 , Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.41/1.82 ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.41/1.82 , Z ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X )
% 1.41/1.82 ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.41/1.82 , Y ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.41/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.41/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.41/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.41/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.41/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Z,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.41/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'( Y,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ),
% 1.41/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.41/1.82 ), Y ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), Z ) ), =( Z,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), Z ), Y ), =( Z,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.82 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.41/1.82 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.41/1.82 ), Y ), Z ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.82 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.41/1.82 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.41/1.82 ), Y ), Z ), Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( hAPP(
% 1.41/1.82 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.41/1.82 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), ~(
% 1.41/1.82 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBC'(
% 1.41/1.82 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Z, X, 'tc_fun'( X, X ), Y )
% 1.41/1.82 , T, Y, X, X ), U, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), W ), T
% 1.41/1.82 ), Y, X ), ~( 'c_Lim_OLIM'( Z, U, W, Y, X ) ) ],
% 1.41/1.82 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.82 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.41/1.82 'c_Int_OMin', X ) ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.41/1.82 ) ],
% 1.41/1.82 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ), hAPP(
% 1.41/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.41/1.82 'c_Groebner__Basis_Ogb__semiring'( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( X ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.41/1.82 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ) ) ],
% 1.41/1.82 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.41/1.82 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ), Y ) ) ],
% 1.41/1.82 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.41/1.82 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBS'(
% 1.41/1.82 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'( X ), Z, X, 'tc_fun'( X, X ), Y ),
% 1.41/1.82 'c_COMBB'( 'c_HOL_Ouminus__class_Ouminus'( X ), T, X, X, Y ), Y, X, X ),
% 1.41/1.82 U, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), W ), hAPP(
% 1.41/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), V0 ) ), Y, X ), ~( 'c_Lim_OLIM'( T,
% 1.41/1.82 U, V0, Y, X ) ), ~( 'c_Lim_OLIM'( Z, U, W, Y, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.41/1.82 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), ~( 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.41/1.82 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ),
% 1.41/1.82 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.41/1.82 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.41/1.82 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Z ), Y ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.41/1.82 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), 'c_lessequals'( Z,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 X ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.41/1.82 , Y ) ), Z ), X ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), =( Y,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.41/1.82 Z, 'tc_nat' ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ),
% 1.41/1.82 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'(
% 1.41/1.82 Z, 'tc_nat' ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 X ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.41/1.82 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.41/1.82 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Z ), T ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.41/1.82 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.41/1.82 ), Z ), Y ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.41/1.82 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.41/1.82 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~(
% 1.41/1.82 'class_OrderedGroup_Omonoid__mult'( X ) ), 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.41/1.82 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.41/1.82 ), Y ), Z ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Z ),
% 1.41/1.82 X ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.41/1.82 , Z, 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.41/1.82 , X ) ), ~( 'c_HOL_Oord__class_Oless'( Y, T, X ) ) ],
% 1.41/1.82 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.41/1.82 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBS'(
% 1.41/1.82 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'( X ), Z, X, 'tc_fun'( X, X ), Y ),
% 1.41/1.82 T, Y, X, X ), U, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), W ), V0 ),
% 1.41/1.82 Y, X ), ~( 'c_Lim_OLIM'( T, U, V0, Y, X ) ), ~( 'c_Lim_OLIM'( Z, U, W, Y
% 1.41/1.82 , X ) ) ],
% 1.41/1.82 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.41/1.82 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBS'(
% 1.41/1.82 'c_COMBB'( 'c_HOL_Ominus__class_Ominus'( X ), Z, X, 'tc_fun'( X, X ), Y )
% 1.41/1.82 , T, Y, X, X ), U, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), W ), V0
% 1.41/1.82 ), Y, X ), ~( 'c_Lim_OLIM'( T, U, V0, Y, X ) ), ~( 'c_Lim_OLIM'( Z, U, W
% 1.41/1.82 , Y, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.41/1.82 X ), Y ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.41/1.82 hAPP( 'c_Power_Opower__class_Opower'( X ), hAPP(
% 1.41/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ), Z
% 1.41/1.82 ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.41/1.82 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.41/1.82 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.41/1.82 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( X )
% 1.41/1.82 , 'c_Power_Opower_Opower'( 'c_HOL_Oone__class_Oone'( X ),
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), X ) ) ],
% 1.41/1.82 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_Series_Osums'(
% 1.41/1.82 'c_COMBC'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'(
% 1.41/1.82 X, X ), 'tc_nat' ), Z, 'tc_nat', X, X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_Series_Osums'( Y
% 1.41/1.82 , T, X ) ) ],
% 1.41/1.82 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_Series_Osums'(
% 1.41/1.82 'c_COMBC'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'(
% 1.41/1.82 X, X ), 'tc_nat' ), Z, 'tc_nat', X, X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_Series_Osums'( Y
% 1.41/1.82 , T, X ) ) ],
% 1.41/1.82 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_SEQ_OLIMSEQ'(
% 1.41/1.82 'c_COMBC'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'(
% 1.41/1.82 X, X ), 'tc_nat' ), Z, 'tc_nat', X, X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_SEQ_OLIMSEQ'( Y,
% 1.41/1.82 T, X ) ) ],
% 1.41/1.82 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_SEQ_OZseq'(
% 1.41/1.82 'c_COMBC'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'(
% 1.41/1.82 X, X ), 'tc_nat' ), Z, 'tc_nat', X, X ), X ), ~( 'c_SEQ_OZseq'( Y, X ) )
% 1.41/1.82 ],
% 1.41/1.82 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_SEQ_OZseq'(
% 1.41/1.82 'c_COMBC'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'(
% 1.41/1.82 X, X ), 'tc_nat' ), Z, 'tc_nat', X, X ), X ), ~( 'c_SEQ_OZseq'( Y, X ) )
% 1.41/1.82 ],
% 1.41/1.82 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Omod'( Y,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.41/1.82 , Y ) ) ],
% 1.41/1.82 [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 1.41/1.82 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.41/1.82 'tc_nat' ) ) ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.41/1.82 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ],
% 1.41/1.82 [ ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.41/1.82 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.41/1.82 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.41/1.82 [ ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), hBOOL(
% 1.41/1.82 hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 'tc_nat' ), 'tc_nat' ) ) ) ],
% 1.41/1.82 [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ), ~( hBOOL( hAPP( X
% 1.41/1.82 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.41/1.82 'tc_nat' ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 'tc_nat' ), 'tc_nat' ) ],
% 1.41/1.82 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.41/1.82 ), 'tc_nat' ) ) ],
% 1.41/1.82 [ ~( 'c_HOL_Oord__class_Oless'( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.41/1.82 ), 'tc_nat' ) ) ],
% 1.41/1.82 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ),
% 1.41/1.82 ~( 'c_Groebner__Basis_Ogb__semiring'( T, U, X, W, Z, V0 ) ) ],
% 1.41/1.82 [ ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ],
% 1.41/1.82 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ],
% 1.41/1.82 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.41/1.82 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), X ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.41/1.82 [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 1.41/1.82 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.41/1.82 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 1.41/1.82 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' )
% 1.41/1.82 ],
% 1.41/1.82 [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 1.41/1.82 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.41/1.82 ), Z ) ), T ) ) ],
% 1.41/1.82 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.41/1.82 'c_lessequals'( hAPP( 'c_HOL_Oabs__class_Oabs'( X ),
% 1.41/1.82 'c_Finite__Set_Osetsum'( Y, Z, T, X ) ), 'c_Finite__Set_Osetsum'(
% 1.41/1.82 'c_COMBB'( 'c_HOL_Oabs__class_Oabs'( X ), Y, X, X, T ), Z, T, X ), X ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( Y ), X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.82 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.41/1.82 Y, X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.41/1.82 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.41/1.82 'c_Int_OMin', X ) ), Y ), 'c_Int_Onumber__class_Onumber__of'(
% 1.41/1.82 'c_Int_OMin', X ) ), 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), 'c_Finite__Set_Osetsum'( Y, Z, T, X
% 1.41/1.82 ) ), U ), 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBB'(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y, X, 'tc_fun'( X, X ), T ), U, T,
% 1.41/1.82 X, X ), Z, T, X ) ) ],
% 1.41/1.82 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), 'c_Finite__Set_Osetsum'( Y, Z, T, X
% 1.41/1.82 ) ), U ), 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBB'(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y, X, 'tc_fun'( X, X ), T ), U, T,
% 1.41/1.82 X, X ), Z, T, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.41/1.82 , X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.41/1.82 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.41/1.82 'c_Int_OBit1'( 'c_Int_OPls' ), 'tc_Int_Oint' ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.41/1.82 'c_HOL_Oone__class_Oone'( X ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'(
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.41/1.82 , X ), ~( 'c_lessequals'( Y, 'c_Int_OBit1'( 'c_Int_OPls' ), 'tc_Int_Oint'
% 1.41/1.82 ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( Y, 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ), 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Oone__class_Oone'( X )
% 1.41/1.82 , X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.41/1.82 , X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( 'c_Int_OPls' ), Y,
% 1.41/1.82 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_Int_OBit1'( 'c_Int_OPls' ), Y, 'tc_Int_Oint' ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'(
% 1.41/1.82 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.41/1.82 , X ), ~( 'c_lessequals'( 'c_Int_OBit1'( 'c_Int_OPls' ), Y, 'tc_Int_Oint'
% 1.41/1.82 ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ), Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.41/1.82 'c_HOL_Oone__class_Oone'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.41/1.82 , X ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.41/1.82 'tc_nat' ), X ), hAPP( 'c_Suc', Y ) ), X, 'tc_nat' ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.41/1.82 'tc_nat' ) ) ],
% 1.41/1.82 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc',
% 1.41/1.82 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.41/1.82 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ), ~(
% 1.41/1.82 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.41/1.82 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.41/1.82 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.41/1.82 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), ~(
% 1.41/1.82 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.41/1.82 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc',
% 1.41/1.82 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.41/1.82 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP(
% 1.41/1.82 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ) ) ),
% 1.41/1.82 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.41/1.82 [ =( hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' )
% 1.41/1.82 , X ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ),
% 1.41/1.82 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.41/1.82 'tc_nat' ) ) ],
% 1.41/1.82 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.41/1.82 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.41/1.82 [ ~( =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'tc_nat' ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ),
% 1.41/1.82 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.41/1.82 [ =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.41/1.82 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.41/1.82 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.41/1.82 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 'tc_nat' ) ), ~( 'c_lessequals'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( 'c_Suc', X
% 1.41/1.82 ), hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_lessequals'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ), 'tc_nat' ),
% 1.41/1.82 ~( 'c_lessequals'( X, Y, 'tc_nat' ) ) ],
% 1.41/1.82 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.41/1.82 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'(
% 1.41/1.82 X, Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.41/1.82 [ ~( 'c_lessequals'( hAPP( 'c_Suc', X ), X, 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( 'c_Suc', X
% 1.41/1.82 ), Y, 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_lessequals'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ), ~( 'c_lessequals'(
% 1.41/1.82 X, Y, 'tc_nat' ) ) ],
% 1.41/1.82 [ =( X, Y ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.41/1.82 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_Suc', X ),
% 1.41/1.82 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.41/1.82 [ =( X, Y ), ~( 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ),
% 1.41/1.82 'tc_nat' ) ), 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.41/1.82 , X ) ), hAPP( 'c_Suc', Y ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.41/1.82 'tc_nat' ), X ), Y ) ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( 'c_Suc'
% 1.41/1.82 , U ) ), hAPP( hAPP( Y, T ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z
% 1.41/1.82 ), T ), U ) ) ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.41/1.82 'c_Suc', Y ) ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.82 'tc_nat' ), X ), Y ) ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.41/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Y, Z, X ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Z, T, X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.41/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ) ), =( U,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.41/1.82 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ), hAPP(
% 1.41/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), =( Z,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), =( U, 'c_HOL_Ozero__class_Ozero'( X )
% 1.41/1.82 ), =( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), U ), hAPP(
% 1.41/1.82 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.41/1.82 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.82 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), ~(
% 1.41/1.82 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBB'( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), T, X, X, Y ), U, hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), W ), Y, X ), ~( 'c_Lim_OLIM'( T,
% 1.41/1.82 U, W, Y, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.41/1.82 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.41/1.82 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.82 ) ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.41/1.82 X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), =(
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.82 ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.41/1.82 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.82 ) ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), ~( =( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.82 ) ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =(
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.82 ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.41/1.82 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.41/1.82 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.82 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), Z ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.41/1.82 , X ) ), T ) ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.41/1.82 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.41/1.82 , X ) ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ) ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( 'class_Int_Onumber'( X )
% 1.41/1.82 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), ~( 'class_Int_Onumber'(
% 1.41/1.82 X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.82 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 X ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.41/1.82 ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.41/1.82 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_lessequals'( Y, T, X ) )
% 1.41/1.82 ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~( 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ), =( Z,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.82 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_SEQ_OLIMSEQ'(
% 1.41/1.82 'c_COMBB'( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X,
% 1.41/1.82 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.41/1.82 , ~( 'c_SEQ_OLIMSEQ'( Z, T, X ) ) ],
% 1.41/1.82 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_SEQ_OZseq'(
% 1.41/1.82 'c_COMBB'( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X,
% 1.41/1.82 'tc_nat' ), X ), ~( 'c_SEQ_OZseq'( Z, X ) ) ],
% 1.41/1.82 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_SEQ_OZseq'(
% 1.41/1.82 'c_COMBB'( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X,
% 1.41/1.82 'tc_nat' ), X ), ~( 'c_SEQ_OZseq'( Z, X ) ) ],
% 1.41/1.82 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_Series_Osums'(
% 1.41/1.82 'c_COMBB'( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X,
% 1.41/1.82 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.41/1.82 , ~( 'c_Series_Osums'( Z, T, X ) ) ],
% 1.41/1.82 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_Series_Osums'(
% 1.41/1.82 'c_COMBB'( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X,
% 1.41/1.82 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.41/1.82 , ~( 'c_Series_Osums'( Z, T, X ) ) ],
% 1.41/1.82 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.41/1.82 'c_Finite__Set_Osetsum'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.41/1.82 'tc_bool' ) ), Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.82 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.41/1.82 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.41/1.82 , 'tc_nat' ), 'tc_nat' ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.41/1.82 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'(
% 1.41/1.82 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.41/1.82 , 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.41/1.82 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.41/1.82 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.41/1.82 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.41/1.82 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.41/1.82 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.41/1.82 , 'tc_nat' ), 'tc_nat' ), =( 'c_Int_Onumber__class_Onumber__of'( Z,
% 1.41/1.82 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ), ~(
% 1.41/1.82 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.41/1.82 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.41/1.82 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.41/1.82 'c_Finite__Set_Osetsum'( 'c_COMBB'( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.41/1.82 Y, X, X, Z ), T, Z, X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.41/1.82 'c_Finite__Set_Osetsum'( Y, T, Z, X ) ) ) ],
% 1.41/1.82 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ), =( hAPP(
% 1.41/1.82 'c_HOL_Oabs__class_Oabs'( X ), 'c_Finite__Set_Osetsum'( 'c_COMBB'(
% 1.41/1.82 'c_HOL_Oabs__class_Oabs'( X ), Y, X, X, Z ), T, Z, X ) ),
% 1.41/1.82 'c_Finite__Set_Osetsum'( 'c_COMBB'( 'c_HOL_Oabs__class_Oabs'( X ), Y, X,
% 1.41/1.82 X, Z ), T, Z, X ) ) ],
% 1.41/1.82 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Int_Onumber__class_Onumber__of'(
% 1.41/1.82 'c_Int_OPls', X ) ), Y ) ],
% 1.41/1.82 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.41/1.82 'c_Int_OPls', X ) ), Y ), Y ) ],
% 1.41/1.82 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.41/1.82 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), Y ) ) ],
% 1.41/1.82 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.41/1.82 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.41/1.82 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.41/1.82 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.41/1.82 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP( 'c_Suc',
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.41/1.82 [ ~( =( hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) )
% 1.41/1.82 , Y ) ), =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat'
% 1.41/1.82 ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.41/1.82 hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.41/1.82 hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.41/1.82 [ =( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X
% 1.41/1.82 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 X, hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.41/1.82 ), 'tc_nat' ) ) ],
% 1.41/1.82 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 'tc_nat' ) ), 'tc_nat' ) ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 'tc_nat' ) ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.41/1.82 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.41/1.82 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.41/1.82 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.41/1.82 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, hAPP( 'c_Suc'
% 1.41/1.82 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.41/1.82 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc',
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ) ],
% 1.41/1.82 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.41/1.82 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, hAPP(
% 1.41/1.82 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.41/1.82 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.41/1.82 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP( 'c_Suc',
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.41/1.82 [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 'tc_nat' ) ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) )
% 1.41/1.82 ],
% 1.41/1.82 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.41/1.82 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.41/1.82 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.41/1.82 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.41/1.82 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, hAPP(
% 1.41/1.82 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, hAPP( 'c_Suc'
% 1.41/1.82 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.41/1.82 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc',
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.41/1.82 [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 'tc_nat' ) ) ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( 'c_Suc',
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.41/1.82 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.41/1.82 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.41/1.82 'c_HOL_Oone__class_Oone'( X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.41/1.82 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ) ],
% 1.41/1.82 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', 'tc_nat' ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OPls',
% 1.41/1.82 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OPls',
% 1.41/1.82 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls',
% 1.41/1.82 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.41/1.82 'c_Int_OPls', 'c_Int_OBit1'( X ), 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ 'c_lessequals'( 'c_Int_OPls', 'c_Int_OBit1'( X ), 'tc_Int_Oint' ), ~(
% 1.41/1.82 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.41/1.82 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.41/1.82 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.41/1.82 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ),
% 1.41/1.82 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.41/1.82 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint'
% 1.41/1.82 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.41/1.82 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint'
% 1.41/1.82 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.41/1.82 'c_Int_OPls', 'c_Int_OBit0'( X ), 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ 'c_lessequals'( 'c_Int_OPls', 'c_Int_OBit0'( X ), 'tc_Int_Oint' ), ~(
% 1.41/1.82 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OPls',
% 1.41/1.82 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OPls',
% 1.41/1.82 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls',
% 1.41/1.82 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OBit0'( X ),
% 1.41/1.82 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OBit0'( X ),
% 1.41/1.82 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X,
% 1.41/1.82 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ 'c_lessequals'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.41/1.82 'c_Int_OBit0'( X ), 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OPls', 'tc_Int_Oint' ), ~(
% 1.41/1.82 'c_lessequals'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.41/1.82 'c_Suc', X ) ) ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 1.41/1.82 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.41/1.82 'c_Suc', Y ) ) ), 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 1.41/1.82 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.41/1.82 'c_Suc', X ) ) ), Y, 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), Y, 'tc_nat' ) ) ],
% 1.41/1.82 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.41/1.82 'c_Suc', Y ) ) ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ), 'tc_nat' ) ) ],
% 1.41/1.82 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.41/1.82 'c_Suc', X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.41/1.82 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.41/1.82 Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.41/1.82 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP(
% 1.41/1.82 'c_Suc', X ) ) ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.41/1.82 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.41/1.82 Y, 'tc_nat' ), 'tc_nat' ) ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.41/1.82 , X ) ), Y ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ),
% 1.41/1.82 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.41/1.82 'tc_nat' ) ) ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ), Y, 'tc_nat'
% 1.41/1.82 ) ) ],
% 1.41/1.82 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.41/1.82 V3, V4 ) ), =( hAPP( hAPP( 'c_Power_Opower_Opower'( V1, V2, V4 ), Z ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ],
% 1.41/1.82 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( Z, hAPP( hAPP( T, hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower_Opower'( U, W, V0 ), X ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( U
% 1.41/1.82 , W, V0 ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.41/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), Y ) ) ), ~(
% 1.41/1.82 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, T, Z, V4, V5, U, W, V6,
% 1.41/1.82 V0 ) ) ],
% 1.41/1.82 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( Z, hAPP( hAPP( T, hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower_Opower'( U, W, V0 ), V1 ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( U
% 1.41/1.82 , W, V0 ), X ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.41/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), Y ) ) ), ~(
% 1.41/1.82 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, T, Z, V4, V5, U, W, V6,
% 1.41/1.82 V0 ) ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, U ) ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y
% 1.41/1.82 , Z ), U ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.41/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~(
% 1.41/1.82 'c_Ring__and__Field_Ocomm__ring__1'( X, Y, W, T, V0, V1, Z ) ) ],
% 1.41/1.82 [ 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.41/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ),
% 1.41/1.82 ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ), ~(
% 1.41/1.82 'c_Parity_Oeven__odd__class_Oeven'( 'c_Divides_Odiv__class_Omod'( X,
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.41/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ) ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.41/1.82 X ) ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.82 'tc_nat' ), X ), Y ) ) ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.41/1.82 X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.41/1.82 'c_Suc', Y ) ) ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y ) ),
% 1.41/1.82 hAPP( 'c_Suc', Z ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.41/1.82 ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z )
% 1.41/1.82 ) ],
% 1.41/1.82 [ =( X, hAPP( 'c_Suc', Y ) ), 'c_lessequals'( X, Y, 'tc_nat' ), ~(
% 1.41/1.82 'c_lessequals'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ],
% 1.41/1.82 [ ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Y, hAPP( 'c_Suc', X ), 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( X, X, 'tc_nat' ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', Y ), 'tc_nat' ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.41/1.82 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', Z ) ), hAPP( hAPP( T, Y ), hAPP(
% 1.41/1.82 hAPP( X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W,
% 1.41/1.82 V0, V1 ) ) ],
% 1.41/1.82 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', Z ) ), hAPP( hAPP( T, Y ), hAPP(
% 1.41/1.82 hAPP( X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W,
% 1.41/1.82 V0, V1 ) ) ],
% 1.41/1.82 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ), hAPP( hAPP( Y, Z ),
% 1.41/1.82 hAPP( 'c_Suc', T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Y, W
% 1.41/1.82 , V0, V1 ) ) ],
% 1.41/1.82 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ), hAPP( hAPP( Z, Y ),
% 1.41/1.82 hAPP( 'c_Suc', T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Z, W
% 1.41/1.82 , V0, V1 ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( X, hAPP( 'c_Suc', X ), 'tc_nat' ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Z, Y, 'tc_nat' ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_Fun_Oinj__on'( 'c_Suc', X, 'tc_nat', 'tc_nat' ) ],
% 1.41/1.82 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.41/1.82 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =(
% 1.41/1.82 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), =( hAPP(
% 1.41/1.82 'c_Suc', X ), Y ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ 'c_lessequals'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ), 'c_lessequals'( Y,
% 1.41/1.82 X, 'tc_nat' ) ],
% 1.41/1.82 [ ~( 'c_lessequals'( X, Y, 'tc_nat' ) ), ~( 'c_lessequals'( hAPP(
% 1.41/1.82 'c_Suc', Y ), X, 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_lessequals'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', X ), 'tc_nat' ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ), ~(
% 1.41/1.82 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', X ), 'tc_nat' ) ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', X ), 'tc_nat' ),
% 1.41/1.82 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 1.41/1.82 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 1.41/1.82 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ),
% 1.41/1.82 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ) ) ],
% 1.41/1.82 [ =( 'c_Int_OBit1'( 'c_Int_OMin' ), 'c_Int_OMin' ) ],
% 1.41/1.82 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OMin' ) ), =( X, 'c_Int_OMin' ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ ~( =( 'c_Int_OMin', 'c_Int_OBit1'( X ) ) ), =( 'c_Int_OMin', X ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ 'c_lessequals'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint'
% 1.41/1.82 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.41/1.82 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ 'c_lessequals'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint'
% 1.41/1.82 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.41/1.82 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.41/1.82 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.41/1.82 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.41/1.82 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ),
% 1.41/1.82 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ =( 'c_Int_OMin', 'c_Int_OBit1'( 'c_Int_OMin' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OBit1'( X ),
% 1.41/1.82 'tc_Int_Oint' ), ~( 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ) ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ 'c_lessequals'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OBit1'( X ),
% 1.41/1.82 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ 'c_lessequals'( 'c_Int_OBit1'( X ), 'c_Int_OPls', 'tc_Int_Oint' ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ), ~(
% 1.41/1.82 'c_lessequals'( 'c_Int_OBit1'( X ), 'c_Int_OPls', 'tc_Int_Oint' ) ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), Y, X ) ) ],
% 1.41/1.82 [ ~( =( 'c_Int_OPls', 'c_Int_OMin' ) ) ],
% 1.41/1.82 [ ~( =( 'c_Int_OMin', 'c_Int_OPls' ) ) ],
% 1.41/1.82 [ ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', 'c_Int_OPls',
% 1.41/1.82 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ 'c_lessequals'( 'c_Int_OPls', 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.41/1.82 [ 'c_lessequals'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint'
% 1.41/1.82 ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.41/1.82 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ 'c_lessequals'( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint'
% 1.41/1.82 ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.41/1.82 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ),
% 1.41/1.82 'tc_Int_Oint' ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ),
% 1.41/1.82 'tc_Int_Oint' ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ), 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.41/1.82 'tc_nat' ) ), Y ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.41/1.82 'tc_nat' ) ), Y ) ],
% 1.41/1.82 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y )
% 1.41/1.82 , 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP(
% 1.41/1.82 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.41/1.82 X ), Y ), Z ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), hAPP(
% 1.41/1.82 'c_HOL_Oabs__class_Oabs'( X ), Y ) ), Z ) ) ],
% 1.41/1.82 [ ~( =( 'c_Int_OMin', 'c_Int_OBit0'( X ) ) ) ],
% 1.41/1.82 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OMin' ) ) ],
% 1.41/1.82 [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint'
% 1.41/1.82 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.41/1.82 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ 'c_lessequals'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint'
% 1.41/1.82 ), ~( 'c_lessequals'( X, Y, 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ 'c_lessequals'( X, Y, 'tc_Int_Oint' ), ~( 'c_lessequals'(
% 1.41/1.82 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ), 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.41/1.82 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.41/1.82 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.41/1.82 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ),
% 1.41/1.82 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ =( X, 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.82 'tc_nat' ), Z ), hAPP( 'c_Suc', X ) ), 'tc_nat' ) ), ~( 'c_lessequals'(
% 1.41/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), Y,
% 1.41/1.82 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.41/1.82 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.41/1.82 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.41/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ),
% 1.41/1.82 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.41/1.82 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.41/1.82 , ~( 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.41/1.82 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ), Y ),
% 1.41/1.82 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.41/1.82 'tc_nat' ) ) ],
% 1.41/1.82 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ), X ),
% 1.41/1.82 ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.41/1.82 'tc_nat' ) ) ],
% 1.41/1.82 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.41/1.82 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.41/1.82 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.82 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z )
% 1.41/1.82 , 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 'tc_nat' ), X, 'tc_nat' ) ],
% 1.41/1.82 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.82 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y )
% 1.41/1.82 , 'tc_nat' ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 'tc_nat' ), Y, 'tc_nat' ) ],
% 1.41/1.82 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.82 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z )
% 1.41/1.82 , 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.41/1.82 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ), 'tc_nat' ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.41/1.82 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.41/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z )
% 1.41/1.82 , X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ),
% 1.41/1.82 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ), ~(
% 1.41/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X )
% 1.41/1.82 , Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ),
% 1.41/1.82 'tc_nat' ) ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' ), ~(
% 1.41/1.82 'c_lessequals'( X, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ 'c_lessequals'( X, 'c_Int_OPls', 'tc_Int_Oint' ), 'c_lessequals'( X, Y
% 1.41/1.82 , 'tc_Int_Oint' ), ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'(
% 1.41/1.82 X, 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.41/1.82 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( X,
% 1.41/1.82 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ), 'tc_nat' )
% 1.41/1.82 , ~( 'c_HOL_Oord__class_Oless'( X, Y, 'tc_Int_Oint' ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', Y, 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', X, 'tc_Int_Oint' ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Y, X, 'tc_Int_Oint' ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.41/1.82 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ), 'tc_nat' )
% 1.41/1.82 ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.41/1.82 , Y ) ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ) ), ~(
% 1.41/1.82 'c_Parity_Oeven__odd__class_Oeven'( 'c_Int_Onumber__class_Onumber__of'( Z
% 1.41/1.82 , 'tc_nat' ), 'tc_nat' ) ) ],
% 1.41/1.82 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_SEQ_OLIMSEQ'(
% 1.41/1.82 'c_COMBS'( 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'( X ), Y, X, 'tc_fun'( X
% 1.41/1.82 , X ), 'tc_nat' ), 'c_COMBB'( 'c_HOL_Ouminus__class_Ouminus'( X ), Z, X,
% 1.41/1.82 X, 'tc_nat' ), 'tc_nat', X, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.82 X ), T ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), U ) ), X ), ~(
% 1.41/1.82 'c_SEQ_OLIMSEQ'( Z, U, X ) ), ~( 'c_SEQ_OLIMSEQ'( Y, T, X ) ) ],
% 1.41/1.82 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ) ), Y, 'tc_nat'
% 1.41/1.82 ), 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', Z ), Y, 'tc_nat' ) ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_Series_Osums'(
% 1.41/1.82 'c_COMBS'( 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'( X ), Y, X, 'tc_fun'( X
% 1.41/1.82 , X ), 'tc_nat' ), Z, 'tc_nat', X, X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~( 'c_Series_Osums'( Z, U
% 1.41/1.82 , X ) ), ~( 'c_Series_Osums'( Y, T, X ) ) ],
% 1.41/1.82 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_SEQ_OLIMSEQ'(
% 1.41/1.82 'c_COMBS'( 'c_COMBB'( 'c_HOL_Ominus__class_Ominus'( X ), Y, X, 'tc_fun'(
% 1.41/1.82 X, X ), 'tc_nat' ), Z, 'tc_nat', X, X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Ominus__class_Ominus'( X ), T ), U ), X ), ~( 'c_SEQ_OLIMSEQ'( Z,
% 1.41/1.82 U, X ) ), ~( 'c_SEQ_OLIMSEQ'( Y, T, X ) ) ],
% 1.41/1.82 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_SEQ_OLIMSEQ'(
% 1.41/1.82 'c_COMBS'( 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'( X ), Y, X, 'tc_fun'( X
% 1.41/1.82 , X ), 'tc_nat' ), Z, 'tc_nat', X, X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~( 'c_SEQ_OLIMSEQ'( Z, U
% 1.41/1.82 , X ) ), ~( 'c_SEQ_OLIMSEQ'( Y, T, X ) ) ],
% 1.41/1.82 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_SEQ_OZseq'(
% 1.41/1.82 'c_COMBS'( 'c_COMBB'( 'c_HOL_Ominus__class_Ominus'( X ), Y, X, 'tc_fun'(
% 1.41/1.82 X, X ), 'tc_nat' ), Z, 'tc_nat', X, X ), X ), ~( 'c_SEQ_OZseq'( Z, X ) )
% 1.41/1.82 , ~( 'c_SEQ_OZseq'( Y, X ) ) ],
% 1.41/1.82 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_Series_Osums'(
% 1.41/1.82 'c_COMBS'( 'c_COMBB'( 'c_HOL_Ominus__class_Ominus'( X ), Y, X, 'tc_fun'(
% 1.41/1.82 X, X ), 'tc_nat' ), Z, 'tc_nat', X, X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Ominus__class_Ominus'( X ), T ), U ), X ), ~( 'c_Series_Osums'( Z
% 1.41/1.82 , U, X ) ), ~( 'c_Series_Osums'( Y, T, X ) ) ],
% 1.41/1.82 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_SEQ_OZseq'(
% 1.41/1.82 'c_COMBS'( 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'( X ), Y, X, 'tc_fun'( X
% 1.41/1.82 , X ), 'tc_nat' ), Z, 'tc_nat', X, X ), X ), ~( 'c_SEQ_OZseq'( Z, X ) ),
% 1.41/1.82 ~( 'c_SEQ_OZseq'( Y, X ) ) ],
% 1.41/1.82 [ ~( 'class_RealVector_Ometric__space'( X ) ), 'c_SEQ_OLIMSEQ'(
% 1.41/1.82 'c_COMBB'( Y, 'c_COMBC'( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z,
% 1.41/1.82 'tc_nat', 'tc_nat', 'tc_nat' ), 'tc_nat', X, 'tc_nat' ), T, X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.41/1.82 'tc_nat' ) ), ~( 'c_SEQ_OLIMSEQ'( Y, T, X ) ) ],
% 1.41/1.82 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.41/1.82 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.41/1.82 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, hAPP( hAPP( Z, hAPP(
% 1.41/1.82 hAPP( 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.41/1.82 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.41/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), Z, V2, V3, V4, T, U, V5
% 1.41/1.82 , W ) ), =( V0, hAPP( hAPP( Z, hAPP( hAPP( 'c_Power_Opower_Opower'( T, U
% 1.41/1.82 , W ), V0 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.41/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower_Opower'( T, U, W ), V1 ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.41/1.82 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, hAPP( hAPP( Z, hAPP(
% 1.41/1.82 hAPP( 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.41/1.82 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.41/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), Z, V2, V3, V4, T, U, V5
% 1.41/1.82 , W ) ), =( V1, hAPP( hAPP( Z, hAPP( hAPP( 'c_Power_Opower_Opower'( T, U
% 1.41/1.82 , W ), V0 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.41/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower_Opower'( T, U, W ), V1 ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.41/1.82 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.41/1.82 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.41/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), ~(
% 1.41/1.82 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, Z, X, V4, V5, T, U, V6, W
% 1.41/1.82 ) ) ],
% 1.41/1.82 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.41/1.82 V3, V4 ) ), hBOOL( hAPP( hAPP( U, hAPP( hAPP( T, hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower_Opower'( V1, V2, V4 ), Z ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( V1
% 1.41/1.82 , V2, V4 ), Z ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.41/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), Z ) ) ],
% 1.41/1.82 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.41/1.82 U ), W ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.41/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), ~(
% 1.41/1.82 'c_Ring__and__Field_Oordered__idom'( V0, V1, Y, V2, X, V3, V4, Z, T, V5,
% 1.41/1.82 U ) ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( Y, T ), T ) ), ~(
% 1.41/1.82 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.41/1.82 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower_Opower'( Z, T, U ), W ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), V0, V1, V2, V3, Z, T, V4, U ) ), =( W,
% 1.41/1.82 hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T, U ), W ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.41/1.82 [ =( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ), U ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( Y
% 1.41/1.82 , Z, T ), U ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.41/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~(
% 1.41/1.82 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, V4, X, Y, Z, V5,
% 1.41/1.82 T ) ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, U ) ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y
% 1.41/1.82 , Z ), U ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.41/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~(
% 1.41/1.82 'c_Ring__and__Field_Oordered__idom'( W, V0, V1, V2, V3, V4, T, X, Y, V5,
% 1.41/1.82 Z ) ) ],
% 1.41/1.82 [ ~( 'c_Ring__and__Field_Oordered__idom'( X, Y, Z, T, U, W, V0, V1, V2,
% 1.41/1.82 V3, V4 ) ), =( hAPP( hAPP( T, hAPP( hAPP( 'c_Power_Opower_Opower'( V1, V2
% 1.41/1.82 , V4 ), Z ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.41/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower_Opower'( V1, V2, V4 ), Z ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), Z ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.41/1.82 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.41/1.82 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.41/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.41/1.82 [ ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T
% 1.41/1.82 ), U ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), W ) ) ), ~(
% 1.41/1.82 'c_Ring__and__Field_Oordered__idom'( V0, V1, W, V2, V3, X, V4, Y, Z, V5,
% 1.41/1.82 T ) ) ],
% 1.41/1.82 [ ~( hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z,
% 1.41/1.82 T, U ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.41/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), ~(
% 1.41/1.82 'c_Ring__and__Field_Oordered__idom'( W, V0, Y, V1, V2, X, V3, Z, T, V4, U
% 1.41/1.82 ) ) ],
% 1.41/1.82 [ ~( hBOOL( hAPP( hAPP( X, hAPP( hAPP( Y, hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower_Opower'( Z, T, U ), W ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z
% 1.41/1.82 , T, U ), V0 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.41/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), V1 ) ) ), ~(
% 1.41/1.82 'c_Ring__and__Field_Oordered__idom'( V2, V3, V1, Y, V4, X, V5, Z, T, V6,
% 1.41/1.82 U ) ) ],
% 1.41/1.82 [ ~( hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower_Opower'( T, U, W ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.41/1.82 , U, W ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.41/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ) ), ~(
% 1.41/1.82 'c_Ring__and__Field_Oordered__idom'( V0, V1, Y, Z, V2, X, V3, T, U, V4, W
% 1.41/1.82 ) ) ],
% 1.41/1.82 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), X ) ],
% 1.41/1.82 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.41/1.82 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.41/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), =( V0, Y ), ~(
% 1.41/1.82 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, Z, V4, X, V5, T, U, V6, W
% 1.41/1.82 ) ) ],
% 1.41/1.82 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower_Opower'( T, U, W ), V0 ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP( 'c_Power_Opower_Opower'( T
% 1.41/1.82 , U, W ), V1 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.41/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ), =( V1, Y ), ~(
% 1.41/1.82 'c_Ring__and__Field_Oordered__idom'( V2, V3, Y, Z, V4, X, V5, T, U, V6, W
% 1.41/1.82 ) ) ],
% 1.41/1.82 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.41/1.82 U ), W ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.41/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), =( W, Y ), ~(
% 1.41/1.82 'c_Ring__and__Field_Oordered__idom'( V0, V1, Y, V2, V3, X, V4, Z, T, V5,
% 1.41/1.82 U ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.82 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.41/1.82 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' )
% 1.41/1.82 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.41/1.82 , Y, 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.82 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.41/1.82 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.41/1.82 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.41/1.82 , X, 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.82 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.41/1.82 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.82 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.41/1.82 ), Z ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y, 'tc_nat' ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( X, Z, 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.82 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.41/1.82 ), Z ), Y ), 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.82 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.41/1.82 ), X ), Z ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' )
% 1.41/1.82 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.41/1.82 , X, 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.41/1.82 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X
% 1.41/1.82 ), 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.41/1.82 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.41/1.82 ), 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.41/1.82 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.41/1.82 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ) ) ],
% 1.41/1.82 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.41/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.41/1.82 'tc_nat' ) ), =( Y, Z ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.41/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat'
% 1.41/1.82 ), ~( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.41/1.82 , Y, 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ],
% 1.41/1.82 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 'tc_nat' ) ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y ), 'tc_nat' ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.41/1.82 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.41/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ) ) ), =( Z, T ), =( Y
% 1.41/1.82 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.41/1.82 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.41/1.82 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), =( X,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.41/1.82 [ ~( =( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.41/1.82 ) ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.41/1.82 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.41/1.82 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.82 hAPP( 'c_Suc', X ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.82 'tc_nat' ), hAPP( 'c_Suc', X ) ), Z ), 'tc_nat' ), ~( 'c_lessequals'( Y,
% 1.41/1.82 Z, 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_lessequals'( X, Y, 'tc_nat' ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), X ), hAPP(
% 1.41/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), Y )
% 1.41/1.82 , 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.82 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Z ),
% 1.41/1.82 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( Y, Z, 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.82 'tc_nat' ), hAPP( 'c_Suc', Z ) ), X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), Y ),
% 1.41/1.82 'tc_nat' ) ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.41/1.82 , X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ),
% 1.41/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.41/1.82 'c_Suc', Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.41/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), ~(
% 1.41/1.82 'class_OrderedGroup_Omonoid__mult'( X ) ), =( 'c_Finite__Set_Osetsum'(
% 1.41/1.82 'c_COMBC'( 'c_COMBB'( 'c_HOL_Ominus__class_Ominus'( X ), 'c_COMBS'(
% 1.41/1.82 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), 'c_COMBB'( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP(
% 1.41/1.82 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ), X
% 1.41/1.82 , 'tc_fun'( X, X ), 'tc_nat' ), hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.41/1.82 , Y ), 'tc_nat', X, X ), X, 'tc_fun'( X, X ), 'tc_nat' ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ), T ), 'tc_nat', X, X ),
% 1.41/1.82 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 'tc_nat' ), T, 'tc_nat' ), 'tc_nat', X ), 'c_Finite__Set_Osetsum'(
% 1.41/1.82 'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ), X, 'tc_fun'( X, X ), 'tc_nat' )
% 1.41/1.82 , 'c_COMBS'( 'c_COMBB'( 'c_HOL_Ominus__class_Ominus'( X ), 'c_COMBB'(
% 1.41/1.82 hAPP( 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP(
% 1.41/1.82 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ), X
% 1.41/1.82 , 'tc_fun'( X, X ), 'tc_nat' ), 'c_COMBB'( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ), hAPP(
% 1.41/1.82 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ),
% 1.41/1.82 'tc_nat', X, X ), 'tc_nat', X, X ),
% 1.41/1.82 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 'tc_nat' ), T, 'tc_nat' ), 'tc_nat', X ) ) ],
% 1.41/1.82 [ =( 'c_SetInterval_Oord__class_OatLeastLessThan'( X,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ),
% 1.41/1.82 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_nat', 'tc_bool' ) ) ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ ~( 'class_RealVector_Ometric__space'( X ) ), 'c_SEQ_OLIMSEQ'( Y, Z, X
% 1.41/1.82 ), ~( 'c_SEQ_OLIMSEQ'( 'c_COMBB'( Y, 'c_Suc', 'tc_nat', X, 'tc_nat' ), Z
% 1.41/1.82 , X ) ) ],
% 1.41/1.82 [ ~( 'class_RealVector_Ometric__space'( X ) ), 'c_SEQ_OLIMSEQ'(
% 1.41/1.82 'c_COMBB'( Y, 'c_Suc', 'tc_nat', X, 'tc_nat' ), Z, X ), ~(
% 1.41/1.82 'c_SEQ_OLIMSEQ'( Y, Z, X ) ) ],
% 1.41/1.82 [ =( 'c_Set_Oimage'( 'c_Suc',
% 1.41/1.82 'c_SetInterval_Oord__class_OatLeastLessThan'( X, Y, 'tc_nat' ), 'tc_nat'
% 1.41/1.82 , 'tc_nat' ), 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( 'c_Suc'
% 1.41/1.82 , X ), hAPP( 'c_Suc', Y ), 'tc_nat' ) ) ],
% 1.41/1.82 [ =( 'c_SetInterval_Oord__class_OatLeastLessThan'( X, hAPP( 'c_Suc', Y )
% 1.41/1.82 , 'tc_nat' ), 'c_SetInterval_Oord__class_OatLeastAtMost'( X, Y, 'tc_nat'
% 1.41/1.82 ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.41/1.82 'v_m', 'tc_nat' ) ],
% 1.41/1.82 [ 'c_lessequals'( 'v_m', 'v_i', 'tc_nat' ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), X ) ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), X ) ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.82 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.41/1.82 ), Y ), Y ) ) ],
% 1.41/1.82 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.41/1.82 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.41/1.82 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.41/1.82 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.41/1.82 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.41/1.82 ), 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.41/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), =(
% 1.41/1.82 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.41/1.82 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.41/1.82 ), 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), =(
% 1.41/1.82 'c_Divides_Odiv__class_Omod'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.41/1.82 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.41/1.82 ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), U ) ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.41/1.82 X, Y, Z ), T ), U ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.41/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~(
% 1.41/1.82 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.41/1.82 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_Power_Opower_Opower'( Z, T,
% 1.41/1.82 U ), W ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), V0 ) ) ) ), ~(
% 1.41/1.82 'c_Ring__and__Field_Oordered__idom'( V1, V2, Y, V3, X, V4, V5, Z, T, V6,
% 1.41/1.82 U ) ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, U ) ),
% 1.41/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), W ) ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower_Opower'( X, Y, Z ), U ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), W ) ) ), ~(
% 1.41/1.82 'c_Ring__and__Field_Ocomm__ring__1'( X, Y, V0, T, V1, V2, Z ) ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, X ) ),
% 1.41/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), U ) ), X ), ~(
% 1.41/1.82 'c_Ring__and__Field_Ocomm__ring__1'( X, Y, W, T, V0, V1, Z ) ) ],
% 1.41/1.82 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), ~(
% 1.41/1.82 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBB'( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), T, X, X, Y ), U,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_Lim_OLIM'( T, U,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.82 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), ~(
% 1.41/1.82 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBB'( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ), T, X, X, Y ), U,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_Lim_OLIM'( T, U,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X ), hAPP(
% 1.41/1.82 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y ), =(
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.82 ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), =( Y, hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =(
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.82 ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.41/1.82 X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), =(
% 1.41/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z ), =( T,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.41/1.82 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =(
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.41/1.82 , X ) ), Z ) ), Z ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y,
% 1.41/1.82 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.41/1.82 , X ) ), Z ) ), Z ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'( Y, X )
% 1.41/1.82 , hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.41/1.82 , X ) ), Z ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), =( Y, hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =(
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.82 ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.82 X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y ), =(
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.82 ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.41/1.82 , X ) ), Z ) ), Z ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), =( Z,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), ~( =( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ) ), =( Y, hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( T
% 1.41/1.82 , X ) ), Z ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ) ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.82 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.82 X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.41/1.82 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), ~(
% 1.41/1.82 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBS'(
% 1.41/1.82 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Z, X, 'tc_fun'( X, X ), Y )
% 1.41/1.82 , T, Y, X, X ), U, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), W ), V0
% 1.41/1.82 ), Y, X ), ~( 'c_Lim_OLIM'( T, U, V0, Y, X ) ), ~( 'c_Lim_OLIM'( Z, U, W
% 1.41/1.82 , Y, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.41/1.82 ), X ) ), 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 'tc_nat' ) ), X ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.41/1.82 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.41/1.82 ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( 'c_lessequals'(
% 1.41/1.82 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.41/1.82 , X ) ) ],
% 1.41/1.82 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_Finite__Set_Osetsum'( Y, Z, T, X )
% 1.41/1.82 ), U ), 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBB'(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'( X, X ), T ), U, T, X,
% 1.41/1.82 X ), Z, T, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_Finite__Set_Osetsum'( Y, Z, T, X )
% 1.41/1.82 ), U ), 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBB'(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'( X, X ), T ), U, T, X,
% 1.41/1.82 X ), Z, T, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.41/1.82 hAPP( 'c_Power_Opower__class_Opower'( X ), T ), hAPP( 'c_Suc', Z ) ) ) )
% 1.41/1.82 , =( Y, T ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) )
% 1.41/1.82 , ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.41/1.82 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.41/1.82 ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.41/1.82 hAPP( 'c_Suc', T ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Z
% 1.41/1.82 ), hAPP( 'c_Suc', T ) ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.41/1.82 ), Y ), 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_lessequals'( Y,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Oone__class_Oone'( X )
% 1.41/1.82 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X )
% 1.41/1.82 ) ],
% 1.41/1.82 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ),
% 1.41/1.82 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ) )
% 1.41/1.82 , Y ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ) )
% 1.41/1.82 , Y ) ],
% 1.41/1.82 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.41/1.82 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.82 X ), Y, X, 'tc_fun'( X, X ), Z ), T, Z, X, X ), U, Z, X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'( Y, U, Z, X ) )
% 1.41/1.82 , 'c_Finite__Set_Osetsum'( T, U, Z, X ) ) ) ],
% 1.41/1.82 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.41/1.82 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'(
% 1.41/1.82 'c_HOL_Ominus__class_Ominus'( X ), Y, X, 'tc_fun'( X, X ), Z ), T, Z, X,
% 1.41/1.82 X ), U, Z, X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ),
% 1.41/1.82 'c_Finite__Set_Osetsum'( Y, U, Z, X ) ), 'c_Finite__Set_Osetsum'( T, U, Z
% 1.41/1.82 , X ) ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.41/1.82 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.41/1.82 ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.82 X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ), =( Z, 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.41/1.82 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.41/1.82 ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) )
% 1.41/1.82 ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Y, Z, X ), ~( 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.41/1.82 [ ~( =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), =( Y,
% 1.41/1.82 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ),
% 1.41/1.82 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ), ~(
% 1.41/1.82 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.41/1.82 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ),
% 1.41/1.82 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.41/1.82 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.41/1.82 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.41/1.82 , Z ) ],
% 1.41/1.82 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.41/1.82 , Z ) ],
% 1.41/1.82 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.41/1.82 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), ~(
% 1.41/1.82 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.41/1.82 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.41/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.41/1.82 'c_Groebner__Basis_Ogb__semiring'( U, W, X, V0, V1, V2 ) ) ],
% 1.41/1.82 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.41/1.82 ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), X ) )
% 1.41/1.82 , 'tc_nat' ) ],
% 1.41/1.82 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.82 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T )
% 1.41/1.82 , 'tc_nat' ), ~( 'c_lessequals'( Y, T, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 1.41/1.82 , Z, 'tc_nat' ) ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.41/1.82 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.41/1.82 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.82 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y )
% 1.41/1.82 , 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.82 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z )
% 1.41/1.82 , 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.82 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z )
% 1.41/1.82 , 'tc_nat' ), ~( 'c_lessequals'( Y, Z, 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.82 X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y )
% 1.41/1.82 , 'tc_nat' ), ~( 'c_lessequals'( X, Z, 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.82 'tc_nat' ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.41/1.82 ), Z ), Y ), 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( X, Y, 'tc_nat' ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.82 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.41/1.82 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.41/1.82 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Oone__class_Oone'(
% 1.41/1.82 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.82 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ), X ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.41/1.82 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), X ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.41/1.82 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.41/1.82 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( X, 'c_HOL_Oone__class_Oone'(
% 1.41/1.82 'tc_nat' ) ) ],
% 1.41/1.82 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.41/1.82 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ), =( Y, 'c_HOL_Oone__class_Oone'(
% 1.41/1.82 'tc_nat' ) ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ), T ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), T ) ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.41/1.82 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.41/1.82 [ 'c_lessequals'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.41/1.82 ), X ), X ), 'tc_nat' ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.82 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'(
% 1.41/1.82 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.82 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Z ),
% 1.41/1.82 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.82 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.41/1.82 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.41/1.82 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ),
% 1.41/1.82 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.82 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.41/1.82 ), X ), Z ), 'tc_nat' ) ) ],
% 1.41/1.82 [ =( 'c_SetInterval_Oord__class_OatLeastLessThan'( X, hAPP( 'c_Suc', Y )
% 1.41/1.82 , 'tc_nat' ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_nat',
% 1.41/1.82 'tc_bool' ) ) ), 'c_lessequals'( X, Y, 'tc_nat' ) ],
% 1.41/1.82 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.41/1.82 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastAtMost'( Z
% 1.41/1.82 , hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( X ), hAPP( Y, Z ) ), 'c_Finite__Set_Osetsum'(
% 1.41/1.82 'c_COMBB'( Y, 'c_Suc', 'tc_nat', X, 'tc_nat' ),
% 1.41/1.82 'c_SetInterval_Oord__class_OatLeastAtMost'( Z, T, 'tc_nat' ), 'tc_nat', X
% 1.41/1.82 ) ) ), 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', T ), Z, 'tc_nat' ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_Series_Osums'(
% 1.41/1.82 'c_COMBB'( Y, 'c_COMBC'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z,
% 1.41/1.82 'tc_nat', 'tc_nat', 'tc_nat' ), 'tc_nat', X, 'tc_nat' ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Ominus__class_Ominus'( X ), T ), 'c_Finite__Set_Osetsum'( Y,
% 1.41/1.82 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ) ), X ), ~( 'c_Series_Osums'( Y,
% 1.41/1.82 T, X ) ) ],
% 1.41/1.82 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'( Y,
% 1.41/1.82 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ), 'tc_nat'
% 1.41/1.82 , X ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.41/1.82 'c_SetInterval_Oord__class_OatLeastLessThan'( T, U, 'tc_nat' ), 'tc_nat'
% 1.41/1.82 , X ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.41/1.82 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, U, 'tc_nat' ), 'tc_nat'
% 1.41/1.82 , X ) ), ~( 'c_lessequals'( T, U, 'tc_nat' ) ), ~( 'c_lessequals'( Z, T,
% 1.41/1.82 'tc_nat' ) ) ],
% 1.41/1.82 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Ominus__class_Ominus'( X ), 'c_Finite__Set_Osetsum'( Y,
% 1.41/1.82 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ), 'tc_nat'
% 1.41/1.82 , X ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.41/1.82 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, U, 'tc_nat' ), 'tc_nat'
% 1.41/1.82 , X ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.41/1.82 'c_SetInterval_Oord__class_OatLeastLessThan'( U, T, 'tc_nat' ), 'tc_nat'
% 1.41/1.82 , X ) ), ~( 'c_lessequals'( U, T, 'tc_nat' ) ), ~( 'c_lessequals'( Z, U,
% 1.41/1.82 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.41/1.82 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.82 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat' ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.41/1.82 'tc_nat' ) ) ],
% 1.41/1.82 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_HOL_Oone__class_Oone'(
% 1.41/1.82 'tc_nat' ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.41/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.41/1.82 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.41/1.82 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.41/1.82 ), 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.41/1.82 [ ~( =( 'c_FFT__Mirabelle_Oroot'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 'tc_Complex_Ocomplex' ) ) ) ],
% 1.41/1.82 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.41/1.82 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( Z, T, U, Y, X ),
% 1.41/1.82 ~( 'c_Lim_OLIM'( W, T, U, Y, X ) ), ~( 'c_Lim_OLIM'( 'c_COMBS'( 'c_COMBB'(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( X ), Z, X, 'tc_fun'( X, X ), Y ), 'c_COMBB'(
% 1.41/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), W, X, X, Y ), Y, X, X ), T,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( 'c_Finite__Set_Osetsum'(
% 1.41/1.82 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.41/1.82 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), 'c_HOL_Oone__class_Oone'(
% 1.41/1.82 X ) ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ),
% 1.41/1.82 'c_HOL_Oone__class_Oone'( X ) ) ) ), =( Y, 'c_HOL_Oone__class_Oone'( X )
% 1.41/1.82 ) ],
% 1.41/1.82 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.41/1.82 'c_Finite__Set_Osetsum'( 'c_COMBB'( Y, 'c_COMBC'(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z, 'tc_nat', 'tc_nat', 'tc_nat' )
% 1.41/1.82 , 'tc_nat', X, 'tc_nat' ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), T, 'tc_nat' ), 'tc_nat', X ),
% 1.41/1.82 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), 'c_Finite__Set_Osetsum'( Y
% 1.41/1.82 , 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), Z ), 'tc_nat' ), 'tc_nat', X
% 1.41/1.82 ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.41/1.82 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ) ) ) ],
% 1.41/1.82 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.41/1.82 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ), 'tc_nat' ), 'tc_nat', X
% 1.41/1.82 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'(
% 1.41/1.82 'c_COMBB'( Y, 'c_COMBC'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T,
% 1.41/1.82 'tc_nat', 'tc_nat', 'tc_nat' ), 'tc_nat', X, 'tc_nat' ),
% 1.41/1.82 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ) ), 'c_Finite__Set_Osetsum'( Y,
% 1.41/1.82 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 'tc_nat' ), T, 'tc_nat' ), 'tc_nat', X ) ) ) ],
% 1.41/1.82 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), ~(
% 1.41/1.82 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBC'(
% 1.41/1.82 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Z, X, 'tc_fun'( X, X ), Y )
% 1.41/1.82 , T, Y, X, X ), U, 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.41/1.82 'c_Lim_OLIM'( Z, U, 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.82 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), ~(
% 1.41/1.82 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBC'(
% 1.41/1.82 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Z, X, 'tc_fun'( X, X ), Y )
% 1.41/1.82 , T, Y, X, X ), U, 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.41/1.82 'c_Lim_OLIM'( Z, U, 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), 'c_lessequals'( Y, hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~( 'c_lessequals'( Y,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~( 'c_lessequals'(
% 1.41/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~( 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~( 'c_lessequals'(
% 1.41/1.82 Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), 'c_lessequals'(
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~( 'c_lessequals'(
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.82 ), X ) ), ~( 'c_lessequals'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.82 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.41/1.82 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.41/1.82 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.41/1.82 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( T, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.41/1.82 ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.41/1.82 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'( T,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.41/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.41/1.82 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'( T,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.41/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.41/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.41/1.82 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.41/1.82 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.41/1.82 ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.41/1.82 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.41/1.82 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.41/1.82 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.41/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.41/1.82 ), X ), ~( 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Z, X
% 1.41/1.82 ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), T ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.41/1.82 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Z
% 1.41/1.82 , X ) ), T ), X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ), X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.41/1.82 , 'c_Int_Onumber__class_Onumber__of'( Y, X ) ), T ), Z, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.41/1.82 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), 'c_lessequals'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~( 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( T, X
% 1.41/1.82 ), X ) ), ~( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.41/1.82 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.41/1.82 'c_lessequals'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.41/1.82 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.41/1.82 , X ) ), Z ), T, X ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Z, X ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Z, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.41/1.82 ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.41/1.82 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.41/1.82 , T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.41/1.82 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ), X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Z, 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.41/1.82 , 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), Y, X ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.41/1.82 ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.41/1.82 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), T, X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.41/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( T, X ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'( Z,
% 1.41/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.41/1.82 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_Int_Onumber__class_Onumber__of'( Z, X ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), Y, X ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.41/1.82 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Z ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.41/1.82 , Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.41/1.82 X ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oinverse__class_Odivide'( X ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), T, X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Z, X ), X ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.41/1.82 ), T ), 'c_Int_Onumber__class_Onumber__of'( Z, X ) ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.41/1.82 'class_Ring__and__Field_Odivision__by__zero'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber'( X ) ), 'c_HOL_Oord__class_Oless'( Y, hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), Z ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ) ), X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( T, X ), X ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.41/1.82 ), Y ), 'c_Int_Onumber__class_Onumber__of'( T, X ) ), Z, X ) ) ],
% 1.41/1.82 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~(
% 1.41/1.82 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBS'(
% 1.41/1.82 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'( X ), Z, X, 'tc_fun'( X, X ), Y ),
% 1.41/1.82 T, Y, X, X ), U, 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_Lim_OLIM'(
% 1.41/1.82 T, U, 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~( 'c_Lim_OLIM'( Z, U,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.41/1.82 , Y ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP(
% 1.41/1.82 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ ~( 'class_OrderedGroup_Opordered__ab__group__add__abs'( X ) ),
% 1.41/1.82 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), 'c_Finite__Set_Osetsum'(
% 1.41/1.82 'c_COMBB'( 'c_HOL_Oabs__class_Oabs'( X ), Y, X, X, Z ), T, Z, X ), X ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.82 ), X ), ~( 'c_HOL_Oord__class_Oless'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) )
% 1.41/1.82 ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( Y,
% 1.41/1.82 'c_Int_OPls', 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.82 ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'(
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.82 ), X ), ~( 'c_lessequals'( Y, 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( Y, 'c_Int_OPls',
% 1.41/1.82 'tc_Int_Oint' ), ~( 'c_lessequals'( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.41/1.82 , X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.41/1.82 ), X ), ~( 'c_HOL_Oord__class_Oless'( 'c_Int_OPls', Y, 'tc_Int_Oint' ) )
% 1.41/1.82 ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber__ring'( X ) ), 'c_HOL_Oord__class_Oless'( 'c_Int_OPls'
% 1.41/1.82 , Y, 'tc_Int_Oint' ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.41/1.82 ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), 'c_Int_Onumber__class_Onumber__of'( Y, X
% 1.41/1.82 ), X ), ~( 'c_lessequals'( 'c_Int_OPls', Y, 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.41/1.82 'class_Int_Onumber__ring'( X ) ), 'c_lessequals'( 'c_Int_OPls', Y,
% 1.41/1.82 'tc_Int_Oint' ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.41/1.82 ), X ) ), ~( 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.41/1.82 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_lessequals'( Y,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), X ) ),
% 1.41/1.82 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.41/1.82 'c_Parity_Oeven__odd__class_Oeven'( Z, 'tc_nat' ), =( Z,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.41/1.82 'c_Parity_Oeven__odd__class_Oeven'( Y, 'tc_nat' ) ), =( Y,
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_lessequals'( hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.41/1.82 ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ), =( Y, T ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z,
% 1.41/1.82 'tc_nat' ) ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), T, X )
% 1.41/1.82 ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.82 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.82 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( Y ), X ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ),
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.41/1.82 ), Y ), hAPP( 'c_Suc', Z ) ), 'c_HOL_Oone__class_Oone'( X ), X ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Y, 'c_HOL_Oone__class_Oone'( X ), X ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( X ), X ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ), Y
% 1.41/1.82 ), Z ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.41/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.41/1.82 [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), ~( 'c_lessequals'( X
% 1.41/1.82 , 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ) ), 'c_lessequals'( X
% 1.41/1.82 , 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.41/1.82 [ =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_lessequals'( X,
% 1.41/1.82 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.41/1.82 [ ~( =( 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_lessequals'( X,
% 1.41/1.82 'c_Int_OPls', 'tc_Int_Oint' ) ],
% 1.41/1.82 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_SEQ_OZseq'(
% 1.41/1.82 'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'(
% 1.41/1.82 X, X ), 'tc_nat' ), Z, 'tc_nat', X, X ), X ), ~( 'c_SEQ_OZseq'( Z, X ) )
% 1.41/1.82 , ~( 'c_SEQ_OZseq'( Y, X ) ) ],
% 1.41/1.82 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_SEQ_OLIMSEQ'(
% 1.41/1.82 'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'(
% 1.41/1.82 X, X ), 'tc_nat' ), Z, 'tc_nat', X, X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_SEQ_OLIMSEQ'( Z,
% 1.41/1.82 U, X ) ), ~( 'c_SEQ_OLIMSEQ'( Y, T, X ) ) ],
% 1.41/1.82 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ) ), 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ), 'tc_nat' ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.41/1.82 Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc',
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.41/1.82 ), X, 'tc_nat' ), ~( 'c_lessequals'( hAPP( 'c_Suc',
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.41/1.82 ), X, 'tc_nat' ), ~( 'c_lessequals'( hAPP( 'c_Suc',
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.82 'tc_nat' ), X ), Y ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.41/1.82 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_HOL_Oord__class_Oless'( X, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.82 'tc_nat' ), Y ), X ), 'tc_nat' ), ~( 'c_HOL_Oord__class_Oless'( hAPP(
% 1.41/1.82 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y, 'tc_nat' ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.41/1.82 [ 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' )
% 1.41/1.82 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.41/1.82 'tc_nat' ), ~( 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 'tc_nat' ) ), Y, 'tc_nat' ) ), ~( 'c_lessequals'( hAPP( 'c_Suc',
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X, 'tc_nat' ) ) ],
% 1.41/1.82 [ =( 'c_HOL_Oone__class_Oone'( 'tc_nat' ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.41/1.82 'tc_nat' ) ) ],
% 1.41/1.82 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.41/1.82 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( T, X ) ),
% 1.41/1.82 hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), U ) ) ), hAPP( T, X ) ), ~(
% 1.41/1.82 'c_Ring__and__Field_Ocomm__ring__1'( X, Y, W, T, V0, V1, Z ) ) ],
% 1.41/1.82 [ =( hAPP( hAPP( 'c_Power_Opower_Opower'( X, Y, Z ), T ), hAPP( 'c_Suc'
% 1.41/1.82 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), U ) ) ), hAPP( hAPP( Y, T ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower_Opower'( X, Y, Z ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.41/1.82 X, Y, Z ), T ), U ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.41/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), ~(
% 1.41/1.82 'c_OrderedGroup_Omonoid__mult'( X, Y, Z ) ) ],
% 1.41/1.82 [ hBOOL( hAPP( hAPP( X, hAPP( hAPP( 'c_Power_Opower_Opower'( Y, Z, T ),
% 1.41/1.82 U ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.41/1.82 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), W ) ) ) ), V0 ) ), ~( hBOOL( hAPP( hAPP(
% 1.41/1.82 X, U ), V0 ) ) ), ~( 'c_Ring__and__Field_Oordered__idom'( V1, V2, V0, V3
% 1.41/1.82 , V4, X, V5, Y, Z, V6, T ) ) ],
% 1.41/1.82 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( X, Y ), hAPP(
% 1.41/1.82 hAPP( 'c_Power_Opower_Opower'( T, U, W ), Z ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), V0 ) ) ) ) ) ), ~(
% 1.41/1.82 'c_Ring__and__Field_Oordered__idom'( V1, V2, Y, V3, X, V4, V5, T, U, V6,
% 1.41/1.82 W ) ) ],
% 1.41/1.82 [ =( X, hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.82 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.41/1.82 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ),
% 1.41/1.82 'c_Parity_Osko__Parity__Xodd__Suc__mult__two__ex__1__1'( X ) ) ) ),
% 1.41/1.82 'c_Parity_Oeven__odd__class_Oeven'( X, 'tc_nat' ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.41/1.82 X ), 'c_HOL_Oone__class_Oone'( X ) ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ), 'c_HOL_Oone__class_Oone'( X ) ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ =( 'c_Finite__Set_Osetsum'( hAPP( 'c_Power_Opower__class_Opower'(
% 1.41/1.82 'tc_Complex_Ocomplex' ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.41/1.82 'tc_Complex_Ocomplex' ), 'c_FFT__Mirabelle_Oroot'( X ) ), Y ) ),
% 1.41/1.82 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 'tc_nat' ), X, 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex' ),
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_Complex_Ocomplex' ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( Y, X, 'tc_nat' ) ), ~(
% 1.41/1.82 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Y,
% 1.41/1.82 'tc_nat' ) ) ],
% 1.41/1.82 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.41/1.82 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastAtMost'(
% 1.41/1.82 hAPP( 'c_Suc', Z ), hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ),
% 1.41/1.82 'c_Finite__Set_Osetsum'( 'c_COMBB'( Y, 'c_Suc', 'tc_nat', X, 'tc_nat' ),
% 1.41/1.82 'c_SetInterval_Oord__class_OatLeastAtMost'( Z, T, 'tc_nat' ), 'tc_nat', X
% 1.41/1.82 ) ) ],
% 1.41/1.82 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Set_Oimage'( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ),
% 1.41/1.82 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 'tc_nat' ), X, 'tc_nat' ), 'tc_nat', 'tc_nat' ), 'c_Set_Oimage'(
% 1.41/1.82 'c_COMBB'( 'c_Suc', hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_nat', 'tc_nat' ),
% 1.41/1.82 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 'tc_nat' ), X, 'tc_nat' ), 'tc_nat', 'tc_nat' ), 'tc_fun'( 'tc_nat',
% 1.41/1.82 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( 'tc_nat',
% 1.41/1.82 'tc_bool' ) ) ) ],
% 1.41/1.82 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.41/1.82 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.41/1.82 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ) ), Z ) ) ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP( 'c_Power_Opower_Opower'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), X ),
% 1.41/1.82 hAPP( hAPP( 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.82 'c_HOL_Oplus__class_Oplus'( X ), X ), Y ), Z ) ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.41/1.82 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.41/1.82 'c_Int_OMin', X ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.41/1.82 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ), 'c_HOL_Oone__class_Oone'( X ) ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ =( hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' )
% 1.41/1.82 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), 'c_HOL_Oone__class_Oone'( 'tc_nat'
% 1.41/1.82 ) ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.82 'tc_nat' ) ) ],
% 1.41/1.82 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.82 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.41/1.82 X ), 'c_HOL_Oone__class_Oone'( X ) ) ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.41/1.82 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.82 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ) ), hAPP(
% 1.41/1.82 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ]
% 1.41/1.82 ,
% 1.41/1.82 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.41/1.82 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.41/1.82 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.41/1.82 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.41/1.83 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ), 'tc_nat' ), 'tc_nat', X )
% 1.41/1.83 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.83 X ), hAPP( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( Y,
% 1.41/1.83 'c_HOL_Oone__class_Oone'( 'tc_nat' ) ) ) ), hAPP( Y,
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( Y,
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.41/1.83 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), ~(
% 1.41/1.83 'class_RealVector_Ometric__space'( Y ) ), 'c_Lim_OLIM'( 'c_COMBS'(
% 1.41/1.83 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Z, X, 'tc_fun'( X, X ), Y )
% 1.41/1.83 , T, Y, X, X ), U, 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~(
% 1.41/1.83 'c_Lim_OLIM'( T, U, 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ), ~(
% 1.41/1.83 'c_Lim_OLIM'( Z, U, 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.41/1.83 'class_Power_Opower'( X ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y
% 1.41/1.83 , 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.41/1.83 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =(
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Oord__class_Oless'(
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =(
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), X ) ),
% 1.41/1.83 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( X ), X ) ],
% 1.41/1.83 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), ~( =( hAPP( Y,
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.41/1.83 ) ), 'c_Series_Osums'( Y, Z, X ), ~( 'c_Series_Osums'( 'c_COMBB'( Y,
% 1.41/1.83 'c_Suc', 'tc_nat', X, 'tc_nat' ), Z, X ) ) ],
% 1.41/1.83 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ) ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.41/1.83 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, Y ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( T
% 1.41/1.83 , X, Z, U, W, V0 ) ) ],
% 1.41/1.83 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ), Z ) ),
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.41/1.83 , 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.41/1.83 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( X, 'tc_nat' ) ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'( X
% 1.41/1.83 , 'c_Int_OPls', 'tc_Int_Oint' ) ) ],
% 1.41/1.83 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.41/1.83 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.41/1.83 Z, hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ),
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_HOL_Oord__class_Oless'( T, Z,
% 1.41/1.83 'tc_nat' ) ) ],
% 1.41/1.83 [ =( 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( 'tc_Complex_Ocomplex' ), 'c_COMBB'( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.41/1.83 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.83 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.41/1.83 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_m' ) ) ), hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'v_i' ), 'tc_nat',
% 1.41/1.83 'tc_Complex_Ocomplex', 'tc_nat' ), 'tc_Complex_Ocomplex', 'tc_fun'(
% 1.41/1.83 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ), 'tc_nat' ), 'v_a',
% 1.41/1.83 'tc_nat', 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ),
% 1.41/1.83 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.83 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_m' ), 'tc_nat' ), 'tc_nat',
% 1.41/1.83 'tc_Complex_Ocomplex' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.83 'tc_Complex_Ocomplex' ), 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( 'tc_Complex_Ocomplex' ), 'c_COMBB'( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.41/1.83 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.83 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.41/1.83 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_m' ) ) ), 'c_COMBB'(
% 1.41/1.83 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'v_i' ), hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_nat', 'tc_nat' ), 'tc_nat'
% 1.41/1.83 , 'tc_Complex_Ocomplex', 'tc_nat' ), 'tc_Complex_Ocomplex', 'tc_fun'(
% 1.41/1.83 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ), 'tc_nat' ), 'c_COMBB'(
% 1.41/1.83 'v_a', hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat'
% 1.41/1.83 ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ),
% 1.41/1.83 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.83 'tc_nat' ), 'v_m', 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex' ) ),
% 1.41/1.83 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( 'tc_Complex_Ocomplex' ), 'c_COMBB'( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.41/1.83 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.83 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.41/1.83 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_m' ) ) ), 'c_COMBB'(
% 1.41/1.83 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'v_i' ), 'c_COMBC'(
% 1.41/1.83 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_nat' )
% 1.41/1.83 , 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat', 'tc_nat',
% 1.41/1.83 'tc_nat' ), 'tc_nat', 'tc_nat', 'tc_nat' ), 'tc_nat',
% 1.41/1.83 'tc_Complex_Ocomplex', 'tc_nat' ), 'tc_Complex_Ocomplex', 'tc_fun'(
% 1.41/1.83 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ), 'tc_nat' ), 'c_COMBB'(
% 1.41/1.83 'v_a', 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_nat' )
% 1.41/1.83 , 'tc_nat' ), 'c_HOL_Oone__class_Oone'( 'tc_nat' ), 'tc_nat', 'tc_nat',
% 1.41/1.83 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ), 'tc_nat',
% 1.41/1.83 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ),
% 1.41/1.83 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.83 'tc_nat' ), 'v_m', 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex' ) ) ) ]
% 1.41/1.83 ,
% 1.41/1.83 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' )
% 1.41/1.83 , 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.83 'tc_nat' ), X ), Y ) ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.83 'tc_nat' ), X ), Z ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.41/1.83 'tc_Complex_Ocomplex' ), 'c_FFT__Mirabelle_Oroot'( Y ) ), Z ) ), ~(
% 1.41/1.83 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X,
% 1.41/1.83 'tc_nat' ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), ~(
% 1.41/1.83 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ), hAPP(
% 1.41/1.83 hAPP( 'c_Power_Opower__class_Opower'( X ), T ), hAPP( 'c_Suc', Z ) ) ),
% 1.41/1.83 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), 'c_Finite__Set_Osetsum'(
% 1.41/1.83 'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ), X, 'tc_fun'( X, X ), 'tc_nat' )
% 1.41/1.83 , 'c_COMBB'( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), hAPP(
% 1.41/1.83 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), 'tc_nat', X, 'tc_nat' ),
% 1.41/1.83 'tc_nat', X, X ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', Z ), 'tc_nat' ),
% 1.41/1.83 'tc_nat', X ) ) ) ],
% 1.41/1.83 [ =( 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'tc_nat' ),
% 1.41/1.83 'c_Lattices_Oupper__semilattice__class_Osup'( 'c_Set_Oimage'( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ),
% 1.41/1.83 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.83 'tc_nat' ), X, 'tc_nat' ), 'tc_nat', 'tc_nat' ), 'c_Set_Oimage'(
% 1.41/1.83 'c_COMBB'( 'c_Suc', hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_nat', 'tc_nat' ),
% 1.41/1.83 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.83 'tc_nat' ), X, 'tc_nat' ), 'tc_nat', 'tc_nat' ), 'tc_fun'( 'tc_nat',
% 1.41/1.83 'tc_bool' ) ) ) ],
% 1.41/1.83 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y )
% 1.41/1.83 , Y ) ) ],
% 1.41/1.83 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.41/1.83 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ],
% 1.41/1.83 [ 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ],
% 1.41/1.83 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X
% 1.41/1.83 , 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.41/1.83 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ) ) ]
% 1.41/1.83 ,
% 1.41/1.83 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( 'c_Suc', hAPP( 'c_Suc', X ) )
% 1.41/1.83 ) ],
% 1.41/1.83 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( 'c_Suc', hAPP( 'c_Suc', X ) ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc',
% 1.41/1.83 'c_Divides_Odiv__class_Odiv'( X, 'c_Int_Onumber__class_Onumber__of'(
% 1.41/1.83 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) )
% 1.41/1.83 ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP(
% 1.41/1.83 'c_HOL_Oabs__class_Oabs'( X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.41/1.83 X ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.41/1.83 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.41/1.83 X ), Y ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.41/1.83 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Oabs__class_Oabs'( X )
% 1.41/1.83 , Y ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.41/1.83 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), X ) ) ],
% 1.41/1.83 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.41/1.83 'tc_nat' ), X ), X ) ) ],
% 1.41/1.83 [ 'c_Parity_Oeven__odd__class_Oeven'( hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), 'tc_nat' ) ],
% 1.41/1.83 [ 'c_Fun_Oinj__on'( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), X, 'tc_nat', 'tc_nat' ) ],
% 1.41/1.83 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.83 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.41/1.83 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP( T, hAPP(
% 1.41/1.83 hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ), ~(
% 1.41/1.83 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.41/1.83 [ =( 'c_FFT__Mirabelle_Oroot'( 'c_Int_Onumber__class_Onumber__of'(
% 1.41/1.83 'c_Int_OBit0'( 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat'
% 1.41/1.83 ) ), 'c_Complex_Oii' ) ],
% 1.41/1.83 [ ~( 'class_RealVector_Oreal__normed__algebra__1'( X ) ), =(
% 1.41/1.83 'c_Series_Osuminf'( 'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X
% 1.41/1.83 ), Y, X, 'tc_fun'( X, X ), 'tc_nat' ), hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.41/1.83 'tc_nat', X, X ), X ), hAPP( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.41/1.83 ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.41/1.83 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), X ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.83 ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), =( Y, Z ), ~( 'c_lessequals'(
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ), ~( 'c_lessequals'(
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( X ), Y, X ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.41/1.83 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.41/1.83 =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.41/1.83 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.41/1.83 =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), 'c_lessequals'(
% 1.41/1.83 Y, Z, X ), ~( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), Z, X ) ),
% 1.41/1.83 ~( 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.41/1.83 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~(
% 1.41/1.83 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.41/1.83 ), Y ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ]
% 1.41/1.83 ,
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.41/1.83 ,
% 1.41/1.83 [ =( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X
% 1.41/1.83 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( 'c_HOL_Oord__class_Oless'(
% 1.41/1.83 X, 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ), 'tc_nat' ) ) ],
% 1.41/1.83 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP( T, Y ), hAPP( hAPP(
% 1.41/1.83 T, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, Y ), Z ) ) ) ), ~(
% 1.41/1.83 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W, V0, V1 ) ) ],
% 1.41/1.83 [ ~( 'c_Parity_Oeven__odd__class_Oeven'( hAPP( 'c_Suc', hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), 'tc_nat' ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Ocomm__ring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.41/1.83 X ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ) ],
% 1.41/1.83 [ =( 'c_FFT__Mirabelle_OIDFT'( X, Y, 'v_i' ), 'c_Finite__Set_Osetsum'(
% 1.41/1.83 'c_COMBS'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'(
% 1.41/1.83 'tc_Complex_Ocomplex' ), Y, 'tc_Complex_Ocomplex', 'tc_fun'(
% 1.41/1.83 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ), 'tc_nat' ), 'c_COMBB'(
% 1.41/1.83 hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.41/1.83 'c_FFT__Mirabelle_Oroot'( X ) ), hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.83 'tc_nat' ), 'v_i' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ),
% 1.41/1.83 'tc_nat', 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ),
% 1.41/1.83 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.83 'tc_nat' ), X, 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex' ) ) ],
% 1.41/1.83 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.41/1.83 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ) ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.41/1.83 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), X ) ), Y ) ), Z ) ) ) ]
% 1.41/1.83 ,
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_lessequals'( hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.41/1.83 ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), X ) ],
% 1.41/1.83 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( hAPP(
% 1.41/1.83 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.41/1.83 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ) ), X ) ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit0'(
% 1.41/1.83 'c_Int_OBit1'( 'c_Int_OPls' ) ) ), 'tc_nat' ) ), X ) ), =( X,
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.41/1.83 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( hAPP(
% 1.41/1.83 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), 'c_Int_Onumber__class_Onumber__of'(
% 1.41/1.83 'c_Int_OBit0'( 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ), hAPP(
% 1.41/1.83 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ), =( X, 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.83 'tc_nat' ) ) ],
% 1.41/1.83 [ 'c_Fun_Oinj__on'( 'c_COMBB'( 'c_Suc', hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_nat', 'tc_nat' ), X,
% 1.41/1.83 'tc_nat', 'tc_nat' ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), 'c_lessequals'(
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), ~( 'c_lessequals'(
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), X ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ),
% 1.41/1.83 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.41/1.83 ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.83 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.41/1.83 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ),
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( X ), X ), ~( 'c_HOL_Oord__class_Oless'( Y,
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( X ), X ) ) ],
% 1.41/1.83 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.41/1.83 'c_Int_OMin', X ) ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), Y ) ) ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OMin', X ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), ~(
% 1.41/1.83 'class_OrderedGroup_Omonoid__mult'( X ) ), =( 'c_Finite__Set_Osetsum'(
% 1.41/1.83 'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ), X, 'tc_fun'( X, X ), 'tc_nat' )
% 1.41/1.83 , 'c_COMBB'( hAPP( 'c_Power_Opower__class_Opower'( X ), Z ), hAPP(
% 1.41/1.83 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc', T ) ), 'tc_nat'
% 1.41/1.83 , X, 'tc_nat' ), 'tc_nat', X, X ),
% 1.41/1.83 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.83 'tc_nat' ), hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Z ), 'c_Finite__Set_Osetsum'(
% 1.41/1.83 'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ), X, 'tc_fun'( X, X ), 'tc_nat' )
% 1.41/1.83 , 'c_COMBB'( hAPP( 'c_Power_Opower__class_Opower'( X ), Z ), hAPP(
% 1.41/1.83 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ),
% 1.41/1.83 'tc_nat', X, X ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', T ), 'tc_nat' ),
% 1.41/1.83 'tc_nat', X ) ) ) ],
% 1.41/1.83 [ ~( 'class_Power_Opower'( X ) ), ~(
% 1.41/1.83 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.41/1.83 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_Power_Opower__class_Opower'(
% 1.41/1.83 X ), Y ), X, 'tc_fun'( X, X ), 'tc_nat' ), 'c_COMBB'( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Z ), hAPP(
% 1.41/1.83 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ),
% 1.41/1.83 'tc_nat', X, X ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', T ), 'tc_nat' ),
% 1.41/1.83 'tc_nat', X ), 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), 'c_COMBB'( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ), hAPP(
% 1.41/1.83 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ), X
% 1.41/1.83 , 'tc_fun'( X, X ), 'tc_nat' ), hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.41/1.83 , Z ), 'tc_nat', X, X ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', T ), 'tc_nat' ),
% 1.41/1.83 'tc_nat', X ) ) ],
% 1.41/1.83 [ =( 'c_FFT__Mirabelle_ODFT'( X, Y, 'v_i' ), 'c_Finite__Set_Osetsum'(
% 1.41/1.83 'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( 'tc_Complex_Ocomplex'
% 1.41/1.83 ), 'c_COMBB'( hAPP( 'c_Power_Opower__class_Opower'(
% 1.41/1.83 'tc_Complex_Ocomplex' ), 'c_FFT__Mirabelle_Oroot'( X ) ), hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'v_i' ), 'tc_nat',
% 1.41/1.83 'tc_Complex_Ocomplex', 'tc_nat' ), 'tc_Complex_Ocomplex', 'tc_fun'(
% 1.41/1.83 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ), 'tc_nat' ), Y, 'tc_nat',
% 1.41/1.83 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ),
% 1.41/1.83 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.83 'tc_nat' ), X, 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex' ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.83 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.41/1.83 [ =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ) ) ],
% 1.41/1.83 [ ~( 'class_Int_Onumber__ring'( X ) ), =( 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.83 ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.41/1.83 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ) ) ],
% 1.41/1.83 [ =( 'c_Int_OBit0'( 'c_Int_OPls' ), 'c_Int_OPls' ) ],
% 1.41/1.83 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ),
% 1.41/1.83 'tc_nat' ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.41/1.83 ,
% 1.41/1.83 [ ~( =( hAPP( 'c_Suc', X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.41/1.83 ,
% 1.41/1.83 [ ~( =( hAPP( 'c_Suc', X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.41/1.83 ,
% 1.41/1.83 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', 'tc_nat' ),
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.41/1.83 [ ~( 'class_Int_Onumber__ring'( X ) ), =(
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OPls', X ),
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( =( hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y
% 1.41/1.83 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.41/1.83 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.83 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.41/1.83 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.41/1.83 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.41/1.83 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.41/1.83 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.41/1.83 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.83 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.41/1.83 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.83 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.41/1.83 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.83 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.83 'tc_nat' ) ) ],
% 1.41/1.83 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.83 'tc_nat' ) ) ],
% 1.41/1.83 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.41/1.83 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.83 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.41/1.83 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.41/1.83 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.41/1.83 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.83 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.41/1.83 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.41/1.83 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.41/1.83 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.41/1.83 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Int_Onumber__class_Onumber__of'( Y
% 1.41/1.83 , 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ), =(
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.41/1.83 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), =( 'c_Int_Onumber__class_Onumber__of'(
% 1.41/1.83 Y, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.41/1.83 [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X, Y ) ],
% 1.41/1.83 [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X, Y ) ],
% 1.41/1.83 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.41/1.83 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( Y
% 1.41/1.83 , Z ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.41/1.83 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.41/1.83 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( X
% 1.41/1.83 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 1.41/1.83 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.41/1.83 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), =( Y
% 1.41/1.83 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 1.41/1.83 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.41/1.83 [ ~( =( 'c_Int_OPls', 'c_Int_OBit1'( X ) ) ) ],
% 1.41/1.83 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.41/1.83 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.41/1.83 hAPP( 'c_Suc', Z ), hAPP( 'c_Suc', T ), 'tc_nat' ), 'tc_nat', X ),
% 1.41/1.83 'c_Finite__Set_Osetsum'( 'c_COMBB'( Y, 'c_Suc', 'tc_nat', X, 'tc_nat' ),
% 1.41/1.83 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ), 'tc_nat'
% 1.41/1.83 , X ) ) ],
% 1.41/1.83 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), ~( 'class_Int_Onumber'(
% 1.41/1.83 X ) ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.83 X ), 'c_Int_Onumber__class_Onumber__of'( Y, X ) ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( Y, X ) ) ) ],
% 1.41/1.83 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' )
% 1.41/1.83 , 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.83 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.41/1.83 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), X ) ) ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.41/1.83 'c_FFT__Mirabelle_Oroot'( X ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.83 'tc_nat' ), Y ), Z ) ) ) ],
% 1.41/1.83 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OPls' ) ) ],
% 1.41/1.83 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OPls' ) ), =( X, 'c_Int_OPls' ) ]
% 1.41/1.83 ,
% 1.41/1.83 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit0'( Y ) ) ), =( X, Y ) ],
% 1.41/1.83 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ) ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Finite__Set_Osetsum'( Z, T, U
% 1.41/1.83 , X ) ), 'c_Finite__Set_Osetsum'( 'c_COMBB'( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X, U ), T, U, X ) ) ],
% 1.41/1.83 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Finite__Set_Osetsum'( Z, T, U
% 1.41/1.83 , X ) ), 'c_Finite__Set_Osetsum'( 'c_COMBB'( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X, U ), T, U, X ) ) ],
% 1.41/1.83 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ) ) ],
% 1.41/1.83 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit0'( Y ) ) ) ],
% 1.41/1.83 [ =( 'c_Int_OPls', 'c_Int_OBit0'( 'c_Int_OPls' ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.41/1.83 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.41/1.83 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.41/1.83 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.83 X ), Y ), Y ) ) ],
% 1.41/1.83 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.41/1.83 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP(
% 1.41/1.83 'c_Suc', X ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.41/1.83 , hAPP( 'c_Suc', X ) ), Z ) ) ), =( Y, Z ) ],
% 1.41/1.83 [ =( 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc', hAPP( 'c_Suc'
% 1.41/1.83 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ],
% 1.41/1.83 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.41/1.83 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), Y ) ],
% 1.41/1.83 [ ~( =( hAPP( 'c_Suc', X ), X ) ) ],
% 1.41/1.83 [ ~( =( X, hAPP( 'c_Suc', X ) ) ) ],
% 1.41/1.83 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.83 'tc_nat' ) ), Y ) ) ],
% 1.41/1.83 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.83 'tc_nat' ) ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.41/1.83 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.41/1.83 ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.83 'tc_nat' ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.41/1.83 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.41/1.83 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.41/1.83 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.41/1.83 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 1.41/1.83 =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.83 ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.41/1.83 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.41/1.83 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.41/1.83 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.83 ) ) ],
% 1.41/1.83 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.41/1.83 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), U ) ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.41/1.83 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.41/1.83 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.41/1.83 ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ),
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =( hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( Y, 'tc_nat' ) ),
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.41/1.83 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.83 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.41/1.83 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.83 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.41/1.83 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.83 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.83 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.41/1.83 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), 'c_Int_Onumber__class_Onumber__of'(
% 1.41/1.83 'c_Int_OBit1'( 'c_Int_OPls' ), X ) ), Y ), Y ) ],
% 1.41/1.83 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OPls' ), X ) )
% 1.41/1.83 , Y ) ],
% 1.41/1.83 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.41/1.83 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, hAPP(
% 1.41/1.83 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.41/1.83 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.41/1.83 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.41/1.83 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.41/1.83 [ ~( =( 'c_Int_OPls', 'c_Int_OBit0'( X ) ) ), =( 'c_Int_OPls', X ) ]
% 1.41/1.83 ,
% 1.41/1.83 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 1.41/1.83 ,
% 1.41/1.83 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 1.41/1.83 ,
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.41/1.83 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.41/1.83 hAPP( 'c_Suc', Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.41/1.83 [ ~( =( 'c_Int_OBit1'( X ), 'c_Int_OBit1'( Y ) ) ), =( X, Y ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.41/1.83 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.41/1.83 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.41/1.83 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ) ) ],
% 1.41/1.83 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.41/1.83 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.41/1.83 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.41/1.83 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.41/1.83 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.41/1.83 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.41/1.83 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.41/1.83 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.41/1.83 ) ) ],
% 1.41/1.83 [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 1.41/1.83 ,
% 1.41/1.83 [ =( hAPP( 'c_COMBS'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), hAPP( Y
% 1.41/1.83 , W ) ) ) ],
% 1.41/1.83 [ =( hAPP( 'c_Suc', hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.41/1.83 ) ) ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ) ],
% 1.41/1.83 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), ~( =( hAPP( Y,
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.41/1.83 ) ), =( 'c_Finite__Set_Osetsum'( Y,
% 1.41/1.83 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( 'c_Suc',
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z, 'tc_nat' ), 'tc_nat', X ),
% 1.41/1.83 'c_Finite__Set_Osetsum'( Y, 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ), 'tc_nat', X ) ) ]
% 1.41/1.83 ,
% 1.41/1.83 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit1'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.83 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), Y ) ) ]
% 1.41/1.83 ,
% 1.41/1.83 [ ~( 'class_Int_Oring__char__0'( X ) ), ~( 'class_Int_Onumber__ring'( X
% 1.41/1.83 ) ), ~( =( 'c_Int_Onumber__class_Onumber__of'( Y, X ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( Z, X ) ) ), =( Y, Z ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), Z ) ), hAPP( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.41/1.83 [ ~( =( 'c_Int_OBit0'( X ), 'c_Int_OBit1'( Y ) ) ) ],
% 1.41/1.83 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.41/1.83 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.41/1.83 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.41/1.83 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( Z, 'tc_nat' ) ),
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.41/1.83 ) ) ],
% 1.41/1.83 [ ~( =( 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( 'tc_Complex_Ocomplex' ), 'c_COMBB'( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( 'tc_Complex_Ocomplex' ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.41/1.83 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.83 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.41/1.83 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_m' ) ) ), 'v_i' ) ),
% 1.41/1.83 'c_COMBB'( hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' )
% 1.41/1.83 , 'c_FFT__Mirabelle_Oroot'( 'v_m' ) ), hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.83 'tc_nat' ), 'v_i' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ),
% 1.41/1.83 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex', 'tc_nat' ),
% 1.41/1.83 'tc_Complex_Ocomplex', 'tc_fun'( 'tc_Complex_Ocomplex',
% 1.41/1.83 'tc_Complex_Ocomplex' ), 'tc_nat' ), 'c_COMBB'( 'v_a', 'c_COMBB'( 'c_Suc'
% 1.41/1.83 , hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.41/1.83 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'( 'c_Int_OBit1'(
% 1.41/1.83 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_nat', 'tc_nat' ), 'tc_nat'
% 1.41/1.83 , 'tc_Complex_Ocomplex', 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex',
% 1.41/1.83 'tc_Complex_Ocomplex' ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.41/1.83 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'v_m', 'tc_nat' ), 'tc_nat',
% 1.41/1.83 'tc_Complex_Ocomplex' ), 'c_Finite__Set_Osetsum'( 'c_COMBB'( hAPP(
% 1.41/1.83 'c_HOL_Otimes__class_Otimes'( 'tc_Complex_Ocomplex' ), hAPP( hAPP(
% 1.41/1.83 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.41/1.83 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.83 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.41/1.83 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), 'v_m' ) ) ), 'v_i' ) ),
% 1.41/1.83 'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( 'tc_Complex_Ocomplex'
% 1.41/1.83 ), hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ), hAPP(
% 1.41/1.83 hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.41/1.83 'c_FFT__Mirabelle_Oroot'( 'v_m' ) ), 'v_i' ) ), 'tc_Complex_Ocomplex',
% 1.41/1.83 'tc_fun'( 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ), 'tc_nat' ),
% 1.41/1.83 'c_COMBB'( 'v_a', 'c_COMBB'( 'c_Suc', hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.41/1.83 'tc_nat' ), 'c_Int_Onumber__class_Onumber__of'( 'c_Int_OBit0'(
% 1.41/1.83 'c_Int_OBit1'( 'c_Int_OPls' ) ), 'tc_nat' ) ), 'tc_nat', 'tc_nat',
% 1.41/1.83 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ), 'tc_nat',
% 1.41/1.83 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ), 'tc_Complex_Ocomplex',
% 1.41/1.83 'tc_Complex_Ocomplex', 'tc_nat' ),
% 1.41/1.83 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.41/1.83 'tc_nat' ), 'v_m', 'tc_nat' ), 'tc_nat', 'tc_Complex_Ocomplex' ) ) ) ]
% 1.41/1.83 ,
% 1.41/1.83 [ 'class_Lattices_Oupper__semilattice'( 'tc_fun'( X, Y ) ), ~(
% 1.41/1.83 'class_Lattices_Olattice'( Y ) ) ],
% 1.41/1.83 [ 'class_Lattices_Olower__semilattice'( 'tc_fun'( X, Y ) ), ~(
% 1.41/1.83 'class_Lattices_Olattice'( Y ) ) ],
% 1.41/1.83 [ 'class_Lattices_Odistrib__lattice'( 'tc_fun'( X, Y ) ), ~(
% 1.41/1.83 'class_Lattices_Odistrib__lattice'( Y ) ) ],
% 1.41/1.83 [ 'class_Lattices_Obounded__lattice'( 'tc_fun'( X, Y ) ), ~(
% 1.41/1.83 'class_Lattices_Obounded__lattice'( Y ) ) ],
% 1.41/1.83 [ 'class_Lattices_Oboolean__algebra'( 'tc_fun'( X, Y ) ), ~(
% 1.41/1.83 'class_Lattices_Oboolean__algebra'( Y ) ) ],
% 1.41/1.83 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 1.41/1.83 'class_Orderings_Opreorder'( Y ) ) ],
% 1.41/1.83 [ 'class_Lattices_Olattice'( 'tc_fun'( X, Y ) ), ~(
% 1.41/1.83 'class_Lattices_Olattice'( Y ) ) ],
% 1.41/1.83 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 1.41/1.83 'class_Orderings_Oorder'( Y ) ) ],
% 1.41/1.83 [ 'class_Orderings_Obot'( 'tc_fun'( X, Y ) ), ~( 'class_Orderings_Obot'(
% 1.41/1.83 Y ) ) ],
% 1.41/1.83 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.41/1.83 ],
% 1.41/1.83 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.41/1.83 ) ],
% 1.41/1.83 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.41/1.83 ],
% 1.41/1.83 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 1.41/1.83 ,
% 1.41/1.83 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.41/1.83 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 1.41/1.83 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.41/1.83 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.41/1.83 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.41/1.83 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 1.41/1.83 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 1.41/1.83 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.41/1.83 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.41/1.83 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.41/1.83 [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_nat' ) ],
% 1.41/1.83 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.41/1.83 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.41/1.83 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.41/1.83 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.41/1.83 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.41/1.83 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.41/1.83 [ 'class_Lattices_Oupper__semilattice'( 'tc_nat' ) ],
% 1.41/1.83 [ 'class_Lattices_Olower__semilattice'( 'tc_nat' ) ],
% 1.41/1.83 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.41/1.83 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.41/1.83 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.41/1.83 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.41/1.83 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.41/1.83 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.41/1.83 [ 'class_Lattices_Odistrib__lattice'( 'tc_nat' ) ],
% 1.41/1.83 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.41/1.83 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.41/1.83 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 1.41/1.83 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.41/1.83 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.41/1.83 [ 'class_Lattices_Olattice'( 'tc_nat' ) ],
% 1.41/1.83 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.41/1.83 [ 'class_Orderings_Obot'( 'tc_nat' ) ],
% 1.41/1.83 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 1.41/1.83 [ 'class_Int_Onumber'( 'tc_nat' ) ],
% 1.41/1.83 [ 'class_Lattices_Oupper__semilattice'( 'tc_bool' ) ],
% 1.41/1.83 [ 'class_Lattices_Olower__semilattice'( 'tc_bool' ) ],
% 1.41/1.83 [ 'class_Lattices_Odistrib__lattice'( 'tc_bool' ) ],
% 1.41/1.83 [ 'class_Lattices_Obounded__lattice'( 'tc_bool' ) ],
% 1.41/1.83 [ 'class_Lattices_Oboolean__algebra'( 'tc_bool' ) ],
% 1.41/1.83 [ 'class_Orderings_Opreorder'( 'tc_bool' ) ],
% 1.41/1.83 [ 'class_Lattices_Olattice'( 'tc_bool' ) ],
% 1.41/1.83 [ 'class_Orderings_Oorder'( 'tc_bool' ) ],
% 1.41/1.83 [ 'class_Orderings_Obot'( 'tc_bool' ) ],
% 1.41/1.83 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'(
% 1.41/1.83 'tc_Int_Oint' ) ],
% 1.41/1.83 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'(
% 1.41/1.83 'tc_Int_Oint' ) ],
% 1.41/1.83 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'(
% 1.41/1.83 'tc_Int_Oint' ) ],
% 1.41/1.83 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_Int_Oint' )
% 1.41/1.83 ],
% 1.41/1.83 [ 'class_OrderedGroup_Olordered__ab__group__add__meet'( 'tc_Int_Oint' )
% 1.41/1.83 ],
% 1.41/1.83 [ 'class_OrderedGroup_Olordered__ab__group__add__join'( 'tc_Int_Oint' )
% 1.41/1.83 ],
% 1.41/1.83 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'( 'tc_Int_Oint' )
% 1.41/1.83 ],
% 1.41/1.83 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_Int_Oint' ) ]
% 1.41/1.83 ,
% 1.41/1.83 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.41/1.83 ,
% 1.41/1.83 [ 'class_OrderedGroup_Opordered__ab__group__add__abs'( 'tc_Int_Oint' ) ]
% 1.41/1.83 ,
% 1.41/1.83 [ 'class_OrderedGroup_Olordered__ab__group__add__abs'( 'tc_Int_Oint' ) ]
% 1.41/1.83 ,
% 1.41/1.83 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_Int_Oint' ) ]
% 1.41/1.83 ,
% 1.41/1.83 [ 'class_Ring__and__Field_Oring__no__zero__divisors'( 'tc_Int_Oint' ) ]
% 1.41/1.83 ,
% 1.41/1.83 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_Int_Oint' ) ]
% 1.41/1.83 ,
% 1.41/1.83 [ 'class_Ring__and__Field_Oordered__ring__strict'( 'tc_Int_Oint' ) ]
% 1.41/1.83 ,
% 1.41/1.83 [ 'class_OrderedGroup_Opordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.41/1.83 [ 'class_OrderedGroup_Olordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.41/1.83 [ 'class_OrderedGroup_Oordered__ab__group__add'( 'tc_Int_Oint' ) ],
% 1.41/1.83 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.41/1.83 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_Int_Oint' ) ],
% 1.41/1.83 [ 'class_Ring__and__Field_Opordered__ring__abs'( 'tc_Int_Oint' ) ],
% 1.41/1.83 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_Int_Oint' ) ],
% 1.41/1.83 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Int_Oint' ) ],
% 1.41/1.83 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_Int_Oint' ) ],
% 1.41/1.83 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Int_Oint' ) ],
% 1.41/1.83 [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_Int_Oint' ) ],
% 1.41/1.83 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Int_Oint' ) ],
% 1.41/1.83 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Int_Oint' ) ],
% 1.41/1.83 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Int_Oint' ) ],
% 1.41/1.83 [ 'class_Ring__and__Field_Opordered__ring'( 'tc_Int_Oint' ) ],
% 1.41/1.83 [ 'class_Ring__and__Field_Olordered__ring'( 'tc_Int_Oint' ) ],
% 1.41/1.83 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Int_Oint' ) ],
% 1.41/1.84 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Int_Oint' ) ],
% 1.41/1.84 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Int_Oint' ) ],
% 1.41/1.84 [ 'class_Ring__and__Field_Oordered__idom'( 'tc_Int_Oint' ) ],
% 1.41/1.84 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Int_Oint' ) ],
% 1.41/1.84 [ 'class_Lattices_Oupper__semilattice'( 'tc_Int_Oint' ) ],
% 1.41/1.84 [ 'class_Lattices_Olower__semilattice'( 'tc_Int_Oint' ) ],
% 1.41/1.84 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Int_Oint' ) ],
% 1.41/1.84 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Int_Oint' ) ],
% 1.41/1.84 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_Int_Oint' ) ],
% 1.41/1.84 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Int_Oint' ) ],
% 1.41/1.84 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Int_Oint' ) ],
% 1.41/1.84 [ 'class_Ring__and__Field_Omult__mono'( 'tc_Int_Oint' ) ],
% 1.41/1.84 [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_Int_Oint' ) ],
% 1.41/1.84 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Int_Oint' ) ],
% 1.41/1.84 [ 'class_Lattices_Odistrib__lattice'( 'tc_Int_Oint' ) ],
% 1.41/1.84 [ 'class_Ring__and__Field_Osemiring'( 'tc_Int_Oint' ) ],
% 1.41/1.84 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Int_Oint' ) ],
% 1.41/1.84 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Int_Oint' ) ],
% 1.41/1.84 [ 'class_Ring__and__Field_Oring__1'( 'tc_Int_Oint' ) ],
% 1.41/1.84 [ 'class_Ring__and__Field_Oabs__if'( 'tc_Int_Oint' ) ],
% 1.41/1.84 [ 'class_Divides_Osemiring__div'( 'tc_Int_Oint' ) ],
% 1.41/1.84 [ 'class_Ring__and__Field_Oring'( 'tc_Int_Oint' ) ],
% 1.41/1.84 [ 'class_Ring__and__Field_Oidom'( 'tc_Int_Oint' ) ],
% 1.41/1.84 [ 'class_Orderings_Opreorder'( 'tc_Int_Oint' ) ],
% 1.41/1.84 [ 'class_Orderings_Olinorder'( 'tc_Int_Oint' ) ],
% 1.41/1.84 [ 'class_Lattices_Olattice'( 'tc_Int_Oint' ) ],
% 1.41/1.84 [ 'class_Divides_Oring__div'( 'tc_Int_Oint' ) ],
% 1.41/1.84 [ 'class_Orderings_Oorder'( 'tc_Int_Oint' ) ],
% 1.41/1.84 [ 'class_Int_Oring__char__0'( 'tc_Int_Oint' ) ],
% 1.41/1.84 [ 'class_Int_Onumber__ring'( 'tc_Int_Oint' ) ],
% 1.41/1.84 [ 'class_Power_Opower'( 'tc_Int_Oint' ) ],
% 1.41/1.84 [ 'class_Int_Onumber'( 'tc_Int_Oint' ) ],
% 1.41/1.84 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 1.41/1.84 'tc_Complex_Ocomplex' ) ],
% 1.41/1.84 [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 1.41/1.84 'tc_Complex_Ocomplex' ) ],
% 1.41/1.84 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 1.41/1.84 'tc_Complex_Ocomplex' ) ],
% 1.41/1.84 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Complex_Ocomplex' )
% 1.41/1.84 ],
% 1.41/1.84 [ 'class_RealVector_Oreal__normed__algebra__1'( 'tc_Complex_Ocomplex' )
% 1.41/1.84 ],
% 1.41/1.84 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Complex_Ocomplex' )
% 1.41/1.84 ],
% 1.41/1.84 [ 'class_Ring__and__Field_Odivision__by__zero'( 'tc_Complex_Ocomplex' )
% 1.41/1.84 ],
% 1.41/1.84 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.41/1.84 ,
% 1.41/1.84 [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_Complex_Ocomplex' ) ]
% 1.41/1.84 ,
% 1.41/1.84 [ 'class_RealVector_Oreal__normed__algebra'( 'tc_Complex_Ocomplex' ) ]
% 1.41/1.84 ,
% 1.41/1.84 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.41/1.84 ,
% 1.41/1.84 [ 'class_RealVector_Oreal__normed__vector'( 'tc_Complex_Ocomplex' ) ]
% 1.41/1.84 ,
% 1.41/1.84 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.41/1.84 ,
% 1.41/1.84 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Complex_Ocomplex' ) ]
% 1.41/1.84 ,
% 1.41/1.84 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Complex_Ocomplex' ) ]
% 1.41/1.84 ,
% 1.41/1.84 [ 'class_RealVector_Oreal__normed__field'( 'tc_Complex_Ocomplex' ) ]
% 1.41/1.84 ,
% 1.41/1.84 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Complex_Ocomplex' ) ]
% 1.41/1.84 ,
% 1.41/1.84 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Complex_Ocomplex' ) ]
% 1.41/1.84 ,
% 1.41/1.84 [ 'class_Ring__and__Field_Ocomm__ring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.41/1.84 ,
% 1.41/1.84 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.41/1.84 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Complex_Ocomplex' ) ],
% 1.41/1.84 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Complex_Ocomplex' ) ],
% 1.41/1.84 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Complex_Ocomplex' ) ],
% 1.41/1.84 [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_Complex_Ocomplex' ) ],
% 1.41/1.84 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Complex_Ocomplex' ) ],
% 1.41/1.84 [ 'class_Ring__and__Field_Osemiring'( 'tc_Complex_Ocomplex' ) ],
% 1.41/1.84 [ 'class_RealVector_Ometric__space'( 'tc_Complex_Ocomplex' ) ],
% 1.41/1.84 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Complex_Ocomplex' ) ],
% 1.41/1.84 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Complex_Ocomplex' ) ],
% 1.41/1.84 [ 'class_Ring__and__Field_Oring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.41/1.84 [ 'class_RealVector_Oreal__field'( 'tc_Complex_Ocomplex' ) ],
% 1.41/1.84 [ 'class_Ring__and__Field_Ofield'( 'tc_Complex_Ocomplex' ) ],
% 1.41/1.84 [ 'class_Ring__and__Field_Oring'( 'tc_Complex_Ocomplex' ) ],
% 1.41/1.84 [ 'class_Ring__and__Field_Oidom'( 'tc_Complex_Ocomplex' ) ],
% 1.41/1.84 [ 'class_Int_Oring__char__0'( 'tc_Complex_Ocomplex' ) ],
% 1.41/1.84 [ 'class_Int_Onumber__ring'( 'tc_Complex_Ocomplex' ) ],
% 1.41/1.84 [ 'class_Power_Opower'( 'tc_Complex_Ocomplex' ) ],
% 1.41/1.84 [ 'class_Int_Onumber'( 'tc_Complex_Ocomplex' ) ],
% 1.41/1.84 [ =( hAPP( 'c_COMBS'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), hAPP( Y
% 1.41/1.84 , W ) ) ) ],
% 1.41/1.84 [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), Y ) ) ]
% 1.41/1.84 ,
% 1.41/1.84 [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 1.41/1.84 ,
% 1.41/1.84 [ 'c_fequal'( X, X, Y ) ],
% 1.41/1.84 [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ]
% 1.41/1.84 ] .
% 1.41/1.84
% 1.41/1.84
% 1.41/1.84 percentage equality = 0.228014, percentage horn = 0.864537
% 1.41/1.84 This is a problem with some equality
% 1.41/1.84
% 1.41/1.84
% 1.41/1.84
% 1.41/1.84 Options Used:
% 1.41/1.84
% 1.41/1.84 useres = 1
% 1.41/1.84 useparamod = 1
% 1.41/1.84 useeqrefl = 1
% 1.41/1.84 useeqfact = 1
% 1.41/1.84 usefactor = 1
% 1.41/1.84 usesimpsplitting = 0
% 1.41/1.84 usesimpdemod = 5
% 1.41/1.84 usesimpres = 3
% 1.41/1.84
% 1.41/1.84 resimpinuse = 1000
% 1.41/1.84 resimpclauses = 20000
% 1.41/1.84 substype = eqrewr
% 1.41/1.84 backwardsubs = 1
% 1.41/1.84 selectoldest = 5
% 1.41/1.84
% 1.41/1.84 litorderings [0] = split
% 1.41/1.84 litorderings [1] = extend the termordering, first sorting on arguments
% 1.41/1.84
% 1.41/1.84 termordering = kbo
% 1.41/1.84
% 1.41/1.84 litapriori = 0
% 1.41/1.84 termapriori = 1
% 1.41/1.84 litaposteriori = 0
% 1.41/1.84 termaposteriori = 0
% 1.41/1.84 demodaposteriori = 0
% 1.41/1.84 ordereqreflfact = 0
% 1.41/1.84
% 1.41/1.84 litselect = negord
% 1.41/1.84
% 1.41/1.84 maxweight = 15
% 1.41/1.84 maxdepth = 30000
% 1.41/1.84 maxlength = 115
% 1.41/1.84 maxnrvars = 195
% 1.41/1.84 excuselevel = 1
% 1.41/1.84 increasemaxweight = 1
% 1.41/1.84
% 1.41/1.84 maxselected = 10000000
% 1.41/1.84 maxnrclauses = 10000000
% 1.41/1.84
% 1.41/1.84 showgenerated = 0
% 1.41/1.84 showkept = 0
% 1.41/1.84 showselected = 0
% 1.41/1.84 showdeleted = 0
% 1.41/1.84 showresimp = 1
% 1.41/1.84 showstatus = 2000
% 1.41/1.84
% 1.41/1.84 prologoutput = 1
% 1.41/1.84 nrgoals = 5000000
% 1.41/1.84 totalproof = 1
% 1.41/1.84
% 1.41/1.84 Symbols occurring in the translation:
% 1.41/1.84
% 1.41/1.84 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.41/1.84 . [1, 2] (w:1, o:188, a:1, s:1, b:0),
% 1.41/1.84 ! [4, 1] (w:0, o:91, a:1, s:1, b:0),
% 1.41/1.84 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.41/1.84 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.41/1.84 'c_Power_Opower_Opower' [43, 3] (w:1, o:220, a:1, s:1, b:0),
% 1.41/1.84 hAPP [46, 2] (w:1, o:213, a:1, s:1, b:0),
% 1.41/1.84 'c_Ring__and__Field_Oordered__idom' [54, 11] (w:1, o:243, a:1, s:1
% 1.41/1.84 , b:0),
% 1.41/1.84 'class_Ring__and__Field_Oordered__semidom' [55, 1] (w:1, o:98, a:1
% 1.41/1.84 , s:1, b:0),
% 1.41/1.84 'c_HOL_Oplus__class_Oplus' [57, 1] (w:1, o:100, a:1, s:1, b:0),
% 1.41/1.84 'c_HOL_Oord__class_Oless' [59, 3] (w:1, o:221, a:1, s:1, b:0),
% 1.41/1.84 'c_HOL_Ozero__class_Ozero' [60, 1] (w:1, o:101, a:1, s:1, b:0),
% 1.41/1.84 'tc_nat' [61, 0] (w:1, o:50, a:1, s:1, b:0),
% 1.41/1.84 'c_HOL_Otimes__class_Otimes' [62, 1] (w:1, o:102, a:1, s:1, b:0),
% 1.41/1.84 'c_Divides_Odiv__class_Omod' [63, 3] (w:1, o:222, a:1, s:1, b:0),
% 1.41/1.84 'c_Divides_Odiv__class_Odiv' [64, 3] (w:1, o:223, a:1, s:1, b:0),
% 1.41/1.84 hBOOL [65, 1] (w:1, o:103, a:1, s:1, b:0),
% 1.41/1.84 'c_HOL_Ominus__class_Ominus' [69, 1] (w:1, o:104, a:1, s:1, b:0),
% 1.41/1.84 'class_Orderings_Olinorder' [70, 1] (w:1, o:105, a:1, s:1, b:0),
% 1.41/1.84 'class_OrderedGroup_Olordered__ab__group__add' [71, 1] (w:1, o:106
% 1.41/1.84 , a:1, s:1, b:0),
% 1.41/1.84 'c_HOL_Ouminus__class_Ouminus' [72, 1] (w:1, o:107, a:1, s:1, b:0),
% 1.41/1.84 'c_Lattices_Oupper__semilattice__class_Osup' [73, 3] (w:1, o:224, a:1
% 1.41/1.84 , s:1, b:0),
% 1.41/1.84 'c_Suc' [74, 0] (w:1, o:54, a:1, s:1, b:0),
% 1.41/1.84 'c_lessequals' [75, 3] (w:1, o:225, a:1, s:1, b:0),
% 1.41/1.84 'class_Lattices_Oupper__semilattice' [76, 1] (w:1, o:108, a:1, s:1
% 1.41/1.84 , b:0),
% 1.41/1.84 'class_Orderings_Oorder' [80, 1] (w:1, o:109, a:1, s:1, b:0),
% 1.41/1.84 'c_SetInterval_Oord__class_OatLeastLessThan' [81, 3] (w:1, o:226, a:1
% 1.41/1.84 , s:1, b:0),
% 1.41/1.84 'tc_bool' [82, 0] (w:1, o:61, a:1, s:1, b:0),
% 1.41/1.84 'tc_fun' [83, 2] (w:1, o:214, a:1, s:1, b:0),
% 1.41/1.84 'c_Orderings_Obot__class_Obot' [84, 1] (w:1, o:110, a:1, s:1, b:0),
% 1.41/1.84 'c_Int_OMin' [85, 0] (w:1, o:62, a:1, s:1, b:0),
% 1.41/1.84 'tc_Int_Oint' [86, 0] (w:1, o:63, a:1, s:1, b:0),
% 1.41/1.84 'class_Ring__and__Field_Oordered__idom' [87, 1] (w:1, o:111, a:1, s:1
% 1.41/1.84 , b:0),
% 1.41/1.84 'class_Int_Onumber__ring' [88, 1] (w:1, o:112, a:1, s:1, b:0),
% 1.41/1.84 'c_HOL_Oabs__class_Oabs' [89, 1] (w:1, o:113, a:1, s:1, b:0),
% 1.41/1.84 'c_Int_Onumber__class_Onumber__of' [90, 2] (w:1, o:215, a:1, s:1, b:0
% 1.41/1.84 ),
% 1.41/1.84 'c_HOL_Oone__class_Oone' [91, 1] (w:1, o:99, a:1, s:1, b:0),
% 1.41/1.84 'c_OrderedGroup_Omonoid__mult' [92, 3] (w:1, o:219, a:1, s:1, b:0),
% 1.41/1.84 'c_Set_Oimage' [96, 4] (w:1, o:234, a:1, s:1, b:0),
% 1.41/1.84 'class_RealVector_Oreal__normed__vector' [97, 1] (w:1, o:114, a:1, s:
% 1.41/1.84 1, b:0),
% 1.41/1.84 'class_RealVector_Ometric__space' [98, 1] (w:1, o:115, a:1, s:1, b:0)
% 1.41/1.84 ,
% 1.41/1.84 'c_Lim_OLIM' [100, 5] (w:1, o:237, a:1, s:1, b:0),
% 1.41/1.84 'c_COMBB' [101, 5] (w:1, o:238, a:1, s:1, b:0),
% 1.41/1.84 'c_COMBC' [102, 5] (w:1, o:239, a:1, s:1, b:0),
% 1.41/1.84 'class_Lattices_Odistrib__lattice' [103, 1] (w:1, o:116, a:1, s:1, b:
% 1.41/1.84 0),
% 1.41/1.84 'c_Lattices_Olower__semilattice__class_Oinf' [104, 3] (w:1, o:227, a:
% 1.41/1.84 1, s:1, b:0),
% 1.41/1.84 'class_OrderedGroup_Ogroup__add' [107, 1] (w:1, o:117, a:1, s:1, b:0)
% 1.41/1.84 ,
% 1.41/1.84 'class_OrderedGroup_Ocomm__monoid__add' [108, 1] (w:1, o:118, a:1, s:
% 1.41/1.84 1, b:0),
% 1.41/1.84 'class_OrderedGroup_Opordered__ab__group__add__abs' [109, 1] (w:1, o:
% 1.41/1.84 120, a:1, s:1, b:0),
% 1.41/1.84 'class_Divides_Osemiring__div' [110, 1] (w:1, o:122, a:1, s:1, b:0),
% 1.41/1.84
% 1.41/1.84 'class_RealVector_Oreal__normed__algebra' [111, 1] (w:1, o:123, a:1
% 1.41/1.84 , s:1, b:0),
% 1.41/1.84 'class_Power_Opower' [112, 1] (w:1, o:143, a:1, s:1, b:0),
% 1.41/1.84 'c_Power_Opower__class_Opower' [113, 1] (w:1, o:144, a:1, s:1, b:0),
% 1.41/1.84
% 1.41/1.84 'c_SEQ_OLIMSEQ' [115, 3] (w:1, o:228, a:1, s:1, b:0),
% 1.41/1.84 'class_Lattices_Olower__semilattice' [116, 1] (w:1, o:145, a:1, s:1
% 1.41/1.84 , b:0),
% 1.41/1.84 'class_Lattices_Olattice' [117, 1] (w:1, o:146, a:1, s:1, b:0),
% 1.41/1.84 'class_Ring__and__Field_Oordered__field' [118, 1] (w:1, o:147, a:1
% 1.41/1.84 , s:1, b:0),
% 1.41/1.84 'class_Ring__and__Field_Odivision__by__zero' [119, 1] (w:1, o:153, a:
% 1.41/1.84 1, s:1, b:0),
% 1.41/1.84 'class_Int_Onumber' [120, 1] (w:1, o:154, a:1, s:1, b:0),
% 1.41/1.84 'c_HOL_Oinverse__class_Odivide' [121, 1] (w:1, o:155, a:1, s:1, b:0)
% 1.41/1.84 ,
% 1.41/1.84 'class_OrderedGroup_Opordered__ab__group__add' [123, 1] (w:1, o:124
% 1.41/1.84 , a:1, s:1, b:0),
% 1.41/1.84 'c_SetInterval_Oord__class_OatLeastAtMost' [125, 3] (w:1, o:229, a:1
% 1.41/1.84 , s:1, b:0),
% 1.41/1.84 'c_Finite__Set_Osetsum' [126, 4] (w:1, o:235, a:1, s:1, b:0),
% 1.41/1.84 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [127, 1]
% 1.41/1.84 (w:1, o:125, a:1, s:1, b:0),
% 1.41/1.84 'class_OrderedGroup_Opordered__ab__semigroup__add' [128, 1] (w:1, o:
% 1.41/1.84 126, a:1, s:1, b:0),
% 1.41/1.84 'c_Parity_Oeven__odd__class_Oeven' [131, 2] (w:1, o:216, a:1, s:1, b:
% 1.41/1.84 0),
% 1.41/1.84 'class_RealVector_Oreal__normed__algebra__1' [132, 1] (w:1, o:156, a:
% 1.41/1.84 1, s:1, b:0),
% 1.41/1.84 'class_Lattices_Oboolean__algebra' [136, 1] (w:1, o:157, a:1, s:1, b:
% 1.41/1.84 0),
% 1.41/1.84 'class_OrderedGroup_Olordered__ab__group__add__abs' [137, 1] (w:1, o:
% 1.41/1.84 127, a:1, s:1, b:0),
% 1.41/1.84 'c_SEQ_OZseq' [140, 2] (w:1, o:217, a:1, s:1, b:0),
% 1.41/1.84 'class_OrderedGroup_Opordered__comm__monoid__add' [142, 1] (w:1, o:
% 1.41/1.84 128, a:1, s:1, b:0),
% 1.41/1.84 'class_Lattices_Obounded__lattice' [143, 1] (w:1, o:158, a:1, s:1, b:
% 1.41/1.84 0),
% 1.41/1.84 'class_Ring__and__Field_Ofield' [146, 1] (w:1, o:159, a:1, s:1, b:0)
% 1.41/1.84 ,
% 1.41/1.84 'c_Int_OPls' [147, 0] (w:1, o:77, a:1, s:1, b:0),
% 1.41/1.84 'class_Divides_Oring__div' [148, 1] (w:1, o:121, a:1, s:1, b:0),
% 1.41/1.84 'class_OrderedGroup_Oab__group__add' [149, 1] (w:1, o:129, a:1, s:1
% 1.41/1.84 , b:0),
% 1.41/1.84 'c_COMBS' [150, 5] (w:1, o:240, a:1, s:1, b:0),
% 1.41/1.84 'class_RealVector_Oreal__normed__field' [151, 1] (w:1, o:160, a:1, s:
% 1.41/1.84 1, b:0),
% 1.41/1.84 'c_Series_Osums' [152, 3] (w:1, o:230, a:1, s:1, b:0),
% 1.41/1.84 'class_Ring__and__Field_Ocomm__semiring__1' [153, 1] (w:1, o:151, a:1
% 1.41/1.84 , s:1, b:0),
% 1.41/1.84 'c_Int_OBit1' [155, 1] (w:1, o:162, a:1, s:1, b:0),
% 1.41/1.84 'class_Ring__and__Field_Oabs__if' [157, 1] (w:1, o:163, a:1, s:1, b:0
% 1.41/1.84 ),
% 1.41/1.84 'c_Fun_Oinj__on' [158, 4] (w:1, o:236, a:1, s:1, b:0),
% 1.41/1.84 'class_Ring__and__Field_Opordered__ring' [159, 1] (w:1, o:167, a:1
% 1.41/1.84 , s:1, b:0),
% 1.41/1.84 'c_Int_OBit0' [161, 1] (w:1, o:161, a:1, s:1, b:0),
% 5.77/6.14 'class_Orderings_Obot' [162, 1] (w:1, o:130, a:1, s:1, b:0),
% 5.77/6.14 'class_Ring__and__Field_Oring' [163, 1] (w:1, o:168, a:1, s:1, b:0),
% 5.77/6.14
% 5.77/6.14 'class_Ring__and__Field_Olordered__ring' [164, 1] (w:1, o:169, a:1
% 5.77/6.14 , s:1, b:0),
% 5.77/6.14 'c_Groebner__Basis_Ogb__semiring' [170, 6] (w:1, o:241, a:1, s:1, b:0
% 5.77/6.14 ),
% 5.77/6.14 'class_Ring__and__Field_Oidom' [175, 1] (w:1, o:170, a:1, s:1, b:0),
% 5.77/6.14
% 5.77/6.14 'class_OrderedGroup_Ocancel__ab__semigroup__add' [176, 1] (w:1, o:131
% 5.77/6.14 , a:1, s:1, b:0),
% 5.77/6.14 'class_OrderedGroup_Ocancel__semigroup__add' [177, 1] (w:1, o:132, a:
% 5.77/6.14 1, s:1, b:0),
% 5.77/6.14 'class_Ring__and__Field_Ocomm__ring__1' [178, 1] (w:1, o:148, a:1, s:
% 5.77/6.14 1, b:0),
% 5.77/6.14 'class_OrderedGroup_Olordered__ab__group__add__meet' [180, 1] (w:1
% 5.77/6.14 , o:133, a:1, s:1, b:0),
% 5.77/6.14 'class_OrderedGroup_Olordered__ab__group__add__join' [181, 1] (w:1
% 5.77/6.14 , o:134, a:1, s:1, b:0),
% 5.77/6.14 'class_Orderings_Opreorder' [182, 1] (w:1, o:135, a:1, s:1, b:0),
% 5.77/6.14 'class_OrderedGroup_Oab__semigroup__add' [183, 1] (w:1, o:136, a:1
% 5.77/6.14 , s:1, b:0),
% 5.77/6.14 'class_RealVector_Oreal__field' [188, 1] (w:1, o:171, a:1, s:1, b:0)
% 5.77/6.14 ,
% 5.77/6.14 'class_OrderedGroup_Oordered__ab__group__add' [190, 1] (w:1, o:119
% 5.77/6.14 , a:1, s:1, b:0),
% 5.77/6.14 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [195, 1]
% 5.77/6.14 (w:1, o:137, a:1, s:1, b:0),
% 5.77/6.14 'c_Series_Osuminf' [197, 2] (w:1, o:218, a:1, s:1, b:0),
% 5.77/6.14 'c_Complex_Oii' [199, 0] (w:1, o:83, a:1, s:1, b:0),
% 5.77/6.14 'tc_Complex_Ocomplex' [200, 0] (w:1, o:84, a:1, s:1, b:0),
% 5.77/6.14 'class_Ring__and__Field_Ozero__neq__one' [201, 1] (w:1, o:172, a:1
% 5.77/6.14 , s:1, b:0),
% 5.77/6.14 'class_OrderedGroup_Omonoid__add' [202, 1] (w:1, o:138, a:1, s:1, b:0
% 5.77/6.14 ),
% 5.77/6.14 'class_Ring__and__Field_Oordered__semiring__strict' [203, 1] (w:1, o:
% 5.77/6.14 164, a:1, s:1, b:0),
% 5.77/6.14 'class_Ring__and__Field_Oordered__ring__strict' [204, 1] (w:1, o:97
% 5.77/6.14 , a:1, s:1, b:0),
% 5.77/6.14 'class_Ring__and__Field_Opordered__ring__abs' [205, 1] (w:1, o:173
% 5.77/6.14 , a:1, s:1, b:0),
% 5.77/6.14 'class_Ring__and__Field_Oordered__semiring' [206, 1] (w:1, o:165, a:1
% 5.77/6.14 , s:1, b:0),
% 5.77/6.14 'class_Ring__and__Field_Ocomm__semiring' [207, 1] (w:1, o:152, a:1
% 5.77/6.14 , s:1, b:0),
% 5.77/6.14 'class_OrderedGroup_Omonoid__mult' [208, 1] (w:1, o:139, a:1, s:1, b:
% 5.77/6.14 0),
% 5.77/6.14 'class_OrderedGroup_Ocomm__monoid__mult' [209, 1] (w:1, o:140, a:1
% 5.77/6.14 , s:1, b:0),
% 5.77/6.14 'class_Ring__and__Field_Osemiring' [210, 1] (w:1, o:177, a:1, s:1, b:
% 5.77/6.14 0),
% 5.77/6.14 'c_FFT__Mirabelle_ODFT' [212, 3] (w:1, o:231, a:1, s:1, b:0),
% 5.77/6.14 'c_FFT__Mirabelle_Oroot' [213, 1] (w:1, o:178, a:1, s:1, b:0),
% 5.77/6.14 'class_Ring__and__Field_Oordered__comm__semiring__strict' [214, 1]
% 5.77/6.14 (w:1, o:166, a:1, s:1, b:0),
% 5.77/6.14 'class_Ring__and__Field_Omult__mono1' [215, 1] (w:1, o:179, a:1, s:1
% 5.77/6.14 , b:0),
% 5.77/6.14 'class_Ring__and__Field_Omult__mono' [216, 1] (w:1, o:180, a:1, s:1
% 5.77/6.14 , b:0),
% 5.77/6.14 'class_Ring__and__Field_Opordered__cancel__semiring' [217, 1] (w:1
% 5.77/6.14 , o:181, a:1, s:1, b:0),
% 5.77/6.14 'class_Ring__and__Field_Opordered__semiring' [218, 1] (w:1, o:182, a:
% 5.77/6.14 1, s:1, b:0),
% 5.77/6.14 'class_Ring__and__Field_Oring__1' [219, 1] (w:1, o:174, a:1, s:1, b:0
% 5.77/6.14 ),
% 5.77/6.14 'c_Ring__and__Field_Ocomm__ring__1' [222, 7] (w:1, o:242, a:1, s:1
% 5.77/6.14 , b:0),
% 5.77/6.14 'class_Ring__and__Field_Ocomm__ring' [223, 1] (w:1, o:149, a:1, s:1
% 5.77/6.14 , b:0),
% 5.77/6.14 'v_m' [224, 0] (w:1, o:86, a:1, s:1, b:0),
% 5.77/6.14 'v_i' [225, 0] (w:1, o:87, a:1, s:1, b:0),
% 5.77/6.14 'class_Ring__and__Field_Osemiring__0' [226, 1] (w:1, o:183, a:1, s:1
% 5.77/6.14 , b:0),
% 5.77/6.14 'c_Parity_Osko__Parity__Xodd__Suc__mult__two__ex__1__1' [227, 1] (w:1
% 5.77/6.14 , o:184, a:1, s:1, b:0),
% 5.77/6.14 'v_a' [228, 0] (w:1, o:88, a:1, s:1, b:0),
% 5.77/6.14 'class_Ring__and__Field_Osemiring__1' [229, 1] (w:1, o:185, a:1, s:1
% 5.77/6.14 , b:0),
% 5.77/6.14 'c_FFT__Mirabelle_OIDFT' [230, 3] (w:1, o:232, a:1, s:1, b:0),
% 5.77/6.14 'class_Ring__and__Field_Ocomm__semiring__0' [231, 1] (w:1, o:150, a:1
% 5.77/6.14 , s:1, b:0),
% 5.77/6.14 'class_Ring__and__Field_Oring__no__zero__divisors' [233, 1] (w:1, o:
% 5.77/6.14 175, a:1, s:1, b:0),
% 5.77/6.14 'class_Ring__and__Field_Omult__zero' [234, 1] (w:1, o:186, a:1, s:1
% 5.77/6.14 , b:0),
% 5.77/6.14 'class_Ring__and__Field_Ono__zero__divisors' [235, 1] (w:1, o:96, a:1
% 21.16/21.57 , s:1, b:0),
% 21.16/21.57 'class_OrderedGroup_Oab__semigroup__mult' [237, 1] (w:1, o:141, a:1
% 21.16/21.57 , s:1, b:0),
% 21.16/21.57 'class_OrderedGroup_Oab__semigroup__idem__mult' [238, 1] (w:1, o:142
% 21.16/21.57 , a:1, s:1, b:0),
% 21.16/21.57 'class_Ring__and__Field_Oring__1__no__zero__divisors' [239, 1] (w:1
% 21.16/21.57 , o:176, a:1, s:1, b:0),
% 21.16/21.57 'class_Int_Oring__char__0' [240, 1] (w:1, o:187, a:1, s:1, b:0),
% 21.16/21.57 'c_fequal' [243, 3] (w:1, o:233, a:1, s:1, b:0).
% 21.16/21.57
% 21.16/21.57
% 21.16/21.57 Starting Search:
% 21.16/21.57
% 21.16/21.57 Resimplifying inuse:
% 21.16/21.57 Done
% 21.16/21.57
% 21.16/21.57
% 21.16/21.57 Intermediate Status:
% 21.16/21.57 Generated: 2932
% 21.16/21.57 Kept: 2008
% 21.16/21.57 Inuse: 84
% 21.16/21.57 Deleted: 2
% 21.16/21.57 Deletedinuse: 0
% 21.16/21.57
% 21.16/21.57 Resimplifying inuse:
% 21.16/21.57 Done
% 21.16/21.57
% 21.16/21.57
% 21.16/21.57 Intermediate Status:
% 21.16/21.57 Generated: 8680
% 21.16/21.57 Kept: 4034
% 21.16/21.57 Inuse: 326
% 21.16/21.57 Deleted: 10
% 21.16/21.57 Deletedinuse: 0
% 21.16/21.57
% 21.16/21.57 Resimplifying inuse:
% 21.16/21.57 Done
% 21.16/21.57
% 21.16/21.57 Resimplifying inuse:
% 21.16/21.57 Done
% 21.16/21.57
% 21.16/21.57
% 21.16/21.57 Intermediate Status:
% 21.16/21.57 Generated: 17324
% 21.16/21.57 Kept: 6172
% 21.16/21.57 Inuse: 346
% 21.16/21.57 Deleted: 10
% 21.16/21.57 Deletedinuse: 0
% 21.16/21.57
% 21.16/21.57 Resimplifying inuse:
% 21.16/21.57 Done
% 21.16/21.57
% 21.16/21.57 Resimplifying inuse:
% 21.16/21.57 Done
% 21.16/21.57
% 21.16/21.57
% 21.16/21.57 Intermediate Status:
% 21.16/21.57 Generated: 26840
% 21.16/21.57 Kept: 8531
% 21.16/21.57 Inuse: 366
% 21.16/21.57 Deleted: 10
% 21.16/21.57 Deletedinuse: 0
% 21.16/21.57
% 21.16/21.57 Resimplifying inuse:
% 21.16/21.57 Done
% 21.16/21.57
% 21.16/21.57 Resimplifying inuse:
% 21.16/21.57 Done
% 21.16/21.57
% 21.16/21.57
% 21.16/21.57 Intermediate Status:
% 21.16/21.57 Generated: 35221
% 21.16/21.57 Kept: 10535
% 21.16/21.57 Inuse: 417
% 21.16/21.57 Deleted: 10
% 21.16/21.57 Deletedinuse: 0
% 21.16/21.57
% 21.16/21.57 Resimplifying inuse:
% 21.16/21.57 Done
% 21.16/21.57
% 21.16/21.57 Resimplifying inuse:
% 21.16/21.57 Done
% 21.16/21.57
% 21.16/21.57
% 21.16/21.57 Intermediate Status:
% 21.16/21.57 Generated: 41841
% 21.16/21.57 Kept: 13006
% 21.16/21.57 Inuse: 466
% 21.16/21.57 Deleted: 10
% 21.16/21.57 Deletedinuse: 0
% 21.16/21.57
% 21.16/21.57 Resimplifying inuse:
% 21.16/21.57 Done
% 21.16/21.57
% 21.16/21.57 Resimplifying inuse:
% 21.16/21.57 Done
% 21.16/21.57
% 21.16/21.57
% 21.16/21.57 Intermediate Status:
% 21.16/21.57 Generated: 49102
% 21.16/21.57 Kept: 15747
% 21.16/21.57 Inuse: 499
% 21.16/21.57 Deleted: 10
% 21.16/21.57 Deletedinuse: 0
% 21.16/21.57
% 21.16/21.57 Resimplifying inuse:
% 21.16/21.57 Done
% 21.16/21.57
% 21.16/21.57 Resimplifying inuse:
% 21.16/21.57 Done
% 21.16/21.57
% 21.16/21.57
% 21.16/21.57 Intermediate Status:
% 21.16/21.57 Generated: 56765
% 21.16/21.57 Kept: 17848
% 21.16/21.57 Inuse: 571
% 21.16/21.57 Deleted: 10
% 21.16/21.57 Deletedinuse: 0
% 21.16/21.57
% 21.16/21.57 Resimplifying inuse:
% 21.16/21.57 Done
% 21.16/21.57
% 21.16/21.57 Resimplifying inuse:
% 21.16/21.57 Done
% 21.16/21.57
% 21.16/21.57
% 21.16/21.57 Intermediate Status:
% 21.16/21.57 Generated: 64061
% 21.16/21.57 Kept: 19998
% 21.16/21.57 Inuse: 641
% 21.16/21.57 Deleted: 11
% 21.16/21.57 Deletedinuse: 1
% 21.16/21.57
% 21.16/21.57 Resimplifying inuse:
% 21.16/21.57 Done
% 21.16/21.57
% 21.16/21.57 Resimplifying clauses:
% 21.16/21.57 Done
% 21.16/21.57
% 21.16/21.57
% 21.16/21.57 Intermediate Status:
% 21.16/21.57 Generated: 68629
% 21.16/21.57 Kept: 22127
% 21.16/21.57 Inuse: 651
% 21.16/21.57 Deleted: 291
% 21.16/21.57 Deletedinuse: 2
% 21.16/21.57
% 21.16/21.57 Resimplifying inuse:
% 21.16/21.57 Done
% 21.16/21.57
% 21.16/21.57
% 21.16/21.57 Intermediate Status:
% 21.16/21.57 Generated: 72559
% 21.16/21.57 Kept: 24318
% 21.16/21.57 Inuse: 656
% 21.16/21.57 Deleted: 291
% 21.16/21.57 Deletedinuse: 2
% 21.16/21.57
% 21.16/21.57 Resimplifying inuse:
% 21.16/21.57 Done
% 21.16/21.57
% 21.16/21.57
% 21.16/21.57 Intermediate Status:
% 21.16/21.57 Generated: 76487
% 21.16/21.57 Kept: 26571
% 21.16/21.57 Inuse: 661
% 21.16/21.57 Deleted: 291
% 21.16/21.57 Deletedinuse: 2
% 21.16/21.57
% 21.16/21.57 Resimplifying inuse:
% 21.16/21.57 Done
% 21.16/21.57
% 21.16/21.57 Resimplifying inuse:
% 21.16/21.57 Done
% 21.16/21.57
% 21.16/21.57
% 21.16/21.57 Intermediate Status:
% 21.16/21.57 Generated: 81377
% 21.16/21.57 Kept: 28753
% 21.16/21.57 Inuse: 671
% 21.16/21.57 Deleted: 291
% 21.16/21.57 Deletedinuse: 2
% 21.16/21.57
% 21.16/21.57
% 21.16/21.57 Intermediate Status:
% 21.16/21.57 Generated: 90014
% 21.16/21.57 Kept: 31366
% 21.16/21.57 Inuse: 681
% 21.16/21.57 Deleted: 291
% 21.16/21.57 Deletedinuse: 2
% 21.16/21.57
% 21.16/21.57 Resimplifying inuse:
% 21.16/21.57 Done
% 21.16/21.57
% 21.16/21.57 Resimplifying inuse:
% 21.16/21.57 Done
% 21.16/21.57
% 21.16/21.57
% 21.16/21.57 Intermediate Status:
% 21.16/21.57 Generated: 97136
% 21.16/21.57 Kept: 33703
% 21.16/21.57 Inuse: 716
% 21.16/21.57 Deleted: 291
% 21.16/21.57 Deletedinuse: 2
% 21.16/21.57
% 21.16/21.57 Resimplifying inuse:
% 21.16/21.57 Done
% 21.16/21.57
% 21.16/21.57 Resimplifying inuse:
% 21.16/21.57 Done
% 21.16/21.57
% 21.16/21.57
% 21.16/21.57 Intermediate Status:
% 21.16/21.57 Generated: 103836
% 21.16/21.57 Kept: 36052
% 21.16/21.57 Inuse: 746
% 21.16/21.57 Deleted: 292
% 21.16/21.57 Deletedinuse: 3
% 21.16/21.57
% 21.16/21.57 Resimplifying inuse:
% 21.16/21.57 Done
% 21.16/21.57
% 21.16/21.57 Resimplifying inuse:
% 21.16/21.57 Done
% 21.16/21.57
% 21.16/21.57
% 21.16/21.57 Intermediate Status:
% 21.16/21.57 Generated: 110682
% 21.16/21.57 Kept: 38250
% 21.16/21.57 Inuse: 776
% 21.16/21.57 Deleted: 292
% 21.16/21.57 Deletedinuse: 3
% 21.16/21.57
% 21.16/21.57 Resimplifying inuse:
% 21.16/21.57 Done
% 21.16/21.57
% 21.16/21.57 Resimplifying inuse:
% 21.16/21.57 Done
% 21.16/21.57
% 21.16/21.57 Resimplifying clauses:
% 21.16/21.57 Done
% 21.16/21.57
% 21.16/21.57
% 21.16/21.57 Intermediate Status:
% 21.16/21.57 Generated: 119328
% 21.16/21.57 Kept: 40350
% 21.16/21.57 Inuse: 826
% 21.16/21.57 Deleted: 790
% 21.16/21.57 Deletedinuse: 3
% 21.16/21.57
% 21.16/21.57 Resimplifying inuse:
% 21.16/21.57 Done
% 21.16/21.57
% 21.16/21.57 Resimplifying inuse:
% 21.16/21.57 Done
% 21.16/21.57
% 21.16/21.57
% 21.16/21.57 Intermediate Status:
% 21.16/21.57 Generated: 124881
% 21.16/21.57 Kept: 42354
% 21.16/21.57 Inuse: 865
% 21.16/21.57 Deleted: 790
% 21.16/21.57 Deletedinuse: 3
% 21.16/21.57
% 21.16/21.57 Resimplifying inuse:
% 21.16/21.57 Done
% 21.16/21.57
% 21.16/21.57
% 21.16/21.57 Intermediate Status:
% 21.16/21.57 Generated: 134146
% 21.16/21.57 Kept: 44362
% 21.16/21.57 Inuse: 901
% 21.16/21.57 Deleted: 790
% 21.16/21.57 Deletedinuse: 3
% 21.16/21.57
% 21.16/21.57 Resimplifying inuse:
% 21.16/21.57 Done
% 21.16/21.57
% 21.16/21.57 Resimplifying inuse:
% 21.16/21.57 Done
% 21.16/21.57
% 21.16/21.57
% 21.16/21.57 Intermediate Status:
% 21.16/21.57 Generated: 140331
% 21.16/21.57 Kept: 46397
% 21.16/21.57 Inuse: 930
% 21.16/21.57 Deleted: 790
% 21.16/21.57 Deletedinuse: 3
% 21.16/21.57
% 21.16/21.57 Resimplifying inuse:
% 21.16/21.57 Done
% 21.16/21.57
% 21.16/21.57 Resimplifying inuse:
% 21.16/21.57 Done
% 21.16/21.57
% 21.16/21.57
% 21.16/21.57 Intermediate Status:
% 21.16/21.57 Generated: 146109
% 21.16/21.57 Kept: 48497
% 21.16/21.57 Inuse: 946
% 21.16/21.57 Deleted: 790
% 21.16/21.57 Deletedinuse: 3
% 21.16/21.57
% 21.16/21.57 Resimplifying inuse:
% 21.16/21.57 Done
% 55.37/55.75
% 55.37/55.75
% 55.37/55.75 Intermediate Status:
% 55.37/55.75 Generated: 152429
% 55.37/55.75 Kept: 50635
% 55.37/55.75 Inuse: 961
% 55.37/55.75 Deleted: 790
% 55.37/55.75 Deletedinuse: 3
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75
% 55.37/55.75 Intermediate Status:
% 55.37/55.75 Generated: 164277
% 55.37/55.75 Kept: 53706
% 55.37/55.75 Inuse: 986
% 55.37/55.75 Deleted: 790
% 55.37/55.75 Deletedinuse: 3
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75
% 55.37/55.75 Intermediate Status:
% 55.37/55.75 Generated: 174146
% 55.37/55.75 Kept: 56259
% 55.37/55.75 Inuse: 1006
% 55.37/55.75 Deleted: 790
% 55.37/55.75 Deletedinuse: 3
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75
% 55.37/55.75 Intermediate Status:
% 55.37/55.75 Generated: 183211
% 55.37/55.75 Kept: 58380
% 55.37/55.75 Inuse: 1019
% 55.37/55.75 Deleted: 790
% 55.37/55.75 Deletedinuse: 3
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75 Resimplifying clauses:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75
% 55.37/55.75 Intermediate Status:
% 55.37/55.75 Generated: 189967
% 55.37/55.75 Kept: 60386
% 55.37/55.75 Inuse: 1047
% 55.37/55.75 Deleted: 953
% 55.37/55.75 Deletedinuse: 3
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75
% 55.37/55.75 Intermediate Status:
% 55.37/55.75 Generated: 197499
% 55.37/55.75 Kept: 62447
% 55.37/55.75 Inuse: 1080
% 55.37/55.75 Deleted: 953
% 55.37/55.75 Deletedinuse: 3
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75
% 55.37/55.75 Intermediate Status:
% 55.37/55.75 Generated: 212162
% 55.37/55.75 Kept: 66058
% 55.37/55.75 Inuse: 1105
% 55.37/55.75 Deleted: 954
% 55.37/55.75 Deletedinuse: 3
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75
% 55.37/55.75 Intermediate Status:
% 55.37/55.75 Generated: 215848
% 55.37/55.75 Kept: 68270
% 55.37/55.75 Inuse: 1108
% 55.37/55.75 Deleted: 954
% 55.37/55.75 Deletedinuse: 3
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75
% 55.37/55.75 Intermediate Status:
% 55.37/55.75 Generated: 221493
% 55.37/55.75 Kept: 70651
% 55.37/55.75 Inuse: 1120
% 55.37/55.75 Deleted: 954
% 55.37/55.75 Deletedinuse: 3
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75
% 55.37/55.75 Intermediate Status:
% 55.37/55.75 Generated: 226384
% 55.37/55.75 Kept: 72712
% 55.37/55.75 Inuse: 1130
% 55.37/55.75 Deleted: 954
% 55.37/55.75 Deletedinuse: 3
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75
% 55.37/55.75 Intermediate Status:
% 55.37/55.75 Generated: 233247
% 55.37/55.75 Kept: 74713
% 55.37/55.75 Inuse: 1154
% 55.37/55.75 Deleted: 954
% 55.37/55.75 Deletedinuse: 3
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75
% 55.37/55.75 Intermediate Status:
% 55.37/55.75 Generated: 240651
% 55.37/55.75 Kept: 77020
% 55.37/55.75 Inuse: 1180
% 55.37/55.75 Deleted: 958
% 55.37/55.75 Deletedinuse: 7
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75
% 55.37/55.75 Intermediate Status:
% 55.37/55.75 Generated: 247409
% 55.37/55.75 Kept: 79046
% 55.37/55.75 Inuse: 1204
% 55.37/55.75 Deleted: 958
% 55.37/55.75 Deletedinuse: 7
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75 Resimplifying clauses:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75
% 55.37/55.75 Intermediate Status:
% 55.37/55.75 Generated: 254162
% 55.37/55.75 Kept: 81136
% 55.37/55.75 Inuse: 1225
% 55.37/55.75 Deleted: 1342
% 55.37/55.75 Deletedinuse: 7
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75
% 55.37/55.75 Intermediate Status:
% 55.37/55.75 Generated: 260136
% 55.37/55.75 Kept: 83154
% 55.37/55.75 Inuse: 1241
% 55.37/55.75 Deleted: 1342
% 55.37/55.75 Deletedinuse: 7
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75
% 55.37/55.75 Intermediate Status:
% 55.37/55.75 Generated: 266288
% 55.37/55.75 Kept: 85217
% 55.37/55.75 Inuse: 1250
% 55.37/55.75 Deleted: 1342
% 55.37/55.75 Deletedinuse: 7
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75
% 55.37/55.75 Intermediate Status:
% 55.37/55.75 Generated: 272099
% 55.37/55.75 Kept: 87233
% 55.37/55.75 Inuse: 1263
% 55.37/55.75 Deleted: 1342
% 55.37/55.75 Deletedinuse: 7
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75
% 55.37/55.75 Intermediate Status:
% 55.37/55.75 Generated: 277935
% 55.37/55.75 Kept: 89244
% 55.37/55.75 Inuse: 1285
% 55.37/55.75 Deleted: 1342
% 55.37/55.75 Deletedinuse: 7
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75
% 55.37/55.75 Intermediate Status:
% 55.37/55.75 Generated: 284491
% 55.37/55.75 Kept: 91270
% 55.37/55.75 Inuse: 1307
% 55.37/55.75 Deleted: 1342
% 55.37/55.75 Deletedinuse: 7
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75
% 55.37/55.75 Intermediate Status:
% 55.37/55.75 Generated: 292357
% 55.37/55.75 Kept: 93384
% 55.37/55.75 Inuse: 1335
% 55.37/55.75 Deleted: 1342
% 55.37/55.75 Deletedinuse: 7
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75
% 55.37/55.75 Intermediate Status:
% 55.37/55.75 Generated: 301786
% 55.37/55.75 Kept: 95695
% 55.37/55.75 Inuse: 1365
% 55.37/55.75 Deleted: 1342
% 55.37/55.75 Deletedinuse: 7
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75
% 55.37/55.75 Intermediate Status:
% 55.37/55.75 Generated: 306420
% 55.37/55.75 Kept: 97707
% 55.37/55.75 Inuse: 1376
% 55.37/55.75 Deleted: 1342
% 55.37/55.75 Deletedinuse: 7
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75
% 55.37/55.75 Intermediate Status:
% 55.37/55.75 Generated: 311154
% 55.37/55.75 Kept: 99973
% 55.37/55.75 Inuse: 1385
% 55.37/55.75 Deleted: 1342
% 55.37/55.75 Deletedinuse: 7
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75 Resimplifying clauses:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75
% 55.37/55.75 Intermediate Status:
% 55.37/55.75 Generated: 318101
% 55.37/55.75 Kept: 102056
% 55.37/55.75 Inuse: 1405
% 55.37/55.75 Deleted: 1425
% 55.37/55.75 Deletedinuse: 7
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 55.37/55.75 Resimplifying inuse:
% 55.37/55.75 Done
% 55.37/55.75
% 112.56/112.89
% 112.56/112.89 Intermediate Status:
% 112.56/112.89 Generated: 325840
% 112.56/112.89 Kept: 104426
% 112.56/112.89 Inuse: 1425
% 112.56/112.89 Deleted: 1425
% 112.56/112.89 Deletedinuse: 7
% 112.56/112.89
% 112.56/112.89 Resimplifying inuse:
% 112.56/112.89 Done
% 112.56/112.89
% 112.56/112.89 Resimplifying inuse:
% 112.56/112.89 Done
% 112.56/112.89
% 112.56/112.89
% 112.56/112.89 Intermediate Status:
% 112.56/112.89 Generated: 333121
% 112.56/112.89 Kept: 106436
% 112.56/112.89 Inuse: 1441
% 112.56/112.89 Deleted: 1425
% 112.56/112.89 Deletedinuse: 7
% 112.56/112.89
% 112.56/112.89 Resimplifying inuse:
% 112.56/112.89 Done
% 112.56/112.89
% 112.56/112.89
% 112.56/112.89 Intermediate Status:
% 112.56/112.89 Generated: 340633
% 112.56/112.89 Kept: 108554
% 112.56/112.89 Inuse: 1455
% 112.56/112.89 Deleted: 1425
% 112.56/112.89 Deletedinuse: 7
% 112.56/112.89
% 112.56/112.89 Resimplifying inuse:
% 112.56/112.89 Done
% 112.56/112.89
% 112.56/112.89 Resimplifying inuse:
% 112.56/112.89 Done
% 112.56/112.89
% 112.56/112.89
% 112.56/112.89 Intermediate Status:
% 112.56/112.89 Generated: 347934
% 112.56/112.89 Kept: 110603
% 112.56/112.89 Inuse: 1470
% 112.56/112.89 Deleted: 1425
% 112.56/112.89 Deletedinuse: 7
% 112.56/112.89
% 112.56/112.89 Resimplifying inuse:
% 112.56/112.89 Done
% 112.56/112.89
% 112.56/112.89
% 112.56/112.89 Intermediate Status:
% 112.56/112.89 Generated: 355825
% 112.56/112.89 Kept: 113005
% 112.56/112.89 Inuse: 1490
% 112.56/112.89 Deleted: 1425
% 112.56/112.89 Deletedinuse: 7
% 112.56/112.89
% 112.56/112.89 Resimplifying inuse:
% 112.56/112.89 Done
% 112.56/112.89
% 112.56/112.89 Resimplifying inuse:
% 112.56/112.89 Done
% 112.56/112.89
% 112.56/112.89
% 112.56/112.89 Intermediate Status:
% 112.56/112.89 Generated: 372574
% 112.56/112.89 Kept: 115905
% 112.56/112.89 Inuse: 1510
% 112.56/112.89 Deleted: 1426
% 112.56/112.89 Deletedinuse: 8
% 112.56/112.89
% 112.56/112.89 Resimplifying inuse:
% 112.56/112.89 Done
% 112.56/112.89
% 112.56/112.89 Resimplifying inuse:
% 112.56/112.89 Done
% 112.56/112.89
% 112.56/112.89
% 112.56/112.89 Intermediate Status:
% 112.56/112.89 Generated: 397702
% 112.56/112.90 Kept: 119618
% 112.56/112.90 Inuse: 1520
% 112.56/112.90 Deleted: 1426
% 112.56/112.90 Deletedinuse: 8
% 112.56/112.90
% 112.56/112.90 Resimplifying inuse:
% 112.56/112.90 Done
% 112.56/112.90
% 112.56/112.90 Resimplifying inuse:
% 112.56/112.90 Done
% 112.56/112.90
% 112.56/112.90 Resimplifying clauses:
% 112.56/112.90 Done
% 112.56/112.90
% 112.56/112.90
% 112.56/112.90 Intermediate Status:
% 112.56/112.90 Generated: 423540
% 112.56/112.90 Kept: 123316
% 112.56/112.90 Inuse: 1530
% 112.56/112.90 Deleted: 2027
% 112.56/112.90 Deletedinuse: 8
% 112.56/112.90
% 112.56/112.90 Resimplifying inuse:
% 112.56/112.90 Done
% 112.56/112.90
% 112.56/112.90 Resimplifying inuse:
% 112.56/112.90 Done
% 112.56/112.90
% 112.56/112.90
% 112.56/112.90 Intermediate Status:
% 112.56/112.90 Generated: 438243
% 112.56/112.90 Kept: 125639
% 112.56/112.90 Inuse: 1540
% 112.56/112.90 Deleted: 2027
% 112.56/112.90 Deletedinuse: 8
% 112.56/112.90
% 112.56/112.90 Resimplifying inuse:
% 112.56/112.90 Done
% 112.56/112.90
% 112.56/112.90 Resimplifying inuse:
% 112.56/112.90 Done
% 112.56/112.90
% 112.56/112.90
% 112.56/112.90 Intermediate Status:
% 112.56/112.90 Generated: 448127
% 112.56/112.90 Kept: 127821
% 112.56/112.90 Inuse: 1570
% 112.56/112.90 Deleted: 2027
% 112.56/112.90 Deletedinuse: 8
% 112.56/112.90
% 112.56/112.90 Resimplifying inuse:
% 112.56/112.90 Done
% 112.56/112.90
% 112.56/112.90
% 112.56/112.90 Intermediate Status:
% 112.56/112.90 Generated: 463005
% 112.56/112.90 Kept: 131989
% 112.56/112.90 Inuse: 1585
% 112.56/112.90 Deleted: 2027
% 112.56/112.90 Deletedinuse: 8
% 112.56/112.90
% 112.56/112.90 Resimplifying inuse:
% 112.56/112.90 Done
% 112.56/112.90
% 112.56/112.90 Resimplifying inuse:
% 112.56/112.90 Done
% 112.56/112.90
% 112.56/112.90
% 112.56/112.90 Intermediate Status:
% 112.56/112.90 Generated: 470740
% 112.56/112.90 Kept: 134201
% 112.56/112.90 Inuse: 1600
% 112.56/112.90 Deleted: 2027
% 112.56/112.90 Deletedinuse: 8
% 112.56/112.90
% 112.56/112.90 Resimplifying inuse:
% 112.56/112.90 Done
% 112.56/112.90
% 112.56/112.90 Resimplifying inuse:
% 112.56/112.90 Done
% 112.56/112.90
% 112.56/112.90
% 112.56/112.90 Intermediate Status:
% 112.56/112.90 Generated: 479830
% 112.56/112.90 Kept: 136426
% 112.56/112.90 Inuse: 1620
% 112.56/112.90 Deleted: 2027
% 112.56/112.90 Deletedinuse: 8
% 112.56/112.90
% 112.56/112.90 Resimplifying inuse:
% 112.56/112.90 Done
% 112.56/112.90
% 112.56/112.90 Resimplifying inuse:
% 112.56/112.90 Done
% 112.56/112.90
% 112.56/112.90
% 112.56/112.90 Intermediate Status:
% 112.56/112.90 Generated: 496903
% 112.56/112.90 Kept: 140498
% 112.56/112.90 Inuse: 1650
% 112.56/112.90 Deleted: 2028
% 112.56/112.90 Deletedinuse: 9
% 112.56/112.90
% 112.56/112.90 Resimplifying inuse:
% 112.56/112.90 Done
% 112.56/112.90
% 112.56/112.90
% 112.56/112.90 Intermediate Status:
% 112.56/112.90 Generated: 509559
% 112.56/112.90 Kept: 143691
% 112.56/112.90 Inuse: 1665
% 112.56/112.90 Deleted: 2028
% 112.56/112.90 Deletedinuse: 9
% 112.56/112.90
% 112.56/112.90 Resimplifying inuse:
% 112.56/112.90 Done
% 112.56/112.90
% 112.56/112.90 Resimplifying clauses:
% 112.56/112.90 Done
% 112.56/112.90
% 112.56/112.90 Resimplifying inuse:
% 112.56/112.90 Done
% 112.56/112.90
% 112.56/112.90
% 112.56/112.90 Intermediate Status:
% 112.56/112.90 Generated: 521108
% 112.56/112.90 Kept: 146093
% 112.56/112.90 Inuse: 1685
% 112.56/112.90 Deleted: 2126
% 112.56/112.90 Deletedinuse: 9
% 112.56/112.90
% 112.56/112.90 Resimplifying inuse:
% 112.56/112.90 Done
% 112.56/112.90
% 112.56/112.90 Resimplifying inuse:
% 112.56/112.90 Done
% 112.56/112.90
% 112.56/112.90
% 112.56/112.90 Intermediate Status:
% 112.56/112.90 Generated: 537527
% 112.56/112.90 Kept: 148276
% 112.56/112.90 Inuse: 1715
% 112.56/112.90 Deleted: 2126
% 112.56/112.90 Deletedinuse: 9
% 112.56/112.90
% 112.56/112.90 Resimplifying inuse:
% 112.56/112.90 Done
% 112.56/112.90
% 112.56/112.90
% 112.56/112.90 Intermediate Status:
% 112.56/112.90 Generated: 545691
% 112.56/112.90 Kept: 151483
% 112.56/112.90 Inuse: 1722
% 112.56/112.90 Deleted: 2126
% 112.56/112.90 Deletedinuse: 9
% 112.56/112.90
% 112.56/112.90 Resimplifying inuse:
% 112.56/112.90 Done
% 112.56/112.90
% 112.56/112.90 Resimplifying inuse:
% 112.56/112.90 Done
% 112.56/112.90
% 112.56/112.90
% 112.56/112.90 Intermediate Status:
% 112.56/112.90 Generated: 552316
% 112.56/112.90 Kept: 153702
% 112.56/112.90 Inuse: 1739
% 112.56/112.90 Deleted: 2127
% 112.56/112.90 Deletedinuse: 9
% 112.56/112.90
% 112.56/112.90 Resimplifying inuse:
% 112.56/112.90 Done
% 112.56/112.90
% 112.56/112.90 Resimplifying inuse:
% 112.56/112.90 Done
% 112.56/112.90
% 112.56/112.90
% 112.56/112.90 Intermediate Status:
% 112.56/112.90 Generated: 560712
% 112.56/112.90 Kept: 155723
% 112.56/112.90 Inuse: 1766
% 112.56/112.90 Deleted: 2127
% 112.56/112.90 Deletedinuse: 9
% 112.56/112.90
% 112.56/112.90 Resimplifying inuse:
% 112.56/112.90 Done
% 112.56/112.90
% 112.56/112.90 Resimplifying inuse:
% 112.56/112.90 Done
% 112.56/112.90
% 112.56/112.90
% 112.56/112.90 Intermediate Status:
% 112.56/112.90 Generated: 567785
% 112.56/112.90 Kept: 157750
% 112.56/112.90 Inuse: 1786
% 112.56/112.90 Deleted: 2127
% 112.56/112.90 Deletedinuse: 9
% 112.56/112.90
% 112.56/112.90 Resimplifying inuse:
% 112.56/112.90 Done
% 112.56/112.90
% 112.56/112.90 Resimplifying inuse:
% 112.56/112.90 Done
% 112.56/112.90
% 112.56/112.90
% 112.56/112.90 Intermediate Status:
% 112.56/112.90 Generated: 576347
% 112.56/112.90 Kept: 159858
% 112.56/112.90 Inuse: 1814
% 112.56/112.90 Deleted: 2127
% 112.56/112.90 Deletedinuse: 9
% 112.56/112.90
% 112.56/112.90 Resimplifying inuse:
% 112.56/112.90 Done
% 112.56/112.90
% 112.56/112.90 Resimplifying inuse:
% 112.56/112.90 Done
% 112.56/112.90
% 112.56/112.90
% 112.56/112.90 Intermediate Status:
% 112.56/112.90 Generated: 585326
% 112.56/112.90 Kept: 162212
% 112.56/112.90 Inuse: 1834
% 112.56/112.90 Deleted: 2129
% 112.56/112.90 Deletedinuse: 11
% 112.56/112.90
% 112.56/112.90 Resimplifying inuse:
% 112.56/112.90 Done
% 112.56/112.90
% 112.56/112.90 Resimplifying clauses:
% 112.56/112.90 Done
% 112.56/112.90
% 112.56/112.90 Resimplifying inuse:
% 112.56/112.90 Done
% 112.56/112.90
% 112.56/112.90
% 112.56/112.90 Intermediate Status:
% 112.56/112.90 Generated: 598264
% 112.56/112.90 Kept: 164323
% 112.56/112.90 Inuse: 1859
% 112.56/112.90 Deleted: 3088
% 112.56/112.90 Deletedinuse: 11
% 112.56/112.90
% 112.56/112.90 Resimplifying inuse:
% 112.56/112.90 Done
% 112.56/112.90
% 112.56/112.90 Resimplifying inuse:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18
% 190.76/191.18 Intermediate Status:
% 190.76/191.18 Generated: 606014
% 190.76/191.18 Kept: 166600
% 190.76/191.18 Inuse: 1879
% 190.76/191.18 Deleted: 3089
% 190.76/191.18 Deletedinuse: 12
% 190.76/191.18
% 190.76/191.18 Resimplifying inuse:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18 Resimplifying inuse:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18
% 190.76/191.18 Intermediate Status:
% 190.76/191.18 Generated: 613375
% 190.76/191.18 Kept: 168616
% 190.76/191.18 Inuse: 1904
% 190.76/191.18 Deleted: 3090
% 190.76/191.18 Deletedinuse: 13
% 190.76/191.18
% 190.76/191.18
% 190.76/191.18 Intermediate Status:
% 190.76/191.18 Generated: 622549
% 190.76/191.18 Kept: 171101
% 190.76/191.18 Inuse: 1909
% 190.76/191.18 Deleted: 3090
% 190.76/191.18 Deletedinuse: 13
% 190.76/191.18
% 190.76/191.18 Resimplifying inuse:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18 Resimplifying inuse:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18
% 190.76/191.18 Intermediate Status:
% 190.76/191.18 Generated: 630603
% 190.76/191.18 Kept: 173143
% 190.76/191.18 Inuse: 1928
% 190.76/191.18 Deleted: 3090
% 190.76/191.18 Deletedinuse: 13
% 190.76/191.18
% 190.76/191.18 Resimplifying inuse:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18 Resimplifying inuse:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18
% 190.76/191.18 Intermediate Status:
% 190.76/191.18 Generated: 639244
% 190.76/191.18 Kept: 175547
% 190.76/191.18 Inuse: 1944
% 190.76/191.18 Deleted: 3090
% 190.76/191.18 Deletedinuse: 13
% 190.76/191.18
% 190.76/191.18 Resimplifying inuse:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18
% 190.76/191.18 Intermediate Status:
% 190.76/191.18 Generated: 664177
% 190.76/191.18 Kept: 179189
% 190.76/191.18 Inuse: 1959
% 190.76/191.18 Deleted: 3090
% 190.76/191.18 Deletedinuse: 13
% 190.76/191.18
% 190.76/191.18 Resimplifying inuse:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18 Resimplifying inuse:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18
% 190.76/191.18 Intermediate Status:
% 190.76/191.18 Generated: 677183
% 190.76/191.18 Kept: 181213
% 190.76/191.18 Inuse: 1997
% 190.76/191.18 Deleted: 3090
% 190.76/191.18 Deletedinuse: 13
% 190.76/191.18
% 190.76/191.18 Resimplifying inuse:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18 Resimplifying inuse:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18
% 190.76/191.18 Intermediate Status:
% 190.76/191.18 Generated: 687403
% 190.76/191.18 Kept: 183268
% 190.76/191.18 Inuse: 2019
% 190.76/191.18 Deleted: 3090
% 190.76/191.18 Deletedinuse: 13
% 190.76/191.18
% 190.76/191.18 Resimplifying inuse:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18 Resimplifying clauses:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18 Resimplifying inuse:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18
% 190.76/191.18 Intermediate Status:
% 190.76/191.18 Generated: 697621
% 190.76/191.18 Kept: 185417
% 190.76/191.18 Inuse: 2039
% 190.76/191.18 Deleted: 3530
% 190.76/191.18 Deletedinuse: 13
% 190.76/191.18
% 190.76/191.18 Resimplifying inuse:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18 Resimplifying inuse:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18
% 190.76/191.18 Intermediate Status:
% 190.76/191.18 Generated: 706387
% 190.76/191.18 Kept: 187434
% 190.76/191.18 Inuse: 2058
% 190.76/191.18 Deleted: 3530
% 190.76/191.18 Deletedinuse: 13
% 190.76/191.18
% 190.76/191.18 Resimplifying inuse:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18 Resimplifying inuse:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18
% 190.76/191.18 Intermediate Status:
% 190.76/191.18 Generated: 717617
% 190.76/191.18 Kept: 189696
% 190.76/191.18 Inuse: 2079
% 190.76/191.18 Deleted: 3530
% 190.76/191.18 Deletedinuse: 13
% 190.76/191.18
% 190.76/191.18 Resimplifying inuse:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18
% 190.76/191.18 Intermediate Status:
% 190.76/191.18 Generated: 735330
% 190.76/191.18 Kept: 192605
% 190.76/191.18 Inuse: 2099
% 190.76/191.18 Deleted: 3530
% 190.76/191.18 Deletedinuse: 13
% 190.76/191.18
% 190.76/191.18 Resimplifying inuse:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18 Resimplifying inuse:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18
% 190.76/191.18 Intermediate Status:
% 190.76/191.18 Generated: 745360
% 190.76/191.18 Kept: 194802
% 190.76/191.18 Inuse: 2124
% 190.76/191.18 Deleted: 3530
% 190.76/191.18 Deletedinuse: 13
% 190.76/191.18
% 190.76/191.18 Resimplifying inuse:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18 Resimplifying inuse:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18
% 190.76/191.18 Intermediate Status:
% 190.76/191.18 Generated: 760385
% 190.76/191.18 Kept: 198989
% 190.76/191.18 Inuse: 2139
% 190.76/191.18 Deleted: 3530
% 190.76/191.18 Deletedinuse: 13
% 190.76/191.18
% 190.76/191.18 Resimplifying inuse:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18
% 190.76/191.18 Intermediate Status:
% 190.76/191.18 Generated: 769891
% 190.76/191.18 Kept: 201170
% 190.76/191.18 Inuse: 2159
% 190.76/191.18 Deleted: 3530
% 190.76/191.18 Deletedinuse: 13
% 190.76/191.18
% 190.76/191.18 Resimplifying inuse:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18
% 190.76/191.18 Intermediate Status:
% 190.76/191.18 Generated: 777474
% 190.76/191.18 Kept: 204292
% 190.76/191.18 Inuse: 2169
% 190.76/191.18 Deleted: 3531
% 190.76/191.18 Deletedinuse: 14
% 190.76/191.18
% 190.76/191.18 Resimplifying inuse:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18 Resimplifying clauses:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18
% 190.76/191.18 Intermediate Status:
% 190.76/191.18 Generated: 788972
% 190.76/191.18 Kept: 207776
% 190.76/191.18 Inuse: 2174
% 190.76/191.18 Deleted: 3699
% 190.76/191.18 Deletedinuse: 14
% 190.76/191.18
% 190.76/191.18 Resimplifying inuse:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18 Resimplifying inuse:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18
% 190.76/191.18 Intermediate Status:
% 190.76/191.18 Generated: 797588
% 190.76/191.18 Kept: 209870
% 190.76/191.18 Inuse: 2194
% 190.76/191.18 Deleted: 3699
% 190.76/191.18 Deletedinuse: 14
% 190.76/191.18
% 190.76/191.18 Resimplifying inuse:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18 Resimplifying inuse:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18
% 190.76/191.18 Intermediate Status:
% 190.76/191.18 Generated: 808879
% 190.76/191.18 Kept: 212146
% 190.76/191.18 Inuse: 2224
% 190.76/191.18 Deleted: 3699
% 190.76/191.18 Deletedinuse: 14
% 190.76/191.18
% 190.76/191.18 Resimplifying inuse:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18 Resimplifying inuse:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18
% 190.76/191.18 Intermediate Status:
% 190.76/191.18 Generated: 818673
% 190.76/191.18 Kept: 214347
% 190.76/191.18 Inuse: 2249
% 190.76/191.18 Deleted: 3699
% 190.76/191.18 Deletedinuse: 14
% 190.76/191.18
% 190.76/191.18 Resimplifying inuse:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18
% 190.76/191.18 Intermediate Status:
% 190.76/191.18 Generated: 838774
% 190.76/191.18 Kept: 218870
% 190.76/191.18 Inuse: 2264
% 190.76/191.18 Deleted: 3699
% 190.76/191.18 Deletedinuse: 14
% 190.76/191.18
% 190.76/191.18 Resimplifying inuse:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18
% 190.76/191.18 Intermediate Status:
% 190.76/191.18 Generated: 848943
% 190.76/191.18 Kept: 221489
% 190.76/191.18 Inuse: 2269
% 190.76/191.18 Deleted: 3699
% 190.76/191.18 Deletedinuse: 14
% 190.76/191.18
% 190.76/191.18 Resimplifying inuse:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18 Resimplifying inuse:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18
% 190.76/191.18 Intermediate Status:
% 190.76/191.18 Generated: 860406
% 190.76/191.18 Kept: 223552
% 190.76/191.18 Inuse: 2294
% 190.76/191.18 Deleted: 3699
% 190.76/191.18 Deletedinuse: 14
% 190.76/191.18
% 190.76/191.18 Resimplifying inuse:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18 Resimplifying clauses:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18 Resimplifying inuse:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18
% 190.76/191.18 Intermediate Status:
% 190.76/191.18 Generated: 879089
% 190.76/191.18 Kept: 225933
% 190.76/191.18 Inuse: 2314
% 190.76/191.18 Deleted: 3841
% 190.76/191.18 Deletedinuse: 15
% 190.76/191.18
% 190.76/191.18 Resimplifying inuse:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18 Resimplifying inuse:
% 190.76/191.18 Done
% 190.76/191.18
% 190.76/191.18
% 190.76/191.18 Intermediate Status:
% 190.76/191.18 Generated: 891359
% 190.76/191.18 Kept: 228135
% 190.76/191.18 InCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------