TSTP Solution File: SWV692-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV692-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n011.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 16:27:49 EDT 2022
% Result : Timeout 300.07s 300.60s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV692-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : bliksem %s
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % DateTime : Wed Jun 15 08:32:20 EDT 2022
% 0.14/0.35 % CPUTime :
% 1.18/1.56 *** allocated 10000 integers for termspace/termends
% 1.18/1.56 *** allocated 10000 integers for clauses
% 1.18/1.56 *** allocated 10000 integers for justifications
% 1.18/1.56 *** allocated 15000 integers for termspace/termends
% 1.18/1.56 *** allocated 22500 integers for termspace/termends
% 1.18/1.56 *** allocated 33750 integers for termspace/termends
% 1.18/1.56 Bliksem 1.12
% 1.18/1.56
% 1.18/1.56
% 1.18/1.56 Automatic Strategy Selection
% 1.18/1.56
% 1.18/1.56 Clauses:
% 1.18/1.56 [
% 1.18/1.56 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Y ) ) ) ],
% 1.18/1.56 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Y ) ) ) ],
% 1.18/1.56 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP( 'c_lessequals'( Z
% 1.18/1.56 , X ), Y ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.18/1.56 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), X ) ) ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), X ) ) ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ ~( 'class_Orderings_Oorder'( X ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Y ) ) ) ],
% 1.18/1.56 [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.56 'tc_nat' ) ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.18/1.56 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.18/1.56 [ =( X, Y ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y )
% 1.18/1.56 ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP(
% 1.18/1.56 'c_Suc', Y ) ) ) ) ],
% 1.18/1.56 [ =( X, Y ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ),
% 1.18/1.56 hAPP( 'c_Suc', X ) ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.56 'tc_nat' ), X ) ) ],
% 1.18/1.56 [ =( X, Y ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ),
% 1.18/1.56 hAPP( 'c_Suc', Y ) ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X,
% 1.18/1.56 'tc_nat' ), Y ) ) ],
% 1.18/1.56 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.18/1.56 , Z ) ],
% 1.18/1.56 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.18/1.56 , Z ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.18/1.56 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.18/1.56 Y, X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.56 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.18/1.56 ) ), Z ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.18/1.56 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) )
% 1.18/1.56 ), ~( hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), X ) ), Y ) ), U ) ) ) ),
% 1.18/1.56 ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), T ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), T ) ), U ) ) ), ~(
% 1.18/1.56 hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.56 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T
% 1.18/1.56 ) ), X ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.18/1.56 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ), U ) )
% 1.18/1.56 ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.56 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y
% 1.18/1.56 ) ), Z ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.18/1.56 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) )
% 1.18/1.56 ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), T ) ), Y ) ), Z ),
% 1.18/1.56 'tc_nat' ), U ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( T, 'tc_nat' ), X ) )
% 1.18/1.56 ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.56 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ) ), T ),
% 1.18/1.56 'tc_nat' ), U ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), T ), 'tc_nat' ),
% 1.18/1.56 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), U ) ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X )
% 1.18/1.56 , Z ), 'tc_nat' ), Y ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.18/1.56 'tc_nat' ), X ), Y ), 'tc_nat' ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.18/1.56 X, 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y
% 1.18/1.56 ) ) ) ) ],
% 1.18/1.56 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, hAPP(
% 1.18/1.56 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, hAPP( 'c_Suc'
% 1.18/1.56 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.18/1.56 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.56 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.56 'tc_nat' ) ) ) ) ],
% 1.18/1.56 [ ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ), =( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), Z ) ), T ) ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), T ) ) ],
% 1.18/1.56 [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X, Y ) ],
% 1.18/1.56 [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X, Y ) ],
% 1.18/1.56 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, Z ), U ) )
% 1.18/1.56 , hAPP( hAPP( Y, Z ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' )
% 1.18/1.56 , T ), U ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, Y, V0, V1, V2
% 1.18/1.56 ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 1.18/1.56 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.18/1.56 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.18/1.56 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), Y ) ) ), hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), T ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.18/1.56 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.18/1.56 'c_Groebner__Basis_Ogb__semiring'( U, W, X, V0, V1, V2 ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.18/1.56 'c_Suc', Y ) ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.56 'tc_nat' ), X ), Y ) ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.18/1.56 X ) ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.56 'tc_nat' ), X ), Y ) ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ) ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), X ) ), Y ) ), U ) ) ), ~(
% 1.18/1.56 hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), T ) ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ) ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), T ) ), Y ) ), Z ) ), U ) )
% 1.18/1.56 , ~( hBOOL( hAPP( 'c_lessequals'( T, 'tc_nat' ), X ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.56 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.56 'tc_nat' ), Z ), T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ),
% 1.18/1.56 T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Z ) ) ) ],
% 1.18/1.56 [ ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), X ) ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc', Y ) ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.18/1.56 Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP(
% 1.18/1.56 'c_Suc', X ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.56 'tc_nat' ) ), 'tc_nat' ), X ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP(
% 1.18/1.56 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.56 'tc_nat' ) ), 'tc_nat' ), X ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP(
% 1.18/1.56 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ) ) ],
% 1.18/1.56 [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.56 'tc_nat' ) ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) )
% 1.18/1.56 ],
% 1.18/1.56 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP( 'c_Suc',
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.18/1.56 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, hAPP(
% 1.18/1.56 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.18/1.56 X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.18/1.56 'c_Suc', Y ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc',
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.56 'tc_nat' ) ), 'tc_nat' ), X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.56 'tc_nat' ) ), 'tc_nat' ), Y ) ) ) ],
% 1.18/1.56 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.18/1.56 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.18/1.56 ) ],
% 1.18/1.56 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.18/1.56 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.18/1.56 ) ],
% 1.18/1.56 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.18/1.56 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 1.18/1.56 ) ],
% 1.18/1.56 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.18/1.56 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.18/1.56 'c_Groebner__Basis_Ogb__semiring'( W, Y, X, V0, V1, V2 ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( Z, hAPP(
% 1.18/1.56 hAPP( X, Y ), T ) ), hAPP( hAPP( X, Y ), U ) ) ), ~(
% 1.18/1.56 'c_Groebner__Basis_Ogb__semiring'( Z, X, W, V0, V1, V2 ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.18/1.56 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.18/1.56 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.18/1.56 , V0, V1, V2 ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.18/1.56 T, X, U, W, Y, V0 ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.18/1.56 T, X, U, Y, W, V0 ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.18/1.56 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.18/1.56 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.18/1.56 , V0, V1, V2 ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.18/1.56 X, T, U, Y, W, V0 ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.18/1.56 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.18/1.56 , V0, V1, V2 ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.18/1.56 'c_Groebner__Basis_Ogb__semiring'( X, T, U, W, V0, V1 ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.18/1.56 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U, W
% 1.18/1.56 , V0, V1, V2 ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.18/1.56 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.18/1.56 W, V0, V1, V2 ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.18/1.56 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, U,
% 1.18/1.56 W, V0, V1, V2 ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.18/1.56 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.18/1.56 ~( 'c_Groebner__Basis_Ogb__semiring'( X, W, V0, V1, V2, V3 ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, Z ),
% 1.18/1.56 hAPP( hAPP( X, Y ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.18/1.56 W, V0, V1, V2 ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), T ) ), hAPP( hAPP( X, hAPP(
% 1.18/1.56 hAPP( X, Y ), Z ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.18/1.56 , V0, V1, V2 ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, Y ),
% 1.18/1.56 hAPP( hAPP( X, Z ), T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X,
% 1.18/1.56 W, V0, V1, V2 ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), T ), hAPP( hAPP( X, hAPP(
% 1.18/1.56 hAPP( X, Y ), T ) ), Z ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, W
% 1.18/1.56 , V0, V1, V2 ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.18/1.56 , hAPP( hAPP( X, T ), hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), U ) ) ),
% 1.18/1.56 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.18/1.56 , hAPP( hAPP( X, Y ), hAPP( hAPP( X, Z ), hAPP( hAPP( X, T ), U ) ) ) ),
% 1.18/1.56 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( X, hAPP( hAPP( X, Y ), Z ) ), hAPP( hAPP( X, T ), U ) )
% 1.18/1.56 , hAPP( hAPP( X, hAPP( hAPP( X, Y ), T ) ), hAPP( hAPP( X, Z ), U ) ) ),
% 1.18/1.56 ~( 'c_Groebner__Basis_Ogb__semiring'( W, X, V0, V1, V2, V3 ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.18/1.56 T, X, U, W, Z, V0 ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.18/1.56 T, X, U, W, Y, V0 ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.18/1.56 T, X, U, Z, W, V0 ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.18/1.56 T, X, U, Y, W, V0 ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), U ), hAPP( hAPP( Y, hAPP(
% 1.18/1.56 hAPP( X, Z ), U ) ), hAPP( hAPP( X, T ), U ) ) ), ~(
% 1.18/1.56 'c_Groebner__Basis_Ogb__semiring'( Y, X, W, V0, V1, V2 ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Z ), Y ) ), ~(
% 1.18/1.56 'c_Groebner__Basis_Ogb__semiring'( T, X, U, W, V0, V1 ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( X, Y ), Z ), Y ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.18/1.56 X, T, U, Z, W, V0 ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( X, Y ), Z ), Z ), ~( 'c_Groebner__Basis_Ogb__semiring'(
% 1.18/1.56 X, T, U, Y, W, V0 ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( X, Y ), Y ), hAPP( hAPP( Z, hAPP( hAPP( X, T ), T ) ),
% 1.18/1.56 Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, U, W, T, V0 ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), Y ) ), hAPP( hAPP( Z, hAPP(
% 1.18/1.56 hAPP( X, T ), U ) ), Y ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Z, W
% 1.18/1.56 , V0, U, V1 ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), T ), hAPP( hAPP( Y, hAPP(
% 1.18/1.56 hAPP( X, Z ), U ) ), T ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( X, Y, W
% 1.18/1.56 , V0, U, V1 ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), T ) )
% 1.18/1.56 , hAPP( hAPP( Y, hAPP( hAPP( X, Z ), U ) ), T ) ), ~(
% 1.18/1.56 'c_Groebner__Basis_Ogb__semiring'( X, Y, W, V0, V1, V2 ) ) ],
% 1.18/1.56 [ =( X, hAPP( 'c_Suc', Y ) ), hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' )
% 1.18/1.56 , Y ) ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( 'c_Suc', Y
% 1.18/1.56 ) ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.18/1.56 Y ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), X ) ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ), ~(
% 1.18/1.56 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), hAPP( 'c_Suc', X )
% 1.18/1.56 ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), X ) ), hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), X ) ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.56 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, 'tc_nat' ), T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X
% 1.18/1.56 , 'tc_nat' ), Z ) ) ) ],
% 1.18/1.56 [ ~( =( X, hAPP( hAPP( Y, X ), Z ) ) ), ~(
% 1.18/1.56 'c_Groebner__Basis_Osemiringb'( Y, T, U, W, V0, V1 ) ), =( Z, W ) ],
% 1.18/1.56 [ ~( =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( X, Y ), T ) ) ), ~(
% 1.18/1.56 'c_Groebner__Basis_Osemiringb'( X, U, W, V0, V1, V2 ) ), =( Z, T ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z )
% 1.18/1.56 , X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~(
% 1.18/1.56 hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, 'tc_nat' ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.18/1.56 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), X ), hAPP(
% 1.18/1.56 hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), T ) ) ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, 'tc_nat' ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.18/1.56 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Y ), X ), hAPP(
% 1.18/1.56 hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), T ) ) ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.56 'tc_nat' ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 1.18/1.56 ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.56 'tc_nat' ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat'
% 1.18/1.56 ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Y ) ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.18/1.56 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), =( Z, Y ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.18/1.56 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.18/1.56 Y, X ), Z ) ) ), =( Z, Y ) ],
% 1.18/1.56 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.18/1.56 Y, X ), Z ) ) ) ],
% 1.18/1.56 [ ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ) ), =( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), X ), Y ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ) ],
% 1.18/1.56 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X
% 1.18/1.56 ), Z ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ],
% 1.18/1.56 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y
% 1.18/1.56 , X ), Z ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) )
% 1.18/1.56 ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.18/1.56 X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.18/1.56 X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ) ) ],
% 1.18/1.56 [ ~( 'c_Groebner__Basis_Osemiringb'( X, Y, Z, T, U, W ) ), =( V0, hAPP(
% 1.18/1.56 hAPP( X, V0 ), T ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, Z ), U ) )
% 1.18/1.56 , hAPP( hAPP( X, hAPP( hAPP( Y, Z ), U ) ), hAPP( hAPP( Y, Z ), T ) ) ),
% 1.18/1.56 ~( 'c_Groebner__Basis_Osemiringb'( X, Y, W, V0, V1, V2 ) ) ],
% 1.18/1.56 [ ~( 'c_Groebner__Basis_Osemiringb'( X, Y, Z, T, U, W ) ), =( hAPP( hAPP(
% 1.18/1.56 X, hAPP( hAPP( Y, V0 ), V1 ) ), hAPP( hAPP( Y, V0 ), V2 ) ), hAPP( hAPP(
% 1.18/1.56 X, hAPP( hAPP( Y, V0 ), V2 ) ), hAPP( hAPP( Y, V0 ), V1 ) ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Y ), X ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), Y ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.18/1.56 [ ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ), =( Y, hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), X ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, 'tc_nat' ), X ) ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.56 'tc_nat' ), Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.56 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.56 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.56 'tc_nat' ), Y ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( 'c_Suc', Y ) ) ),
% 1.18/1.56 ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( hAPP( 'c_Suc', X ), 'tc_nat' ), Y ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.56 'tc_nat' ) ), 'tc_nat' ), Y ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.56 'tc_nat' ) ), 'tc_nat' ), X ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.56 'tc_nat' ) ), 'tc_nat' ), Y ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.56 'tc_nat' ) ), 'tc_nat' ), X ) ) ) ],
% 1.18/1.56 [ ~( hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_Suc', X ), 'tc_nat' ), X ) )
% 1.18/1.56 ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y
% 1.18/1.56 , 'tc_nat' ), X ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.18/1.56 'tc_nat' ), X ), Z ), 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z
% 1.18/1.56 , 'tc_nat' ), X ) ) ) ],
% 1.18/1.56 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), Y ) ) ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), X ) ) ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.56 'tc_nat' ), X ), Z ), 'tc_nat' ), Y ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), Z ) ), ~(
% 1.18/1.56 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.56 'tc_nat' ), Z ), X ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.56 'tc_nat' ), Z ), Y ) ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.56 'tc_nat' ) ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.56 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_Suc',
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), Y ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.18/1.56 ) ), 'tc_nat' ), X ) ) ) ],
% 1.18/1.56 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y
% 1.18/1.56 , X ), Y ) ) ],
% 1.18/1.56 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X
% 1.18/1.56 ), Y ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), X ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X
% 1.18/1.56 , 'tc_nat' ), Z ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), X ) ) ],
% 1.18/1.56 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.18/1.56 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.18/1.56 T, X ), Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T ) )
% 1.18/1.56 ) ],
% 1.18/1.56 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y
% 1.18/1.56 , X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( T, X ), Z ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.18/1.56 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( T, X ), Z ) ) ) ],
% 1.18/1.56 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.18/1.56 Y, X ), T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ), Z ) )
% 1.18/1.56 ) ],
% 1.18/1.56 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X
% 1.18/1.56 ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( T, X ), Z ) ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( 'c_Suc',
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.18/1.56 [ =( X, Y ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ),
% 1.18/1.56 hAPP( 'c_Suc', Y ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ),
% 1.18/1.56 X ) ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), Y ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), X ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_Suc', X ), 'tc_nat' ), hAPP(
% 1.18/1.56 'c_Suc', Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) )
% 1.18/1.56 ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( hAPP( 'c_Suc', X ), 'tc_nat' ), hAPP( 'c_Suc', Y ) ) ) )
% 1.18/1.56 ],
% 1.18/1.56 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ) ],
% 1.18/1.56 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y
% 1.18/1.56 , X ), Z ) ), hBOOL( hAPP( 'c_lessequals'( Z, X ), Y ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, 'tc_nat' ), X ) ) ],
% 1.18/1.56 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ) ],
% 1.18/1.56 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ) ],
% 1.18/1.56 [ ~( 'class_Orderings_Oorder'( X ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), hAPP( hAPP(
% 1.18/1.56 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.56 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.56 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.18/1.56 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), T ) ),
% 1.18/1.56 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.56 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), T ) ) ), Y ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( T, 'tc_nat' ), Z ) ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.56 'c_Finite__Set_Osetsum'( 'tc_nat', X ), Y ),
% 1.18/1.56 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, hAPP( 'c_Suc', T ),
% 1.18/1.56 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( T, 'tc_nat' ), Z ) ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.56 'c_Finite__Set_Osetsum'( 'tc_nat', X ), Y ),
% 1.18/1.56 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, hAPP( 'c_Suc', T ),
% 1.18/1.56 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.56 'c_Finite__Set_Osetsum'( 'tc_nat', X ), Y ),
% 1.18/1.56 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ) ) ), hAPP(
% 1.18/1.56 Y, T ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, 'tc_nat' ), Z ) )
% 1.18/1.56 ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.18/1.56 'c_Finite__Set_Osetsum'( 'tc_nat', X ), Y ),
% 1.18/1.56 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ) ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( Y, Z ) ), hAPP( hAPP(
% 1.18/1.56 'c_Finite__Set_Osetsum'( 'tc_nat', X ), Y ),
% 1.18/1.56 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( 'c_Suc', Z ), T,
% 1.18/1.56 'tc_nat' ) ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, 'tc_nat'
% 1.18/1.56 ), T ) ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' )
% 1.18/1.56 , 'c_FFT__Mirabelle_Oroot'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.56 'tc_nat' ), X ), Y ) ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.56 'tc_nat' ), X ), Z ) ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.18/1.56 'tc_Complex_Ocomplex' ), 'c_FFT__Mirabelle_Oroot'( Y ) ), Z ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.56 'tc_nat' ), X ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.56 , T ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y )
% 1.18/1.56 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.56 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.18/1.56 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ), ~(
% 1.18/1.56 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.56 , T ), Y ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.18/1.56 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.56 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.18/1.56 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) ), ~(
% 1.18/1.56 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.56 X ), Y ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.56 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.18/1.56 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.56 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T
% 1.18/1.56 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.56 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.18/1.56 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) ), ~(
% 1.18/1.56 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.56 X ), Y ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.56 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.18/1.56 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ), ~(
% 1.18/1.56 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.56 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.18/1.56 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( T, X ), Y ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.56 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.18/1.56 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.56 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.18/1.56 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ), ~(
% 1.18/1.56 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.56 X ), Z ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.56 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.18/1.56 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ), Y ) ) ), ~(
% 1.18/1.56 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.18/1.56 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.18/1.56 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.18/1.56 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.56 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z
% 1.18/1.56 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.18/1.56 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.18/1.56 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.18/1.56 , Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z )
% 1.18/1.56 , Y ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.18/1.56 , Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z )
% 1.18/1.56 , Y ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.56 X ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.18/1.56 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.56 X ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.18/1.56 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.56 X ), X ), Y ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.56 X ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.18/1.56 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.56 X ), X ), Z ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.18/1.56 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~(
% 1.18/1.56 hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) )
% 1.18/1.56 ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.18/1.56 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~(
% 1.18/1.56 hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) )
% 1.18/1.56 ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.18/1.56 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~(
% 1.18/1.56 hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) )
% 1.18/1.56 ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.18/1.56 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~(
% 1.18/1.56 hBOOL( hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.18/1.56 ), ~( hBOOL( hAPP( 'c_lessequals'( T, X ), Z ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.18/1.56 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~(
% 1.18/1.56 hBOOL( hAPP( 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.18/1.56 ), ~( hBOOL( hAPP( 'c_lessequals'( T, X ), Y ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, X ), Z ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.56 Y, X ), Z ) ) ],
% 1.18/1.56 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.18/1.56 Y, X ), Z ) ) ), =( Y, Z ) ],
% 1.18/1.56 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), =( X, Y
% 1.18/1.56 ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.18/1.56 [ =( X, Y ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y )
% 1.18/1.56 ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), =( X, Y
% 1.18/1.56 ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.18/1.56 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.18/1.56 Y, X ), Z ) ) ) ],
% 1.18/1.56 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, X ), Z ) ) ) ],
% 1.18/1.56 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.18/1.56 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.18/1.56 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, hAPP( 'c_Suc'
% 1.18/1.56 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.18/1.56 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.18/1.56 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.18/1.56 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.18/1.56 , X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ],
% 1.18/1.56 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP(
% 1.18/1.56 'c_Suc', X ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' )
% 1.18/1.56 , hAPP( 'c_Suc', X ) ), Z ) ) ), =( Y, Z ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), 'tc_nat' ), Y ) ) )
% 1.18/1.56 ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.18/1.56 Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) )
% 1.18/1.56 ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.56 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( X, 'tc_nat' ), Z ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.56 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.56 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.56 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( X, 'tc_nat' ), Z ) ) ) ],
% 1.18/1.56 [ ~( =( hAPP( 'c_Suc', X ), X ) ) ],
% 1.18/1.56 [ ~( =( X, hAPP( 'c_Suc', X ) ) ) ],
% 1.18/1.56 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ) ) ), =( Z, T ), =( Y
% 1.18/1.56 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.56 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ),
% 1.18/1.56 'c_Deriv_Odifferentiable'( Y, Z, X ), ~( 'c_Deriv_Oderiv'( Y, Z, T, X ) )
% 1.18/1.56 ],
% 1.18/1.56 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ),
% 1.18/1.56 'c_Deriv_Odifferentiable'( Y, Z, X ), ~( 'c_Deriv_Oderiv'( Y, Z, T, X ) )
% 1.18/1.56 ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.56 'tc_nat' ), Z ), X ), 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.56 'tc_nat' ), X ), Z ), 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', Z ) ), hAPP( hAPP( T, Y ), hAPP(
% 1.18/1.56 hAPP( X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W,
% 1.18/1.56 V0, V1 ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( X, Y ), hAPP( 'c_Suc', Z ) ), hAPP( hAPP( T, Y ), hAPP(
% 1.18/1.56 hAPP( X, Y ), Z ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, T, X, W,
% 1.18/1.56 V0, V1 ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), Z ), hAPP( hAPP( Y, Z ),
% 1.18/1.56 hAPP( 'c_Suc', T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Y, W
% 1.18/1.56 , V0, V1 ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, Y ), T ) ), hAPP( hAPP( Z, Y ),
% 1.18/1.56 hAPP( 'c_Suc', T ) ) ), ~( 'c_Groebner__Basis_Ogb__semiring'( U, X, Z, W
% 1.18/1.56 , V0, V1 ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.56 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.56 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ),
% 1.18/1.56 Z ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ),
% 1.18/1.56 X ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z )
% 1.18/1.56 , Y ) ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.56 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.56 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ),
% 1.18/1.56 Z ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.18/1.56 X ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.18/1.56 X ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), 'tc_nat' )
% 1.18/1.56 , Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), Y ) )
% 1.18/1.56 ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP(
% 1.18/1.56 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) )
% 1.18/1.56 ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), hAPP( 'c_Suc', Y ) )
% 1.18/1.56 ), ~( hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ), =( Z, Y ) ],
% 1.18/1.56 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ],
% 1.18/1.56 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ],
% 1.18/1.56 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), =( Z, Y ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ],
% 1.18/1.56 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, X ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ),
% 1.18/1.56 Y ) ) ) ],
% 1.18/1.56 [ =( X, Y ), ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) ) ), ~(
% 1.18/1.56 hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), X ) ), =( Y, X ) ],
% 1.18/1.56 [ ~( 'class_RealVector_Ometric__space'( X ) ), =( Y, Z ), ~(
% 1.18/1.56 'c_SEQ_OLIMSEQ'( T, Z, X ) ), ~( 'c_SEQ_OLIMSEQ'( T, Y, X ) ) ],
% 1.18/1.56 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( Y, Z ), ~(
% 1.18/1.56 'c_Deriv_Oderiv'( T, U, Z, X ) ), ~( 'c_Deriv_Oderiv'( T, U, Y, X ) ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ), =( Z, Y ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), Y ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), X ) ), =( Y, X ) ],
% 1.18/1.56 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Z, X ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.18/1.56 Z ) ) ) ],
% 1.18/1.56 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ), =( Z, Y ) ],
% 1.18/1.56 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Z, X ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.18/1.56 Z ) ) ) ],
% 1.18/1.56 [ =( 'c_HOL_Oord__class_Oless'( 'v_n', 'tc_nat' ), 'c_lessequals'( hAPP(
% 1.18/1.56 'c_Suc', 'v_n' ), 'tc_nat' ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ), Y ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( Z, 'tc_nat' ), X ) ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.18/1.56 'c_Suc', Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.18/1.56 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.18/1.56 , X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ),
% 1.18/1.56 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.56 'tc_nat' ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.56 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Y ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.56 'tc_nat' ), X ) ) ) ],
% 1.18/1.56 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( X, 'tc_nat' ), T ) ) ), =( Z, hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), X ) ), Y ) ), U ) ) ],
% 1.18/1.56 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( T, 'tc_nat' ), X ) ) ), =( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), T ) ), Y ) ), Z ), U ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ), =( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), Z ) ), T ) ) ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 1.18/1.56 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.18/1.56 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ],
% 1.18/1.56 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.18/1.56 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, hAPP(
% 1.18/1.56 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.18/1.56 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.18/1.56 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.18/1.56 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.18/1.56 , X ) ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.18/1.56 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ),
% 1.18/1.56 X ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.56 'tc_nat' ), X ), Z ), 'tc_nat' ), Y ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_Suc', X ), 'tc_nat' ), Y ) ),
% 1.18/1.56 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( hAPP( 'c_Suc', X ), 'tc_nat' ), Y ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_Suc', X ), 'tc_nat' ), Y ) ),
% 1.18/1.56 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( hAPP( 'c_Suc', X ), 'tc_nat' ), Y ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.56 'tc_nat' ), X ), Y ), 'tc_nat' ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.18/1.56 X, 'tc_nat' ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z )
% 1.18/1.56 , Y ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.18/1.56 Z ), 'tc_nat' ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ),
% 1.18/1.56 Y ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.18/1.56 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.18/1.56 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.18/1.56 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), 'tc_nat' ),
% 1.18/1.56 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), X ) ), Y ) ), U ) ) ) ),
% 1.18/1.56 ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), T ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), T ) ), U ) ) ), ~(
% 1.18/1.56 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), X ), 'tc_nat' ),
% 1.18/1.56 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ), U ) ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), 'tc_nat' ),
% 1.18/1.56 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), T ), Y ) ), U ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.56 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), T ) ), Y ) ), Z ),
% 1.18/1.56 'tc_nat' ), U ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( T, 'tc_nat' ), X ) )
% 1.18/1.56 ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ) ), T ),
% 1.18/1.56 'tc_nat' ), U ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), T ), 'tc_nat' ),
% 1.18/1.56 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), U ) ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.18/1.56 , hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ) ), Z )
% 1.18/1.56 , hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc', X
% 1.18/1.56 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ),
% 1.18/1.56 ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.56 'tc_nat' ) ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ),
% 1.18/1.56 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, 'tc_nat' ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.18/1.56 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), X ),
% 1.18/1.56 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.18/1.56 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc',
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_RealVector_Ometric__space'( X ) ), 'c_SEQ_OLIMSEQ'(
% 1.18/1.56 'c_COMBB'( Y, 'c_Suc', 'tc_nat', X, 'tc_nat' ), Z, X ), ~(
% 1.18/1.56 'c_SEQ_OLIMSEQ'( Y, Z, X ) ) ],
% 1.18/1.56 [ ~( 'class_RealVector_Ometric__space'( X ) ), 'c_SEQ_OLIMSEQ'( Y, Z, X
% 1.18/1.56 ), ~( 'c_SEQ_OLIMSEQ'( 'c_COMBB'( Y, 'c_Suc', 'tc_nat', X, 'tc_nat' ), Z
% 1.18/1.56 , X ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.56 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.56 'tc_nat' ), X ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.56 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.56 'tc_nat' ), Y ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.18/1.56 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ],
% 1.18/1.56 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ) ],
% 1.18/1.56 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.56 'tc_nat' ), 'tc_nat' ), X ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.56 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X )
% 1.18/1.56 ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( X, 'tc_nat' ), Z ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.18/1.56 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), ~(
% 1.18/1.56 hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) )
% 1.18/1.56 ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.18/1.56 , T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), U ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.18/1.56 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), ~(
% 1.18/1.56 hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) )
% 1.18/1.56 ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X )
% 1.18/1.56 , Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), U ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.18/1.56 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.56 X ), Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.18/1.56 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.56 X ), Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.56 X ), Y ), Y ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.18/1.56 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.18/1.56 Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.18/1.56 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.18/1.56 , Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.18/1.56 , Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.18/1.56 , Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.18/1.56 , Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y )
% 1.18/1.56 , Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ),
% 1.18/1.56 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.18/1.56 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), T ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.56 , Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.18/1.56 ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ),
% 1.18/1.56 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.18/1.56 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), T ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.56 , Z ), Y ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y )
% 1.18/1.56 ) ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.56 X ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.18/1.56 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.18/1.56 ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.56 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z )
% 1.18/1.56 , T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.56 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z )
% 1.18/1.56 , T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), Z ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.18/1.56 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), =( Y,
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.18/1.56 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), =( Z,
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.18/1.56 ), Y ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.18/1.56 ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.18/1.56 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.18/1.56 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.18/1.56 ), Y ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.18/1.56 ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.56 X ), Z ), T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T )
% 1.18/1.56 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.18/1.56 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.56 ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ) ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.18/1.56 ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.56 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.18/1.56 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.56 X ), X ), Y ) ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y
% 1.18/1.56 ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), X
% 1.18/1.56 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.18/1.56 Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z
% 1.18/1.56 ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.18/1.56 'c_COMBB'( Y, Z, X, X, X ), T, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.56 X ), U ), W ), X ), ~( 'c_Deriv_Oderiv'( Z, T, W, X ) ), ~(
% 1.18/1.56 'c_Deriv_Oderiv'( Y, hAPP( Z, T ), U, X ) ) ],
% 1.18/1.56 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.18/1.56 'c_COMBB'( Y, Z, X, X, X ), T, hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.56 X ), U ), W ), X ), ~( 'c_Deriv_Oderiv'( Y, hAPP( Z, T ), U, X ) ), ~(
% 1.18/1.56 'c_Deriv_Oderiv'( Z, T, W, X ) ) ],
% 1.18/1.56 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.18/1.56 'c_COMBB'( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X, X ), T
% 1.18/1.56 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ), X ), ~(
% 1.18/1.56 'c_Deriv_Oderiv'( Z, T, U, X ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ),
% 1.18/1.56 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.18/1.56 Y, X ), Z ) ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), X ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X )
% 1.18/1.56 , Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X )
% 1.18/1.56 , Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.56 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), X ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.56 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.18/1.56 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.56 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), Z ) ) ),
% 1.18/1.56 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X )
% 1.18/1.56 , X ), Y ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.56 X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP(
% 1.18/1.56 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.18/1.56 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_Power_Opower__class_Opower'( X ), Y ), Z ), X ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z )
% 1.18/1.56 , X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ), ~(
% 1.18/1.56 hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) )
% 1.18/1.56 ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.18/1.56 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.18/1.56 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.56 hAPP( 'c_Suc', Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.18/1.56 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.18/1.56 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.18/1.56 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.18/1.56 ],
% 1.18/1.56 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_SEQ_OLIMSEQ'(
% 1.18/1.56 'c_COMBB'( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X,
% 1.18/1.56 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X )
% 1.18/1.56 , ~( 'c_SEQ_OLIMSEQ'( Z, T, X ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.18/1.56 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.56 X ), Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), X ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.18/1.56 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.56 X ), Z ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ), X ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.18/1.56 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.18/1.56 ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.18/1.56 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.18/1.56 ), Z ), Y ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z
% 1.18/1.56 ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z
% 1.18/1.56 ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.18/1.56 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.56 X ), Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.18/1.56 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.56 X ), Z ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.18/1.56 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.56 X ), Z ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.18/1.56 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.56 X ), Y ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oinverse__class_Odivide'( X ), Z ), Y ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z
% 1.18/1.56 ), X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) ),
% 1.18/1.56 ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z )
% 1.18/1.56 ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z
% 1.18/1.56 ), X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) ),
% 1.18/1.56 ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.18/1.56 ) ), ~( hBOOL( hAPP( 'c_lessequals'( T, X ), Y ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.18/1.56 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ),
% 1.18/1.56 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ), Y ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.18/1.56 ), Y ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.18/1.56 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.56 X ), Z ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.18/1.56 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ),
% 1.18/1.56 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.18/1.56 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.18/1.56 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.18/1.56 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.56 X ), X ), Y ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.18/1.56 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.56 X ), X ), Y ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.18/1.56 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.18/1.56 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T )
% 1.18/1.56 , Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.18/1.56 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T )
% 1.18/1.56 , Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( T, X ), Y ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y
% 1.18/1.56 ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z
% 1.18/1.56 ), Y ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y
% 1.18/1.56 ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Z
% 1.18/1.56 ), Y ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.18/1.56 ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.18/1.56 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.18/1.56 ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.18/1.56 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.56 X ), X ), Y ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.18/1.56 ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.18/1.56 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.56 X ), X ), Y ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.18/1.56 ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.18/1.56 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.18/1.56 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.56 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.56 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.18/1.56 Z ), 'tc_nat' ), Y ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ),
% 1.18/1.56 X ), 'tc_nat' ), Y ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( X, 'tc_nat' ), Y ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( X, 'tc_nat' ), Z ) ) ) ],
% 1.18/1.56 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.18/1.56 Y, X ), Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), Y ) )
% 1.18/1.56 ) ],
% 1.18/1.56 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP( 'c_lessequals'( Z
% 1.18/1.56 , X ), Y ) ) ],
% 1.18/1.56 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.18/1.56 Y, X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Y ) )
% 1.18/1.56 ) ],
% 1.18/1.56 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Y ) ), hBOOL( hAPP( 'c_lessequals'( Y
% 1.18/1.56 , X ), Y ) ) ],
% 1.18/1.56 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Z, X ), Y ) ) ) ],
% 1.18/1.56 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( 'c_lessequals'( Y
% 1.18/1.56 , X ), Z ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP( 'c_lessequals'( Z
% 1.18/1.56 , X ), Y ) ) ],
% 1.18/1.56 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.18/1.56 Y, X ), Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), Y ) )
% 1.18/1.56 ) ],
% 1.18/1.56 [ ~( =( hAPP( hAPP( X, Y ), hAPP( hAPP( Z, T ), U ) ), hAPP( hAPP( X, Y
% 1.18/1.56 ), hAPP( hAPP( Z, T ), W ) ) ) ), =( U, W ), =( T, V0 ), ~(
% 1.18/1.56 'c_Groebner__Basis_Osemiringb'( X, Z, V1, V0, V2, V3 ) ) ],
% 1.18/1.56 [ ~( =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), W
% 1.18/1.56 ) ), hAPP( hAPP( X, hAPP( hAPP( Y, Z ), W ) ), hAPP( hAPP( Y, U ), T ) )
% 1.18/1.56 ) ), ~( 'c_Groebner__Basis_Osemiringb'( X, Y, V0, V1, V2, V3 ) ), =( T,
% 1.18/1.56 W ), =( Z, U ) ],
% 1.18/1.56 [ ~( =( hAPP( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( Y, U ), W
% 1.18/1.56 ) ), hAPP( hAPP( X, hAPP( hAPP( Y, Z ), W ) ), hAPP( hAPP( Y, U ), T ) )
% 1.18/1.56 ) ), =( T, W ), =( Z, U ), ~( 'c_Groebner__Basis_Osemiringb'( X, Y, V0,
% 1.18/1.56 V1, V2, V3 ) ) ],
% 1.18/1.56 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.18/1.56 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~(
% 1.18/1.56 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.56 'tc_nat' ), 'tc_nat' ), X ) ) ), =( Y, Z ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.56 'tc_nat' ), 'tc_nat' ), X ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.56 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat'
% 1.18/1.56 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) )
% 1.18/1.56 ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.56 'tc_nat' ), 'tc_nat' ), X ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.56 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ), 'tc_nat'
% 1.18/1.56 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ) ) ) )
% 1.18/1.56 ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.56 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.56 'tc_nat' ), X ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z )
% 1.18/1.56 , X ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.18/1.56 Z ), Y ) ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Z ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.56 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ), 'tc_nat' ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.56 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ) ],
% 1.18/1.56 [ =( X, hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X
% 1.18/1.56 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), hAPP( 'c_Suc', hAPP( 'c_Suc',
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.56 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.56 'tc_nat' ), 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ), T ) ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), T ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.56 'tc_nat' ), 'tc_nat' ), X ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.56 'tc_nat' ), 'tc_nat' ), X ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.56 'tc_nat' ), hAPP( 'c_Suc', Z ) ), X ), 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), Y ) ) ) )
% 1.18/1.56 ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y ),
% 1.18/1.56 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP(
% 1.18/1.56 'c_Suc', X ) ), Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.56 'tc_nat' ), Z ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), 'tc_nat' )
% 1.18/1.56 , Y ) ), =( hAPP( 'c_Suc', X ), Y ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_Suc', X ), 'tc_nat' ), Y ) ),
% 1.18/1.56 hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) ) ],
% 1.18/1.56 [ ~( hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( hAPP( 'c_Suc', Y ), 'tc_nat' ), X ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), Z ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.18/1.56 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.18/1.56 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP( 'c_Suc',
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.18/1.56 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.18/1.56 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.18/1.56 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.18/1.56 hAPP( 'c_Suc', Z ) ), X ), 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', Z ) ), Y ) ) ) )
% 1.18/1.56 ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.56 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Z ) ) ),
% 1.18/1.56 ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.18/1.56 X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( hAPP( 'c_Suc', X ), 'tc_nat' ), hAPP(
% 1.18/1.56 'c_Suc', X ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), X ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.56 'tc_nat' ), X ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.56 'tc_nat' ), Z ), X ), 'tc_nat' ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.56 'tc_nat' ), Z ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.56 'tc_nat' ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X,
% 1.18/1.56 'tc_nat' ), Z ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.56 'tc_nat' ), X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.56 'tc_nat' ), Z ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.56 'tc_nat' ), X ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.56 'tc_nat' ), Y ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.56 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.56 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.18/1.56 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Z, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.18/1.56 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Z, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), 'tc_nat' )
% 1.18/1.56 , hAPP( 'c_Suc', Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X,
% 1.18/1.56 'tc_nat' ), Y ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), 'tc_nat' ), hAPP(
% 1.18/1.56 'c_Suc', Y ) ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( 'c_Suc', X ), 'tc_nat' )
% 1.18/1.56 , hAPP( 'c_Suc', Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X,
% 1.18/1.56 'tc_nat' ), Y ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.56 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U
% 1.18/1.56 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( Z, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.56 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U
% 1.18/1.56 ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.56 X ), Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Z, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.56 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U
% 1.18/1.56 ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.56 X ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.56 X ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), U )
% 1.18/1.56 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.56 X ), Y ), T ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T
% 1.18/1.56 ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.56 X ), T ), Y ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z
% 1.18/1.56 ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.56 , Y ), T ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T )
% 1.18/1.56 ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.56 , T ), Y ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.18/1.56 ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.56 X ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U
% 1.18/1.56 ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.56 X ), Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Z, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.18/1.56 , ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.18/1.56 , ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.18/1.56 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~(
% 1.18/1.56 hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.18/1.56 ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.18/1.56 ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.18/1.56 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~(
% 1.18/1.56 hBOOL( hAPP( 'c_lessequals'( T, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.18/1.56 ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.18/1.56 ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.56 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.56 X ), Z ), T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ), ~(
% 1.18/1.56 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.56 X ), Z ) ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.56 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.18/1.56 ) ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.56 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.18/1.56 , ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.18/1.56 ) ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.56 X ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.18/1.56 , ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.56 ) ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.56 X ), Y ), Z ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.56 ) ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.56 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.56 X ), Z ), T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T )
% 1.18/1.56 ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X
% 1.18/1.56 ), Z ) ) ) ],
% 1.18/1.56 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ),
% 1.18/1.56 'c_Deriv_Odifferentiable'( 'c_COMBB'( Y, Z, X, X, X ), T, X ), ~(
% 1.18/1.56 'c_Deriv_Odifferentiable'( Z, T, X ) ), ~( 'c_Deriv_Odifferentiable'( Y,
% 1.18/1.56 hAPP( Z, T ), X ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.56 , Z ), T ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.18/1.56 ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Z, X ), Y ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.56 , T ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y )
% 1.18/1.56 ) ) ) ],
% 1.18/1.56 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.18/1.56 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, Y, X ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z )
% 1.18/1.56 , T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( U, X ), T ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.18/1.56 , Z ), U ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.18/1.56 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.56 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.56 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.18/1.56 ), T ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) )
% 1.18/1.56 ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.18/1.56 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.56 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.56 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T
% 1.18/1.56 ), Y ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ) )
% 1.18/1.56 ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.18/1.56 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Z, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ), hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z
% 1.18/1.56 ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~(
% 1.18/1.56 hBOOL( hAPP( 'c_lessequals'( Z, X ), U ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.56 , hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.18/1.56 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z )
% 1.18/1.56 ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.56 , hBOOL( hAPP( 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X
% 1.18/1.56 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.56 , hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.18/1.56 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T )
% 1.18/1.56 ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.18/1.56 , hBOOL( hAPP( 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ), X
% 1.18/1.56 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ), hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z
% 1.18/1.56 ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), ~(
% 1.18/1.56 hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ), hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z
% 1.18/1.56 ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), ~(
% 1.18/1.56 hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.18/1.56 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( 'c_Suc', Y ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.18/1.56 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.18/1.56 hAPP( 'c_Suc', T ) ), X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.18/1.56 ), Z ), hAPP( 'c_Suc', T ) ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.18/1.56 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.18/1.56 hAPP( 'c_Power_Opower__class_Opower'( X ), T ), hAPP( 'c_Suc', Z ) ) ) )
% 1.18/1.56 , =( Y, T ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.56 X ), X ), T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.18/1.56 ), Y ), T ), X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Z ),
% 1.18/1.56 T ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( U, X ), T ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), Y
% 1.18/1.56 ) ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Z, X ), Y ) ), ~( hBOOL( hAPP( 'c_lessequals'( U, X ), T
% 1.18/1.56 ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.56 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.18/1.56 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.18/1.56 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.18/1.56 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.18/1.56 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.18/1.56 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.18/1.56 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.56 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.56 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.18/1.56 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.56 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.56 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.56 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.18/1.56 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.56 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.56 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.18/1.56 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), X ), hAPP( hAPP(
% 1.18/1.56 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.18/1.56 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.18/1.56 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) ),
% 1.18/1.56 =( Z, T ) ],
% 1.18/1.56 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.18/1.56 hAPP( 'c_COMBC'( 'c_COMBB'( 'c_Power_Opower__class_Opower'( X ), Y, X,
% 1.18/1.56 'tc_fun'( 'tc_nat', X ), X ), X, 'tc_nat', X ), hAPP( 'c_Suc', Z ) ), T,
% 1.18/1.56 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.18/1.56 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), U ), hAPP( hAPP(
% 1.18/1.56 'c_Power_Opower__class_Opower'( X ), hAPP( Y, T ) ), Z ) ) ), X ), ~(
% 1.18/1.56 'c_Deriv_Oderiv'( Y, T, U, X ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.56 'tc_nat' ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.18/1.56 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.56 'tc_nat' ), X ) ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Y ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.56 'tc_nat' ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X
% 1.18/1.56 ) ) ) ) ],
% 1.18/1.56 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.18/1.56 X, 'tc_nat' ), Y ) ) ) ],
% 1.18/1.56 [ ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hBOOL( hAPP( 'c_lessequals'(
% 1.18/1.56 X, 'tc_nat' ), Y ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ) ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), X ) ),
% 1.18/1.56 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.56 'tc_nat' ), 'tc_nat' ), X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.18/1.56 'tc_nat' ), Y ) ) ) ],
% 1.18/1.56 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.18/1.56 hAPP( 'c_COMBC'( 'c_COMBB'( 'c_Power_Opower__class_Opower'( X ), Y, X,
% 1.18/1.56 'tc_fun'( 'tc_nat', X ), X ), X, 'tc_nat', X ), Z ), T, hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.18/1.56 Z, X ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), hAPP( hAPP(
% 1.18/1.56 'c_Power_Opower__class_Opower'( X ), hAPP( Y, T ) ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), hAPP( 'c_Suc',
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ), X ), ~(
% 1.18/1.56 'c_Deriv_Oderiv'( Y, T, U, X ) ) ],
% 1.18/1.56 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'v_i', 'tc_nat' ), 'v_n' ) ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ) ), =( Y,
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ) ), =( Z,
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), X ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), X ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.56 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.18/1.56 ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.56 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), X ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ), X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.56 ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.18/1.56 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.18/1.56 X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.18/1.56 'c_HOL_Oone__class_Oone'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.18/1.56 X ), Y ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ),
% 1.18/1.56 'c_HOL_Oone__class_Oone'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.18/1.56 'c_HOL_Oone__class_Oone'( X ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ) ), U ), X ), W ) ),
% 1.18/1.56 ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.18/1.56 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), U ), X ),
% 1.18/1.56 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), W ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.56 X ), U ), Z ) ), W ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.56 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T
% 1.18/1.56 ), X ), W ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), U ) ), W ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), Y ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.56 X ), Z ), U ) ), W ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.56 X ), U ), Z ) ), W ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( T, X ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.18/1.56 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ) ), U ), X ), W ) ),
% 1.18/1.56 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.18/1.56 X ), Y ), T ) ), U ), X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.18/1.56 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), W ) ) ) ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.18/1.56 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), X ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.18/1.56 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T ), X ), W ) ) ) ]
% 1.18/1.56 ,
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.56 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), U ) ), W ) ) ), ~( hBOOL(
% 1.18/1.56 hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.56 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), Y ), X )
% 1.18/1.56 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ), W ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.18/1.56 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), X ), hAPP(
% 1.18/1.56 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.18/1.56 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z
% 1.18/1.56 ), X ), T ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.18/1.56 X ), Y ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X )
% 1.18/1.56 , Z ), T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z
% 1.18/1.56 , X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ), ~(
% 1.18/1.56 hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.18/1.56 ), Y ), T ), X ), Z ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.18/1.56 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ), X ), Z ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.18/1.56 ), Y ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.56 , Y ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.18/1.56 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), Z ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.18/1.56 ), Y ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X
% 1.18/1.56 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ), ~(
% 1.18/1.56 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.56 X ), Z ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.56 , Y ), T ), X ), Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.18/1.56 ), Y ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X
% 1.18/1.56 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.56 , T ), Z ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X
% 1.18/1.56 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.18/1.56 ), Y ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.56 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.56 , T ), Z ), X ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X
% 1.18/1.56 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.18/1.56 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.56 , Y ), T ), X ), Z ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.18/1.56 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), hAPP( hAPP(
% 1.18/1.56 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ), ~( hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.56 , Y ), T ), X ), Z ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.56 , Y ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X )
% 1.18/1.56 , 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.18/1.56 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ),
% 1.18/1.56 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.56 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ), Y ) ) ) ],
% 1.18/1.56 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.56 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.18/1.57 ), Y ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X
% 1.18/1.57 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.18/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.57 , T ), Z ), X ), Y ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ],
% 1.18/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.18/1.57 ), Y ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.57 , T ), Z ), X ), Y ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ],
% 1.18/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.18/1.57 ), Y ), Z ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), hBOOL( hAPP(
% 1.18/1.57 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.18/1.57 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.18/1.57 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.18/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.57 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.18/1.57 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.57 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.18/1.57 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X )
% 1.18/1.57 , X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), hAPP(
% 1.18/1.57 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ) ) ) ],
% 1.18/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.57 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.18/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.57 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.18/1.57 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), hAPP( hAPP(
% 1.18/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ), hBOOL( hAPP(
% 1.18/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ]
% 1.18/1.57 ,
% 1.18/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.57 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.18/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.57 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.18/1.57 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), hAPP( hAPP(
% 1.18/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ), hBOOL( hAPP(
% 1.18/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ]
% 1.18/1.57 ,
% 1.18/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.57 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.18/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.18/1.57 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.18/1.57 , hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ),
% 1.18/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.18/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.18/1.57 , Y ), T ), X ), Z ) ) ) ],
% 1.18/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.18/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.18/1.57 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y )
% 1.18/1.57 , T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.18/1.57 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ), ~( hBOOL( hAPP(
% 1.18/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.18/1.57 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ), Z ) ) ) ],
% 1.18/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.18/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.18/1.57 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y )
% 1.18/1.57 , T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.18/1.57 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ), ~( hBOOL( hAPP(
% 1.18/1.57 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.18/1.57 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ), T ) ) ) ],
% 1.18/1.57 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ),
% 1.18/1.57 'c_Deriv_Odifferentiable'( 'c_COMBS'( 'c_COMBB'(
% 1.18/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'( X, X ), X ), Z, X, X,
% 1.18/1.57 X ), T, X ), ~( 'c_Deriv_Odifferentiable'( Z, T, X ) ), ~(
% 1.18/1.57 'c_Deriv_Odifferentiable'( Y, T, X ) ) ],
% 1.18/1.57 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.18/1.57 'c_COMBS'( 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'( X ), Y, X, 'tc_fun'( X
% 1.18/1.57 , X ), X ), Z, X, X, X ), T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.18/1.57 , U ), W ), X ), ~( 'c_Deriv_Oderiv'( Z, T, W, X ) ), ~( 'c_Deriv_Oderiv'(
% 1.18/1.57 Y, T, U, X ) ) ],
% 1.18/1.57 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ),
% 1.18/1.57 'c_Deriv_Odifferentiable'( 'c_COMBS'( 'c_COMBB'(
% 1.18/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y, X, 'tc_fun'( X, X ), X ), Z, X, X, X
% 1.18/1.57 ), T, X ), ~( 'c_Deriv_Odifferentiable'( Z, T, X ) ), ~(
% 1.18/1.57 'c_Deriv_Odifferentiable'( Y, T, X ) ) ],
% 1.18/1.57 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), =( Y,
% 1.18/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.18/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.18/1.57 hAPP( 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.57 ) ), Y ) ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.18/1.57 ],
% 1.18/1.57 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP(
% 1.18/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.18/1.57 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.18/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.18/1.57 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), ~( hBOOL( hAPP(
% 1.18/1.57 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.18/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.57 X ) ) ) ) ],
% 1.18/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.57 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), ~( hBOOL(
% 1.18/1.57 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.18/1.57 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.18/1.57 ) ) ) ) ],
% 1.18/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.57 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.18/1.57 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.18/1.57 ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.18/1.57 X ), Y ) ) ) ],
% 1.18/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.57 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL(
% 1.18/1.57 hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ),
% 1.18/1.57 'c_HOL_Oone__class_Oone'( X ) ), Y ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.57 ) ) ) ) ],
% 1.18/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.57 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ),
% 1.18/1.57 'c_HOL_Oone__class_Oone'( X ) ), Y ), X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.57 ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.18/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.57 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.18/1.57 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.18/1.57 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.18/1.57 ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.18/1.57 ), 'c_HOL_Oone__class_Oone'( X ) ), Y ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.57 X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.18/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.18/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ),
% 1.18/1.57 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.18/1.57 ), X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ),
% 1.18/1.57 'c_HOL_Oone__class_Oone'( X ) ), Y ) ) ) ) ],
% 1.18/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.18/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.18/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP(
% 1.18/1.57 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X )
% 1.18/1.57 ), Y ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.18/1.57 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.18/1.57 'c_COMBS'( 'c_COMBB'( 'c_HOL_Ominus__class_Ominus'( X ), Y, X, 'tc_fun'(
% 1.18/1.57 X, X ), X ), Z, X, X, X ), T, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.18/1.57 ), U ), W ), X ), ~( 'c_Deriv_Oderiv'( Z, T, W, X ) ), ~(
% 1.18/1.57 'c_Deriv_Oderiv'( Y, T, U, X ) ) ],
% 1.18/1.57 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ),
% 1.18/1.57 'c_Deriv_Odifferentiable'( 'c_COMBS'( 'c_COMBB'(
% 1.18/1.57 'c_HOL_Ominus__class_Ominus'( X ), Y, X, 'tc_fun'( X, X ), X ), Z, X, X,
% 1.18/1.57 X ), T, X ), ~( 'c_Deriv_Odifferentiable'( Z, T, X ) ), ~(
% 1.18/1.57 'c_Deriv_Odifferentiable'( Y, T, X ) ) ],
% 1.18/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.18/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), hAPP( hAPP(
% 1.18/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.18/1.57 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ), ~( hBOOL( hAPP(
% 1.18/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) ) ]
% 1.18/1.57 ,
% 1.18/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.18/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.18/1.57 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.18/1.57 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ), ~( hBOOL(
% 1.18/1.57 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), Y )
% 1.18/1.57 ) ) ],
% 1.18/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.18/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.18/1.57 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.57 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.18/1.57 'c_HOL_Oone__class_Oone'( X ) ) ), X ), Z ) ), ~( hBOOL( hAPP(
% 1.18/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ) ],
% 1.18/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.18/1.57 'c_HOL_Oord__class_Oless'( Y, X ), hAPP( hAPP(
% 1.18/1.57 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.18/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.18/1.57 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.18/1.57 'c_HOL_Oone__class_Oone'( X ) ) ) ) ), ~( hBOOL( hAPP(
% 1.18/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ) ],
% 1.18/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.18/1.57 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.18/1.57 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.18/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ), hAPP( hAPP(
% 1.18/1.57 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.18/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), U ), Z ) ) ), hAPP( hAPP(
% 1.18/1.57 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.18/1.57 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.18/1.57 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.18/1.57 'c_Power_Opower__class_Opower'( X ), Y ), U ) ) ), Z ) ), =( Y,
% 1.18/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.18/1.57 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.18/1.57 hAPP( 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Y, X,
% 1.18/1.57 'tc_fun'( X, X ), X ), X, X, X ), Z ), T, hAPP( hAPP(
% 1.18/1.57 'c_HOL_Oinverse__class_Odivide'( X ), U ), Z ), X ), ~( 'c_Deriv_Oderiv'(
% 1.18/1.57 Y, T, U, X ) ) ],
% 1.18/1.57 [ =( hAPP( hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat',
% 1.18/1.57 'tc_Complex_Ocomplex' ), hAPP( 'c_Power_Opower__class_Opower'(
% 1.18/1.57 'tc_Complex_Ocomplex' ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.18/1.57 'tc_Complex_Ocomplex' ), 'c_FFT__Mirabelle_Oroot'( X ) ), Y ) ) ),
% 1.18/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.57 'tc_nat' ), X, 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.18/1.57 'tc_Complex_Ocomplex' ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y,
% 1.18/1.57 'tc_nat' ), X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.18/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Y ) ) ) ],
% 1.18/1.57 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_SEQ_OLIMSEQ'(
% 1.18/1.57 'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'(
% 1.18/1.57 X, X ), 'tc_nat' ), Z, 'tc_nat', X, X ), hAPP( hAPP(
% 1.18/1.57 'c_HOL_Otimes__class_Otimes'( X ), T ), U ), X ), ~( 'c_SEQ_OLIMSEQ'( Z,
% 1.18/1.57 U, X ) ), ~( 'c_SEQ_OLIMSEQ'( Y, T, X ) ) ],
% 1.18/1.57 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_SEQ_OLIMSEQ'(
% 1.18/1.57 'c_COMBS'( 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'( X ), Y, X, 'tc_fun'( X
% 1.18/1.57 , X ), 'tc_nat' ), Z, 'tc_nat', X, X ), hAPP( hAPP(
% 1.18/1.57 'c_HOL_Oplus__class_Oplus'( X ), T ), U ), X ), ~( 'c_SEQ_OLIMSEQ'( Z, U
% 1.18/1.57 , X ) ), ~( 'c_SEQ_OLIMSEQ'( Y, T, X ) ) ],
% 1.18/1.57 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), 'c_SEQ_OLIMSEQ'(
% 1.18/1.57 hAPP( 'c_COMBC'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Y, X,
% 1.18/1.57 'tc_fun'( X, X ), 'tc_nat' ), 'tc_nat', X, X ), Z ), hAPP( hAPP(
% 1.18/1.57 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), ~( 'c_SEQ_OLIMSEQ'( Y,
% 1.18/1.57 T, X ) ) ],
% 1.18/1.57 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_SEQ_OLIMSEQ'(
% 1.18/1.57 hAPP( 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'( X ), Y, X,
% 1.18/1.57 'tc_fun'( X, X ), 'tc_nat' ), 'tc_nat', X, X ), Z ), hAPP( hAPP(
% 1.18/1.57 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ), X ), ~( 'c_SEQ_OLIMSEQ'( Y, T
% 1.18/1.57 , X ) ) ],
% 1.18/1.57 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_SEQ_OLIMSEQ'(
% 1.18/1.57 'c_COMBS'( 'c_COMBB'( 'c_HOL_Ominus__class_Ominus'( X ), Y, X, 'tc_fun'(
% 1.18/1.57 X, X ), 'tc_nat' ), Z, 'tc_nat', X, X ), hAPP( hAPP(
% 1.18/1.57 'c_HOL_Ominus__class_Ominus'( X ), T ), U ), X ), ~( 'c_SEQ_OLIMSEQ'( Z,
% 1.18/1.57 U, X ) ), ~( 'c_SEQ_OLIMSEQ'( Y, T, X ) ) ],
% 1.18/1.57 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_SEQ_OLIMSEQ'(
% 1.18/1.57 hAPP( 'c_COMBC'( 'c_COMBB'( 'c_HOL_Ominus__class_Ominus'( X ), Y, X,
% 1.18/1.57 'tc_fun'( X, X ), 'tc_nat' ), 'tc_nat', X, X ), Z ), hAPP( hAPP(
% 1.18/1.57 'c_HOL_Ominus__class_Ominus'( X ), T ), Z ), X ), ~( 'c_SEQ_OLIMSEQ'( Y,
% 1.18/1.57 T, X ) ) ],
% 1.18/1.57 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_SEQ_OLIMSEQ'(
% 1.18/1.57 hAPP( 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Y, X,
% 1.20/1.57 'tc_fun'( X, X ), 'tc_nat' ), 'tc_nat', X, X ), Z ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ), ~( 'c_SEQ_OLIMSEQ'(
% 1.20/1.57 Y, T, X ) ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_Finite__Set_Osetsum'(
% 1.20/1.57 'tc_nat', X ), Y ), 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T,
% 1.20/1.57 'tc_nat' ) ) ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', X ), Y ),
% 1.20/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( T, U, 'tc_nat' ) ) ), hAPP(
% 1.20/1.57 hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', X ), Y ),
% 1.20/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, U, 'tc_nat' ) ) ), ~(
% 1.20/1.57 hBOOL( hAPP( 'c_lessequals'( T, 'tc_nat' ), U ) ) ), ~( hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( Z, 'tc_nat' ), T ) ) ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_Finite__Set_Osetsum'(
% 1.20/1.57 'tc_nat', X ), Y ), 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T,
% 1.20/1.57 'tc_nat' ) ) ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', X ), Y ),
% 1.20/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, U, 'tc_nat' ) ) ), hAPP(
% 1.20/1.57 hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', X ), Y ),
% 1.20/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( U, T, 'tc_nat' ) ) ), ~(
% 1.20/1.57 hBOOL( hAPP( 'c_lessequals'( U, 'tc_nat' ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( Z, 'tc_nat' ), U ) ) ) ],
% 1.20/1.57 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ),
% 1.20/1.57 'c_Deriv_Odifferentiable'( hAPP( 'c_COMBC'( 'c_COMBB'(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), Y, X, 'tc_fun'( 'tc_nat', X ), X ),
% 1.20/1.57 X, 'tc_nat', X ), Z ), T, X ), ~( 'c_Deriv_Odifferentiable'( Y, T, X ) )
% 1.20/1.57 ],
% 1.20/1.57 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), ~(
% 1.20/1.57 'class_Power_Opower'( X ) ), 'c_SEQ_OLIMSEQ'( hAPP( 'c_COMBC'( 'c_COMBB'(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), Y, X, 'tc_fun'( 'tc_nat', X ),
% 1.20/1.57 'tc_nat' ), 'tc_nat', 'tc_nat', X ), Z ), hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), T ), Z ), X ), ~( 'c_SEQ_OLIMSEQ'( Y
% 1.20/1.57 , T, X ) ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_Finite__Set_Osetsum'( 'tc_nat', X ), Y ),
% 1.20/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( 'c_Suc', Z ), hAPP(
% 1.20/1.57 'c_Suc', T ), 'tc_nat' ) ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat'
% 1.20/1.57 , X ), 'c_COMBB'( Y, 'c_Suc', 'tc_nat', X, 'tc_nat' ) ),
% 1.20/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, T, 'tc_nat' ) ) ) ],
% 1.20/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), 'v_i' ), 'tc_nat' ), 'v_n'
% 1.20/1.57 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), 'v_n' ) )
% 1.20/1.57 ) ],
% 1.20/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 'v_i' ), X ), 'tc_nat' ), 'v_n'
% 1.20/1.57 ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.20/1.57 , Y ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), X ),
% 1.20/1.57 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.20/1.57 hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.20/1.57 ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.20/1.57 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.20/1.57 'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'(
% 1.20/1.57 X, X ), X ), Z, X, X, X ), T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.20/1.57 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( Y, T ) ), U ) ),
% 1.20/1.57 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), W ), hAPP( Z, T ) ) ), X )
% 1.20/1.57 , ~( 'c_Deriv_Oderiv'( Z, T, U, X ) ), ~( 'c_Deriv_Oderiv'( Y, T, W, X )
% 1.20/1.57 ) ],
% 1.20/1.57 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.20/1.57 'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'(
% 1.20/1.57 X, X ), X ), Z, X, X, X ), T, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.20/1.57 , hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), hAPP( Z, T ) ) ),
% 1.20/1.57 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), W ), hAPP( Y, T ) ) ), X )
% 1.20/1.57 , ~( 'c_Deriv_Oderiv'( Z, T, W, X ) ), ~( 'c_Deriv_Oderiv'( Y, T, U, X )
% 1.20/1.57 ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.20/1.57 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), hBOOL( hAPP(
% 1.20/1.57 'c_HOL_Oord__class_Oless'( T, X ), U ) ), ~( hBOOL( hAPP(
% 1.20/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ) ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.20/1.57 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), hBOOL( hAPP(
% 1.20/1.57 'c_HOL_Oord__class_Oless'( Y, X ), Z ) ), ~( hBOOL( hAPP(
% 1.20/1.57 'c_HOL_Oord__class_Oless'( T, X ), U ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z
% 1.20/1.57 ), X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ) ),
% 1.20/1.57 ~( hBOOL( hAPP( 'c_lessequals'( U, X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), U ) ) )
% 1.20/1.57 , ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.57 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.57 , ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.20/1.57 ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.20/1.57 , ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.20/1.57 ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.20/1.57 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T )
% 1.20/1.57 , U ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( U, X ), Z ) ) ), ~( hBOOL(
% 1.20/1.57 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), U
% 1.20/1.57 ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ), ~(
% 1.20/1.57 hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) )
% 1.20/1.57 ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z
% 1.20/1.57 ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.20/1.57 , ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.20/1.57 ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z
% 1.20/1.57 ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.57 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) )
% 1.20/1.57 , ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.20/1.57 ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X
% 1.20/1.57 ), Y ), Z ), X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T )
% 1.20/1.57 , U ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( U, X ), Z ) ) ),
% 1.20/1.57 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.57 ), X ), U ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), T ) ) ), ~(
% 1.20/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.57 X ), Y ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X )
% 1.20/1.57 , Z ), T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.20/1.57 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.57 X ), T ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hBOOL( hAPP(
% 1.20/1.57 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.57 X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z
% 1.20/1.57 ), X ), T ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), hBOOL( hAPP(
% 1.20/1.57 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.57 X ), Z ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ), hBOOL( hAPP(
% 1.20/1.57 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.57 X ), Z ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ), Y ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.20/1.57 ), Y ), Z ), X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ),
% 1.20/1.57 Z ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Z ) ) ), ~( hBOOL(
% 1.20/1.57 hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ), ~(
% 1.20/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ), T ) ) ) ],
% 1.20/1.57 [ hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.20/1.57 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.20/1.57 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ]
% 1.20/1.57 ,
% 1.20/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 'tc_nat' ), 'tc_nat' ), X ) ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.20/1.57 ) ) ],
% 1.20/1.57 [ ~( =( hAPP( 'c_Suc', X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.20/1.57 ,
% 1.20/1.57 [ ~( =( hAPP( 'c_Suc', X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.20/1.57 ,
% 1.20/1.57 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 'tc_nat' ) ) ],
% 1.20/1.57 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 'tc_nat' ) ) ],
% 1.20/1.57 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.20/1.57 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( Y
% 1.20/1.57 , Z ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.20/1.57 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.20/1.57 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( X
% 1.20/1.57 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 1.20/1.57 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.20/1.57 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), =( Y
% 1.20/1.57 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 1.20/1.57 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.20/1.57 [ ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.20/1.57 [ =( hAPP( hAPP( X, Y ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z ),
% 1.20/1.57 ~( 'c_Groebner__Basis_Ogb__semiring'( T, U, X, W, Z, V0 ) ) ],
% 1.20/1.57 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 'tc_nat' ) ), Y ) ) ],
% 1.20/1.57 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 'tc_nat' ) ) ) ],
% 1.20/1.57 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) )
% 1.20/1.57 ) ],
% 1.20/1.57 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.20/1.57 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.20/1.57 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.20/1.57 [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 1.20/1.57 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.20/1.57 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 1.20/1.57 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.20/1.57 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 1.20/1.57 ,
% 1.20/1.57 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 1.20/1.57 ,
% 1.20/1.57 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.20/1.57 [ hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.20/1.57 'tc_nat' ), X ) ) ],
% 1.20/1.57 [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.20/1.57 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.20/1.57 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.20/1.57 ), Y ), Z ), X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.20/1.57 T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), T ) )
% 1.20/1.57 ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'(
% 1.20/1.57 X ), X ), Y ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.57 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ), ~( hBOOL( hAPP(
% 1.20/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.20/1.57 ), T ), Y ), X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ),
% 1.20/1.57 Z ) ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.57 'c_HOL_Oone__class_Oone'( X ), X ), T ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.20/1.57 ), Y ), Z ), X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.20/1.57 T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.57 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.20/1.57 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), T ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.57 'c_HOL_Oord__class_Oless'( Y, 'tc_nat' ), Z ) ), ~( hBOOL( hAPP(
% 1.20/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.20/1.57 ), T ), Y ), X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), T ),
% 1.20/1.57 Z ) ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.57 'c_HOL_Oone__class_Oone'( X ), X ), T ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X ), hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ) ), ~(
% 1.20/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Oone__class_Oone'( X ), X
% 1.20/1.57 ), Y ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z )
% 1.20/1.57 , X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~(
% 1.20/1.57 hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Oone__class_Oone'( X ), X ), Y ) ) )
% 1.20/1.57 , ~( hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ), T ) ) ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =(
% 1.20/1.57 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.20/1.57 Y, X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), ~( hBOOL(
% 1.20/1.57 hAPP( 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.20/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP( 'c_Suc', Y ) ),
% 1.20/1.57 'tc_nat' ), X ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), X ) ) ) ],
% 1.20/1.57 [ =( hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' )
% 1.20/1.57 , X ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ),
% 1.20/1.57 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 'tc_nat' ), 'tc_nat' ), X ) ) ) ],
% 1.20/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), Z ) ),
% 1.20/1.57 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( X, 'tc_nat' ), Z ) ) ) ],
% 1.20/1.57 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.20/1.57 , X ) ), hAPP( 'c_Suc', Y ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.20/1.57 'tc_nat' ), X ), Y ) ) ],
% 1.20/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP(
% 1.20/1.57 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL(
% 1.20/1.57 hAPP( 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), X ) ) ), ~( hBOOL( hAPP(
% 1.20/1.57 'c_HOL_Oord__class_Oless'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.20/1.57 [ ~( hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.20/1.57 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), Y ) )
% 1.20/1.57 ) ), hBOOL( hAPP( X, Z ) ) ],
% 1.20/1.57 [ ~( hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.20/1.57 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), Y ) )
% 1.20/1.57 ) ), hBOOL( hAPP( X, Z ) ) ],
% 1.20/1.57 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ],
% 1.20/1.57 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ) ],
% 1.20/1.57 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y ) ),
% 1.20/1.57 hAPP( 'c_Suc', Z ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.20/1.57 ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z )
% 1.20/1.57 ) ],
% 1.20/1.57 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP(
% 1.20/1.57 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Y ), ~( hBOOL(
% 1.20/1.57 hAPP( 'c_lessequals'( Y, 'tc_nat' ), X ) ) ) ],
% 1.20/1.57 [ hBOOL( hAPP( 'c_lessequals'( X, 'tc_nat' ), Y ) ), ~( hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X )
% 1.20/1.57 , Z ), 'tc_nat' ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.20/1.57 Y ), Z ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ),
% 1.20/1.57 ~( hBOOL( hAPP( 'c_lessequals'( Z, 'tc_nat' ), X ) ) ) ],
% 1.20/1.57 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.20/1.57 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( X, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y
% 1.20/1.57 , 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), X )
% 1.20/1.57 ) ) ],
% 1.20/1.57 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.20/1.57 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( X, 'tc_nat' ), Z ) ) ) ],
% 1.20/1.57 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.20/1.57 'tc_nat' ), X ), Y ), 'tc_nat' ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( Z, 'tc_nat' ), Y ) ) ) ],
% 1.20/1.57 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.20/1.57 [ ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ),
% 1.20/1.57 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ), ~(
% 1.20/1.57 hBOOL( hAPP( 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( Y, 'tc_nat' ), X ) ) ), =( X, Z ) ],
% 1.20/1.57 [ hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.20/1.57 'tc_nat' ), X ), Y ), 'tc_nat' ), X ) ) ],
% 1.20/1.57 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.20/1.57 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.20/1.57 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.20/1.57 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ), ~( hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( Y, 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y
% 1.20/1.57 , 'tc_nat' ), X ) ) ) ],
% 1.20/1.57 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), X ), Y ) ],
% 1.20/1.57 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Y ), X ) ],
% 1.20/1.57 [ ~( 'class_RealVector_Ometric__space'( X ) ), 'c_SEQ_OLIMSEQ'(
% 1.20/1.57 'c_COMBB'( Y, hAPP( 'c_COMBC'( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.20/1.57 'tc_nat', 'tc_nat', 'tc_nat' ), Z ), 'tc_nat', X, 'tc_nat' ), T, X ), ~(
% 1.20/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 'tc_nat' ), 'tc_nat' ), Z ) ) ), ~( 'c_SEQ_OLIMSEQ'( Y, T, X ) ) ],
% 1.20/1.57 [ ~( 'class_RealVector_Ometric__space'( X ) ), 'c_SEQ_OLIMSEQ'(
% 1.20/1.57 'c_COMBB'( Y, hAPP( 'c_COMBC'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.20/1.57 'tc_nat', 'tc_nat', 'tc_nat' ), Z ), 'tc_nat', X, 'tc_nat' ), T, X ), ~(
% 1.20/1.57 'c_SEQ_OLIMSEQ'( Y, T, X ) ) ],
% 1.20/1.57 [ ~( 'class_RealVector_Ometric__space'( X ) ), 'c_SEQ_OLIMSEQ'( Y, Z, X
% 1.20/1.57 ), ~( 'c_SEQ_OLIMSEQ'( 'c_COMBB'( Y, hAPP( 'c_COMBC'(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'tc_nat', 'tc_nat', 'tc_nat' ), T
% 1.20/1.57 ), 'tc_nat', X, 'tc_nat' ), Z, X ) ) ],
% 1.20/1.57 [ ~( =( 'c_FFT__Mirabelle_Oroot'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 'tc_Complex_Ocomplex' ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X )
% 1.20/1.57 , Z ), T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z
% 1.20/1.57 , X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ),
% 1.20/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.57 X ), T ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z
% 1.20/1.57 ), T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.20/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ),
% 1.20/1.57 ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z
% 1.20/1.57 ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.57 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), Y ) ) ),
% 1.20/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.57 X ), Z ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.20/1.57 X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.20/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ),
% 1.20/1.57 ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ), X ), Y ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X )
% 1.20/1.57 , Z ), T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), hBOOL( hAPP(
% 1.20/1.57 'c_HOL_Oord__class_Oless'( T, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.57 ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.57 X ), Y ), T ), X ), Z ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X )
% 1.20/1.57 , Z ), T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z
% 1.20/1.57 , X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ),
% 1.20/1.57 hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.20/1.57 X ), T ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z
% 1.20/1.57 ), X ), T ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), hBOOL( hAPP(
% 1.20/1.57 'c_HOL_Oord__class_Oless'( Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.20/1.57 ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z
% 1.20/1.57 ), X ), T ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ),
% 1.20/1.57 X ), Y ) ) ), hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X )
% 1.20/1.57 , Z ), T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, X ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z
% 1.20/1.57 , X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ), ~(
% 1.20/1.57 hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.20/1.57 ), Y ), T ), X ), Z ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z
% 1.20/1.57 ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Z, X ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.57 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X ), Y ) ) ),
% 1.20/1.57 ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X )
% 1.20/1.57 , Z ), T ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) )
% 1.20/1.57 ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z
% 1.20/1.57 ), X ), T ) ), ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) )
% 1.20/1.57 ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X )
% 1.20/1.57 , Z ), T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ),
% 1.20/1.57 X ), Z ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.20/1.57 X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X )
% 1.20/1.57 , T ), Z ) ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z
% 1.20/1.57 ), X ), T ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T
% 1.20/1.57 ), Z ) ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( Y, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z
% 1.20/1.57 ), T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T
% 1.20/1.57 ), X ), Z ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z
% 1.20/1.57 ), X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ) ),
% 1.20/1.57 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.57 ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ),
% 1.20/1.57 ~( hBOOL( hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.20/1.57 ) ), ~( hBOOL( hAPP( 'c_lessequals'( Z, X ), T ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__field'( X ) ), hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z
% 1.20/1.57 ), X ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ) ),
% 1.20/1.57 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.57 ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ),
% 1.20/1.57 ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y )
% 1.20/1.57 ) ), ~( hBOOL( hAPP( 'c_lessequals'( T, X ), Z ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z )
% 1.20/1.57 , X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~(
% 1.20/1.57 hBOOL( hAPP( 'c_lessequals'( Y, X ), 'c_HOL_Oone__class_Oone'( X ) ) ) )
% 1.20/1.57 , ~( hBOOL( hAPP( 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.20/1.57 ) ) ), ~( hBOOL( hAPP( 'c_lessequals'( T, 'tc_nat' ), Z ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.20/1.57 ), Y ), Z ), X ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.20/1.57 T ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.20/1.57 'c_HOL_Oone__class_Oone'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.20/1.57 , ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( T, 'tc_nat' ), Z ) ) ) ]
% 1.20/1.57 ,
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.20/1.57 'c_HOL_Oord__class_Oless'( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X
% 1.20/1.57 ), Y ), hAPP( 'c_Suc', Z ) ), X ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.20/1.57 ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y, X ),
% 1.20/1.57 'c_HOL_Oone__class_Oone'( X ) ) ) ), ~( hBOOL( hAPP(
% 1.20/1.57 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) )
% 1.20/1.57 ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( =( hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), Y ), Z ), hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), T ), Z ) ) ), =( Y, T ), ~( hBOOL(
% 1.20/1.57 hAPP( 'c_HOL_Oord__class_Oless'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.20/1.57 'tc_nat' ), Z ) ) ), ~( hBOOL( hAPP( 'c_lessequals'(
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ), X ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( 'c_HOL_Ozero__class_Ozero'( X ), X ), Y ) ) ) ],
% 1.20/1.57 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ),
% 1.20/1.57 'c_Deriv_Odifferentiable'( 'c_COMBS'( 'c_COMBB'(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Y, X, 'tc_fun'( X, X ), X ), Z, X,
% 1.20/1.57 X, X ), T, X ), =( hAPP( Z, T ), 'c_HOL_Ozero__class_Ozero'( X ) ), ~(
% 1.20/1.57 'c_Deriv_Odifferentiable'( Z, T, X ) ), ~( 'c_Deriv_Odifferentiable'( Y,
% 1.20/1.57 T, X ) ) ],
% 1.20/1.57 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.20/1.57 'c_COMBS'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Y, X,
% 1.20/1.57 'tc_fun'( X, X ), X ), Z, X, X, X ), T, hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), U ), hAPP( Z, T ) ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), W ), hAPP( Y, T ) ) ) ), hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), hAPP( Z, T ) ), hAPP( 'c_Suc', hAPP(
% 1.20/1.57 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ), X ), =( hAPP( Z
% 1.20/1.57 , T ), 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Deriv_Oderiv'( Z, T, W, X
% 1.20/1.57 ) ), ~( 'c_Deriv_Oderiv'( Y, T, U, X ) ) ],
% 1.20/1.57 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_SEQ_OLIMSEQ'( Y
% 1.20/1.57 , Z, X ), ~( 'c_SEQ_OLIMSEQ'( 'c_COMBS'( 'c_COMBB'(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), Y, X, 'tc_fun'( X, X ), 'tc_nat' ), T
% 1.20/1.57 , 'tc_nat', X, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.20/1.57 'c_SEQ_OLIMSEQ'( T, Z, X ) ) ],
% 1.20/1.57 [ ~( 'class_RealVector_Oreal__normed__vector'( X ) ), 'c_SEQ_OLIMSEQ'( Y
% 1.20/1.57 , Z, X ), ~( 'c_SEQ_OLIMSEQ'( 'c_COMBS'( 'c_COMBB'(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), T, X, 'tc_fun'( X, X ), 'tc_nat' ), Y
% 1.20/1.57 , 'tc_nat', X, X ), 'c_HOL_Ozero__class_Ozero'( X ), X ) ), ~(
% 1.20/1.57 'c_SEQ_OLIMSEQ'( T, Z, X ) ) ],
% 1.20/1.57 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_SEQ_OLIMSEQ'(
% 1.20/1.57 'c_COMBS'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Y, X,
% 1.20/1.57 'tc_fun'( X, X ), 'tc_nat' ), Z, 'tc_nat', X, X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ), X ), =( U,
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_SEQ_OLIMSEQ'( Z, U, X ) ), ~(
% 1.20/1.57 'c_SEQ_OLIMSEQ'( Y, T, X ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( T, 'tc_nat' ), Z ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 X ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.20/1.57 'c_lessequals'( T, 'tc_nat' ), Z ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 X ) ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), ~( =( hAPP( Y,
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.20/1.57 ) ), =( hAPP( hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', X ), Y ),
% 1.20/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( 'c_Suc',
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Z, 'tc_nat' ) ), hAPP( hAPP(
% 1.20/1.57 'c_Finite__Set_Osetsum'( 'tc_nat', X ), Y ),
% 1.20/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 'tc_nat' ), Z, 'tc_nat' ) ) ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_Finite__Set_Osetsum'( 'tc_nat', X ), Y ),
% 1.20/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), U ), T ), 'tc_nat' ) ), hAPP(
% 1.20/1.57 hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', X ), 'c_COMBB'( Y, hAPP(
% 1.20/1.57 'c_COMBC'( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'tc_nat', 'tc_nat',
% 1.20/1.57 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ) ),
% 1.20/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( Z, U, 'tc_nat' ) ) ) ],
% 1.20/1.57 [ =( hAPP( hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat',
% 1.20/1.57 'tc_Complex_Ocomplex' ), hAPP( 'c_Power_Opower__class_Opower'(
% 1.20/1.57 'tc_Complex_Ocomplex' ), hAPP( hAPP( 'c_Power_Opower__class_Opower'(
% 1.20/1.57 'tc_Complex_Ocomplex' ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.20/1.57 'tc_Complex_Ocomplex' ), 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex'
% 1.20/1.57 ) ), 'c_FFT__Mirabelle_Oroot'( X ) ) ), Y ) ) ),
% 1.20/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 'tc_nat' ), X, 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 'tc_Complex_Ocomplex' ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( Y,
% 1.20/1.57 'tc_nat' ), X ) ) ), ~( hBOOL( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ), Y ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ),
% 1.20/1.57 'c_Groebner__Basis_Ogb__semiring'( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( X ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.20/1.57 ,
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.20/1.57 X ) ), 'c_Groebner__Basis_Osemiringb'( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( X ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ), X ) ]
% 1.20/1.57 ,
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.20/1.57 ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), Z ) ) )
% 1.20/1.57 , hBOOL( hAPP( 'c_lessequals'( T, 'tc_nat' ), Z ) ), =( Y,
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.57 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), 'c_Deriv_Oderiv'(
% 1.20/1.57 'c_COMBS'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Y, X,
% 1.20/1.57 'tc_fun'( X, X ), X ), Z, X, X, X ), T, hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), U ), hAPP( Z, T ) ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( Y, T ) ), W ) ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( Z, T ) ), hAPP( Z, T ) ) ), X )
% 1.20/1.57 , =( hAPP( Z, T ), 'c_HOL_Ozero__class_Ozero'( X ) ), ~( 'c_Deriv_Oderiv'(
% 1.20/1.57 Z, T, W, X ) ), ~( 'c_Deriv_Oderiv'( Y, T, U, X ) ) ],
% 1.20/1.57 [ ~( 'class_RealVector_Oreal__normed__algebra__1'( X ) ), =(
% 1.20/1.57 'c_Series_Osuminf'( 'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X
% 1.20/1.57 ), Y, X, 'tc_fun'( X, X ), 'tc_nat' ), hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.20/1.57 'tc_nat', X, X ), X ), hAPP( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.20/1.57 ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_Finite__Set_Osetsum'( 'tc_nat', X ), Y ),
% 1.20/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T )
% 1.20/1.57 , 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.20/1.57 'c_Finite__Set_Osetsum'( 'tc_nat', X ), 'c_COMBB'( Y, hAPP( 'c_COMBC'(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'tc_nat', 'tc_nat', 'tc_nat' ), T
% 1.20/1.57 ), 'tc_nat', X, 'tc_nat' ) ),
% 1.20/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 'tc_nat' ), Z, 'tc_nat' ) ) ), hAPP( hAPP( 'c_Finite__Set_Osetsum'(
% 1.20/1.57 'tc_nat', X ), Y ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), T, 'tc_nat' ) ) ) ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_Finite__Set_Osetsum'( 'tc_nat', X ), 'c_COMBB'( Y, hAPP( 'c_COMBC'(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'tc_nat', 'tc_nat', 'tc_nat' ), Z
% 1.20/1.57 ), 'tc_nat', X, 'tc_nat' ) ),
% 1.20/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 'tc_nat' ), T, 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.20/1.57 ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', X ), Y ),
% 1.20/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), Z )
% 1.20/1.57 , 'tc_nat' ) ) ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', X ), Y )
% 1.20/1.57 , 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ) ) ],
% 1.20/1.57 [ =( 'c_FFT__Mirabelle_ODFT'( X, Y, 'v_i' ), hAPP( hAPP(
% 1.20/1.57 'c_Finite__Set_Osetsum'( 'tc_nat', 'tc_Complex_Ocomplex' ), 'c_COMBS'(
% 1.20/1.57 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( 'tc_Complex_Ocomplex' ),
% 1.20/1.57 'c_COMBB'( hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' )
% 1.20/1.57 , 'c_FFT__Mirabelle_Oroot'( X ) ), hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.57 'tc_nat' ), 'v_i' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ),
% 1.20/1.57 'tc_Complex_Ocomplex', 'tc_fun'( 'tc_Complex_Ocomplex',
% 1.20/1.57 'tc_Complex_Ocomplex' ), 'tc_nat' ), Y, 'tc_nat', 'tc_Complex_Ocomplex',
% 1.20/1.57 'tc_Complex_Ocomplex' ) ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X, 'tc_nat' ) ) ) ],
% 1.20/1.57 [ =( 'c_FFT__Mirabelle_OIDFT'( X, Y, 'v_i' ), hAPP( hAPP(
% 1.20/1.57 'c_Finite__Set_Osetsum'( 'tc_nat', 'tc_Complex_Ocomplex' ), 'c_COMBS'(
% 1.20/1.57 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( 'tc_Complex_Ocomplex' ), Y,
% 1.20/1.57 'tc_Complex_Ocomplex', 'tc_fun'( 'tc_Complex_Ocomplex',
% 1.20/1.57 'tc_Complex_Ocomplex' ), 'tc_nat' ), 'c_COMBB'( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.20/1.57 'c_FFT__Mirabelle_Oroot'( X ) ), hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.57 'tc_nat' ), 'v_i' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ),
% 1.20/1.57 'tc_nat', 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ) ),
% 1.20/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 'tc_nat' ), X, 'tc_nat' ) ) ) ],
% 1.20/1.57 [ =( hAPP( hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat',
% 1.20/1.57 'tc_Complex_Ocomplex' ), 'c_COMBS'( 'c_COMBB'(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_Complex_Ocomplex' ), hAPP( 'c_COMBC'(
% 1.20/1.57 'c_COMBB'( 'c_Finite__Set_Osetsum'( 'tc_nat', 'tc_Complex_Ocomplex' ),
% 1.20/1.57 'c_COMBB'( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.20/1.57 'c_COMBS'( 'c_COMBS'( 'c_COMBB'( 'c_HOL_OIf'( 'tc_Complex_Ocomplex' ),
% 1.20/1.57 'c_lessequals'( 'v_i', 'tc_nat' ), 'tc_bool', 'tc_fun'(
% 1.20/1.57 'tc_Complex_Ocomplex', 'tc_fun'( 'tc_Complex_Ocomplex',
% 1.20/1.57 'tc_Complex_Ocomplex' ) ), 'tc_nat' ), 'c_COMBB'( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.20/1.57 'c_FFT__Mirabelle_Oroot'( 'v_n' ) ), hAPP( 'c_COMBC'(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 'tc_nat', 'tc_nat', 'tc_nat' )
% 1.20/1.57 , 'v_i' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ), 'tc_nat',
% 1.20/1.57 'tc_Complex_Ocomplex', 'tc_fun'( 'tc_Complex_Ocomplex',
% 1.20/1.57 'tc_Complex_Ocomplex' ) ), 'c_COMBB'( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( 'tc_Complex_Ocomplex' ),
% 1.20/1.57 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ),
% 1.20/1.57 'c_FFT__Mirabelle_Oroot'( 'v_n' ) ) ), hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.20/1.57 'tc_nat' ), 'v_i' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ),
% 1.20/1.57 'tc_nat', 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ),
% 1.20/1.57 'tc_Complex_Ocomplex', 'tc_fun'( 'tc_nat', 'tc_Complex_Ocomplex' ),
% 1.20/1.57 'tc_nat' ), 'tc_fun'( 'tc_nat', 'tc_Complex_Ocomplex' ), 'tc_fun'(
% 1.20/1.57 'tc_fun'( 'tc_nat', 'tc_bool' ), 'tc_Complex_Ocomplex' ), 'tc_nat' ),
% 1.20/1.57 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ), 'tc_Complex_Ocomplex' ),
% 1.20/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 'tc_nat' ), 'v_n', 'tc_nat' ) ), 'tc_Complex_Ocomplex', 'tc_fun'(
% 1.20/1.57 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ), 'tc_nat' ), 'v_a',
% 1.20/1.57 'tc_nat', 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ) ),
% 1.20/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 'tc_nat' ), 'v_n', 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.57 'tc_Complex_Ocomplex' ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat',
% 1.20/1.57 'tc_Complex_Ocomplex' ), 'c_COMBS'( 'c_COMBB'(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_Complex_Ocomplex' ), hAPP( 'c_COMBC'(
% 1.20/1.57 'c_COMBB'( 'c_Finite__Set_Osetsum'( 'tc_nat', 'tc_Complex_Ocomplex' ),
% 1.20/1.57 'c_COMBB'( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.20/1.57 'c_COMBB'( hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' )
% 1.20/1.57 , hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( 'tc_Complex_Ocomplex' ),
% 1.20/1.57 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ),
% 1.20/1.57 'c_FFT__Mirabelle_Oroot'( 'v_n' ) ) ), hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.20/1.57 'tc_nat' ), 'v_i' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ),
% 1.20/1.57 'tc_Complex_Ocomplex', 'tc_fun'( 'tc_nat', 'tc_Complex_Ocomplex' ),
% 1.20/1.57 'tc_nat' ), 'tc_fun'( 'tc_nat', 'tc_Complex_Ocomplex' ), 'tc_fun'(
% 1.20/1.57 'tc_fun'( 'tc_nat', 'tc_bool' ), 'tc_Complex_Ocomplex' ), 'tc_nat' ),
% 1.20/1.57 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ), 'tc_Complex_Ocomplex' ),
% 1.20/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 'tc_nat' ), 'v_n', 'tc_nat' ) ), 'tc_Complex_Ocomplex', 'tc_fun'(
% 1.20/1.57 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ), 'tc_nat' ), 'v_a',
% 1.20/1.57 'tc_nat', 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ) ),
% 1.20/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 'tc_nat' ), 'v_i', 'tc_nat' ) ) ), hAPP( hAPP( 'c_Finite__Set_Osetsum'(
% 1.20/1.57 'tc_nat', 'tc_Complex_Ocomplex' ), 'c_COMBS'( 'c_COMBB'(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_Complex_Ocomplex' ), hAPP( 'c_COMBC'(
% 1.20/1.57 'c_COMBB'( 'c_Finite__Set_Osetsum'( 'tc_nat', 'tc_Complex_Ocomplex' ),
% 1.20/1.57 'c_COMBB'( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.20/1.57 'c_COMBB'( hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' )
% 1.20/1.57 , 'c_FFT__Mirabelle_Oroot'( 'v_n' ) ), hAPP( 'c_COMBC'(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 'tc_nat', 'tc_nat', 'tc_nat' )
% 1.20/1.57 , 'v_i' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ),
% 1.20/1.57 'tc_Complex_Ocomplex', 'tc_fun'( 'tc_nat', 'tc_Complex_Ocomplex' ),
% 1.20/1.57 'tc_nat' ), 'tc_fun'( 'tc_nat', 'tc_Complex_Ocomplex' ), 'tc_fun'(
% 1.20/1.57 'tc_fun'( 'tc_nat', 'tc_bool' ), 'tc_Complex_Ocomplex' ), 'tc_nat' ),
% 1.20/1.57 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ), 'tc_Complex_Ocomplex' ),
% 1.20/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 'tc_nat' ), 'v_n', 'tc_nat' ) ), 'tc_Complex_Ocomplex', 'tc_fun'(
% 1.20/1.57 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ), 'tc_nat' ), 'v_a',
% 1.20/1.57 'tc_nat', 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ) ),
% 1.20/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( 'v_i', 'v_n', 'tc_nat' ) )
% 1.20/1.57 ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_Finite__Set_Osetsum'(
% 1.20/1.57 'tc_nat', X ), Y ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_nat' ) ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.20/1.57 Z, X ) ), T ) ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', X ), hAPP(
% 1.20/1.57 'c_COMBC'( 'c_COMBB'( 'c_HOL_Ominus__class_Ominus'( X ), Y, X, 'tc_fun'(
% 1.20/1.57 X, X ), 'tc_nat' ), 'tc_nat', X, X ), T ) ),
% 1.20/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 'tc_nat' ), Z, 'tc_nat' ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__0'( X ) ), ~(
% 1.20/1.57 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_Finite__Set_Osetsum'( 'tc_nat', X ), 'c_COMBS'( 'c_COMBB'(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_Power_Opower__class_Opower'(
% 1.20/1.57 X ), Y ), X, 'tc_fun'( X, X ), 'tc_nat' ), 'c_COMBB'( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), Z ), hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc', T ) ), 'tc_nat'
% 1.20/1.57 , X, 'tc_nat' ), 'tc_nat', X, X ) ),
% 1.20/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 'tc_nat' ), hAPP( 'c_Suc', T ), 'tc_nat' ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.20/1.57 'c_Finite__Set_Osetsum'( 'tc_nat', X ), 'c_COMBS'( 'c_COMBB'(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_Power_Opower__class_Opower'(
% 1.20/1.57 X ), Y ), X, 'tc_fun'( X, X ), 'tc_nat' ), 'c_COMBB'( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), Z ), hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ),
% 1.20/1.57 'tc_nat', X, X ) ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', T ), 'tc_nat' ) )
% 1.20/1.57 ) ) ],
% 1.20/1.57 [ ~( 'class_Power_Opower'( X ) ), ~(
% 1.20/1.57 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_Finite__Set_Osetsum'( 'tc_nat', X ), 'c_COMBS'( 'c_COMBB'(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_Power_Opower__class_Opower'(
% 1.20/1.57 X ), Y ), X, 'tc_fun'( X, X ), 'tc_nat' ), 'c_COMBB'( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), Z ), hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ),
% 1.20/1.57 'tc_nat', X, X ) ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', T ), 'tc_nat' ) )
% 1.20/1.57 , hAPP( hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', X ), 'c_COMBS'(
% 1.20/1.57 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), 'c_COMBB'( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), Y ), hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ), X
% 1.20/1.57 , 'tc_fun'( X, X ), 'tc_nat' ), hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.20/1.57 , Z ), 'tc_nat', X, X ) ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', T ), 'tc_nat' ) )
% 1.20/1.57 ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), ~(
% 1.20/1.57 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), Y ), hAPP( 'c_Suc', Z ) ) ), hAPP(
% 1.20/1.57 hAPP( 'c_Power_Opower__class_Opower'( X ), T ), hAPP( 'c_Suc', Z ) ) ),
% 1.20/1.57 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_Finite__Set_Osetsum'( 'tc_nat', X ), 'c_COMBS'( 'c_COMBB'(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_Power_Opower__class_Opower'(
% 1.20/1.57 X ), Y ), X, 'tc_fun'( X, X ), 'tc_nat' ), 'c_COMBB'( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), T ), hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), 'tc_nat', X, 'tc_nat' ),
% 1.20/1.57 'tc_nat', X, X ) ), 'c_SetInterval_Oord__class_OatLeastLessThan'(
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', Z ), 'tc_nat' ) )
% 1.20/1.57 ) ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.20/1.57 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), Y ) ],
% 1.20/1.57 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y
% 1.20/1.57 , X ), Z ), T ) ), U ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y, X ), hAPP(
% 1.20/1.57 'c_COMBC'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Z, X, 'tc_fun'(
% 1.20/1.57 X, X ), Y ), Y, X, X ), U ) ), T ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y
% 1.20/1.57 , X ), Z ), T ) ), U ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y, X ), hAPP(
% 1.20/1.57 'c_COMBC'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ), Z, X, 'tc_fun'(
% 1.20/1.57 X, X ), Y ), Y, X, X ), U ) ), T ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), 'c_HOL_Oone__class_Oone'(
% 1.20/1.57 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, Z ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.57 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.20/1.57 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.20/1.57 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.57 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.20/1.57 ) ) ],
% 1.20/1.57 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.57 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.20/1.57 ) ) ],
% 1.20/1.57 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.57 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.20/1.57 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.20/1.57 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.57 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.20/1.57 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.57 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.20/1.57 ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.57 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.20/1.57 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.57 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.20/1.57 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ), =( U,
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.20/1.57 ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), Z ) ), =( Z,
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), T ) ), =( T,
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.57 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.20/1.57 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.20/1.57 ), Y ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.20/1.57 ,
% 1.20/1.57 [ =( 'c_FFT__Mirabelle_Oroot'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.20/1.57 , 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.20/1.57 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 1.20/1.57 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 1.20/1.57 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.20/1.57 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.20/1.57 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 1.20/1.57 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.20/1.57 'c_Finite__Set_Osetsum'( Z, X ), T ), U ) ), hAPP( hAPP(
% 1.20/1.57 'c_Finite__Set_Osetsum'( Z, X ), 'c_COMBB'( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), T, X, X, Z ) ), U ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.20/1.57 'c_Finite__Set_Osetsum'( Z, X ), T ), U ) ), hAPP( hAPP(
% 1.20/1.57 'c_Finite__Set_Osetsum'( Z, X ), 'c_COMBB'( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), T, X, X, Z ) ), U ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oone__class_Oone'( X ) ) ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y )
% 1.20/1.57 , 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ocomm__ring'( X ) ), ~(
% 1.20/1.57 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_Finite__Set_Osetsum'( 'tc_nat', X ), hAPP( 'c_COMBC'( 'c_COMBB'(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), 'c_COMBS'( 'c_COMBB'(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), 'c_COMBB'( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ), X
% 1.20/1.57 , 'tc_fun'( X, X ), 'tc_nat' ), hAPP( 'c_Power_Opower__class_Opower'( X )
% 1.20/1.57 , Y ), 'tc_nat', X, X ), X, 'tc_fun'( X, X ), 'tc_nat' ), 'tc_nat', X, X
% 1.20/1.57 ), hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), T ) ) ),
% 1.20/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 'tc_nat' ), T, 'tc_nat' ) ), hAPP( hAPP( 'c_Finite__Set_Osetsum'(
% 1.20/1.57 'tc_nat', X ), 'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.20/1.57 hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), X, 'tc_fun'( X, X ),
% 1.20/1.57 'tc_nat' ), 'c_COMBS'( 'c_COMBB'( 'c_HOL_Ominus__class_Ominus'( X ),
% 1.20/1.57 'c_COMBB'( hAPP( 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ), X
% 1.20/1.57 , 'tc_fun'( X, X ), 'tc_nat' ), 'c_COMBB'( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), Y ), hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), T ), 'tc_nat', X, 'tc_nat' ),
% 1.20/1.57 'tc_nat', X, X ), 'tc_nat', X, X ) ),
% 1.20/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 'tc_nat' ), T, 'tc_nat' ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.20/1.57 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) )
% 1.20/1.57 ],
% 1.20/1.57 [ ~( 'class_RealVector_Oreal__field'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), W ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.57 X ), Y ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ), W ) ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), W ) ), U ) ) ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_Finite__Set_Osetsum'( Y, X ), 'c_COMBS'( 'c_COMBB'(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), Z, X, 'tc_fun'( X, X ), Y ), T, Y, X,
% 1.20/1.57 X ) ), U ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.20/1.57 'c_Finite__Set_Osetsum'( Y, X ), Z ), U ) ), hAPP( hAPP(
% 1.20/1.57 'c_Finite__Set_Osetsum'( Y, X ), T ), U ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.57 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.20/1.57 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.57 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T
% 1.20/1.57 ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.57 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.20/1.57 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( hAPP(
% 1.20/1.57 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T ), W ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.57 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.20/1.57 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( T, hAPP(
% 1.20/1.57 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W ) ) ],
% 1.20/1.57 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 'c_Finite__Set_Osetsum'(
% 1.20/1.57 Y, X ), Z ), T ) ), U ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y, X ),
% 1.20/1.57 hAPP( 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Z, X,
% 1.20/1.57 'tc_fun'( X, X ), Y ), Y, X, X ), U ) ), T ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP( 'c_Finite__Set_Osetsum'(
% 1.20/1.57 Y, X ), Z ), T ) ), U ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y, X ),
% 1.20/1.57 hAPP( 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oinverse__class_Odivide'( X ), Z, X,
% 1.20/1.57 'tc_fun'( X, X ), Y ), Y, X, X ), U ) ), T ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), Y ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.57 X ), 'c_HOL_Oone__class_Oone'( X ) ), 'c_HOL_Oone__class_Oone'( X ) ) ),
% 1.20/1.57 Y ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.20/1.57 ), Y ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.20/1.57 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.57 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.20/1.57 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.20/1.57 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.57 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.20/1.57 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.57 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.20/1.57 ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ), =( U,
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.20/1.57 ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), Z ) ), =( Z,
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), Z ), Y ), =( Z,
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.20/1.57 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.20/1.57 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.57 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.20/1.57 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.57 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.20/1.57 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.57 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.20/1.57 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.57 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.20/1.57 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.20/1.57 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.20/1.57 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.20/1.57 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.20/1.57 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.20/1.57 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.20/1.57 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.57 X ), Y ), Z ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP(
% 1.20/1.57 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Oone__class_Oone'( X )
% 1.20/1.57 ) ), Z ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.57 X ), Z ), 'c_HOL_Oone__class_Oone'( X ) ) ), Y ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ), =( Z,
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( hAPP(
% 1.20/1.57 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.20/1.57 ,
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =(
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.57 ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ) ), =( U,
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X )
% 1.20/1.57 ), =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), U ), hAPP(
% 1.20/1.57 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~( =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), =( Z,
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ) ), =( U, 'c_HOL_Ozero__class_Ozero'( X )
% 1.20/1.57 ), =( hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), Y ), U ), hAPP(
% 1.20/1.57 hAPP( 'c_HOL_Oinverse__class_Odivide'( X ), T ), Z ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.20/1.57 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_Finite__Set_Osetsum'( Y, X ), hAPP( 'c_COMBC'( 'c_COMBB'(
% 1.20/1.57 'c_Finite__Set_Osetsum'( Z, X ), T, 'tc_fun'( Z, X ), 'tc_fun'( 'tc_fun'(
% 1.20/1.57 Z, 'tc_bool' ), X ), Y ), Y, 'tc_fun'( Z, 'tc_bool' ), X ), U ) ), W ),
% 1.20/1.57 hAPP( hAPP( 'c_Finite__Set_Osetsum'( Z, X ), hAPP( 'c_COMBC'( 'c_COMBB'(
% 1.20/1.57 'c_Finite__Set_Osetsum'( Y, X ), 'c_COMBC'( T, Y, Z, X ), 'tc_fun'( Y, X
% 1.20/1.57 ), 'tc_fun'( 'tc_fun'( Y, 'tc_bool' ), X ), Z ), Z, 'tc_fun'( Y,
% 1.20/1.57 'tc_bool' ), X ), W ) ), U ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.20/1.57 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.20/1.57 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.20/1.57 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ), =( T, U ), =( Z,
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.20/1.57 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y
% 1.20/1.57 ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 'tc_nat' ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.20/1.57 ), =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.20/1.57 , =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.20/1.57 [ ~( 'class_Power_Opower'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 'tc_nat' ) ), 'c_HOL_Oone__class_Oone'( X ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 1.20/1.57 =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.57 ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.20/1.57 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.57 ) ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.20/1.57 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), T ), U ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.20/1.57 [ ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), Y ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), Z ), T ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ) ), =( Z, hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), Y ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), Y ), Z ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( Y, hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), Z ) ), =( Z,
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), Z ), Y ), =( Z,
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.57 [ =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' )
% 1.20/1.57 , 'c_FFT__Mirabelle_Oroot'( X ) ), X ), 'c_HOL_Oone__class_Oone'(
% 1.20/1.57 'tc_Complex_Ocomplex' ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), U ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~( =(
% 1.20/1.57 'c_HOL_Oone__class_Oone'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.20/1.57 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.57 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.20/1.57 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.57 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.20/1.57 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.57 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ) ],
% 1.20/1.57 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.20/1.57 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.57 ) ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 X ) ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 X ) ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.20/1.57 , Y ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 X ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.20/1.57 X ) ), =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.57 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), X ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.20/1.57 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.20/1.57 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 1.20/1.57 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.57 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), T ), Y ) ), Z ) ), U ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.57 X ), T ), Z ) ), U ) ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.20/1.57 Y ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.20/1.57 Y ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.20/1.57 Y ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.20/1.57 Y ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.20/1.57 Y ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y ),
% 1.20/1.57 Y ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ),
% 1.20/1.57 hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Oone__class_Oone'( X ) ), Y
% 1.20/1.57 ) ), Z ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.20/1.57 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.57 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.20/1.57 ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.20/1.57 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.57 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.20/1.57 ) ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.20/1.57 X ), Y ), Z ) ), Z ), Y ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.20/1.57 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.20/1.57 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.20/1.57 ,
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.57 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.20/1.57 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.57 X ), Y ), Z ) ), T ) ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.57 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.20/1.57 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.57 X ), Y ), Z ) ), T ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.57 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.20/1.57 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.57 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.20/1.57 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.20/1.57 ), ~( =( hAPP( hAPP( 'c_Power_Opower__class_Opower'( X ), Y ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.20/1.57 ) ) ],
% 1.20/1.57 [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 1.20/1.57 ,
% 1.20/1.57 [ =( hAPP( hAPP( 'c_COMBC'( X, Y, Z, T ), U ), W ), hAPP( hAPP( X, W ),
% 1.20/1.57 U ) ) ],
% 1.20/1.57 [ =( hAPP( 'c_COMBS'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), hAPP( Y
% 1.20/1.57 , W ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( Y,
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.20/1.57 X ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.20/1.57 X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Y ), 'c_HOL_Oone__class_Oone'(
% 1.20/1.57 X ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ) ), =( Z, T ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), T ), T ) ) ), =( Y, Z ) ],
% 1.20/1.57 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 'tc_nat' ) ) ],
% 1.20/1.57 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.57 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), U ) ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ) ) ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_Finite__Set_Osetsum'( Y, X ), 'c_COMBS'( 'c_COMBB'(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Z, X, 'tc_fun'( X, X ), Y ), T, Y, X, X
% 1.20/1.57 ) ), U ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.20/1.57 'c_Finite__Set_Osetsum'( Y, X ), Z ), U ) ), hAPP( hAPP(
% 1.20/1.57 'c_Finite__Set_Osetsum'( Y, X ), T ), U ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.57 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.57 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), U )
% 1.20/1.57 ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 X ) ) ), =( Y, Z ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 X ) ) ), =( Y, Z ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.20/1.57 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 1.20/1.57 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.20/1.57 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.20/1.57 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.20/1.57 [ ~( 'class_RealVector_Oreal__normed__algebra'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.57 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.20/1.57 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), Z ), U ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.20/1.57 Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.57 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.20/1.57 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.57 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.20/1.57 Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.57 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ), Y ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), =( Z,
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ), =( Y,
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), ~(
% 1.20/1.57 'class_Ring__and__Field_Odivision__by__zero'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_Finite__Set_Osetsum'( 'tc_nat', X ), hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), Y ) ),
% 1.20/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 'tc_nat' ), Z, 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Oinverse__class_Odivide'(
% 1.20/1.57 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( X ), Y ), Z ) ), 'c_HOL_Oone__class_Oone'(
% 1.20/1.57 X ) ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ),
% 1.20/1.57 'c_HOL_Oone__class_Oone'( X ) ) ) ), =( Y, 'c_HOL_Oone__class_Oone'( X )
% 1.20/1.57 ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.20/1.57 Y ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.20/1.57 Y ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.20/1.57 Y ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.20/1.57 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.20/1.57 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.20/1.57 Y ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.20/1.57 Y ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.20/1.57 Y ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.20/1.57 Y ) ],
% 1.20/1.57 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.20/1.57 X ), Y ), Z ) ), Z ), Y ) ],
% 1.20/1.57 [ ~( 'class_Ring__and__Field_Ofield'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ) ],
% 1.20/1.57 [ ~( 'class_RealVector_Oreal__normed__field'( X ) ), =( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Y ), T ) ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( X ), Z ), T ) ) ) ],
% 1.20/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( hAPP( hAPP(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 'v_i' ), X ), 'tc_nat' ), 'v_n'
% 1.20/1.57 ) ) ],
% 1.20/1.57 [ hBOOL( hAPP( 'c_HOL_Oord__class_Oless'( 'v_i', 'tc_nat' ), 'v_n' ) ) ]
% 1.20/1.57 ,
% 1.20/1.57 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_Complex_Ocomplex' )
% 1.20/1.57 , hAPP( hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', 'tc_Complex_Ocomplex' )
% 1.20/1.57 , 'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.57 'tc_Complex_Ocomplex' ), hAPP( 'c_COMBC'( 'c_COMBB'(
% 1.20/1.57 'c_Finite__Set_Osetsum'( 'tc_nat', 'tc_Complex_Ocomplex' ), 'c_COMBB'(
% 1.20/1.57 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ), 'c_COMBB'( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ), hAPP( hAPP(
% 1.20/1.57 'c_HOL_Oinverse__class_Odivide'( 'tc_Complex_Ocomplex' ),
% 1.20/1.57 'c_HOL_Oone__class_Oone'( 'tc_Complex_Ocomplex' ) ),
% 1.20/1.57 'c_FFT__Mirabelle_Oroot'( 'v_n' ) ) ), hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.20/1.57 'tc_nat' ), 'v_i' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ),
% 1.20/1.57 'tc_Complex_Ocomplex', 'tc_fun'( 'tc_nat', 'tc_Complex_Ocomplex' ),
% 1.20/1.57 'tc_nat' ), 'tc_fun'( 'tc_nat', 'tc_Complex_Ocomplex' ), 'tc_fun'(
% 1.20/1.57 'tc_fun'( 'tc_nat', 'tc_bool' ), 'tc_Complex_Ocomplex' ), 'tc_nat' ),
% 1.20/1.57 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ), 'tc_Complex_Ocomplex' ),
% 1.20/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 'tc_nat' ), 'v_n', 'tc_nat' ) ), 'tc_Complex_Ocomplex', 'tc_fun'(
% 1.20/1.57 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ), 'tc_nat' ), 'v_a',
% 1.20/1.57 'tc_nat', 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ) ),
% 1.20/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 'tc_nat' ), 'v_i', 'tc_nat' ) ) ), hAPP( hAPP( 'c_Finite__Set_Osetsum'(
% 1.20/1.57 'tc_nat', 'tc_Complex_Ocomplex' ), 'c_COMBS'( 'c_COMBB'(
% 1.20/1.57 'c_HOL_Otimes__class_Otimes'( 'tc_Complex_Ocomplex' ), hAPP( 'c_COMBC'(
% 1.20/1.57 'c_COMBB'( 'c_Finite__Set_Osetsum'( 'tc_nat', 'tc_Complex_Ocomplex' ),
% 1.20/1.57 'c_COMBB'( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.20/1.57 'c_COMBB'( hAPP( 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' )
% 1.20/1.57 , 'c_FFT__Mirabelle_Oroot'( 'v_n' ) ), hAPP( 'c_COMBC'(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 'tc_nat', 'tc_nat', 'tc_nat' )
% 1.20/1.57 , 'v_i' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ),
% 1.20/1.57 'tc_Complex_Ocomplex', 'tc_fun'( 'tc_nat', 'tc_Complex_Ocomplex' ),
% 1.20/1.57 'tc_nat' ), 'tc_fun'( 'tc_nat', 'tc_Complex_Ocomplex' ), 'tc_fun'(
% 1.20/1.57 'tc_fun'( 'tc_nat', 'tc_bool' ), 'tc_Complex_Ocomplex' ), 'tc_nat' ),
% 1.20/1.57 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ), 'tc_Complex_Ocomplex' ),
% 1.20/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 'tc_nat' ), 'v_n', 'tc_nat' ) ), 'tc_Complex_Ocomplex', 'tc_fun'(
% 1.20/1.57 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ), 'tc_nat' ), 'v_a',
% 1.20/1.57 'tc_nat', 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ) ),
% 1.20/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( 'v_i', 'v_n', 'tc_nat' ) )
% 1.20/1.57 ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( 'tc_nat', 'tc_Complex_Ocomplex'
% 1.20/1.57 ), 'c_COMBS'( 'c_COMBB'( 'c_HOL_Otimes__class_Otimes'(
% 1.20/1.57 'tc_Complex_Ocomplex' ), hAPP( 'c_COMBC'( 'c_COMBB'(
% 1.20/1.57 'c_Finite__Set_Osetsum'( 'tc_nat', 'tc_Complex_Ocomplex' ), 'c_COMBB'(
% 1.20/1.57 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ), 'c_COMBB'( hAPP(
% 1.20/1.57 'c_Power_Opower__class_Opower'( 'tc_Complex_Ocomplex' ),
% 1.20/1.57 'c_FFT__Mirabelle_Oroot'( 'v_n' ) ), hAPP( 'c_COMBC'(
% 1.20/1.57 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), 'tc_nat', 'tc_nat', 'tc_nat' )
% 1.20/1.57 , 'v_i' ), 'tc_nat', 'tc_Complex_Ocomplex', 'tc_nat' ),
% 1.20/1.57 'tc_Complex_Ocomplex', 'tc_fun'( 'tc_nat', 'tc_Complex_Ocomplex' ),
% 1.20/1.57 'tc_nat' ), 'tc_fun'( 'tc_nat', 'tc_Complex_Ocomplex' ), 'tc_fun'(
% 1.20/1.57 'tc_fun'( 'tc_nat', 'tc_bool' ), 'tc_Complex_Ocomplex' ), 'tc_nat' ),
% 1.20/1.57 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ), 'tc_Complex_Ocomplex' ),
% 1.20/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( 'c_HOL_Ozero__class_Ozero'(
% 1.20/1.57 'tc_nat' ), 'v_n', 'tc_nat' ) ), 'tc_Complex_Ocomplex', 'tc_fun'(
% 1.20/1.57 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ), 'tc_nat' ), 'v_a',
% 1.20/1.57 'tc_nat', 'tc_Complex_Ocomplex', 'tc_Complex_Ocomplex' ) ),
% 1.20/1.57 'c_SetInterval_Oord__class_OatLeastLessThan'( 'v_i', 'v_n', 'tc_nat' ) )
% 1.20/1.57 ) ) ],
% 1.20/1.57 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 1.20/1.57 'class_Orderings_Opreorder'( Y ) ) ],
% 1.20/1.57 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 1.20/1.57 'class_Orderings_Oorder'( Y ) ) ],
% 1.20/1.57 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.20/1.57 ],
% 1.20/1.57 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.20/1.57 ) ],
% 1.20/1.57 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.20/1.57 ],
% 1.20/1.57 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 1.20/1.57 ,
% 1.20/1.57 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.20/1.57 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 1.20/1.57 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.20/1.57 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.20/1.57 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.20/1.57 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 1.20/1.57 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 1.20/1.57 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.20/1.57 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.20/1.57 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.20/1.57 [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_nat' ) ],
% 1.20/1.57 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.20/1.57 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.20/1.57 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.20/1.57 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.20/1.57 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.20/1.57 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.20/1.57 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.20/1.57 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.20/1.57 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.20/1.57 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.20/1.57 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.20/1.57 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.20/1.57 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.20/1.57 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.20/1.57 [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ],
% 1.20/1.57 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.20/1.57 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.20/1.57 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.20/1.57 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 1.20/1.57 [ 'class_Orderings_Opreorder'( 'tc_bool' ) ],
% 1.20/1.57 [ 'class_Orderings_Oorder'( 'tc_bool' ) ],
% 1.20/1.57 [ 'class_Ring__and__Field_Oring__1__no__zero__divisors'(
% 1.20/1.57 'tc_Complex_Ocomplex' ) ],
% 1.20/1.57 [ 'class_Ring__and__Field_Oring__no__zero__divisors'(
% 1.20/1.57 'tc_Complex_Ocomplex' ) ],
% 1.20/1.57 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'(
% 1.20/1.57 'tc_Complex_Ocomplex' ) ],
% 1.20/1.57 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_Complex_Ocomplex' )
% 1.20/1.57 ],
% 1.20/1.57 [ 'class_RealVector_Oreal__normed__algebra__1'( 'tc_Complex_Ocomplex' )
% 1.20/1.57 ],
% 1.20/1.57 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_Complex_Ocomplex' )
% 1.20/1.57 ],
% 1.20/1.57 [ 'class_Ring__and__Field_Odivision__by__zero'( 'tc_Complex_Ocomplex' )
% 1.20/1.57 ],
% 1.20/1.57 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_Complex_Ocomplex' ) ]
% 1.20/1.57 ,
% 1.20/1.57 [ 'class_Ring__and__Field_Ocomm__semiring__0'( 'tc_Complex_Ocomplex' ) ]
% 1.20/1.57 ,
% 1.20/1.57 [ 'class_RealVector_Oreal__normed__algebra'( 'tc_Complex_Ocomplex' ) ]
% 1.20/1.57 ,
% 1.20/1.57 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.20/1.57 ,
% 1.20/1.57 [ 'class_RealVector_Oreal__normed__vector'( 'tc_Complex_Ocomplex' ) ]
% 1.20/1.57 ,
% 1.20/1.57 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_Complex_Ocomplex' ) ]
% 1.20/1.57 ,
% 1.20/1.57 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_Complex_Ocomplex' ) ]
% 1.20/1.57 ,
% 1.20/1.57 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_Complex_Ocomplex' ) ]
% 1.20/1.57 ,
% 1.20/1.57 [ 'class_RealVector_Oreal__normed__field'( 'tc_Complex_Ocomplex' ) ]
% 1.20/1.57 ,
% 1.20/1.57 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_Complex_Ocomplex' ) ]
% 1.20/1.57 ,
% 1.20/1.57 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_Complex_Ocomplex' ) ]
% 1.20/1.57 ,
% 1.20/1.57 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.20/1.57 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_Complex_Ocomplex' ) ],
% 1.20/1.57 [ 'class_OrderedGroup_Oab__group__add'( 'tc_Complex_Ocomplex' ) ],
% 1.20/1.57 [ 'class_Ring__and__Field_Omult__zero'( 'tc_Complex_Ocomplex' ) ],
% 1.20/1.57 [ 'class_Ring__and__Field_Ocomm__ring'( 'tc_Complex_Ocomplex' ) ],
% 1.20/1.57 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_Complex_Ocomplex' ) ],
% 1.20/1.57 [ 'class_Ring__and__Field_Osemiring'( 'tc_Complex_Ocomplex' ) ],
% 1.20/1.57 [ 'class_RealVector_Ometric__space'( 'tc_Complex_Ocomplex' ) ],
% 1.20/1.57 [ 'class_OrderedGroup_Omonoid__add'( 'tc_Complex_Ocomplex' ) ],
% 1.20/1.57 [ 'class_OrderedGroup_Ogroup__add'( 'tc_Complex_Ocomplex' ) ],
% 1.20/1.57 [ 'class_Ring__and__Field_Oring__1'( 'tc_Complex_Ocomplex' ) ],
% 1.20/1.57 [ 'class_RealVector_Oreal__field'( 'tc_Complex_Ocomplex' ) ],
% 1.20/1.57 [ 'class_Ring__and__Field_Ofield'( 'tc_Complex_Ocomplex' ) ],
% 1.20/1.57 [ 'class_Ring__and__Field_Oring'( 'tc_Complex_Ocomplex' ) ],
% 1.20/1.57 [ 'class_Ring__and__Field_Oidom'( 'tc_Complex_Ocomplex' ) ],
% 1.20/1.57 [ 'class_Nat_Osemiring__char__0'( 'tc_Complex_Ocomplex' ) ],
% 1.20/1.57 [ 'class_Int_Onumber__ring'( 'tc_Complex_Ocomplex' ) ],
% 1.20/1.57 [ 'class_Power_Opower'( 'tc_Complex_Ocomplex' ) ],
% 1.20/1.57 [ =( hAPP( 'c_COMBS'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), hAPP( Y
% 1.20/1.57 , W ) ) ) ],
% 1.20/1.57 [ =( hAPP( hAPP( 'c_COMBC'( X, Y, Z, T ), U ), W ), hAPP( hAPP( X, W ),
% 1.20/1.57 U ) ) ],
% 1.20/1.57 [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 1.20/1.57 ,
% 1.20/1.57 [ 'c_fequal'( X, X, Y ) ],
% 1.20/1.57 [ =( X, Y ), ~( 'c_fequal'( X, Y, Z ) ) ]
% 1.20/1.57 ] .
% 1.20/1.57
% 1.20/1.57
% 1.20/1.57 percentage equality = 0.195162, percentage horn = 0.850348
% 1.20/1.57 This is a problem with some equality
% 1.20/1.57
% 1.20/1.57
% 1.20/1.57
% 1.20/1.57 Options Used:
% 1.20/1.57
% 1.20/1.57 useres = 1
% 1.20/1.57 useparamod = 1
% 1.20/1.57 useeqrefl = 1
% 1.20/1.57 useeqfact = 1
% 1.20/1.57 usefactor = 1
% 1.20/1.57 usesimpsplitting = 0
% 1.20/1.57 usesimpdemod = 5
% 1.20/1.57 usesimpres = 3
% 1.20/1.58
% 1.20/1.58 resimpinuse = 1000
% 1.20/1.58 resimpclauses = 20000
% 1.20/1.58 substype = eqrewr
% 1.20/1.58 backwardsubs = 1
% 1.20/1.58 selectoldest = 5
% 1.20/1.58
% 1.20/1.58 litorderings [0] = split
% 1.20/1.58 litorderings [1] = extend the termordering, first sorting on arguments
% 1.20/1.58
% 1.20/1.58 termordering = kbo
% 1.20/1.58
% 1.20/1.58 litapriori = 0
% 1.20/1.58 termapriori = 1
% 1.20/1.58 litaposteriori = 0
% 1.20/1.58 termaposteriori = 0
% 1.20/1.58 demodaposteriori = 0
% 1.20/1.58 ordereqreflfact = 0
% 1.20/1.58
% 1.20/1.58 litselect = negord
% 1.20/1.58
% 1.20/1.58 maxweight = 15
% 1.20/1.58 maxdepth = 30000
% 1.20/1.58 maxlength = 115
% 1.20/1.58 maxnrvars = 195
% 1.20/1.58 excuselevel = 1
% 1.20/1.58 increasemaxweight = 1
% 1.20/1.58
% 1.20/1.58 maxselected = 10000000
% 1.20/1.58 maxnrclauses = 10000000
% 1.20/1.58
% 1.20/1.58 showgenerated = 0
% 1.20/1.58 showkept = 0
% 1.20/1.58 showselected = 0
% 1.20/1.58 showdeleted = 0
% 1.20/1.58 showresimp = 1
% 1.20/1.58 showstatus = 2000
% 1.20/1.58
% 1.20/1.58 prologoutput = 1
% 1.20/1.58 nrgoals = 5000000
% 1.20/1.58 totalproof = 1
% 1.20/1.58
% 1.20/1.58 Symbols occurring in the translation:
% 1.20/1.58
% 1.20/1.58 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.20/1.58 . [1, 2] (w:1, o:146, a:1, s:1, b:0),
% 1.20/1.58 ! [4, 1] (w:0, o:73, a:1, s:1, b:0),
% 1.20/1.58 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.20/1.58 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.20/1.58 'class_Orderings_Olinorder' [40, 1] (w:1, o:79, a:1, s:1, b:0),
% 1.20/1.58 'c_HOL_Oord__class_Oless' [42, 2] (w:1, o:171, a:1, s:1, b:0),
% 1.20/1.58 hAPP [43, 2] (w:1, o:172, a:1, s:1, b:0),
% 1.20/1.58 hBOOL [44, 1] (w:1, o:80, a:1, s:1, b:0),
% 1.20/1.58 'class_Orderings_Opreorder' [45, 1] (w:1, o:82, a:1, s:1, b:0),
% 1.20/1.58 'c_lessequals' [47, 2] (w:1, o:173, a:1, s:1, b:0),
% 1.20/1.58 'tc_nat' [48, 0] (w:1, o:15, a:1, s:1, b:0),
% 1.20/1.58 'class_Orderings_Oorder' [50, 1] (w:1, o:81, a:1, s:1, b:0),
% 1.20/1.58 'c_Suc' [51, 0] (w:1, o:22, a:1, s:1, b:0),
% 1.20/1.58 'c_HOL_Ozero__class_Ozero' [52, 1] (w:1, o:83, a:1, s:1, b:0),
% 1.20/1.58 'c_HOL_Oplus__class_Oplus' [53, 1] (w:1, o:85, a:1, s:1, b:0),
% 1.20/1.58 'c_HOL_Ominus__class_Ominus' [54, 1] (w:1, o:86, a:1, s:1, b:0),
% 1.20/1.58 'c_HOL_Otimes__class_Otimes' [58, 1] (w:1, o:87, a:1, s:1, b:0),
% 1.20/1.58 'class_Ring__and__Field_Osemiring__1' [66, 1] (w:1, o:93, a:1, s:1
% 1.20/1.58 , b:0),
% 1.20/1.58 'c_Nat_Osemiring__1__class_Oof__nat' [67, 2] (w:1, o:174, a:1, s:1
% 1.20/1.58 , b:0),
% 1.20/1.58 'c_Groebner__Basis_Ogb__semiring' [78, 6] (w:1, o:188, a:1, s:1, b:0)
% 1.20/1.58 ,
% 1.20/1.58 'c_Groebner__Basis_Osemiringb' [84, 6] (w:1, o:189, a:1, s:1, b:0),
% 1.20/1.58 'class_Ring__and__Field_Oordered__semidom' [85, 1] (w:1, o:96, a:1
% 1.20/1.58 , s:1, b:0),
% 1.20/1.58 'c_Power_Opower__class_Opower' [86, 1] (w:1, o:97, a:1, s:1, b:0),
% 1.20/1.58 'c_HOL_Oone__class_Oone' [87, 1] (w:1, o:84, a:1, s:1, b:0),
% 1.20/1.58 'class_OrderedGroup_Omonoid__mult' [89, 1] (w:1, o:99, a:1, s:1, b:0)
% 1.20/1.58 ,
% 1.20/1.58 'class_OrderedGroup_Ocomm__monoid__add' [90, 1] (w:1, o:100, a:1, s:1
% 1.20/1.58 , b:0),
% 1.20/1.58 'c_Finite__Set_Osetsum' [91, 2] (w:1, o:175, a:1, s:1, b:0),
% 1.20/1.58 'c_SetInterval_Oord__class_OatLeastLessThan' [93, 3] (w:1, o:178, a:1
% 1.20/1.58 , s:1, b:0),
% 1.20/1.58 'tc_Complex_Ocomplex' [94, 0] (w:1, o:49, a:1, s:1, b:0),
% 1.20/1.58 'c_FFT__Mirabelle_Oroot' [95, 1] (w:1, o:101, a:1, s:1, b:0),
% 1.20/1.58 'class_Ring__and__Field_Oordered__ring__strict' [96, 1] (w:1, o:95
% 1.20/1.58 , a:1, s:1, b:0),
% 1.20/1.58 'class_Ring__and__Field_Oordered__semiring__strict' [97, 1] (w:1, o:
% 1.20/1.58 102, a:1, s:1, b:0),
% 1.20/1.58 'class_Ring__and__Field_Oordered__comm__semiring__strict' [98, 1] (w:
% 1.20/1.58 1, o:103, a:1, s:1, b:0),
% 1.20/1.58 'class_Ring__and__Field_Omult__mono1' [99, 1] (w:1, o:104, a:1, s:1
% 1.20/1.58 , b:0),
% 1.20/1.58 'class_Ring__and__Field_Omult__mono' [100, 1] (w:1, o:105, a:1, s:1
% 1.20/1.58 , b:0),
% 1.20/1.58 'class_Ring__and__Field_Opordered__ring' [101, 1] (w:1, o:109, a:1
% 1.20/1.58 , s:1, b:0),
% 1.20/1.58 'class_RealVector_Oreal__normed__field' [103, 1] (w:1, o:110, a:1, s:
% 1.20/1.58 1, b:0),
% 1.20/1.58 'c_Deriv_Odifferentiable' [104, 3] (w:1, o:179, a:1, s:1, b:0),
% 1.20/1.58 'c_Deriv_Oderiv' [106, 4] (w:1, o:185, a:1, s:1, b:0),
% 1.20/1.58 'class_Ring__and__Field_Oordered__idom' [107, 1] (w:1, o:106, a:1, s:
% 1.20/1.58 1, b:0),
% 1.20/1.58 'class_RealVector_Ometric__space' [108, 1] (w:1, o:111, a:1, s:1, b:0
% 1.20/1.58 ),
% 1.20/1.58 'c_SEQ_OLIMSEQ' [110, 3] (w:1, o:180, a:1, s:1, b:0),
% 1.20/1.58 'v_n' [113, 0] (w:1, o:57, a:1, s:1, b:0),
% 1.20/1.58 'class_Nat_Osemiring__char__0' [114, 1] (w:1, o:78, a:1, s:1, b:0),
% 1.20/1.58 'c_COMBB' [115, 5] (w:1, o:186, a:1, s:1, b:0),
% 7.53/7.93 'class_Ring__and__Field_Opordered__cancel__semiring' [116, 1] (w:1
% 7.53/7.93 , o:112, a:1, s:1, b:0),
% 7.53/7.93 'class_Ring__and__Field_Opordered__semiring' [117, 1] (w:1, o:113, a:
% 7.53/7.93 1, s:1, b:0),
% 7.53/7.93 'class_OrderedGroup_Opordered__comm__monoid__add' [118, 1] (w:1, o:
% 7.53/7.93 114, a:1, s:1, b:0),
% 7.53/7.93 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [119, 1]
% 7.53/7.93 (w:1, o:115, a:1, s:1, b:0),
% 7.53/7.93 'class_OrderedGroup_Olordered__ab__group__add' [120, 1] (w:1, o:98
% 7.53/7.93 , a:1, s:1, b:0),
% 7.53/7.93 'class_OrderedGroup_Opordered__ab__group__add' [124, 1] (w:1, o:116
% 7.53/7.93 , a:1, s:1, b:0),
% 7.53/7.93 'class_Ring__and__Field_Osemiring__0' [125, 1] (w:1, o:92, a:1, s:1
% 7.53/7.93 , b:0),
% 7.53/7.93 'class_Power_Opower' [126, 1] (w:1, o:128, a:1, s:1, b:0),
% 7.53/7.93 'class_RealVector_Oreal__normed__algebra' [127, 1] (w:1, o:129, a:1
% 7.53/7.93 , s:1, b:0),
% 7.53/7.93 'class_Ring__and__Field_Oordered__field' [128, 1] (w:1, o:107, a:1
% 7.53/7.93 , s:1, b:0),
% 7.53/7.93 'class_Ring__and__Field_Odivision__by__zero' [129, 1] (w:1, o:134, a:
% 7.53/7.93 1, s:1, b:0),
% 7.53/7.93 'c_HOL_Oinverse__class_Odivide' [130, 1] (w:1, o:135, a:1, s:1, b:0)
% 7.53/7.93 ,
% 7.53/7.93 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [131, 1]
% 7.53/7.93 (w:1, o:117, a:1, s:1, b:0),
% 7.53/7.93 'class_Ring__and__Field_Oordered__semiring' [132, 1] (w:1, o:108, a:1
% 7.53/7.93 , s:1, b:0),
% 7.53/7.93 'class_OrderedGroup_Opordered__ab__semigroup__add' [133, 1] (w:1, o:
% 7.53/7.93 118, a:1, s:1, b:0),
% 7.53/7.93 'class_Ring__and__Field_Ocomm__semiring__1' [136, 1] (w:1, o:132, a:1
% 7.53/7.93 , s:1, b:0),
% 7.53/7.93 'tc_fun' [137, 2] (w:1, o:176, a:1, s:1, b:0),
% 7.53/7.93 'c_COMBC' [138, 4] (w:1, o:184, a:1, s:1, b:0),
% 7.53/7.93 'v_i' [139, 0] (w:1, o:59, a:1, s:1, b:0),
% 7.53/7.93 'c_COMBS' [141, 5] (w:1, o:187, a:1, s:1, b:0),
% 7.53/7.93 'class_Ring__and__Field_Ofield' [142, 1] (w:1, o:136, a:1, s:1, b:0)
% 7.53/7.93 ,
% 7.53/7.93 'class_RealVector_Oreal__normed__vector' [144, 1] (w:1, o:137, a:1
% 7.53/7.93 , s:1, b:0),
% 7.53/7.93 'class_OrderedGroup_Oab__group__add' [145, 1] (w:1, o:119, a:1, s:1
% 7.53/7.93 , b:0),
% 7.53/7.93 'class_Ring__and__Field_Oring__1' [147, 1] (w:1, o:88, a:1, s:1, b:0)
% 7.53/7.93 ,
% 7.53/7.93 'class_Ring__and__Field_Oidom' [149, 1] (w:1, o:138, a:1, s:1, b:0),
% 7.53/7.93
% 7.53/7.93 'class_Int_Onumber__ring' [150, 1] (w:1, o:139, a:1, s:1, b:0),
% 7.53/7.93 'class_RealVector_Oreal__normed__algebra__1' [151, 1] (w:1, o:140, a:
% 7.53/7.93 1, s:1, b:0),
% 7.53/7.93 'c_Series_Osuminf' [152, 2] (w:1, o:177, a:1, s:1, b:0),
% 7.53/7.93 'c_FFT__Mirabelle_ODFT' [153, 3] (w:1, o:181, a:1, s:1, b:0),
% 7.53/7.93 'c_FFT__Mirabelle_OIDFT' [154, 3] (w:1, o:182, a:1, s:1, b:0),
% 7.53/7.93 'c_HOL_OIf' [155, 1] (w:1, o:141, a:1, s:1, b:0),
% 7.53/7.93 'tc_bool' [156, 0] (w:1, o:63, a:1, s:1, b:0),
% 7.53/7.93 'v_a' [157, 0] (w:1, o:64, a:1, s:1, b:0),
% 7.53/7.93 'class_Ring__and__Field_Ocomm__semiring__0' [158, 1] (w:1, o:131, a:1
% 7.53/7.93 , s:1, b:0),
% 7.53/7.93 'class_Ring__and__Field_Ocomm__ring' [159, 1] (w:1, o:130, a:1, s:1
% 7.53/7.93 , b:0),
% 7.53/7.93 'class_OrderedGroup_Oab__semigroup__idem__mult' [160, 1] (w:1, o:120
% 7.53/7.93 , a:1, s:1, b:0),
% 7.53/7.93 'class_OrderedGroup_Ocomm__monoid__mult' [163, 1] (w:1, o:121, a:1
% 7.53/7.93 , s:1, b:0),
% 7.53/7.93 'class_OrderedGroup_Oab__semigroup__mult' [164, 1] (w:1, o:122, a:1
% 7.53/7.93 , s:1, b:0),
% 7.53/7.93 'class_Ring__and__Field_Ocomm__semiring' [168, 1] (w:1, o:133, a:1
% 7.53/7.93 , s:1, b:0),
% 7.53/7.93 'class_OrderedGroup_Ocancel__ab__semigroup__add' [169, 1] (w:1, o:123
% 7.53/7.93 , a:1, s:1, b:0),
% 7.53/7.93 'class_OrderedGroup_Ocancel__semigroup__add' [170, 1] (w:1, o:124, a:
% 7.53/7.93 1, s:1, b:0),
% 7.53/7.93 'class_Ring__and__Field_Ozero__neq__one' [171, 1] (w:1, o:142, a:1
% 7.53/7.93 , s:1, b:0),
% 7.53/7.93 'class_RealVector_Oreal__field' [173, 1] (w:1, o:143, a:1, s:1, b:0)
% 7.53/7.93 ,
% 7.53/7.93 'class_Ring__and__Field_Oring' [174, 1] (w:1, o:89, a:1, s:1, b:0),
% 7.53/7.93 'class_Ring__and__Field_Omult__zero' [175, 1] (w:1, o:144, a:1, s:1
% 7.53/7.93 , b:0),
% 7.53/7.93 'class_Ring__and__Field_Oring__no__zero__divisors' [176, 1] (w:1, o:
% 7.53/7.93 90, a:1, s:1, b:0),
% 7.53/7.93 'class_Ring__and__Field_Ono__zero__divisors' [179, 1] (w:1, o:94, a:1
% 7.53/7.93 , s:1, b:0),
% 7.53/7.93 'class_Ring__and__Field_Oring__1__no__zero__divisors' [180, 1] (w:1
% 7.53/7.93 , o:91, a:1, s:1, b:0),
% 7.53/7.93 'class_OrderedGroup_Ogroup__add' [181, 1] (w:1, o:125, a:1, s:1, b:0)
% 7.53/7.93 ,
% 7.53/7.93 'class_OrderedGroup_Oab__semigroup__add' [182, 1] (w:1, o:126, a:1
% 35.61/35.95 , s:1, b:0),
% 35.61/35.95 'class_Ring__and__Field_Osemiring' [185, 1] (w:1, o:145, a:1, s:1, b:
% 35.61/35.95 0),
% 35.61/35.95 'class_OrderedGroup_Omonoid__add' [186, 1] (w:1, o:127, a:1, s:1, b:0
% 35.61/35.95 ),
% 35.61/35.95 'c_fequal' [189, 3] (w:1, o:183, a:1, s:1, b:0).
% 35.61/35.95
% 35.61/35.95
% 35.61/35.95 Starting Search:
% 35.61/35.95
% 35.61/35.95 Resimplifying inuse:
% 35.61/35.95 Done
% 35.61/35.95
% 35.61/35.95
% 35.61/35.95 Intermediate Status:
% 35.61/35.95 Generated: 5779
% 35.61/35.95 Kept: 2118
% 35.61/35.95 Inuse: 75
% 35.61/35.95 Deleted: 1
% 35.61/35.95 Deletedinuse: 0
% 35.61/35.95
% 35.61/35.95 Resimplifying inuse:
% 35.61/35.95 Done
% 35.61/35.95
% 35.61/35.95 Resimplifying inuse:
% 35.61/35.95 Done
% 35.61/35.95
% 35.61/35.95
% 35.61/35.95 Intermediate Status:
% 35.61/35.95 Generated: 15928
% 35.61/35.95 Kept: 4225
% 35.61/35.95 Inuse: 128
% 35.61/35.95 Deleted: 3
% 35.61/35.95 Deletedinuse: 0
% 35.61/35.95
% 35.61/35.95 Resimplifying inuse:
% 35.61/35.95 Done
% 35.61/35.95
% 35.61/35.95 Resimplifying inuse:
% 35.61/35.95 Done
% 35.61/35.95
% 35.61/35.95
% 35.61/35.95 Intermediate Status:
% 35.61/35.95 Generated: 26035
% 35.61/35.95 Kept: 6500
% 35.61/35.95 Inuse: 189
% 35.61/35.95 Deleted: 7
% 35.61/35.95 Deletedinuse: 0
% 35.61/35.95
% 35.61/35.95 Resimplifying inuse:
% 35.61/35.95 Done
% 35.61/35.95
% 35.61/35.95 Resimplifying inuse:
% 35.61/35.95 Done
% 35.61/35.95
% 35.61/35.95
% 35.61/35.95 Intermediate Status:
% 35.61/35.95 Generated: 35094
% 35.61/35.95 Kept: 8718
% 35.61/35.95 Inuse: 204
% 35.61/35.95 Deleted: 7
% 35.61/35.95 Deletedinuse: 0
% 35.61/35.95
% 35.61/35.95 Resimplifying inuse:
% 35.61/35.95 Done
% 35.61/35.95
% 35.61/35.95 Resimplifying inuse:
% 35.61/35.95 Done
% 35.61/35.95
% 35.61/35.95
% 35.61/35.95 Intermediate Status:
% 35.61/35.96 Generated: 43845
% 35.61/35.96 Kept: 10877
% 35.61/35.96 Inuse: 264
% 35.61/35.96 Deleted: 7
% 35.61/35.96 Deletedinuse: 0
% 35.61/35.96
% 35.61/35.96 Resimplifying inuse:
% 35.61/35.96 Done
% 35.61/35.96
% 35.61/35.96 Resimplifying inuse:
% 35.61/35.96 Done
% 35.61/35.96
% 35.61/35.96
% 35.61/35.96 Intermediate Status:
% 35.61/35.96 Generated: 51793
% 35.61/35.96 Kept: 12932
% 35.61/35.96 Inuse: 304
% 35.61/35.96 Deleted: 7
% 35.61/35.96 Deletedinuse: 0
% 35.61/35.96
% 35.61/35.96 Resimplifying inuse:
% 35.61/35.96 Done
% 35.61/35.96
% 35.61/35.96 Resimplifying inuse:
% 35.61/35.96 Done
% 35.61/35.96
% 35.61/35.96
% 35.61/35.96 Intermediate Status:
% 35.61/35.96 Generated: 57787
% 35.61/35.96 Kept: 14935
% 35.61/35.96 Inuse: 324
% 35.61/35.96 Deleted: 7
% 35.61/35.96 Deletedinuse: 0
% 35.61/35.96
% 35.61/35.96 Resimplifying inuse:
% 35.61/35.96 Done
% 35.61/35.96
% 35.61/35.96
% 35.61/35.96 Intermediate Status:
% 35.61/35.96 Generated: 66717
% 35.61/35.96 Kept: 17254
% 35.61/35.96 Inuse: 353
% 35.61/35.96 Deleted: 8
% 35.61/35.96 Deletedinuse: 0
% 35.61/35.96
% 35.61/35.96 Resimplifying inuse:
% 35.61/35.96 Done
% 35.61/35.96
% 35.61/35.96 Resimplifying inuse:
% 35.61/35.96 Done
% 35.61/35.96
% 35.61/35.96
% 35.61/35.96 Intermediate Status:
% 35.61/35.96 Generated: 76185
% 35.61/35.96 Kept: 20262
% 35.61/35.96 Inuse: 391
% 35.61/35.96 Deleted: 10
% 35.61/35.96 Deletedinuse: 0
% 35.61/35.96
% 35.61/35.96 Resimplifying inuse:
% 35.61/35.96 Done
% 35.61/35.96
% 35.61/35.96 Resimplifying clauses:
% 35.61/35.96 Done
% 35.61/35.96
% 35.61/35.96 Resimplifying inuse:
% 35.61/35.96 Done
% 35.61/35.96
% 35.61/35.96
% 35.61/35.96 Intermediate Status:
% 35.61/35.96 Generated: 83712
% 35.61/35.96 Kept: 22608
% 35.61/35.96 Inuse: 411
% 35.61/35.96 Deleted: 310
% 35.61/35.96 Deletedinuse: 0
% 35.61/35.96
% 35.61/35.96 Resimplifying inuse:
% 35.61/35.96 Done
% 35.61/35.96
% 35.61/35.96 Resimplifying inuse:
% 35.61/35.96 Done
% 35.61/35.96
% 35.61/35.96
% 35.61/35.96 Intermediate Status:
% 35.61/35.96 Generated: 93932
% 35.61/35.96 Kept: 25188
% 35.61/35.96 Inuse: 456
% 35.61/35.96 Deleted: 310
% 35.61/35.96 Deletedinuse: 0
% 35.61/35.96
% 35.61/35.96 Resimplifying inuse:
% 35.61/35.96 Done
% 35.61/35.96
% 35.61/35.96 Resimplifying inuse:
% 35.61/35.96 Done
% 35.61/35.96
% 35.61/35.96
% 35.61/35.96 Intermediate Status:
% 35.61/35.96 Generated: 101698
% 35.61/35.96 Kept: 27218
% 35.61/35.96 Inuse: 491
% 35.61/35.96 Deleted: 310
% 35.61/35.96 Deletedinuse: 0
% 35.61/35.96
% 35.61/35.96 Resimplifying inuse:
% 35.61/35.96 Done
% 35.61/35.96
% 35.61/35.96 Resimplifying inuse:
% 35.61/35.96 Done
% 35.61/35.96
% 35.61/35.96
% 35.61/35.96 Intermediate Status:
% 35.61/35.96 Generated: 109091
% 35.61/35.96 Kept: 29493
% 35.61/35.96 Inuse: 526
% 35.61/35.96 Deleted: 310
% 35.61/35.96 Deletedinuse: 0
% 35.61/35.96
% 35.61/35.96 Resimplifying inuse:
% 35.61/35.96 Done
% 35.61/35.96
% 35.61/35.96 Resimplifying inuse:
% 35.61/35.96 Done
% 35.61/35.96
% 35.61/35.96
% 35.61/35.96 Intermediate Status:
% 35.61/35.96 Generated: 118256
% 35.61/35.96 Kept: 31667
% 35.61/35.96 Inuse: 561
% 35.61/35.96 Deleted: 311
% 35.61/35.96 Deletedinuse: 1
% 35.61/35.96
% 35.61/35.96 Resimplifying inuse:
% 35.61/35.96 Done
% 35.61/35.96
% 35.61/35.96
% 35.61/35.96 Intermediate Status:
% 35.61/35.96 Generated: 127593
% 35.61/35.96 Kept: 34142
% 35.61/35.96 Inuse: 586
% 35.61/35.96 Deleted: 311
% 35.61/35.96 Deletedinuse: 1
% 35.61/35.96
% 35.61/35.96 Resimplifying inuse:
% 35.61/35.96 Done
% 35.61/35.96
% 35.61/35.96 Resimplifying inuse:
% 35.61/35.96 Done
% 35.61/35.96
% 35.61/35.96
% 35.61/35.96 Intermediate Status:
% 35.61/35.96 Generated: 135679
% 35.61/35.96 Kept: 36296
% 35.61/35.96 Inuse: 636
% 35.61/35.96 Deleted: 311
% 35.61/35.96 Deletedinuse: 1
% 35.61/35.96
% 35.61/35.96 Resimplifying inuse:
% 35.61/35.96 Done
% 35.61/35.96
% 35.61/35.96 Resimplifying inuse:
% 35.61/35.96 Done
% 35.61/35.96
% 35.61/35.96
% 35.61/35.96 Intermediate Status:
% 35.61/35.96 Generated: 141121
% 35.61/35.96 Kept: 38296
% 35.61/35.96 Inuse: 656
% 35.61/35.96 Deleted: 311
% 35.61/35.96 Deletedinuse: 1
% 35.61/35.96
% 35.61/35.96 Resimplifying inuse:
% 35.61/35.96 Done
% 35.61/35.96
% 35.61/35.96 Resimplifying inuse:
% 35.61/35.96 Done
% 35.61/35.96
% 35.61/35.96
% 35.61/35.96 Intermediate Status:
% 35.61/35.96 Generated: 147680
% 35.61/35.96 Kept: 40520
% 35.61/35.96 Inuse: 681
% 35.61/35.96 Deleted: 311
% 35.61/35.96 Deletedinuse: 1
% 35.61/35.96
% 35.61/35.96 Resimplifying clauses:
% 35.61/35.96 Done
% 35.61/35.96
% 35.61/35.96 Resimplifying inuse:
% 35.61/35.96 Done
% 35.61/35.96
% 35.61/35.96
% 35.61/35.96 Intermediate Status:
% 35.61/35.96 Generated: 154396
% 35.61/35.96 Kept: 42571
% 35.61/35.96 Inuse: 706
% 35.61/35.96 Deleted: 728
% 35.61/35.96 Deletedinuse: 1
% 35.61/35.96
% 35.61/35.96 Resimplifying inuse:
% 35.61/35.96 Done
% 35.61/35.96
% 35.61/35.96 Resimplifying inuse:
% 35.61/35.96 Done
% 35.61/35.96
% 35.61/35.96
% 35.61/35.96 Intermediate Status:
% 35.61/35.96 Generated: 161092
% 35.61/35.96 Kept: 44628
% 35.61/35.96 Inuse: 736
% 35.61/35.96 Deleted: 728
% 35.61/35.96 Deletedinuse: 1
% 35.61/35.96
% 35.61/35.96 Resimplifying inuse:
% 35.61/35.96 Done
% 35.61/35.96
% 35.61/35.96 Resimplifying inuse:
% 35.61/35.96 Done
% 35.61/35.96
% 35.61/35.96
% 35.61/35.96 Intermediate Status:
% 35.61/35.96 Generated: 168186
% 35.61/35.96 Kept: 46729
% 35.61/35.96 Inuse: 761
% 35.61/35.96 Deleted: 728
% 35.61/35.96 Deletedinuse: 1
% 35.61/35.96
% 35.61/35.96 Resimplifying inuse:
% 35.61/35.96 Done
% 35.61/35.96
% 35.61/35.96 Resimplifying inuse:
% 35.61/35.96 Done
% 35.61/35.96
% 35.61/35.96
% 35.61/35.96 Intermediate Status:
% 35.61/35.96 Generated: 176021
% 35.61/35.96 Kept: 48948
% 35.61/35.96 Inuse: 791
% 35.61/35.96 Deleted: 728
% 35.61/35.96 Deletedinuse: 1
% 35.61/35.96
% 35.61/35.96
% 35.61/35.96 Intermediate Status:
% 35.61/35.96 Generated: 185957
% 35.61/35.96 Kept: 51837
% 35.61/35.96 Inuse: 801
% 35.61/35.96 Deleted: 728
% 35.61/35.96 Deletedinuse: 1
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94
% 114.56/114.94 Intermediate Status:
% 114.56/114.94 Generated: 197450
% 114.56/114.94 Kept: 54051
% 114.56/114.94 Inuse: 821
% 114.56/114.94 Deleted: 728
% 114.56/114.94 Deletedinuse: 1
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94
% 114.56/114.94 Intermediate Status:
% 114.56/114.94 Generated: 221890
% 114.56/114.94 Kept: 57701
% 114.56/114.94 Inuse: 836
% 114.56/114.94 Deleted: 728
% 114.56/114.94 Deletedinuse: 1
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94
% 114.56/114.94 Intermediate Status:
% 114.56/114.94 Generated: 229157
% 114.56/114.94 Kept: 60035
% 114.56/114.94 Inuse: 866
% 114.56/114.94 Deleted: 728
% 114.56/114.94 Deletedinuse: 1
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94 Resimplifying clauses:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94
% 114.56/114.94 Intermediate Status:
% 114.56/114.94 Generated: 242655
% 114.56/114.94 Kept: 62744
% 114.56/114.94 Inuse: 886
% 114.56/114.94 Deleted: 1286
% 114.56/114.94 Deletedinuse: 1
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94
% 114.56/114.94 Intermediate Status:
% 114.56/114.94 Generated: 261819
% 114.56/114.94 Kept: 65717
% 114.56/114.94 Inuse: 896
% 114.56/114.94 Deleted: 1286
% 114.56/114.94 Deletedinuse: 1
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94
% 114.56/114.94 Intermediate Status:
% 114.56/114.94 Generated: 281280
% 114.56/114.94 Kept: 68571
% 114.56/114.94 Inuse: 906
% 114.56/114.94 Deleted: 1286
% 114.56/114.94 Deletedinuse: 1
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94
% 114.56/114.94 Intermediate Status:
% 114.56/114.94 Generated: 298812
% 114.56/114.94 Kept: 71496
% 114.56/114.94 Inuse: 916
% 114.56/114.94 Deleted: 1286
% 114.56/114.94 Deletedinuse: 1
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94
% 114.56/114.94 Intermediate Status:
% 114.56/114.94 Generated: 317616
% 114.56/114.94 Kept: 75521
% 114.56/114.94 Inuse: 941
% 114.56/114.94 Deleted: 1286
% 114.56/114.94 Deletedinuse: 1
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94
% 114.56/114.94 Intermediate Status:
% 114.56/114.94 Generated: 328085
% 114.56/114.94 Kept: 77549
% 114.56/114.94 Inuse: 946
% 114.56/114.94 Deleted: 1286
% 114.56/114.94 Deletedinuse: 1
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94
% 114.56/114.94 Intermediate Status:
% 114.56/114.94 Generated: 340308
% 114.56/114.94 Kept: 81112
% 114.56/114.94 Inuse: 956
% 114.56/114.94 Deleted: 1286
% 114.56/114.94 Deletedinuse: 1
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94 Resimplifying clauses:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94
% 114.56/114.94 Intermediate Status:
% 114.56/114.94 Generated: 350691
% 114.56/114.94 Kept: 83468
% 114.56/114.94 Inuse: 981
% 114.56/114.94 Deleted: 1390
% 114.56/114.94 Deletedinuse: 1
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94
% 114.56/114.94 Intermediate Status:
% 114.56/114.94 Generated: 366039
% 114.56/114.94 Kept: 86702
% 114.56/114.94 Inuse: 1011
% 114.56/114.94 Deleted: 1394
% 114.56/114.94 Deletedinuse: 5
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94
% 114.56/114.94 Intermediate Status:
% 114.56/114.94 Generated: 374179
% 114.56/114.94 Kept: 89359
% 114.56/114.94 Inuse: 1021
% 114.56/114.94 Deleted: 1394
% 114.56/114.94 Deletedinuse: 5
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94
% 114.56/114.94 Intermediate Status:
% 114.56/114.94 Generated: 381358
% 114.56/114.94 Kept: 91532
% 114.56/114.94 Inuse: 1036
% 114.56/114.94 Deleted: 1394
% 114.56/114.94 Deletedinuse: 5
% 114.56/114.94
% 114.56/114.94
% 114.56/114.94 Intermediate Status:
% 114.56/114.94 Generated: 391739
% 114.56/114.94 Kept: 93535
% 114.56/114.94 Inuse: 1046
% 114.56/114.94 Deleted: 1394
% 114.56/114.94 Deletedinuse: 5
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94
% 114.56/114.94 Intermediate Status:
% 114.56/114.94 Generated: 402004
% 114.56/114.94 Kept: 95620
% 114.56/114.94 Inuse: 1071
% 114.56/114.94 Deleted: 1394
% 114.56/114.94 Deletedinuse: 5
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94
% 114.56/114.94 Intermediate Status:
% 114.56/114.94 Generated: 416650
% 114.56/114.94 Kept: 97781
% 114.56/114.94 Inuse: 1101
% 114.56/114.94 Deleted: 1394
% 114.56/114.94 Deletedinuse: 5
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94
% 114.56/114.94 Intermediate Status:
% 114.56/114.94 Generated: 428395
% 114.56/114.94 Kept: 99786
% 114.56/114.94 Inuse: 1124
% 114.56/114.94 Deleted: 1395
% 114.56/114.94 Deletedinuse: 6
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94 Resimplifying clauses:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94
% 114.56/114.94 Intermediate Status:
% 114.56/114.94 Generated: 448327
% 114.56/114.94 Kept: 102204
% 114.56/114.94 Inuse: 1140
% 114.56/114.94 Deleted: 2790
% 114.56/114.94 Deletedinuse: 9
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94
% 114.56/114.94 Intermediate Status:
% 114.56/114.94 Generated: 457914
% 114.56/114.94 Kept: 104238
% 114.56/114.94 Inuse: 1155
% 114.56/114.94 Deleted: 2790
% 114.56/114.94 Deletedinuse: 9
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94
% 114.56/114.94 Intermediate Status:
% 114.56/114.94 Generated: 465605
% 114.56/114.94 Kept: 106386
% 114.56/114.94 Inuse: 1165
% 114.56/114.94 Deleted: 2790
% 114.56/114.94 Deletedinuse: 9
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94
% 114.56/114.94 Intermediate Status:
% 114.56/114.94 Generated: 479152
% 114.56/114.94 Kept: 109041
% 114.56/114.94 Inuse: 1185
% 114.56/114.94 Deleted: 2790
% 114.56/114.94 Deletedinuse: 9
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94
% 114.56/114.94 Intermediate Status:
% 114.56/114.94 Generated: 489565
% 114.56/114.94 Kept: 111156
% 114.56/114.94 Inuse: 1200
% 114.56/114.94 Deleted: 2790
% 114.56/114.94 Deletedinuse: 9
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94
% 114.56/114.94 Intermediate Status:
% 114.56/114.94 Generated: 511320
% 114.56/114.94 Kept: 114962
% 114.56/114.94 Inuse: 1220
% 114.56/114.94 Deleted: 2790
% 114.56/114.94 Deletedinuse: 9
% 114.56/114.94
% 114.56/114.94 Resimplifying inuse:
% 114.56/114.94 Done
% 114.56/114.94
% 114.56/114.94
% 114.56/114.94 Intermediate Status:
% 239.36/239.73 Generated: 524049
% 239.36/239.73 Kept: 117299
% 239.36/239.73 Inuse: 1225
% 239.36/239.73 Deleted: 2790
% 239.36/239.73 Deletedinuse: 9
% 239.36/239.73
% 239.36/239.73 Resimplifying inuse:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73 Resimplifying inuse:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73
% 239.36/239.73 Intermediate Status:
% 239.36/239.73 Generated: 533935
% 239.36/239.73 Kept: 119314
% 239.36/239.73 Inuse: 1245
% 239.36/239.73 Deleted: 2790
% 239.36/239.73 Deletedinuse: 9
% 239.36/239.73
% 239.36/239.73 Resimplifying inuse:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73 Resimplifying inuse:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73
% 239.36/239.73 Intermediate Status:
% 239.36/239.73 Generated: 544643
% 239.36/239.73 Kept: 121449
% 239.36/239.73 Inuse: 1265
% 239.36/239.73 Deleted: 2790
% 239.36/239.73 Deletedinuse: 9
% 239.36/239.73
% 239.36/239.73 Resimplifying inuse:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73 Resimplifying clauses:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73 Resimplifying inuse:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73
% 239.36/239.73 Intermediate Status:
% 239.36/239.73 Generated: 555754
% 239.36/239.73 Kept: 123450
% 239.36/239.73 Inuse: 1289
% 239.36/239.73 Deleted: 3084
% 239.36/239.73 Deletedinuse: 9
% 239.36/239.73
% 239.36/239.73 Resimplifying inuse:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73 Resimplifying inuse:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73
% 239.36/239.73 Intermediate Status:
% 239.36/239.73 Generated: 567177
% 239.36/239.73 Kept: 125860
% 239.36/239.73 Inuse: 1310
% 239.36/239.73 Deleted: 3084
% 239.36/239.73 Deletedinuse: 9
% 239.36/239.73
% 239.36/239.73 Resimplifying inuse:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73 Resimplifying inuse:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73
% 239.36/239.73 Intermediate Status:
% 239.36/239.73 Generated: 574316
% 239.36/239.73 Kept: 127865
% 239.36/239.73 Inuse: 1333
% 239.36/239.73 Deleted: 3084
% 239.36/239.73 Deletedinuse: 9
% 239.36/239.73
% 239.36/239.73 Resimplifying inuse:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73 Resimplifying inuse:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73
% 239.36/239.73 Intermediate Status:
% 239.36/239.73 Generated: 585828
% 239.36/239.73 Kept: 129880
% 239.36/239.73 Inuse: 1364
% 239.36/239.73 Deleted: 3084
% 239.36/239.73 Deletedinuse: 9
% 239.36/239.73
% 239.36/239.73
% 239.36/239.73 Intermediate Status:
% 239.36/239.73 Generated: 594677
% 239.36/239.73 Kept: 132450
% 239.36/239.73 Inuse: 1365
% 239.36/239.73 Deleted: 3084
% 239.36/239.73 Deletedinuse: 9
% 239.36/239.73
% 239.36/239.73 Resimplifying inuse:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73 Resimplifying inuse:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73
% 239.36/239.73 Intermediate Status:
% 239.36/239.73 Generated: 604686
% 239.36/239.73 Kept: 134750
% 239.36/239.73 Inuse: 1385
% 239.36/239.73 Deleted: 3084
% 239.36/239.73 Deletedinuse: 9
% 239.36/239.73
% 239.36/239.73 Resimplifying inuse:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73 Resimplifying inuse:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73
% 239.36/239.73 Intermediate Status:
% 239.36/239.73 Generated: 616004
% 239.36/239.73 Kept: 136903
% 239.36/239.73 Inuse: 1405
% 239.36/239.73 Deleted: 3084
% 239.36/239.73 Deletedinuse: 9
% 239.36/239.73
% 239.36/239.73 Resimplifying inuse:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73
% 239.36/239.73 Intermediate Status:
% 239.36/239.73 Generated: 626938
% 239.36/239.73 Kept: 139029
% 239.36/239.73 Inuse: 1419
% 239.36/239.73 Deleted: 3085
% 239.36/239.73 Deletedinuse: 9
% 239.36/239.73
% 239.36/239.73 Resimplifying inuse:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73 Resimplifying inuse:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73
% 239.36/239.73 Intermediate Status:
% 239.36/239.73 Generated: 638122
% 239.36/239.73 Kept: 141035
% 239.36/239.73 Inuse: 1436
% 239.36/239.73 Deleted: 3085
% 239.36/239.73 Deletedinuse: 9
% 239.36/239.73
% 239.36/239.73 Resimplifying inuse:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73 Resimplifying clauses:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73 Resimplifying inuse:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73
% 239.36/239.73 Intermediate Status:
% 239.36/239.73 Generated: 648497
% 239.36/239.73 Kept: 143538
% 239.36/239.73 Inuse: 1449
% 239.36/239.73 Deleted: 3377
% 239.36/239.73 Deletedinuse: 10
% 239.36/239.73
% 239.36/239.73 Resimplifying inuse:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73 Resimplifying inuse:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73
% 239.36/239.73 Intermediate Status:
% 239.36/239.73 Generated: 659633
% 239.36/239.73 Kept: 146029
% 239.36/239.73 Inuse: 1464
% 239.36/239.73 Deleted: 3379
% 239.36/239.73 Deletedinuse: 12
% 239.36/239.73
% 239.36/239.73 Resimplifying inuse:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73
% 239.36/239.73 Intermediate Status:
% 239.36/239.73 Generated: 677345
% 239.36/239.73 Kept: 148680
% 239.36/239.73 Inuse: 1473
% 239.36/239.73 Deleted: 3379
% 239.36/239.73 Deletedinuse: 12
% 239.36/239.73
% 239.36/239.73 Resimplifying inuse:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73 Resimplifying inuse:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73
% 239.36/239.73 Intermediate Status:
% 239.36/239.73 Generated: 686043
% 239.36/239.73 Kept: 151027
% 239.36/239.73 Inuse: 1477
% 239.36/239.73 Deleted: 3387
% 239.36/239.73 Deletedinuse: 13
% 239.36/239.73
% 239.36/239.73 Resimplifying inuse:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73
% 239.36/239.73 Intermediate Status:
% 239.36/239.73 Generated: 695360
% 239.36/239.73 Kept: 153186
% 239.36/239.73 Inuse: 1480
% 239.36/239.73 Deleted: 3399
% 239.36/239.73 Deletedinuse: 13
% 239.36/239.73
% 239.36/239.73 Resimplifying inuse:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73 Resimplifying inuse:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73
% 239.36/239.73 Intermediate Status:
% 239.36/239.73 Generated: 701721
% 239.36/239.73 Kept: 155327
% 239.36/239.73 Inuse: 1483
% 239.36/239.73 Deleted: 3411
% 239.36/239.73 Deletedinuse: 13
% 239.36/239.73
% 239.36/239.73 Resimplifying inuse:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73
% 239.36/239.73 Intermediate Status:
% 239.36/239.73 Generated: 708011
% 239.36/239.73 Kept: 157391
% 239.36/239.73 Inuse: 1486
% 239.36/239.73 Deleted: 3423
% 239.36/239.73 Deletedinuse: 13
% 239.36/239.73
% 239.36/239.73 Resimplifying inuse:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73 Resimplifying inuse:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73
% 239.36/239.73 Intermediate Status:
% 239.36/239.73 Generated: 716370
% 239.36/239.73 Kept: 159943
% 239.36/239.73 Inuse: 1490
% 239.36/239.73 Deleted: 3439
% 239.36/239.73 Deletedinuse: 13
% 239.36/239.73
% 239.36/239.73 Resimplifying inuse:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73 Resimplifying inuse:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73 Resimplifying clauses:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73
% 239.36/239.73 Intermediate Status:
% 239.36/239.73 Generated: 735409
% 239.36/239.73 Kept: 163366
% 239.36/239.73 Inuse: 1494
% 239.36/239.73 Deleted: 5802
% 239.36/239.73 Deletedinuse: 13
% 239.36/239.73
% 239.36/239.73 Resimplifying inuse:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73 Resimplifying inuse:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73
% 239.36/239.73 Intermediate Status:
% 239.36/239.73 Generated: 740521
% 239.36/239.73 Kept: 165457
% 239.36/239.73 Inuse: 1500
% 239.36/239.73 Deleted: 5821
% 239.36/239.73 Deletedinuse: 14
% 239.36/239.73
% 239.36/239.73
% 239.36/239.73 Intermediate Status:
% 239.36/239.73 Generated: 797708
% 239.36/239.73 Kept: 173215
% 239.36/239.73 Inuse: 1501
% 239.36/239.73 Deleted: 5825
% 239.36/239.73 Deletedinuse: 14
% 239.36/239.73
% 239.36/239.73 Resimplifying inuse:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73
% 239.36/239.73 Intermediate Status:
% 239.36/239.73 Generated: 858715
% 239.36/239.73 Kept: 181193
% 239.36/239.73 Inuse: 1502
% 239.36/239.73 Deleted: 5830
% 239.36/239.73 Deletedinuse: 15
% 239.36/239.73
% 239.36/239.73 Resimplifying inuse:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73 Resimplifying inuse:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73 Resimplifying clauses:
% 239.36/239.73 Done
% 239.36/239.73
% 239.36/239.73
% 239.36/239.73 Intermediate Status:
% 239.36/239.73 Generated: 864886
% 239.36/239.73 Kept: 183211
% 239.36/239.73 Inuse: 150Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------