TSTP Solution File: SWV823-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWV823-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 16:28:41 EDT 2022
% Result : Timeout 300.06s 300.50s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWV823-1 : TPTP v8.1.0. Released v4.1.0.
% 0.10/0.12 % Command : bliksem %s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Wed Jun 15 00:47:49 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.16/1.54 *** allocated 10000 integers for termspace/termends
% 1.16/1.54 *** allocated 10000 integers for clauses
% 1.16/1.54 *** allocated 10000 integers for justifications
% 1.16/1.54 *** allocated 15000 integers for termspace/termends
% 1.16/1.54 *** allocated 22500 integers for termspace/termends
% 1.16/1.54 *** allocated 33750 integers for termspace/termends
% 1.16/1.54 Bliksem 1.12
% 1.16/1.54
% 1.16/1.54
% 1.16/1.54 Automatic Strategy Selection
% 1.16/1.54
% 1.16/1.54 Clauses:
% 1.16/1.54 [
% 1.16/1.54 [ =( hAPP( 'c_Collect'( X ), Y ), Y ) ],
% 1.16/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X )
% 1.16/1.54 , Y ), Z ) ) ) ],
% 1.16/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X )
% 1.16/1.54 , Z ), Y ) ) ) ],
% 1.16/1.54 [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OSemi'( Z, T ) ) ), =( Y
% 1.16/1.54 , T ) ],
% 1.16/1.54 [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OSemi'( Z, T ) ) ), =( X
% 1.16/1.54 , Z ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.16/1.54 'c_Finite__Set_Osetsum'( Y, X ), hAPP( 'c_COMBK'( X, Y ),
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( X ) ) ), Z ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.16/1.54 ) ],
% 1.16/1.54 [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OWhile'( Z, T ) ) ) ]
% 1.16/1.54 ,
% 1.16/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.16/1.54 'c_Orderings_Oord__class_Omin'( hAPP( hAPP(
% 1.16/1.54 'c_Orderings_Oord__class_Omax'( X ), Y ), Z ), T, X ), hAPP( hAPP(
% 1.16/1.54 'c_Orderings_Oord__class_Omax'( X ), 'c_Orderings_Oord__class_Omin'( Y, T
% 1.16/1.54 , X ) ), 'c_Orderings_Oord__class_Omin'( Z, T, X ) ) ) ],
% 1.16/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.16/1.54 'c_Orderings_Oord__class_Omin'( Y, hAPP( hAPP(
% 1.16/1.54 'c_Orderings_Oord__class_Omax'( X ), Z ), T ), X ), hAPP( hAPP(
% 1.16/1.54 'c_Orderings_Oord__class_Omax'( X ), 'c_Orderings_Oord__class_Omin'( Y, Z
% 1.16/1.54 , X ) ), 'c_Orderings_Oord__class_Omin'( Y, T, X ) ) ) ],
% 1.16/1.54 [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OCond'( Z, T, U ) ) ) ]
% 1.16/1.54 ,
% 1.16/1.54 [ =( hAPP( 'c_split'( X, Y, Z, T ), hAPP( hAPP( 'c_Pair'( Y, Z ), U ), W
% 1.16/1.54 ) ), hAPP( hAPP( X, U ), W ) ) ],
% 1.16/1.54 [ =( hAPP( 'c_split'( X, Y, Z, T ), hAPP( hAPP( 'c_Pair'( Y, Z ), U ), W
% 1.16/1.54 ) ), hAPP( hAPP( X, U ), W ) ) ],
% 1.16/1.54 [ 'c_Fun_Oinj__on'( 'c_COMBI'( X ), Y, X, X ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.16/1.54 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z
% 1.16/1.54 ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ), ~(
% 1.16/1.54 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.16/1.54 , Z ) ) ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.16/1.54 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z
% 1.16/1.54 ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ) ), ~(
% 1.16/1.54 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.16/1.54 , T ) ) ) ],
% 1.16/1.54 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y
% 1.16/1.54 ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y
% 1.16/1.54 ) ) ) ],
% 1.16/1.54 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.16/1.54 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y
% 1.16/1.54 ) ) ) ],
% 1.16/1.54 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y
% 1.16/1.54 ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y
% 1.16/1.54 ) ) ) ],
% 1.16/1.54 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.16/1.54 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y
% 1.16/1.54 ) ) ) ],
% 1.16/1.54 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL(
% 1.16/1.54 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.16/1.54 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL(
% 1.16/1.54 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.16/1.54 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.16/1.54 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ) ) ],
% 1.16/1.54 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL(
% 1.16/1.54 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.16/1.54 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL(
% 1.16/1.54 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.16/1.54 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.16/1.54 X ), U ), Z ) ), W ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), T )
% 1.16/1.54 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W ) ) ) ) ],
% 1.16/1.54 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.16/1.54 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), U ) ), W ) ) ), ~( hBOOL(
% 1.16/1.54 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.16/1.54 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), Y ) ),
% 1.16/1.54 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ), W ) ) ) ) ],
% 1.16/1.54 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.16/1.54 X ), U ), Z ) ), W ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T ) ), W ) ) ) ]
% 1.16/1.54 ,
% 1.16/1.54 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ) ), U ) ), W ) ), ~(
% 1.16/1.54 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.16/1.54 X ), Y ), T ) ), U ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), W ) ) ) ) ],
% 1.16/1.54 [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OWhile'( T, U ) ) ) ]
% 1.16/1.54 ,
% 1.16/1.54 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.16/1.54 , X ) ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.16/1.54 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat'
% 1.16/1.54 ), Y ), X ) ) ) ],
% 1.16/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Orderings_Oorder'( Y
% 1.16/1.54 ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( Y ), hAPP( Z, T ) ), hAPP( Z, U
% 1.16/1.54 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), T ), U ) ) ), ~( hBOOL(
% 1.16/1.54 'c_Orderings_Oorder__class_Ostrict__mono'( Z, X, Y ) ) ) ],
% 1.16/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Orderings_Oorder'( Y
% 1.16/1.54 ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ), ~( hBOOL( hAPP(
% 1.16/1.54 hAPP( 'c_lessequals'( Y ), hAPP( U, Z ) ), hAPP( U, T ) ) ) ), ~( hBOOL(
% 1.16/1.54 'c_Orderings_Oorder__class_Ostrict__mono'( U, X, Y ) ) ) ],
% 1.16/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Orderings_Oorder'( Y
% 1.16/1.54 ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( Y ), hAPP( Z, T ) ),
% 1.16/1.54 hAPP( Z, U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T
% 1.16/1.54 ), U ) ) ), ~( hBOOL( 'c_Orderings_Oorder__class_Ostrict__mono'( Z, X, Y
% 1.16/1.54 ) ) ) ],
% 1.16/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Orderings_Oorder'( Y
% 1.16/1.54 ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ), ~(
% 1.16/1.54 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( Y ), hAPP( U, Z ) ), hAPP(
% 1.16/1.54 U, T ) ) ) ), ~( hBOOL( 'c_Orderings_Oorder__class_Ostrict__mono'( U, X,
% 1.16/1.54 Y ) ) ) ],
% 1.16/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Orderings_Oorder'( Y
% 1.16/1.54 ) ), ~( =( hAPP( Z, T ), hAPP( Z, U ) ) ), ~( hBOOL(
% 1.16/1.54 'c_Orderings_Oorder__class_Ostrict__mono'( Z, X, Y ) ) ), =( T, U ) ]
% 1.16/1.54 ,
% 1.16/1.54 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'class_Orderings_Oorder'( Y ) )
% 1.16/1.54 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( Y ), hAPP( Z, T ) ), hAPP(
% 1.16/1.54 Z, U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), U
% 1.16/1.54 ) ) ), ~( hBOOL( 'c_Orderings_Oorder__class_Ostrict__mono'( Z, X, Y ) )
% 1.16/1.54 ) ],
% 1.16/1.54 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.16/1.54 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.16/1.54 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.16/1.54 ) ) ) ],
% 1.16/1.54 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.16/1.54 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.16/1.54 ) ],
% 1.16/1.54 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.16/1.54 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.16/1.54 ) ],
% 1.16/1.54 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.16/1.54 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 1.16/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X ), Y )
% 1.16/1.54 , Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ) ),
% 1.16/1.54 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ],
% 1.16/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X ), Y )
% 1.16/1.54 , Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ) ),
% 1.16/1.54 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ],
% 1.16/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X ), Y )
% 1.16/1.54 , Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ) ),
% 1.16/1.54 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ],
% 1.16/1.54 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.16/1.54 hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.16/1.54 'tc_nat' ), X ), Z ) ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.16/1.54 'tc_nat' ), Z ), Y ) ) ) ],
% 1.16/1.54 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ) ), ~( hBOOL( hAPP(
% 1.16/1.54 hAPP( 'c_lessequals'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ) ), ~( hBOOL( hAPP(
% 1.16/1.54 hAPP( 'c_lessequals'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.16/1.54 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP(
% 1.16/1.54 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) )
% 1.16/1.54 ) ],
% 1.16/1.54 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP(
% 1.16/1.54 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) )
% 1.16/1.54 ) ],
% 1.16/1.54 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP(
% 1.16/1.54 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) )
% 1.16/1.54 ) ],
% 1.16/1.54 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.16/1.54 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T ), W ) ],
% 1.16/1.54 [ ~( 'class_Ring__and__Field_Oring'( X ) ), ~( =( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.16/1.54 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), =( T, hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W ) ) ],
% 1.16/1.54 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.16/1.54 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Ominus__class_Ominus'( X ), T ), Y ) ), Z ) ), U ) ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.16/1.54 X ), T ), Z ) ), U ) ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.54 hAPP( 'c_lessequals'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.16/1.54 ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.16/1.54 hAPP( 'c_lessequals'( X ), Z ), Y ) ) ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.54 hAPP( 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ),
% 1.16/1.54 hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ) ) ],
% 1.16/1.54 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.16/1.54 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL(
% 1.16/1.54 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.16/1.54 ) ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z )
% 1.16/1.54 , U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T )
% 1.16/1.54 ) ) ],
% 1.16/1.54 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.16/1.54 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.16/1.54 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.16/1.54 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.16/1.54 ), Y ), T ), Z, X ) ) ],
% 1.16/1.54 [ 'c_Natural_Oevalc'( 'c_Com_Ocom_OWhile'( X, Y ), Z, Z ), hBOOL( hAPP(
% 1.16/1.54 X, Z ) ) ],
% 1.16/1.54 [ hBOOL( hAPP( 'c_Hoare__Mirabelle_Otriple__valid'(
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), X ),
% 1.16/1.54 'c_Hoare__Mirabelle_Otriple_Otriple'( Y, 'c_Com_Ocom_OBODY'( Z ), T, X )
% 1.16/1.54 ) ) ],
% 1.16/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), 'c_Orderings_Oord__class_Omin'( Y, Z, X ) ), Y ) ) ]
% 1.16/1.54 ,
% 1.16/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), 'c_Orderings_Oord__class_Omin'( Y, Z, X ) ), Z ) ) ]
% 1.16/1.54 ,
% 1.16/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), Y ), 'c_Orderings_Oord__class_Omin'( Z, T, X ) ) ),
% 1.16/1.54 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.16/1.54 hAPP( 'c_lessequals'( X ), Y ), Z ) ) ) ],
% 1.16/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), Y ), 'c_Orderings_Oord__class_Omin'( Z, T, X ) ) ),
% 1.16/1.54 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.16/1.54 hAPP( 'c_lessequals'( X ), Y ), Z ) ) ) ],
% 1.16/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), Y ), 'c_Orderings_Oord__class_Omin'( Z, T, X ) ) ),
% 1.16/1.54 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.16/1.54 hAPP( 'c_lessequals'( X ), Y ), Z ) ) ) ],
% 1.16/1.54 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.16/1.54 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.16/1.54 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T
% 1.16/1.54 ) ) ) ],
% 1.16/1.54 [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OWhile'( Y, Z ) ) ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.54 hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~(
% 1.16/1.54 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), hAPP(
% 1.16/1.54 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ) ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.54 hAPP( 'c_lessequals'( X ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X )
% 1.16/1.54 , Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ),
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.54 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), ~(
% 1.16/1.54 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP(
% 1.16/1.54 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), Y ) ) ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.54 hAPP( 'c_lessequals'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.16/1.54 ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.54 hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~(
% 1.16/1.54 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), hAPP(
% 1.16/1.54 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ) ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.54 hAPP( 'c_lessequals'( X ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X )
% 1.16/1.54 , Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ),
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.54 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), ~(
% 1.16/1.54 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP(
% 1.16/1.54 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), Y ) ) ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.54 hAPP( 'c_lessequals'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.16/1.54 ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.16/1.54 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ),
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.16/1.54 [ ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ),
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( 'tc_nat' ), X ), Y ) ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), =( hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), 'c_Orderings_Oord__class_Omin'(
% 1.16/1.54 Y, Z, X ) ), T ), 'c_Orderings_Oord__class_Omin'( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ), X ) ) ],
% 1.16/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.54 'c_Orderings_Oord__class_Omax'( X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.16/1.54 [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OSKIP' ) ) ],
% 1.16/1.54 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.16/1.54 , hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ) ), Z )
% 1.16/1.54 , hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc', X
% 1.16/1.54 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ),
% 1.16/1.54 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Y ), X ) ) ) ],
% 1.16/1.54 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP(
% 1.16/1.54 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ), Z ) ) ),
% 1.16/1.54 hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ],
% 1.16/1.54 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_in'( X ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X,
% 1.16/1.54 'tc_bool' ) ), Z ) ) ) ) ],
% 1.16/1.54 [ ~( =( 'c_Product__Type_OSigma'( X, hAPP( 'c_COMBK'( 'tc_fun'( Y,
% 1.16/1.54 'tc_bool' ), Z ), T ), Z, Y ), 'c_Product__Type_OSigma'( U, hAPP(
% 1.16/1.54 'c_COMBK'( 'tc_fun'( Y, 'tc_bool' ), Z ), T ), Z, Y ) ) ), ~( hBOOL( hAPP(
% 1.16/1.54 hAPP( 'c_in'( Y ), W ), T ) ) ), =( X, U ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.16/1.54 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.16/1.54 ) ],
% 1.16/1.54 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.54 'tc_nat' ) ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.16/1.54 ,
% 1.16/1.54 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.16/1.54 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.16/1.54 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.16/1.54 [ ~( hBOOL( hAPP( X, 'c_Nat_Onat_Onat__case'( Y, Z,
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 't_a' ) ) ) ), hBOOL( hAPP( X, Y
% 1.16/1.54 ) ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.16/1.54 Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.16/1.54 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X
% 1.16/1.54 ) ) ) ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.16/1.54 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X
% 1.16/1.54 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.16/1.54 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.16/1.54 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.16/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_Orderings_Oord__class_Omin'( Z, T
% 1.16/1.54 , X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T )
% 1.16/1.54 ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) )
% 1.16/1.54 ],
% 1.16/1.54 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.16/1.54 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.16/1.54 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.16/1.54 ) ) ],
% 1.16/1.54 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.16/1.54 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.16/1.54 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.16/1.54 ) ) ],
% 1.16/1.54 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'class_Orderings_Oorder'( Y ) )
% 1.16/1.54 , hBOOL( 'c_Orderings_Oorder__class_Omono'( Z, X, Y ) ), ~( hBOOL(
% 1.16/1.54 'c_Orderings_Oorder__class_Ostrict__mono'( Z, X, Y ) ) ) ],
% 1.16/1.54 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP( 'c_Suc',
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.54 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), ~(
% 1.16/1.54 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.16/1.54 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ) ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.54 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.16/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.16/1.54 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Y, Z,
% 1.16/1.54 X ), X ), 'c_Orderings_Oord__class_Omin'( Y, Z, X ) ) ],
% 1.16/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.16/1.54 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP( hAPP(
% 1.16/1.54 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP(
% 1.16/1.54 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), hAPP(
% 1.16/1.54 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.16/1.54 ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.16/1.54 X ), Y ), Z ) ), Z ), Y ) ],
% 1.16/1.54 [ ~( hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.16/1.54 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), Y ) )
% 1.16/1.54 ) ), hBOOL( hAPP( X, Z ) ) ],
% 1.16/1.54 [ ~( hBOOL( hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.16/1.54 ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), Y ) )
% 1.16/1.54 ) ), hBOOL( hAPP( X, Z ) ) ],
% 1.16/1.54 [ =( 'c_split'( hAPP( hAPP( 'c_COMBB'( 'tc_fun'( X, 'tc_prod'( Y, X ) )
% 1.16/1.54 , 'tc_fun'( X, Z ), Y ), hAPP( 'c_COMBB'( 'tc_prod'( Y, X ), Z, X ), T )
% 1.16/1.54 ), 'c_Pair'( Y, X ) ), Y, X, Z ), T ) ],
% 1.16/1.54 [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OSemi'( Y, Z ) ) ) ],
% 1.16/1.54 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.16/1.54 hAPP( 'c_lessequals'( 'tc_nat' ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ), hBOOL(
% 1.16/1.54 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.16/1.54 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.16/1.54 ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), U ) ) ), ~( hBOOL(
% 1.16/1.54 hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.16/1.54 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), Y, hAPP( 'c_Suc', Z ), X ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), 'c_Power_Opower_Opower'(
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X
% 1.16/1.54 ) ), Y ) ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.16/1.54 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), Y, hAPP( 'c_Suc', Z ), X ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Power_Opower_Opower'(
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X
% 1.16/1.54 ) ) ) ],
% 1.16/1.54 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP(
% 1.16/1.54 'c_Suc', Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ),
% 1.16/1.54 Y ) ) ) ],
% 1.16/1.54 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ), ~( hBOOL(
% 1.16/1.54 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP( 'c_Suc', Y
% 1.16/1.54 ) ) ) ) ],
% 1.16/1.54 [ ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), X ) ) ), hBOOL(
% 1.16/1.54 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP( 'c_Suc', X
% 1.16/1.54 ) ) ) ],
% 1.16/1.54 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.16/1.54 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.16/1.54 ,
% 1.16/1.54 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.54 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( hBOOL(
% 1.16/1.54 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), =( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.16/1.54 ,
% 1.16/1.54 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.16/1.54 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), Y, hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ), X ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), 'c_Power_Opower_Opower'(
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X
% 1.16/1.54 ) ), 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), Y, T, X ) ) ) ],
% 1.16/1.54 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), hAPP( 'c_Suc', X )
% 1.16/1.54 ) ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.16/1.54 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.16/1.54 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.16/1.54 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), Y, T, X ) ), 'c_Power_Opower_Opower'(
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), Z, T, X
% 1.16/1.54 ) ) ) ],
% 1.16/1.54 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.16/1.54 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.16/1.54 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.16/1.54 ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__join'( X ) ), =(
% 1.16/1.54 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.16/1.54 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ), hAPP( hAPP(
% 1.16/1.54 'c_Lattices_Oupper__semilattice__class_Osup'( X ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__join'( X ) ), =(
% 1.16/1.54 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.16/1.54 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), T ), hAPP(
% 1.16/1.54 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.16/1.54 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ), hAPP( hAPP(
% 1.16/1.54 'c_Lattices_Oupper__semilattice__class_Osup'( X ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.16/1.54 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), T ), hAPP(
% 1.16/1.54 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.16/1.54 [ ~( hBOOL( hAPP( hAPP( X, Y ), Y ) ) ), ~( 'c_Orderings_Oorder'( Z, X,
% 1.16/1.54 T ) ) ],
% 1.16/1.54 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, Y ), Z ) )
% 1.16/1.54 ), ~( 'c_Orderings_Oorder'( X, T, U ) ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.16/1.54 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL(
% 1.16/1.54 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.16/1.54 ) ],
% 1.16/1.54 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.16/1.54 X, 'tc_bool' ) ), Y ), Y ), Y ) ],
% 1.16/1.54 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =( hAPP( hAPP(
% 1.16/1.54 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Y ), Y ) ],
% 1.16/1.54 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.16/1.54 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ) ],
% 1.16/1.54 [ hBOOL( hAPP( X, 'c_Hilbert__Choice_OEps'( X, Y ) ) ), ~( hBOOL( hAPP(
% 1.16/1.54 X, Z ) ) ), =( 'c_Hilbert__Choice_OEps'( X, Y ), Z ) ],
% 1.16/1.54 [ ~( =( hAPP( X, Y ), hAPP( X, Z ) ) ), ~(
% 1.16/1.54 'c_Lattices_Oboolean__algebra'( T, X, U, W, V0, V1, V2, V3, V4 ) ), =( Y
% 1.16/1.54 , Z ) ],
% 1.16/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.16/1.54 'c_Orderings_Oord__class_Omax'( X ), Y ), Z ), Z ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), Y ), Z ) ) ) ],
% 1.16/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =( hAPP( hAPP(
% 1.16/1.54 'c_Orderings_Oord__class_Omax'( X ), Y ), Z ), Z ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), Y ), Z ) ) ],
% 1.16/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.16/1.54 'c_Orderings_Oord__class_Omax'( X ), Y ), Z ), Y ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), Z ), Y ) ) ) ],
% 1.16/1.54 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.16/1.54 X ), Y ), Z ) ), T ) ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.16/1.54 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.16/1.54 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.16/1.54 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.16/1.54 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.16/1.54 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.16/1.54 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.16/1.54 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Z ), Y ) ) ),
% 1.16/1.54 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), T ) ) ]
% 1.16/1.54 ,
% 1.16/1.54 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.16/1.54 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ),
% 1.16/1.54 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ), ~( hBOOL( hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.54 'tc_nat' ) ), Y ) ) ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Osemigroup__add'( X ) ), =( 'c_List_Ofoldl'(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.16/1.54 X ), Y ), Z ), T, X, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.16/1.54 ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Z, T, X, X ) ) ) ]
% 1.16/1.54 ,
% 1.16/1.54 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Z ), X ) ) ), ~( hBOOL( hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Z ), Y ) ) ) ],
% 1.16/1.54 [ =( 'c_The'( hAPP( hAPP( 'c_COMBC'( X, X, 'tc_bool' ), 'c_fequal'( X )
% 1.16/1.54 ), Y ), X ), Y ) ],
% 1.16/1.54 [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OSemi'( T, U ) ) ) ]
% 1.16/1.54 ,
% 1.16/1.54 [ =( hAPP( hAPP( X, hAPP( 'c_COMBK'( Y, Y ), hAPP( Z, hAPP( T, U ) ) ) )
% 1.16/1.54 , U ), hAPP( hAPP( X, Z ), U ) ), ~( hBOOL(
% 1.16/1.54 'c_Record_Oiso__tuple__update__accessor__cong__assist'( X, T, Y, W ) ) )
% 1.16/1.54 ],
% 1.16/1.54 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.16/1.54 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 1.16/1.54 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.16/1.54 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 1.16/1.54 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.16/1.54 [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 1.16/1.54 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.16/1.54 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.16/1.54 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.16/1.54 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ),
% 1.16/1.54 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ) ],
% 1.16/1.54 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.16/1.54 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.16/1.54 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ),
% 1.16/1.54 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.16/1.54 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ), hBOOL( hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ), ~( hBOOL(
% 1.16/1.54 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ) ],
% 1.16/1.54 [ ~( 'class_Ring__and__Field_Oordered__semiring'( X ) ), hBOOL( hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ), ~( hBOOL(
% 1.16/1.54 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.16/1.54 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ), =( Y, hAPP(
% 1.16/1.54 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), =( Y, Z ) ],
% 1.16/1.54 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.16/1.54 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.16/1.54 , Z, X ) ) ), =( 'c_Divides_Odiv__class_Omod'( hAPP(
% 1.16/1.54 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ),
% 1.16/1.54 'c_Divides_Odiv__class_Omod'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.16/1.54 T ), Z, X ) ) ],
% 1.16/1.54 [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OCond'( T, U, W ) ) )
% 1.16/1.54 , =( Z, W ) ],
% 1.16/1.54 [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OCond'( T, U, W ) ) )
% 1.16/1.54 , =( Y, U ) ],
% 1.16/1.54 [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OCond'( T, U, W ) ) )
% 1.16/1.54 , =( X, T ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.54 X ) ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.54 X ) ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Ominus__class_Ominus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.16/1.54 , Y ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.54 X ) ) ],
% 1.16/1.54 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), X ),
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.16/1.54 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ),
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.16/1.54 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.16/1.54 X ) ), =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ),
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.16/1.54 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.16/1.54 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.16/1.54 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.16/1.54 ) ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.16/1.54 [ 'c_Finite__Set_Ofinite'( hAPP( hAPP(
% 1.16/1.54 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.16/1.54 , Y ), Z ), X ), ~( 'c_Finite__Set_Ofinite'( Z, X ) ), ~(
% 1.16/1.54 'c_Finite__Set_Ofinite'( Y, X ) ) ],
% 1.16/1.54 [ 'c_Finite__Set_Ofinite'( hAPP( hAPP(
% 1.16/1.54 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.16/1.54 , Y ), Z ), X ), ~( 'c_Finite__Set_Ofinite'( Z, X ) ), ~(
% 1.16/1.54 'c_Finite__Set_Ofinite'( Y, X ) ) ],
% 1.16/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.16/1.54 Y ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), hAPP( hAPP(
% 1.16/1.54 'c_Orderings_Oord__class_Omax'( X ), T ), Z ) ) ) ) ],
% 1.16/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.16/1.54 ), Y ), 'c_Orderings_Oord__class_Omin'( T, Z, X ) ) ) ) ],
% 1.16/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.16/1.54 ), Y ), 'c_Orderings_Oord__class_Omin'( Z, T, X ) ) ) ) ],
% 1.16/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), 'c_Orderings_Oord__class_Omin'( Y, Z, X ) ), T ) ),
% 1.16/1.54 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ) ) ],
% 1.16/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), 'c_Orderings_Oord__class_Omin'( Y, Z, X ) ), T ) ),
% 1.16/1.54 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ],
% 1.16/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), 'c_Orderings_Oord__class_Omin'( Y, Z, X ) ), T ) ),
% 1.16/1.54 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ) ) ],
% 1.16/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), 'c_Orderings_Oord__class_Omin'( Y, Z, X ) ), T ) ),
% 1.16/1.54 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ],
% 1.16/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.16/1.54 ), Y ), 'c_Orderings_Oord__class_Omin'( T, Z, X ) ) ) ) ],
% 1.16/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.16/1.54 ), Y ), 'c_Orderings_Oord__class_Omin'( Z, T, X ) ) ) ) ],
% 1.16/1.54 [ =( 'c_Orderings_Oord__class_Omin'( 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.54 'tc_nat' ), X, 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ]
% 1.16/1.54 ,
% 1.16/1.54 [ =( 'c_Orderings_Oord__class_Omin'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.54 'tc_nat' ), 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.16/1.54 [ =( 'c_Nat_Onat_Onat__case'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.16/1.54 ), Z ), X ) ],
% 1.16/1.54 [ =( 'c_Nat_Onat_Onat__case'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.16/1.54 ), Z ), X ) ],
% 1.16/1.54 [ 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( X ), hAPP( hAPP( 'c_COMBC'(
% 1.16/1.54 X, Y, 'tc_bool' ), Z ), T ) ), X ), ~( hBOOL( hAPP( hAPP( 'c_in'( Y ), T
% 1.16/1.54 ), U ) ) ), ~( 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( X ), hAPP(
% 1.16/1.54 hAPP( 'c_COMBB'( 'tc_fun'( Y, 'tc_bool' ), 'tc_bool', X ), 'c_Ex'( Y ) )
% 1.16/1.54 , hAPP( hAPP( 'c_COMBB'( 'tc_fun'( Y, 'tc_bool' ), 'tc_fun'( Y, 'tc_bool'
% 1.16/1.54 ), X ), hAPP( 'c_COMBS'( Y, 'tc_bool', 'tc_bool' ), hAPP( hAPP(
% 1.16/1.54 'c_COMBB'( 'tc_bool', 'tc_fun'( 'tc_bool', 'tc_bool' ), Y ), 'c_and' ),
% 1.16/1.54 hAPP( hAPP( 'c_COMBC'( Y, 'tc_fun'( Y, 'tc_bool' ), 'tc_bool' ), 'c_in'(
% 1.16/1.54 Y ) ), U ) ) ) ), Z ) ) ), X ) ), ~( 'c_Finite__Set_Ofinite'( U, Y ) ) ]
% 1.16/1.54 ,
% 1.16/1.54 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.16/1.54 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.16/1.54 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ), =( Z,
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), ~( =(
% 1.16/1.54 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ),
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.16/1.54 X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ), =( Y,
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.16/1.54 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.16/1.54 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.16/1.54 ) ) ],
% 1.16/1.54 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.16/1.54 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ),
% 1.16/1.54 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), ~( hBOOL( hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.16/1.54 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), U ), Y ) ), Z ) ), W
% 1.16/1.54 ) ) ) ) ],
% 1.16/1.54 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.16/1.54 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ), U ) ), W
% 1.16/1.54 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.16/1.54 X ), T ), U ) ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ), W ) ) ) ) ],
% 1.16/1.54 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.16/1.54 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ),
% 1.16/1.54 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Otimes__class_Otimes'( X ), U ), Z ) ), W ) ) ), ~( hBOOL( hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.16/1.54 X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), U ) ), Z ) ), T
% 1.16/1.54 ) ), W ) ) ) ],
% 1.16/1.54 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.16/1.54 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), T ) ), U ) ), W ) ), ~(
% 1.16/1.54 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.16/1.54 X ), Y ), T ) ), U ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), W ) ) ) ) ],
% 1.16/1.54 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.16/1.54 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.16/1.54 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( 'tc_nat' ), Y ), X ) ) ) ],
% 1.16/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.16/1.54 T ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.16/1.54 'c_Orderings_Oord__class_Omin'( T, Y, X ) ), Z ) ) ) ],
% 1.16/1.54 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.16/1.54 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.16/1.54 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.16/1.54 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.16/1.54 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.16/1.54 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.16/1.54 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.16/1.54 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.16/1.54 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.16/1.54 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.16/1.54 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.16/1.54 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.16/1.54 , U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), W ), T ), Z, X ) ) ],
% 1.16/1.54 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( 'c_Suc',
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.54 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.16/1.54 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.54 X ) ) ) ) ],
% 1.16/1.54 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.16/1.54 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.54 X ) ) ) ) ],
% 1.16/1.54 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.16/1.54 ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.16/1.54 ) ],
% 1.16/1.54 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, hAPP(
% 1.16/1.54 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, hAPP( 'c_Suc'
% 1.16/1.54 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.16/1.54 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.16/1.54 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.16/1.54 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.16/1.54 ) ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ) ],
% 1.16/1.54 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.16/1.54 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.16/1.54 ) ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ) ) ],
% 1.16/1.54 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.16/1.54 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.16/1.54 ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~(
% 1.16/1.54 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.16/1.54 ) ],
% 1.16/1.54 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.16/1.54 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.16/1.54 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.16/1.54 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.16/1.54 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.16/1.54 ) ],
% 1.16/1.54 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_List_Ofoldl'(
% 1.16/1.54 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ), Z, X, X
% 1.16/1.54 ) ), 'c_List_Ofoldl'( 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X, X ) ) ]
% 1.16/1.54 ,
% 1.16/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.16/1.54 ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X ), T ), Y ) ), Z ) ) )
% 1.16/1.54 ],
% 1.16/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.16/1.54 ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X ), Y ), T ) ), Z ) ) )
% 1.16/1.54 ],
% 1.16/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X )
% 1.16/1.54 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ]
% 1.16/1.54 ,
% 1.16/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X )
% 1.16/1.54 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ) ) ]
% 1.16/1.54 ,
% 1.16/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X )
% 1.16/1.54 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ]
% 1.16/1.54 ,
% 1.16/1.54 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.54 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X )
% 1.16/1.54 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ) ) ]
% 1.16/1.55 ,
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.16/1.55 ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X ), T ), Y ) ), Z ) ) )
% 1.16/1.55 ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.16/1.55 ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X ), Y ), T ) ), Z ) ) )
% 1.16/1.55 ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ), Y ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ) ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_Orderings_Oord__class_Omax'( X ), T ), Z ) ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( Z, Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( T,
% 1.16/1.55 'tc_bool' ) ), Z ), X ), Y ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.16/1.55 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ), T ) ), ~( hBOOL( hAPP( Z, T ) ) ) ]
% 1.16/1.55 ,
% 1.16/1.55 [ hBOOL( hAPP( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.16/1.55 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ), T ) ), ~( hBOOL( hAPP( Y, T ) ) ) ]
% 1.16/1.55 ,
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP( 'c_in'(
% 1.16/1.55 X ), Y ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.16/1.55 , T ), Z ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.16/1.55 ) ) ), =( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.16/1.55 ) ) ), =( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z ) ],
% 1.16/1.55 [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OBODY'( T ) ) ) ]
% 1.16/1.55 ,
% 1.16/1.55 [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OCond'( Y, Z, T ) ) ) ]
% 1.16/1.55 ,
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.16/1.55 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.16/1.55 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.16/1.55 'class_Lattices_Oupper__semilattice'( X ) ), =(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( X ),
% 1.16/1.55 'c_Orderings_Oord__class_Omax'( X ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), 'c_Orderings_Oord__class_Omin'( T, Y, X )
% 1.16/1.55 ), Z ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.16/1.55 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.16/1.55 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.16/1.55 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.16/1.55 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.16/1.55 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.16/1.55 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.16/1.55 [ 'c_Finite__Set_Ofinite'( X, Y ), ~( 'c_Finite__Set_Ofinite'( hAPP(
% 1.16/1.55 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Y,
% 1.16/1.55 'tc_bool' ) ), X ), Z ), Y ) ) ],
% 1.16/1.55 [ 'c_Finite__Set_Ofinite'( X, Y ), ~( 'c_Finite__Set_Ofinite'( hAPP(
% 1.16/1.55 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Y,
% 1.16/1.55 'tc_bool' ) ), Z ), X ), Y ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X )
% 1.16/1.55 , Z ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.55 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.16/1.55 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.16/1.55 X ), Y ), Z ) ), T ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.16/1.55 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.16/1.55 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.55 'tc_nat' ) ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.16/1.55 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.16/1.55 ), Y ) ) ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ],
% 1.16/1.55 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.16/1.55 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( Z, T ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_in'( 'tc_prod'( U, X ) ), hAPP( hAPP( 'c_Pair'( U, X ), T ), Y )
% 1.16/1.55 ), 'c_Product__Type_OSigma'( W, Z, U, X ) ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_in'( 'tc_prod'( X, T ) ), hAPP( hAPP( 'c_Pair'( X, T ), Y ), U ) ),
% 1.16/1.55 'c_Product__Type_OSigma'( Z, W, X, T ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 1.16/1.55 [ 'c_Fun_Oinj__on'( 'c_Fun_Oid'( X ), Y, X, X ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ) ), Y ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.16/1.55 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), T, X ),
% 1.16/1.55 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.16/1.55 ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), Z ), T, X ) ) ],
% 1.16/1.55 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), T, X ),
% 1.16/1.55 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.16/1.55 ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( Z, Y ) ) )
% 1.16/1.55 ],
% 1.16/1.55 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), Y ), X ) ) )
% 1.16/1.55 ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.16/1.55 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Y ), Z ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( =(
% 1.16/1.55 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Y ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Y ), Z ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.16/1.55 'c_Orderings_Oord__class_Omin'( Y, Z, X ), Z ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Z ), Y ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), =( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP(
% 1.16/1.55 'c_Orderings_Oord__class_Omax'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.16/1.55 'c_Orderings_Oord__class_Omax'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ) ) ],
% 1.16/1.55 [ =( hAPP( 'c_COMBI'( X ), Y ), Y ) ],
% 1.16/1.55 [ =( hAPP( hAPP( 'c_COMBK'( X, Y ), Z ), T ), Z ) ],
% 1.16/1.55 [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OBODY'( Z ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.16/1.55 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.55 'tc_nat' ) ), Y ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Z ), Y ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Y ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), Y ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), Y ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Y ), Y ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Z ), Y ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Z ), Y ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~(
% 1.16/1.55 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.16/1.55 , hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.16/1.55 [ 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( X ), hAPP( hAPP( 'c_COMBS'(
% 1.16/1.55 X, 'tc_bool', 'tc_bool' ), hAPP( hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'(
% 1.16/1.55 'tc_bool', 'tc_bool' ), X ), 'c_and' ), Y ) ), Z ) ), X ), ~(
% 1.16/1.55 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( X ), Z ), X ) ) ],
% 1.16/1.55 [ 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( X ), hAPP( hAPP( 'c_COMBS'(
% 1.16/1.55 X, 'tc_bool', 'tc_bool' ), hAPP( hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'(
% 1.16/1.55 'tc_bool', 'tc_bool' ), X ), 'c_and' ), Y ) ), Z ) ), X ), ~(
% 1.16/1.55 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( X ), Y ), X ) ) ],
% 1.16/1.55 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.16/1.55 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.16/1.55 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.16/1.55 ), Z ), T, X ) ) ],
% 1.16/1.55 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.16/1.55 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.16/1.55 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T
% 1.16/1.55 , X ) ), T, X ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.16/1.55 'c_Orderings_Oord__class_Omin'( 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 1.16/1.55 , T, X ), 'c_Orderings_Oord__class_Omin'( Y,
% 1.16/1.55 'c_Orderings_Oord__class_Omin'( Z, T, X ), X ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.16/1.55 'c_Orderings_Oord__class_Omin'( Y, 'c_Orderings_Oord__class_Omin'( Z, T,
% 1.16/1.55 X ), X ), 'c_Orderings_Oord__class_Omin'( Z,
% 1.16/1.55 'c_Orderings_Oord__class_Omin'( Y, T, X ), X ) ) ],
% 1.16/1.55 [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.55 'tc_nat' ) ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) )
% 1.16/1.55 ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.16/1.55 , ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( 'tc_nat' ), Z ), Y ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( 'tc_nat' ), Y ), X ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( 'tc_nat' ), Z ), X ) ) ) ],
% 1.16/1.55 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.16/1.55 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.16/1.55 [ 'c_Natural_Oevalc'( 'c_Com_Ocom_OWhile'( X, Y ), Z, T ), ~(
% 1.16/1.55 'c_Natural_Oevalc'( 'c_Com_Ocom_OWhile'( X, Y ), U, T ) ), ~(
% 1.16/1.55 'c_Natural_Oevalc'( Y, Z, U ) ), ~( hBOOL( hAPP( X, Z ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( X ), T ), T ) ) ), =( Y, Z ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( X ), Y ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( X ), Z ), T ) ) ), =( Z, T ) ],
% 1.16/1.55 [ ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ),
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ), ~(
% 1.16/1.55 hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Y ), X ) ) ), =( X, Z ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.16/1.55 'c_Orderings_Oord__class_Omin'( Y, hAPP( hAPP(
% 1.16/1.55 'c_Orderings_Oord__class_Omax'( X ), Y ), Z ), X ), Y ) ],
% 1.16/1.55 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, hAPP(
% 1.16/1.55 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.16/1.55 [ ~( =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP( 'c_Suc',
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.16/1.55 [ 'c_Natural_Oevalc'( 'c_Com_Ocom_OCond'( X, Y, Z ), T, U ), ~(
% 1.16/1.55 'c_Natural_Oevalc'( Y, T, U ) ), ~( hBOOL( hAPP( X, T ) ) ) ],
% 1.16/1.55 [ ~( hBOOL( hAPP( X, Y ) ) ), 'c_Natural_Oevalc'( Z, Y, T ), ~(
% 1.16/1.55 'c_Natural_Oevalc'( 'c_Com_Ocom_OCond'( X, Z, U ), Y, T ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.16/1.55 Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ) ) ), ~(
% 1.16/1.55 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.16/1.55 , Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) )
% 1.16/1.55 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), T ), Z ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.16/1.55 ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ),
% 1.16/1.55 Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ), ~(
% 1.16/1.55 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.16/1.55 , Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) )
% 1.16/1.55 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.16/1.55 Y ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.16/1.55 ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.16/1.55 ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ) ],
% 1.16/1.55 [ 'c_Natural_Oevalc'( 'c_Com_Ocom_OSemi'( X, Y ), Z, T ), ~(
% 1.16/1.55 'c_Natural_Oevalc'( Y, U, T ) ), ~( 'c_Natural_Oevalc'( X, Z, U ) ) ]
% 1.16/1.55 ,
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_Finite__Set_Osetsum'( Z, X ), T ), U ) ), hAPP( hAPP(
% 1.16/1.55 'c_Finite__Set_Osetsum'( Z, X ), hAPP( hAPP( 'c_COMBB'( X, X, Z ), hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ) ), T ) ), U ) ) ],
% 1.16/1.55 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.55 'tc_nat' ) ) ],
% 1.16/1.55 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.16/1.55 X, 'tc_bool' ) ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.16/1.55 , Z ), T ) ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.16/1.55 'tc_fun'( X, 'tc_bool' ) ), Z ), hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.16/1.55 , Y ), T ) ) ) ],
% 1.16/1.55 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.16/1.55 X, 'tc_bool' ) ), hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.16/1.55 , Y ), Z ) ), T ), hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.16/1.55 , Y ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.16/1.55 X, 'tc_bool' ) ), Z ), T ) ) ) ],
% 1.16/1.55 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( X ), hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), T ), hAPP(
% 1.16/1.55 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ) ) ],
% 1.16/1.55 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ), hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), T ) ) ) ],
% 1.16/1.55 [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ), hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), T ) ) ) ],
% 1.16/1.55 [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( X ), hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), T ), hAPP(
% 1.16/1.55 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ) ) ],
% 1.16/1.55 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ) ],
% 1.16/1.55 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ],
% 1.16/1.55 [ ~( =( hAPP( X, Y ), hAPP( X, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T
% 1.16/1.55 ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), U ) ) ), =( Y,
% 1.16/1.55 Z ), ~( 'c_Fun_Oinj__on'( X, U, T, W ) ) ],
% 1.16/1.55 [ ~( =( hAPP( X, Y ), hAPP( X, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T
% 1.16/1.55 ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), U ) ) ), ~(
% 1.16/1.55 'c_Fun_Oinj__on'( X, U, T, W ) ), =( Y, Z ) ],
% 1.16/1.55 [ ~( =( hAPP( X, Y ), hAPP( X, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T
% 1.16/1.55 ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( T ), Y ), U ) ) ), ~(
% 1.16/1.55 'c_Fun_Oinj__on'( X, U, T, W ) ), =( Y, Z ) ],
% 1.16/1.55 [ ~( =( hAPP( X, Y ), hAPP( X, Z ) ) ), ~( 'c_Fun_Oinj__on'( X, T, U, W
% 1.16/1.55 ) ), =( Y, Z ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), Z ), T ) ) ), ~(
% 1.16/1.55 hBOOL( hAPP( hAPP( 'c_in'( U ), Y ), T ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( 'c_Suc', X ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( 'c_Suc', X ) ) ) ],
% 1.16/1.55 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), T ) ), ~(
% 1.16/1.55 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ],
% 1.16/1.55 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ) ) ],
% 1.16/1.55 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), Y ) ) ) ],
% 1.16/1.55 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), T ) ), ~(
% 1.16/1.55 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ],
% 1.16/1.55 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), T ) ), ~(
% 1.16/1.55 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ],
% 1.16/1.55 [ ~( 'class_Lattices_Olattice'( X ) ), hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.16/1.55 X ), Y ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ),
% 1.16/1.55 Z ), Y ) ) ) ],
% 1.16/1.55 [ ~( 'class_Lattices_Olattice'( X ) ), hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.16/1.55 X ), Y ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ),
% 1.16/1.55 Y ), Z ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_Orderings_Oord__class_Omax'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_Orderings_Oord__class_Omax'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_Orderings_Oord__class_Omax'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_Orderings_Oord__class_Omax'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.55 'c_Orderings_Oord__class_Omax'( X ), Y ), T ) ), Z ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.55 'c_Orderings_Oord__class_Omax'( X ), T ), Y ) ), Z ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.55 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.16/1.55 ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_Finite__Set_Osetsum'( Y, X ), Z ), T ), 'c_HOL_Ozero__class_Ozero'( X
% 1.16/1.55 ) ), 'c_Finite__Set_Ofinite'( T, Y ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_Finite__Set_Osetsum'( Y, X ), Z ), T ), 'c_HOL_Ozero__class_Ozero'( X
% 1.16/1.55 ) ), 'c_Finite__Set_Ofinite'( T, Y ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.55 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.16/1.55 ) ],
% 1.16/1.55 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.16/1.55 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.16/1.55 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.16/1.55 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.16/1.55 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.16/1.55 ), U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), W ), T ), Z, X ) ) ],
% 1.16/1.55 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( 'tc_nat' ), Z ), Y ) ) ) ],
% 1.16/1.55 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ), Y ) ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Z ), X ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), hAPP( Y, Z ) ), hAPP( Y, T ) ) ), ~(
% 1.16/1.55 hBOOL( hAPP( hAPP( U, Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 'c_Orderings_Oorder_Ostrict__mono'( U, W, X ), Y ) ) ), ~(
% 1.16/1.55 'c_Orderings_Oorder'( V0, U, W ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.16/1.55 hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X
% 1.16/1.55 ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.16/1.55 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), U ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.16/1.55 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.16/1.55 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.55 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.16/1.55 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.16/1.55 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.16/1.55 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.16/1.55 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.16/1.55 X ), hAPP( Y, Z ) ), hAPP( Y, T ) ) ), ~( hBOOL( hAPP( hAPP( U, Z ), T )
% 1.16/1.55 ) ), ~( hBOOL( hAPP( 'c_Orderings_Oorder_Omono'( U, W, X ), Y ) ) ), ~(
% 1.16/1.55 'c_Orderings_Oorder'( U, V0, W ) ) ],
% 1.16/1.55 [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OWhile'( X, Y ) ) ) ],
% 1.16/1.55 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( 'tc_nat' ), Z ), Y ) ) ) ],
% 1.16/1.55 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( 'c_Suc',
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.16/1.55 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.16/1.55 ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.16/1.55 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ), Y, X )
% 1.16/1.55 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ) ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.16/1.55 [ =( 'c_Product__Type_Oscomp'( hAPP( 'c_Pair'( X, Y ), Z ), T, Y, X, Y,
% 1.16/1.55 U ), hAPP( T, Z ) ) ],
% 1.16/1.55 [ ~( 'c_Orderings_Oorder'( X, Y, Z ) ), hBOOL( hAPP( hAPP( X, T ), T ) )
% 1.16/1.55 ],
% 1.16/1.55 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.16/1.55 [ =( hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.55 'tc_nat' ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Z ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.16/1.55 ), Y ), Z ) ) ) ],
% 1.16/1.55 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), X )
% 1.16/1.55 ) ) ],
% 1.16/1.55 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), X )
% 1.16/1.55 ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Oorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), Y ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), Y ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), Y ) ) ) ],
% 1.16/1.55 [ ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), X ), Y ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.16/1.55 'c_Orderings_Oord__class_Omin'( Y, Y, X ), Y ) ],
% 1.16/1.55 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.16/1.55 ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.16/1.55 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.16/1.55 ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.16/1.55 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_Orderings_Oord__class_Omax'( 'tc_nat' ), X ), Y ) ) ],
% 1.16/1.55 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =( hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), =( Y, Z ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), =( Y, Z ) ],
% 1.16/1.55 [ ~( =( hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) )
% 1.16/1.55 , Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.16/1.55 Z ) ) ), =( Y, Z ) ],
% 1.16/1.55 [ 'c_Natural_Oevalc'( 'c_Com_Ocom_OSKIP', X, X ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ), =( Z, Y ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ],
% 1.16/1.55 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Y ), X )
% 1.16/1.55 ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ) ) ]
% 1.16/1.55 ,
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.16/1.55 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), X ) ), =(
% 1.16/1.55 Y, X ) ],
% 1.16/1.55 [ =( X, Y ), ~( 'c_Natural_Oevalc'( Z, T, X ) ), ~( 'c_Natural_Oevalc'(
% 1.16/1.55 Z, T, Y ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), Z ) ), =( Z, Y ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Z ), Y ) ) ],
% 1.16/1.55 [ ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y, X ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.16/1.55 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), X ) ), =(
% 1.16/1.55 Y, X ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Z ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.16/1.55 X ), Y ), Z ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ), =( Z, Y ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Z ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.16/1.55 X ), Y ), Z ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.16/1.55 X ), Z ), Y ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), =( Z, Y ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ],
% 1.16/1.55 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.16/1.55 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.16/1.55 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.16/1.55 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.16/1.55 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.16/1.55 ), U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( X ), W ), T ), Z, X ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ),
% 1.16/1.55 Z ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X )
% 1.16/1.55 , Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Y ), Z ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_Orderings_Oord__class_Omax'( X ), Y ), Y ), Y ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.16/1.55 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.16/1.55 X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y
% 1.16/1.55 ), Z ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ],
% 1.16/1.55 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ), Y ), ~(
% 1.16/1.55 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), Y ) ) ) ],
% 1.16/1.55 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), ~( =( hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ), Z ) ), hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ) ],
% 1.16/1.55 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ), Z ), ~(
% 1.16/1.55 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.16/1.55 ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), Z ) ]
% 1.16/1.55 ,
% 1.16/1.55 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.16/1.55 ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ), Z ) ]
% 1.16/1.55 ,
% 1.16/1.55 [ ~( =( hAPP( hAPP( hAPP( 'c_Recdef_Ocut'( X, Y ), Z ), T ), U ), hAPP(
% 1.16/1.55 hAPP( hAPP( 'c_Recdef_Ocut'( X, Y ), W ), T ), U ) ) ), =( hAPP( Z, V0 )
% 1.16/1.55 , hAPP( W, V0 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ),
% 1.16/1.55 hAPP( hAPP( 'c_Pair'( X, X ), V0 ), U ) ), T ) ) ) ],
% 1.16/1.55 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP(
% 1.16/1.55 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) )
% 1.16/1.55 ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), hAPP( 'c_Suc', Y ) )
% 1.16/1.55 ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Z ), Y ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.16/1.55 X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.55 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) )
% 1.16/1.55 ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.16/1.55 , hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Y ), T ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.16/1.55 , hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.16/1.55 ), T ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ) ]
% 1.16/1.55 ,
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.16/1.55 , hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Z ), T ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.16/1.55 , hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T
% 1.16/1.55 ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ) ) ]
% 1.16/1.55 ,
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ), hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.16/1.55 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) )
% 1.16/1.55 ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add'( X ) ), hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.16/1.55 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) )
% 1.16/1.55 ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( hAPP( hAPP(
% 1.16/1.55 'c_Natural_Oevaln', T ), U ), W ), Z ) ) ), ~( hBOOL( hAPP( hAPP( V0, Y )
% 1.16/1.55 , U ) ) ), ~( hBOOL( hAPP( 'c_Hoare__Mirabelle_Otriple__valid'( W, 't_a'
% 1.16/1.55 ), 'c_Hoare__Mirabelle_Otriple_Otriple'( V0, T, X, 't_a' ) ) ) ) ],
% 1.16/1.55 [ 'c_Natural_Oevalc'( X, Y, Z ), hBOOL( hAPP( T, Y ) ), ~(
% 1.16/1.55 'c_Natural_Oevalc'( 'c_Com_Ocom_OCond'( T, U, X ), Y, Z ) ) ],
% 1.16/1.55 [ 'c_Natural_Oevalc'( 'c_Com_Ocom_OCond'( X, Y, Z ), T, U ), ~(
% 1.16/1.55 'c_Natural_Oevalc'( Z, T, U ) ), hBOOL( hAPP( X, T ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.16/1.55 X ), Y ) ), Z ) ) ],
% 1.16/1.55 [ ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ) ), =( Y,
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), X ) ) ],
% 1.16/1.55 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), Y ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.16/1.55 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Y ), X ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Y ), X ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.16/1.55 'class_Lattices_Oupper__semilattice'( Y ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( Y ), hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( Y ), hAPP( Z, T ) ), hAPP(
% 1.16/1.55 Z, U ) ) ), hAPP( Z, hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X ), T )
% 1.16/1.55 , U ) ) ) ), ~( hBOOL( 'c_Orderings_Oorder__class_Omono'( Z, X, Y ) ) ) ]
% 1.16/1.55 ,
% 1.16/1.55 [ 'c_Complete__Lattice_Ocomplete__lattice'( X, Y, hAPP( 'c_COMBC'( Z, Z
% 1.16/1.55 , 'tc_bool' ), T ), hAPP( 'c_COMBC'( Z, Z, 'tc_bool' ), U ), W, V0, V1,
% 1.16/1.55 V2, Z ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( Y, X, T, U, V0, W,
% 1.16/1.55 V2, V1, Z ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), =(
% 1.16/1.55 'c_Orderings_Oord__class_Omin'( Y, Z, X ), 'c_Orderings_Oord__class_Omin'(
% 1.16/1.55 Z, Y, X ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.16/1.55 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.16/1.55 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), U )
% 1.16/1.55 ) ],
% 1.16/1.55 [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OCond'( X, Y, Z ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), X ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.16/1.55 ), Y ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X
% 1.16/1.55 ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.16/1.55 ), Y ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.16/1.55 ), Y ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.55 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.16/1.55 ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.16/1.55 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, Z ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.55 X ) ) ), =( Y, Z ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.55 X ) ) ), =( Y, Z ) ],
% 1.16/1.55 [ ~( =( hAPP( hAPP( 'c_COMBC'( X, 'tc_fun'( X, 'tc_bool' ), 'tc_bool' )
% 1.16/1.55 , 'c_in'( X ) ), Y ), hAPP( hAPP( 'c_COMBC'( X, 'tc_fun'( X, 'tc_bool' )
% 1.16/1.55 , 'tc_bool' ), 'c_in'( X ) ), Z ) ) ), =( Y, Z ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Oorder'( X ) ), 'c_Orderings_Oorder'( hAPP(
% 1.16/1.55 'c_COMBC'( X, X, 'tc_bool' ), 'c_lessequals'( X ) ), hAPP( 'c_COMBC'( X,
% 1.16/1.55 X, 'tc_bool' ), 'c_HOL_Oord__class_Oless'( X ) ), X ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.16/1.55 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( Y,
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.16/1.55 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.16/1.55 [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X, 'c_Hilbert__Choice_OEps'(
% 1.16/1.55 X, Z ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( X, 'c_Hilbert__Choice_OEps'( X, Y ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 X, Z ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( 'c_Collect'( X ), Z ) ) ),
% 1.16/1.55 ~( hBOOL( hAPP( Z, Y ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), Y ), hAPP(
% 1.16/1.55 'c_Collect'( Z ), X ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 1.16/1.55 ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T )
% 1.16/1.55 ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 1.16/1.55 ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T )
% 1.16/1.55 ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_Orderings_Oord__class_Omin'( Z, T
% 1.16/1.55 , X ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_Orderings_Oord__class_Omin'( T, Z
% 1.16/1.55 , X ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 1.16/1.55 ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T )
% 1.16/1.55 ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), 'c_Orderings_Oord__class_Omin'( Y, Z, X )
% 1.16/1.55 ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T )
% 1.16/1.55 ) ) ],
% 1.16/1.55 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( 'tc_nat' ), Y ), X ) ) ) ],
% 1.16/1.55 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ), Y ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.16/1.55 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.16/1.55 ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.16/1.55 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.16/1.55 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.16/1.55 X ), hAPP( Y, Z ) ), hAPP( Y, hAPP( 'c_Suc', Z ) ) ) ), ~( hBOOL(
% 1.16/1.55 'c_Orderings_Oorder__class_Omono'( Y, 'tc_nat', X ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( 'tc_nat' ), Y ), X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.16/1.55 , Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.16/1.55 ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.16/1.55 , Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.16/1.55 ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.16/1.55 X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ),
% 1.16/1.55 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.16/1.55 ) ), Y ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.16/1.55 X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ),
% 1.16/1.55 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.16/1.55 X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ),
% 1.16/1.55 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.16/1.55 ) ), Y ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.16/1.55 X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ),
% 1.16/1.55 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.16/1.55 X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ),
% 1.16/1.55 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.16/1.55 ) ), Z ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.55 X ) ) ) ) ],
% 1.16/1.55 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.16/1.55 ) ],
% 1.16/1.55 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 1.16/1.55 ) ],
% 1.16/1.55 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.16/1.55 ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.16/1.55 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 1.16/1.55 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( 'c_HOL_Oinduct__forall'( X, Z ) ) ) ]
% 1.16/1.55 ,
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ),
% 1.16/1.55 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), X ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.16/1.55 , =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.16/1.55 'c_Orderings_Oord__class_Omin'( Y, Z, X ) ), T ),
% 1.16/1.55 'c_Orderings_Oord__class_Omin'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.16/1.55 ), Y ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X )
% 1.16/1.55 ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ), Z ) ) ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Z ), Y ) ) ) ],
% 1.16/1.55 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), T, X ),
% 1.16/1.55 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X
% 1.16/1.55 ), 'c_Divides_Odiv__class_Omod'( Y, T, X ) ),
% 1.16/1.55 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.16/1.55 [ ~( =( hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) )
% 1.16/1.55 , Y ) ), =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat'
% 1.16/1.55 ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.16/1.55 [ =( hAPP( 'c_Product__Type_Oscomp'( X, Y, Z, T, U, W ), V0 ), hAPP(
% 1.16/1.55 'c_split'( Y, T, U, W ), hAPP( X, V0 ) ) ) ],
% 1.16/1.55 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.16/1.55 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.16/1.55 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.16/1.55 ) ), Z ), T, X ) ) ],
% 1.16/1.55 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.16/1.55 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.16/1.55 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z,
% 1.16/1.55 T, X ) ), T, X ) ) ],
% 1.16/1.55 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.16/1.55 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.16/1.55 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.16/1.55 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.16/1.55 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, hAPP( 'c_Suc',
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.16/1.55 [ ~( 'class_Int_Onumber__ring'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ) ), =( Y,
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ) ), =( Z,
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.16/1.55 [ =( hAPP( 'c_Collect'( X ), hAPP( hAPP( 'c_COMBB'( 'tc_bool', 'tc_bool'
% 1.16/1.55 , X ), 'c_Not' ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'(
% 1.16/1.55 X, 'tc_bool' ) ), hAPP( 'c_Collect'( X ), Y ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.16/1.55 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.16/1.55 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( X, hAPP( Y, Z ) ), T ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_in'( U ), T ), Z ) ) ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( Y
% 1.16/1.55 , W, X, V0, V1, V2, V3, V4, U ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( Z, T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_in'( U ), Y ), T ) ) ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( W
% 1.16/1.55 , Z, X, V0, V1, V2, V3, V4, U ) ) ],
% 1.16/1.55 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.16/1.55 X, 'tc_bool' ) ), Y ), Z ), hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.16/1.55 , Z ), Y ) ) ],
% 1.16/1.55 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ), hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), Y ) ) ],
% 1.16/1.55 [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ), hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), Y ) ) ],
% 1.16/1.55 [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OBODY'( Y ) ) ), =( X, Y )
% 1.16/1.55 ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Orderings_Olinorder'(
% 1.16/1.55 Y ) ), =( 'c_Orderings_Oord__class_Omin'( hAPP( Z, T ), hAPP( Z, U ), Y )
% 1.16/1.55 , hAPP( Z, 'c_Orderings_Oord__class_Omin'( T, U, X ) ) ), ~( hBOOL(
% 1.16/1.55 'c_Orderings_Oorder__class_Omono'( Z, X, Y ) ) ) ],
% 1.16/1.55 [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OWhile'( Z, T ) ) ),
% 1.16/1.55 =( X, Z ) ],
% 1.16/1.55 [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OWhile'( Z, T ) ) ),
% 1.16/1.55 =( Y, T ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.16/1.55 , hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_Orderings_Oord__class_Omax'( X ), Y ), Z ), hAPP( hAPP(
% 1.16/1.55 'c_Orderings_Oord__class_Omax'( X ), Z ), Y ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), Z ) ), =( Y, hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), T ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Oorder'( X ) ), ~( 'class_Orderings_Oorder'( Y ) )
% 1.16/1.55 , hBOOL( hAPP( hAPP( 'c_lessequals'( Y ), hAPP( Z, T ) ), hAPP( Z, U ) )
% 1.16/1.55 ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), T ), U ) ) ), ~( hBOOL(
% 1.16/1.55 'c_Orderings_Oorder__class_Omono'( Z, X, Y ) ) ) ],
% 1.16/1.55 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.16/1.55 X, 'tc_bool' ) ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.16/1.55 , Y ), Z ) ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'(
% 1.16/1.55 'tc_fun'( X, 'tc_bool' ) ), Y ), Z ) ) ],
% 1.16/1.55 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ) ],
% 1.16/1.55 [ ~( 'class_Lattices_Olattice'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), Z ) ) ],
% 1.16/1.55 [ =( hAPP( 'c_COMBI'( 't_a' ), 'v_P' ), 'v_P' ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X ),
% 1.16/1.55 'c_Orderings_Oord__class_Omin'( Y, Z, X ) ),
% 1.16/1.55 'c_Orderings_Oord__class_Omin'( Y, T, X ) ) ),
% 1.16/1.55 'c_Orderings_Oord__class_Omin'( Y, hAPP( hAPP(
% 1.16/1.55 'c_Orderings_Oord__class_Omax'( X ), Z ), T ), X ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), ~( hBOOL( hAPP( hAPP( T, Y ), Z ) )
% 1.16/1.55 ), =( Y, Z ), ~( 'c_Orderings_Oorder'( T, X, U ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), =( Y, Z ), ~( hBOOL( hAPP( hAPP( T,
% 1.16/1.55 Y ), Z ) ) ), ~( 'c_Orderings_Oorder'( T, X, U ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), =( Y, Z ), ~( hBOOL( hAPP( hAPP( T,
% 1.16/1.55 Y ), Z ) ) ), ~( 'c_Orderings_Oorder'( T, X, U ) ) ],
% 1.16/1.55 [ =( X, Y ), hBOOL( hAPP( hAPP( Z, X ), Y ) ), ~( hBOOL( hAPP( hAPP( T,
% 1.16/1.55 X ), Y ) ) ), ~( 'c_Orderings_Oorder'( T, Z, U ) ) ],
% 1.16/1.55 [ ~( =( 'c_Com_Ocom_OCond'( X, Y, Z ), 'c_Com_Ocom_OSKIP' ) ) ],
% 1.16/1.55 [ =( hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( 'tc_nat' ), X ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.16/1.55 [ =( hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( 'tc_nat' ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_Orderings_Oord__class_Omax'( X ), Y ), 'c_Orderings_Oord__class_Omin'(
% 1.16/1.55 Y, Z, X ) ), Y ) ],
% 1.16/1.55 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.16/1.55 hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ),
% 1.16/1.55 'c_Divides_Odiv__class_Omod'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.16/1.55 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), Z, X ) ) ],
% 1.16/1.55 [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OCond'( Z, T, U ) ) ) ]
% 1.16/1.55 ,
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.16/1.55 ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.16/1.55 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.16/1.55 ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.16/1.55 X ), T ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y )
% 1.16/1.55 ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.16/1.55 ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.16/1.55 X ), Z ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y )
% 1.16/1.55 ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.16/1.55 X ), Z ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.16/1.55 ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X )
% 1.16/1.55 , Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.55 X ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.16/1.55 ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z )
% 1.16/1.55 ) ) ) ],
% 1.16/1.55 [ ~( =( 'c_Hoare__Mirabelle_Otriple_Otriple'( X, Y, Z, T ),
% 1.16/1.55 'c_Hoare__Mirabelle_Otriple_Otriple'( U, W, V0, T ) ) ), =( X, U ) ],
% 1.16/1.55 [ ~( =( 'c_Hoare__Mirabelle_Otriple_Otriple'( X, Y, Z, T ),
% 1.16/1.55 'c_Hoare__Mirabelle_Otriple_Otriple'( U, W, V0, T ) ) ), =( Y, W ) ],
% 1.16/1.55 [ ~( =( 'c_Hoare__Mirabelle_Otriple_Otriple'( X, Y, Z, T ),
% 1.16/1.55 'c_Hoare__Mirabelle_Otriple_Otriple'( U, W, V0, T ) ) ), =( Z, V0 ) ]
% 1.16/1.55 ,
% 1.16/1.55 [ =( 'c_Nat_Onat_Onat__rec'( X, Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat'
% 1.16/1.55 ), Z ), X ) ],
% 1.16/1.55 [ =( hAPP( hAPP( X, 'c_Fun_Oid'( Y ) ), Z ), Z ), ~( hBOOL(
% 1.16/1.55 'c_Record_Oiso__tuple__update__accessor__cong__assist'( X, T, Y, U ) ) )
% 1.16/1.55 ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.16/1.55 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.16/1.55 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( 'tc_nat' ), Z ), Y ) ) ) ],
% 1.16/1.55 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( 'tc_nat' ), Y ), X ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.16/1.55 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), ~(
% 1.16/1.55 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X
% 1.16/1.55 ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.16/1.55 ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.55 X ) ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), U ) ) ),
% 1.16/1.55 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.16/1.55 ) ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z )
% 1.16/1.55 , U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ],
% 1.16/1.55 [ ~( =( hAPP( X, hAPP( Y, Z ) ), hAPP( T, hAPP( Y, Z ) ) ) ), ~( hBOOL(
% 1.16/1.55 'c_Record_Oiso__tuple__update__accessor__cong__assist'( U, Y, W, V0 ) ) )
% 1.16/1.55 , =( hAPP( hAPP( U, X ), Z ), hAPP( hAPP( U, T ), Z ) ) ],
% 1.16/1.55 [ ~( =( hAPP( X, hAPP( Y, Z ) ), hAPP( Y, Z ) ) ), ~( hBOOL(
% 1.16/1.55 'c_Record_Oiso__tuple__update__accessor__cong__assist'( T, Y, U, W ) ) )
% 1.16/1.55 , =( hAPP( hAPP( T, X ), Z ), Z ) ],
% 1.16/1.55 [ =( hAPP( hAPP( hAPP( 'c_Fun_Ofcomp'( X, Y, Z ), T ), U ), W ), hAPP( U
% 1.16/1.55 , hAPP( T, W ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_Finite__Set_Osetsum'( Y, X ), hAPP( hAPP( 'c_COMBS'( Y, 'tc_fun'( Z,
% 1.16/1.55 'tc_bool' ), X ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( Z, X ), 'tc_fun'(
% 1.16/1.55 'tc_fun'( Z, 'tc_bool' ), X ), Y ), 'c_Finite__Set_Osetsum'( Z, X ) ), T
% 1.16/1.55 ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( Z, 'tc_bool' ), 'tc_fun'( Z,
% 1.16/1.55 'tc_bool' ), Y ), 'c_Collect'( Z ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( Z
% 1.16/1.55 , 'tc_bool' ), 'tc_fun'( Z, 'tc_bool' ), Y ), hAPP( 'c_COMBS'( Z,
% 1.16/1.55 'tc_bool', 'tc_bool' ), hAPP( hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'(
% 1.16/1.55 'tc_bool', 'tc_bool' ), Z ), 'c_and' ), hAPP( hAPP( 'c_COMBC'( Z,
% 1.16/1.55 'tc_fun'( Z, 'tc_bool' ), 'tc_bool' ), 'c_in'( Z ) ), U ) ) ) ), W ) ) )
% 1.16/1.55 ), V0 ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( Z, X ), hAPP( hAPP(
% 1.16/1.55 'c_COMBS'( Z, 'tc_fun'( Y, 'tc_bool' ), X ), hAPP( hAPP( 'c_COMBB'(
% 1.16/1.55 'tc_fun'( Y, X ), 'tc_fun'( 'tc_fun'( Y, 'tc_bool' ), X ), Z ),
% 1.16/1.55 'c_Finite__Set_Osetsum'( Y, X ) ), hAPP( 'c_COMBC'( Y, Z, X ), T ) ) ),
% 1.16/1.55 hAPP( hAPP( 'c_COMBB'( 'tc_fun'( Y, 'tc_bool' ), 'tc_fun'( Y, 'tc_bool' )
% 1.16/1.55 , Z ), 'c_Collect'( Y ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( Y, 'tc_bool'
% 1.16/1.55 ), 'tc_fun'( Y, 'tc_bool' ), Z ), hAPP( 'c_COMBS'( Y, 'tc_bool',
% 1.16/1.55 'tc_bool' ), hAPP( hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'( 'tc_bool',
% 1.16/1.55 'tc_bool' ), Y ), 'c_and' ), hAPP( hAPP( 'c_COMBC'( Y, 'tc_fun'( Y,
% 1.16/1.55 'tc_bool' ), 'tc_bool' ), 'c_in'( Y ) ), V0 ) ) ) ), hAPP( 'c_COMBC'( Y,
% 1.16/1.55 Z, 'tc_bool' ), W ) ) ) ) ), U ) ), ~( 'c_Finite__Set_Ofinite'( U, Z ) )
% 1.16/1.55 , ~( 'c_Finite__Set_Ofinite'( V0, Y ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ), =( X,
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.16/1.55 [ ~( =( 'c_Com_Ocom_OSemi'( X, Y ), 'c_Com_Ocom_OSKIP' ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.16/1.55 X ), Y ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.16/1.55 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.55 'tc_nat' ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.16/1.55 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.16/1.55 , Y ), Z ), Z, X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.16/1.55 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.16/1.55 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.16/1.55 , Y ), Z ), Y, X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ),
% 1.16/1.55 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.55 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.55 X ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.16/1.55 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.55 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.55 X ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ),
% 1.16/1.55 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.16/1.55 , Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.55 X ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.16/1.55 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.16/1.55 , Y ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.55 X ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.55 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.16/1.55 ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.55 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.16/1.55 ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.55 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.16/1.55 ) ],
% 1.16/1.55 [ =( 'c_Hilbert__Choice_OEps'( hAPP( hAPP( 'c_COMBC'( X, X, 'tc_bool' )
% 1.16/1.55 , 'c_fequal'( X ) ), Y ), X ), Y ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), 'c_Power_Opower_Opower'(
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ), 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X
% 1.16/1.55 ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.16/1.55 'c_Power_Opower_Opower'( 'c_HOL_Ozero__class_Ozero'( X ),
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y, Z, X ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), =( hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.16/1.55 ), Y ) ), Z ) ), Z ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.16/1.55 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( 'tc_nat' ), Z ), X ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( 'tc_nat' ), Y ), X ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.16/1.55 ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.16/1.55 'c_Nat_Osemiring__1__class_Oof__nat__aux'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.55 'tc_nat' ), Z, X ), Z ) ],
% 1.16/1.55 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), ~(
% 1.16/1.55 'class_Lattices_Oupper__semilattice'( Y ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( Y ), hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( Y ), hAPP( Z, T ) ), hAPP(
% 1.16/1.55 Z, U ) ) ), hAPP( Z, hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( X ), T ), U ) ) ) ), ~(
% 1.16/1.55 hBOOL( 'c_Orderings_Oorder__class_Omono'( Z, X, Y ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y
% 1.16/1.55 ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~(
% 1.16/1.55 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.55 X ) ) ) ) ],
% 1.16/1.55 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), X ) ) ) ],
% 1.16/1.55 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Y ) ) ) ],
% 1.16/1.55 [ =( hAPP( hAPP( 'c_Fun_Ofcomp'( X, Y, Y ), Z ), 'c_Fun_Oid'( Y ) ), Z )
% 1.16/1.55 ],
% 1.16/1.55 [ =( hAPP( hAPP( 'c_Fun_Ofcomp'( X, X, Y ), 'c_Fun_Oid'( X ) ), Z ), Z )
% 1.16/1.55 ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.16/1.55 Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~(
% 1.16/1.55 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.55 X ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), T ), Y ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.16/1.55 Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~(
% 1.16/1.55 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.55 X ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), T ), Z ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.16/1.55 Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~(
% 1.16/1.55 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.16/1.55 , Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Omult__mono'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.16/1.55 Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~(
% 1.16/1.55 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.16/1.55 , Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Omult__mono1'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.16/1.55 Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~(
% 1.16/1.55 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.16/1.55 , Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), T ) ) ) ],
% 1.16/1.55 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.16/1.55 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.16/1.55 'tc_nat' ), X ), Y ), Y, 'tc_nat' ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), hAPP( hAPP( 'c_Pair'(
% 1.16/1.55 X, X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X
% 1.16/1.55 ) ), hAPP( hAPP( 'c_Pair'( X, X ), U ), Z ) ), T ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_in'( 'tc_prod'( X, X ) ), hAPP( hAPP( 'c_Pair'( X, X ), Y ), U )
% 1.16/1.55 ), T ) ) ), ~( hBOOL( 'c_Relation_Otrans'( T, X ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), hAPP( hAPP( 'c_Pair'(
% 1.16/1.55 X, X ), Y ), Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X
% 1.16/1.55 ) ), hAPP( hAPP( 'c_Pair'( X, X ), U ), Z ) ), T ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_in'( 'tc_prod'( X, X ) ), hAPP( hAPP( 'c_Pair'( X, X ), Y ), U )
% 1.16/1.55 ), T ) ) ), ~( hBOOL( 'c_Relation_Otrans'( T, X ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), ~(
% 1.16/1.55 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), Y ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.16/1.55 ],
% 1.16/1.55 [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OSemi'( Z, T ) ) ) ]
% 1.16/1.55 ,
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.16/1.55 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ), =( T, U ), =( Z,
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.55 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.55 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.16/1.55 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.16/1.55 , Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.55 'tc_nat' ) ) ) ],
% 1.16/1.55 [ =( hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'(
% 1.16/1.55 X, 'tc_bool' ) ), Y ), Z ), hAPP( 'c_Collect'( X ), hAPP( hAPP( 'c_COMBS'(
% 1.16/1.55 X, 'tc_bool', 'tc_bool' ), hAPP( hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'(
% 1.16/1.55 'tc_bool', 'tc_bool' ), X ), 'c_or' ), hAPP( hAPP( 'c_COMBC'( X, 'tc_fun'(
% 1.16/1.55 X, 'tc_bool' ), 'tc_bool' ), 'c_in'( X ) ), Y ) ) ), hAPP( hAPP(
% 1.16/1.55 'c_COMBC'( X, 'tc_fun'( X, 'tc_bool' ), 'tc_bool' ), 'c_in'( X ) ), Z ) )
% 1.16/1.55 ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ) ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( X, Y ) ), =( Z, Y ), ~( 'c_Natural_Oevalc'(
% 1.16/1.55 'c_Com_Ocom_OWhile'( X, T ), Y, Z ) ) ],
% 1.16/1.55 [ =( 'c_Power_Opower_Opower'( X, Y, Z, 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.55 'tc_nat' ), T ), X ) ],
% 1.16/1.55 [ 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( X ), hAPP( hAPP( 'c_COMBC'(
% 1.16/1.55 X, Y, 'tc_bool' ), Z ), T ) ), X ), ~( hBOOL( hAPP( U, T ) ) ), ~(
% 1.16/1.55 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( X ), hAPP( hAPP( 'c_COMBB'(
% 1.16/1.55 'tc_fun'( Y, 'tc_bool' ), 'tc_bool', X ), 'c_Ex'( Y ) ), hAPP( hAPP(
% 1.16/1.55 'c_COMBB'( 'tc_fun'( Y, 'tc_bool' ), 'tc_fun'( Y, 'tc_bool' ), X ), hAPP(
% 1.16/1.55 'c_COMBS'( Y, 'tc_bool', 'tc_bool' ), hAPP( hAPP( 'c_COMBB'( 'tc_bool',
% 1.16/1.55 'tc_fun'( 'tc_bool', 'tc_bool' ), Y ), 'c_and' ), U ) ) ), Z ) ) ), X ) )
% 1.16/1.55 , ~( 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( Y ), U ), Y ) ) ],
% 1.16/1.55 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.16/1.55 ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), T ), Y
% 1.16/1.55 ) ), Z ) ) ) ],
% 1.16/1.55 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.16/1.55 ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), T
% 1.16/1.55 ) ), Z ) ) ) ],
% 1.16/1.55 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ) ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) ) ],
% 1.16/1.55 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ) ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_lessequals'( X ), Y ), Z ) ) ) ],
% 1.16/1.55 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.16/1.55 ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), T ), Y
% 1.16/1.55 ) ), Z ) ) ) ],
% 1.16/1.55 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.16/1.55 ), hAPP( hAPP( 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Y ), T
% 1.16/1.55 ) ), Z ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.16/1.55 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.16/1.55 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.16/1.55 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.16/1.55 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.16/1.55 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.16/1.55 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.16/1.55 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.16/1.55 [ =( hAPP( hAPP( X, Y ), hAPP( Z, Y ) ), T ), ~(
% 1.16/1.55 'c_Lattices_Oboolean__algebra'( U, Z, W, V0, V1, X, V2, T, V3 ) ) ],
% 1.16/1.55 [ =( hAPP( hAPP( X, Y ), hAPP( Z, Y ) ), T ), ~(
% 1.16/1.55 'c_Lattices_Oboolean__algebra'( U, Z, W, V0, X, V1, T, V2, V3 ) ) ],
% 1.16/1.55 [ =( hAPP( hAPP( X, hAPP( Y, Z ) ), Z ), T ), ~(
% 1.16/1.55 'c_Lattices_Oboolean__algebra'( U, Y, W, V0, V1, X, V2, T, V3 ) ) ],
% 1.16/1.55 [ =( hAPP( hAPP( X, hAPP( Y, Z ) ), Z ), T ), ~(
% 1.16/1.55 'c_Lattices_Oboolean__algebra'( U, Y, W, V0, X, V1, T, V2, V3 ) ) ],
% 1.16/1.55 [ =( hAPP( X, hAPP( X, Y ) ), Y ), ~( 'c_Lattices_Oboolean__algebra'( Z
% 1.16/1.55 , X, T, U, W, V0, V1, V2, V3 ) ) ],
% 1.16/1.55 [ ~( 'c_Lattices_Oboolean__algebra'( X, Y, Z, T, U, W, hAPP( hAPP( U, V0
% 1.16/1.55 ), V1 ), hAPP( hAPP( W, V0 ), V1 ), V2 ) ), =( hAPP( Y, V0 ), V1 ) ]
% 1.16/1.55 ,
% 1.16/1.55 [ =( hAPP( X, Y ), Z ), ~( 'c_Lattices_Oboolean__algebra'( T, X, U, W,
% 1.16/1.55 V0, V1, Z, Y, V2 ) ) ],
% 1.16/1.55 [ =( hAPP( X, Y ), Z ), ~( 'c_Lattices_Oboolean__algebra'( T, X, U, W,
% 1.16/1.55 V0, V1, Y, Z, V2 ) ) ],
% 1.16/1.55 [ =( hAPP( hAPP( X, Y ), Z ), hAPP( hAPP( T, Y ), hAPP( U, Z ) ) ), ~(
% 1.16/1.55 'c_Lattices_Oboolean__algebra'( X, U, W, V0, T, V1, V2, V3, V4 ) ) ],
% 1.16/1.55 [ =( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( U, hAPP( X, Z ) ),
% 1.16/1.55 hAPP( X, T ) ) ), ~( 'c_Lattices_Oboolean__algebra'( W, X, V0, V1, Y, U,
% 1.16/1.55 V2, V3, V4 ) ) ],
% 1.16/1.55 [ =( hAPP( X, hAPP( hAPP( Y, Z ), T ) ), hAPP( hAPP( U, hAPP( X, Z ) ),
% 1.16/1.55 hAPP( X, T ) ) ), ~( 'c_Lattices_Oboolean__algebra'( W, X, V0, V1, U, Y,
% 1.16/1.55 V2, V3, V4 ) ) ],
% 1.16/1.55 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Omod'( Y,
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.16/1.55 , Y ) ) ],
% 1.16/1.55 [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 1.16/1.55 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.16/1.55 'tc_nat' ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.16/1.55 X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) )
% 1.16/1.55 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), T ), Z ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ) ],
% 1.16/1.55 [ ~( 'class_Finite__Set_Ofinite_Ofinite'( X ) ), 'c_Finite__Set_Ofinite'(
% 1.16/1.55 Y, X ) ],
% 1.16/1.55 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Y ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Y ), X ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.16/1.55 X ), T ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y )
% 1.16/1.55 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.16/1.55 ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.16/1.55 X ), T ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.16/1.55 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.16/1.55 ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.16/1.55 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ) ]
% 1.16/1.55 ,
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.16/1.55 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ]
% 1.16/1.55 ,
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.16/1.55 ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.16/1.55 ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.16/1.55 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), Y ) ) ) ]
% 1.16/1.55 ,
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.16/1.55 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ]
% 1.16/1.55 ,
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.16/1.55 ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), T ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.16/1.55 ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.16/1.55 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.16/1.55 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ]
% 1.16/1.55 ,
% 1.16/1.55 [ =( hAPP( X, 'c_Fun_Oid'( Y ) ), 'c_Fun_Oid'( Z ) ), ~( hBOOL(
% 1.16/1.55 'c_Record_Oiso__tuple__update__accessor__cong__assist'( X, T, Y, Z ) ) )
% 1.16/1.55 ],
% 1.16/1.55 [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OBODY'( X ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.16/1.55 , =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.16/1.55 'c_Orderings_Oord__class_Omax'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.16/1.55 'c_Orderings_Oord__class_Omax'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.16/1.55 , Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) )
% 1.16/1.55 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.55 X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.16/1.55 X ), Y ), T ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Opordered__semiring'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.16/1.55 , Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) )
% 1.16/1.55 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.55 X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.16/1.55 X ), Y ), T ) ) ) ],
% 1.16/1.55 [ 'c_Orderings_Oorder'( hAPP( 'c_COMBC'( X, X, 'tc_bool' ), Y ), hAPP(
% 1.16/1.55 'c_COMBC'( X, X, 'tc_bool' ), Z ), X ), ~( 'c_Orderings_Oorder'( Y, Z, X
% 1.16/1.55 ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.16/1.55 X ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_Orderings_Oord__class_Omax'( X ), hAPP( hAPP(
% 1.16/1.55 'c_Orderings_Oord__class_Omax'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.16/1.55 'c_Orderings_Oord__class_Omax'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_Orderings_Oord__class_Omax'( X ), Z ), T ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.16/1.55 X ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_Orderings_Oord__class_Omax'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_Orderings_Oord__class_Omax'( X ), Z ), T ) ), hAPP( hAPP(
% 1.16/1.55 'c_Orderings_Oord__class_Omax'( X ), Z ), hAPP( hAPP(
% 1.16/1.55 'c_Orderings_Oord__class_Omax'( X ), Y ), T ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( X ), Y ), hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ],
% 1.16/1.55 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.16/1.55 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.16/1.55 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.16/1.55 , 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 1.16/1.55 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.16/1.55 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.16/1.55 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.16/1.55 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.16/1.55 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.16/1.55 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_Finite__Set_Osetsum'( Y, X ), hAPP( hAPP( 'c_COMBB'( X, X, Y ),
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ) ), Z ) ), T ), hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP( 'c_Finite__Set_Osetsum'(
% 1.16/1.55 Y, X ), Z ), T ) ) ) ],
% 1.16/1.55 [ 'c_Fun_Oinj__on'( X, Y, Z, T ), ~( 'c_Fun_Oinj__on'( X, hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.16/1.55 , U ), Y ), Z, T ) ) ],
% 1.16/1.55 [ 'c_Fun_Oinj__on'( X, Y, Z, T ), ~( 'c_Fun_Oinj__on'( X, hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( Z, 'tc_bool' ) )
% 1.16/1.55 , Y ), U ), Z, T ) ) ],
% 1.16/1.55 [ ~( =( hAPP( hAPP( 'c_COMBC'( X, 'tc_fun'( 'tc_prod'( X, Y ), 'tc_bool'
% 1.16/1.55 ), 'tc_fun'( Y, 'tc_bool' ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( Y,
% 1.16/1.55 'tc_fun'( 'tc_fun'( 'tc_prod'( X, Y ), 'tc_bool' ), 'tc_bool' ) ),
% 1.16/1.55 'tc_fun'( 'tc_fun'( 'tc_prod'( X, Y ), 'tc_bool' ), 'tc_fun'( Y,
% 1.16/1.55 'tc_bool' ) ), X ), 'c_COMBC'( Y, 'tc_fun'( 'tc_prod'( X, Y ), 'tc_bool'
% 1.16/1.55 ), 'tc_bool' ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( Y, 'tc_prod'( X, Y )
% 1.16/1.55 ), 'tc_fun'( Y, 'tc_fun'( 'tc_fun'( 'tc_prod'( X, Y ), 'tc_bool' ),
% 1.16/1.55 'tc_bool' ) ), X ), hAPP( 'c_COMBB'( 'tc_prod'( X, Y ), 'tc_fun'(
% 1.16/1.55 'tc_fun'( 'tc_prod'( X, Y ), 'tc_bool' ), 'tc_bool' ), Y ), 'c_in'(
% 1.16/1.55 'tc_prod'( X, Y ) ) ) ), 'c_Pair'( X, Y ) ) ) ), Z ), hAPP( hAPP(
% 1.16/1.55 'c_COMBC'( X, 'tc_fun'( 'tc_prod'( X, Y ), 'tc_bool' ), 'tc_fun'( Y,
% 1.16/1.55 'tc_bool' ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( Y, 'tc_fun'( 'tc_fun'(
% 1.16/1.55 'tc_prod'( X, Y ), 'tc_bool' ), 'tc_bool' ) ), 'tc_fun'( 'tc_fun'(
% 1.16/1.55 'tc_prod'( X, Y ), 'tc_bool' ), 'tc_fun'( Y, 'tc_bool' ) ), X ),
% 1.16/1.55 'c_COMBC'( Y, 'tc_fun'( 'tc_prod'( X, Y ), 'tc_bool' ), 'tc_bool' ) ),
% 1.16/1.55 hAPP( hAPP( 'c_COMBB'( 'tc_fun'( Y, 'tc_prod'( X, Y ) ), 'tc_fun'( Y,
% 1.16/1.55 'tc_fun'( 'tc_fun'( 'tc_prod'( X, Y ), 'tc_bool' ), 'tc_bool' ) ), X ),
% 1.16/1.55 hAPP( 'c_COMBB'( 'tc_prod'( X, Y ), 'tc_fun'( 'tc_fun'( 'tc_prod'( X, Y )
% 1.16/1.55 , 'tc_bool' ), 'tc_bool' ), Y ), 'c_in'( 'tc_prod'( X, Y ) ) ) ),
% 1.16/1.55 'c_Pair'( X, Y ) ) ) ), T ) ) ), =( Z, T ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.16/1.55 Y ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.16/1.55 Y ) ],
% 1.16/1.55 [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.16/1.55 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 1.16/1.55 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.16/1.55 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.16/1.55 Y ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.16/1.55 Y ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.16/1.55 Y ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.16/1.55 Y ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.16/1.55 Y ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.16/1.55 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y ) ), =( Y,
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_Orderings_Oord__class_Omax'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_Orderings_Oord__class_Omax'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_Orderings_Oord__class_Omax'( X ), Y ), Z ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.16/1.55 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.16/1.55 , Y ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.16/1.55 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.16/1.55 , Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.16/1.55 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.16/1.55 , Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ),
% 1.16/1.55 hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.16/1.55 , Y ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ) ) ],
% 1.16/1.55 [ =( hAPP( 'c_Fun_Oid'( X ), Y ), Y ) ],
% 1.16/1.55 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Y ), X ) ],
% 1.16/1.55 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), X ), Y ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.16/1.55 X ), Y ), Z ) ), Z ), Y ) ],
% 1.16/1.55 [ =( hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ), Y
% 1.16/1.55 ), hAPP( 'c_Collect'( X ), hAPP( hAPP( 'c_COMBB'( 'tc_bool', 'tc_bool',
% 1.16/1.55 X ), 'c_Not' ), hAPP( hAPP( 'c_COMBC'( X, 'tc_fun'( X, 'tc_bool' ),
% 1.16/1.55 'tc_bool' ), 'c_in'( X ) ), Y ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( 'class_Orderings_Olinorder'(
% 1.16/1.55 Y ) ), =( hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( Y ), hAPP( Z, T ) )
% 1.16/1.55 , hAPP( Z, U ) ), hAPP( Z, hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X
% 1.16/1.55 ), T ), U ) ) ), ~( hBOOL( 'c_Orderings_Oorder__class_Omono'( Z, X, Y )
% 1.16/1.55 ) ) ],
% 1.16/1.55 [ =( hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.16/1.55 hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ), Y ) ),
% 1.16/1.55 Y ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.16/1.55 X ), Y ) ), Y ) ],
% 1.16/1.55 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =( hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.16/1.55 X ), Y ) ), Y ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y, hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.16/1.55 X ), Y ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y, hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.16/1.55 X ), Y ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.16/1.55 X ), Y ) ), Y ) ],
% 1.16/1.55 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ) ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ],
% 1.16/1.55 [ ~( 'class_Lattices_Oupper__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( X ), Z ), T ) ) ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( X ), Z ), Y ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.16/1.55 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Y ), T ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.16/1.55 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.16/1.55 [ =( X, Y ), ~( 'c_Natural_Oevalc'( 'c_Com_Ocom_OSKIP', Y, X ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.55 'tc_nat' ) ), Y ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.55 'tc_nat' ) ), X ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.16/1.55 Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.16/1.55 X ), Y ), Y ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.16/1.55 Y ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X )
% 1.16/1.55 , Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X )
% 1.16/1.55 , Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Z ), hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.16/1.55 ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), Y ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y )
% 1.16/1.55 ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), Y ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Z ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.16/1.55 X ), Y ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Z ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.16/1.55 X ), Y ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X )
% 1.16/1.55 , Z ) ), Y ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X )
% 1.16/1.55 , Z ) ), Y ) ) ) ],
% 1.16/1.55 [ =( hAPP( X, Y ), hAPP( Z, hAPP( 'c_Collect'( T ), hAPP( hAPP(
% 1.16/1.55 'c_COMBB'( 'tc_fun'( T, 'tc_bool' ), 'tc_bool', T ), 'c_All'( T ) ), hAPP(
% 1.16/1.55 hAPP( 'c_COMBB'( 'tc_fun'( T, 'tc_bool' ), 'tc_fun'( T, 'tc_bool' ), T )
% 1.16/1.55 , hAPP( 'c_COMBS'( T, 'tc_bool', 'tc_bool' ), hAPP( hAPP( 'c_COMBB'(
% 1.16/1.55 'tc_bool', 'tc_fun'( 'tc_bool', 'tc_bool' ), T ), 'c_implies' ), hAPP(
% 1.16/1.55 hAPP( 'c_COMBC'( T, 'tc_fun'( T, 'tc_bool' ), 'tc_bool' ), 'c_in'( T ) )
% 1.16/1.55 , Y ) ) ) ), hAPP( 'c_COMBC'( T, T, 'tc_bool' ), U ) ) ) ) ) ), ~(
% 1.16/1.55 'c_Complete__Lattice_Ocomplete__lattice'( Z, X, U, W, V0, V1, V2, V3, T )
% 1.16/1.55 ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y
% 1.16/1.55 , X ), Z ), T ) ), U ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y, X ), hAPP(
% 1.16/1.55 hAPP( 'c_COMBC'( Y, X, X ), hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'( X, X ), Y
% 1.16/1.55 ), 'c_HOL_Otimes__class_Otimes'( X ) ), Z ) ), U ) ), T ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_Finite__Set_Osetsum'( Y, X ), hAPP( hAPP( 'c_COMBS'( Y, X, X ), hAPP(
% 1.16/1.55 hAPP( 'c_COMBB'( X, 'tc_fun'( X, X ), Y ), 'c_HOL_Ominus__class_Ominus'(
% 1.16/1.55 X ) ), Z ) ), T ) ), U ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( X ),
% 1.16/1.55 hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y, X ), Z ), U ) ), hAPP( hAPP(
% 1.16/1.55 'c_Finite__Set_Osetsum'( Y, X ), T ), U ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_Finite__Set_Osetsum'( Y, X ), hAPP( hAPP( 'c_COMBS'( Y, X, X ), hAPP(
% 1.16/1.55 hAPP( 'c_COMBB'( X, 'tc_fun'( X, X ), Y ), 'c_HOL_Oplus__class_Oplus'( X
% 1.16/1.55 ) ), Z ) ), T ) ), U ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.16/1.55 hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y, X ), Z ), U ) ), hAPP( hAPP(
% 1.16/1.55 'c_Finite__Set_Osetsum'( Y, X ), T ), U ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( 'c_Suc', X ) ),
% 1.16/1.55 hAPP( 'c_Suc', Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' )
% 1.16/1.55 , X ), Y ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), hAPP(
% 1.16/1.55 'c_Suc', Y ) ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP(
% 1.16/1.55 'c_Suc', Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.16/1.55 'tc_nat' ), X ), Y ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.16/1.55 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP(
% 1.16/1.55 'c_Suc', X ) ), Y ) ) ) ],
% 1.16/1.55 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.16/1.55 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'(
% 1.16/1.55 X, Y, 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.16/1.55 [ ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( 'c_Suc', X ) )
% 1.16/1.55 , X ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), hAPP( 'c_Suc', Y )
% 1.16/1.55 ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ) ) ]
% 1.16/1.55 ,
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y ) ) ) ]
% 1.16/1.55 ,
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP(
% 1.16/1.55 'c_Suc', X ) ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.16/1.55 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.16/1.55 'tc_nat' ), X ), Z ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP(
% 1.16/1.55 'c_Suc', X ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP(
% 1.16/1.55 'c_Suc', X ) ) ) ],
% 1.16/1.55 [ ~( =( hAPP( 'c_Suc', X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.16/1.55 ,
% 1.16/1.55 [ ~( =( hAPP( 'c_Suc', X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ]
% 1.16/1.55 ,
% 1.16/1.55 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.16/1.55 , X ), hAPP( 'c_Suc', Y ) ) ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) ],
% 1.16/1.55 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.16/1.55 , Y ), hAPP( 'c_Suc', X ) ) ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), X ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), T ), Z ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_lessequals'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.16/1.55 X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ),
% 1.16/1.55 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.16/1.55 ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), T ) ) )
% 1.16/1.55 ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), X ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), X ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.16/1.55 X ), Y ), Y ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Y ), Y ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Y ), T ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.16/1.55 ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), U ), T ) ) )
% 1.16/1.55 , ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), hAPP( hAPP( 'c_Pair'(
% 1.16/1.55 X, Y ), Z ), T ) ), 'c_Product__Type_OSigma'( U, W, X, Y ) ) ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_in'( Y ), T ), hAPP( W, Z ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_in'( X ), Z ), U ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), hAPP( hAPP( 'c_Pair'(
% 1.16/1.55 X, Y ), Z ), T ) ), 'c_Product__Type_OSigma'( U, W, X, Y ) ) ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_in'( Y ), T ), hAPP( W, Z ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_in'( X ), Z ), U ) ) ) ],
% 1.16/1.55 [ =( 'c_Orderings_Oord__class_Omin'( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Z ), Y ), 'tc_nat' ), hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ),
% 1.16/1.55 'c_Orderings_Oord__class_Omin'( X, Z, 'tc_nat' ) ), Y ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL(
% 1.16/1.55 hAPP( X, hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), Z ) )
% 1.16/1.55 ) ) ],
% 1.16/1.55 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( 'c_Suc',
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( 'c_Suc',
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP(
% 1.16/1.55 'c_Orderings_Oorder_Omono'( Y, Z, X ), T ) ), ~( hBOOL( hAPP(
% 1.16/1.55 'c_Orderings_Oorder_Ostrict__mono'( U, Z, X ), T ) ) ), ~(
% 1.16/1.55 'c_Orderings_Oorder'( Y, U, Z ) ) ],
% 1.16/1.55 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( Z, Y ), X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 Z, X ), Y ) ) ), ~( 'c_Orderings_Oorder'( Z, T, U ) ) ],
% 1.16/1.55 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( Z, Y ), X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 Z, X ), Y ) ) ), ~( 'c_Orderings_Oorder'( Z, T, U ) ) ],
% 1.16/1.55 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( Z, X ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 Z, Y ), X ) ) ), ~( 'c_Orderings_Oorder'( Z, T, U ) ) ],
% 1.16/1.55 [ =( 'c_Hilbert__Choice_OEps'( hAPP( 'c_fequal'( X ), Y ), X ), Y ) ]
% 1.16/1.55 ,
% 1.16/1.55 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), Y ) ],
% 1.16/1.55 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.16/1.55 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.16/1.55 ), Y ), Z ), Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.16/1.55 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.16/1.55 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.16/1.55 ), Y ), Z ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.16/1.55 [ ~( =( hAPP( hAPP( 'c_Pair'( X, Y ), Z ), T ), hAPP( hAPP( 'c_Pair'( X
% 1.16/1.55 , Y ), U ), W ) ) ), =( Z, U ) ],
% 1.16/1.55 [ ~( =( hAPP( hAPP( 'c_Pair'( X, Y ), Z ), T ), hAPP( hAPP( 'c_Pair'( X
% 1.16/1.55 , Y ), U ), W ) ) ), =( T, W ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.16/1.55 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), U ) ) ),
% 1.16/1.55 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.16/1.55 [ ~( =( 'c_Com_Ocom_OWhile'( X, Y ), 'c_Com_Ocom_OBODY'( Z ) ) ) ],
% 1.16/1.55 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.16/1.55 , X ), hAPP( 'c_Suc', Y ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.16/1.55 'tc_nat' ), Y ), X ) ) ) ],
% 1.16/1.55 [ =( hAPP( hAPP( hAPP( hAPP( 'c_Recdef_Ocut'( X, Y ), Z ), T ), U ), W )
% 1.16/1.55 , hAPP( Z, W ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), hAPP(
% 1.16/1.55 hAPP( 'c_Pair'( X, X ), W ), U ) ), T ) ) ) ],
% 1.16/1.55 [ =( hAPP( hAPP( hAPP( hAPP( 'c_Recdef_Ocut'( X, Y ), Z ), T ), U ), W )
% 1.16/1.55 , hAPP( Z, W ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), hAPP(
% 1.16/1.55 hAPP( 'c_Pair'( X, X ), W ), U ) ), T ) ) ) ],
% 1.16/1.55 [ ~( =( 'c_Com_Ocom_OBODY'( X ), 'c_Com_Ocom_OSKIP' ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.16/1.55 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), X ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.16/1.55 ,
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.16/1.55 ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ),
% 1.16/1.55 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.16/1.55 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.16/1.55 ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ),
% 1.16/1.55 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.16/1.55 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ) ) ) ],
% 1.16/1.55 [ =( 'c_The'( hAPP( 'c_fequal'( X ), Y ), X ), Y ) ],
% 1.16/1.55 [ =( hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' )
% 1.16/1.55 , X ), hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), X ),
% 1.16/1.55 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), X ) ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.16/1.55 'tc_nat' ) ), Y ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( X ), Y )
% 1.16/1.55 , 'c_Orderings_Oord__class_Omin'( Z, T, X ) ) ),
% 1.16/1.55 'c_Orderings_Oord__class_Omin'( hAPP( hAPP(
% 1.16/1.55 'c_Orderings_Oord__class_Omax'( X ), Y ), Z ), hAPP( hAPP(
% 1.16/1.55 'c_Orderings_Oord__class_Omax'( X ), Y ), T ), X ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), U ), T ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.16/1.55 ), Z ), Y ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Z ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X
% 1.16/1.55 ), U ), T ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), T ), U ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Ominus__class_Ominus'( X ), Y ), Z ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( X ), T ), U ) ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), T ), U ) ) ) ],
% 1.16/1.55 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.16/1.55 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.16/1.55 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.16/1.55 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.16/1.55 , Y ), T ), Z, X ) ) ],
% 1.16/1.55 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.16/1.55 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.16/1.55 , Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ),
% 1.16/1.55 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.16/1.55 , Y ), Z ), T, X ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.16/1.55 hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.16/1.55 ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.16/1.55 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.16/1.55 X ), Y ) ) ) ) ],
% 1.16/1.55 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), Y ), X ) ), Y ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), X ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), hAPP( 'c_Suc', Y ) ) ), X
% 1.16/1.55 ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ) ) ],
% 1.16/1.55 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.16/1.55 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, hAPP(
% 1.16/1.55 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, hAPP( 'c_Suc'
% 1.16/1.55 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.16/1.55 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.16/1.55 hAPP( 'c_Suc', 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_Orderings_Oord__class_Omax'( X ), 'c_Orderings_Oord__class_Omin'( Y, Z
% 1.16/1.55 , X ) ), T ), 'c_Orderings_Oord__class_Omin'( hAPP( hAPP(
% 1.16/1.55 'c_Orderings_Oord__class_Omax'( X ), Y ), T ), hAPP( hAPP(
% 1.16/1.55 'c_Orderings_Oord__class_Omax'( X ), Z ), T ), X ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_Orderings_Oord__class_Omax'( X ), Y ), 'c_Orderings_Oord__class_Omin'(
% 1.16/1.55 Z, T, X ) ), 'c_Orderings_Oord__class_Omin'( hAPP( hAPP(
% 1.16/1.55 'c_Orderings_Oord__class_Omax'( X ), Y ), Z ), hAPP( hAPP(
% 1.16/1.55 'c_Orderings_Oord__class_Omax'( X ), Y ), T ), X ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), =( Z, Y ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), Y ), Z ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Y ), Z ) ) ), =( Z, Y ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.16/1.55 =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ) )
% 1.16/1.55 ],
% 1.16/1.55 [ =( X, Y ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X
% 1.16/1.55 ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ) )
% 1.16/1.55 ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.16/1.55 =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ) )
% 1.16/1.55 ],
% 1.16/1.55 [ ~( 'class_Orderings_Oorder'( X ) ), =( Y, Z ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Y ), Z ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), Y ), Z ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), =( Y, Z ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), Y ), Z ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Y ), Z ) ) ), =( Y, Z ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Y ), Z ) ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Y ), Z ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Opordered__cancel__semiring'( X ) ), hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ),
% 1.16/1.55 ~( hBOOL( hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.16/1.55 ) ), Y ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.16/1.55 ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.16/1.55 ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.16/1.55 ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_lessequals'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.16/1.55 ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Opordered__ring'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_lessequals'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.16/1.55 ) ],
% 1.16/1.55 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.16/1.55 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.16/1.55 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.16/1.55 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.16/1.55 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), Z ) ) ],
% 1.16/1.55 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.16/1.55 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.16/1.55 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.16/1.55 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.16/1.55 'c_Divides_Odiv__class_Omod'( Z, T, X ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.16/1.55 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.16/1.55 X ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.16/1.55 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.16/1.55 [ 'c_Natural_Oevalc'( X, Y, Z ), 'c_Natural_Oevalc'( T, Y, Z ), ~(
% 1.16/1.55 'c_Natural_Oevalc'( 'c_Com_Ocom_OCond'( U, T, X ), Y, Z ) ) ],
% 1.16/1.55 [ =( hAPP( 'c_Collect'( X ), hAPP( hAPP( 'c_COMBC'( X, 'tc_fun'( X,
% 1.16/1.55 'tc_bool' ), 'tc_bool' ), 'c_in'( X ) ), Y ) ), Y ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.16/1.55 [ =( hAPP( hAPP( 'c_Fun_Ofcomp'( X, Y, Z ), hAPP( hAPP( 'c_Fun_Ofcomp'(
% 1.16/1.55 X, T, Y ), U ), W ) ), V0 ), hAPP( hAPP( 'c_Fun_Ofcomp'( X, T, Z ), U ),
% 1.16/1.55 hAPP( hAPP( 'c_Fun_Ofcomp'( T, Y, Z ), W ), V0 ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.16/1.55 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.16/1.55 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.16/1.55 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.16/1.55 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.16/1.55 ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.16/1.55 ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.16/1.55 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.16/1.55 ), Z ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ) ],
% 1.16/1.55 [ ~( =( 'c_Com_Ocom_OSKIP', 'c_Com_Ocom_OSemi'( X, Y ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Oorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( 'c_lessequals'( 'tc_nat' ), Y ), X ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_lessequals'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( X ),
% 1.16/1.55 Z ), Y ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ],
% 1.16/1.55 [ =( X, Y ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X
% 1.16/1.55 ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X
% 1.16/1.55 ), hAPP( 'c_Suc', Y ) ) ) ) ],
% 1.16/1.55 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc'
% 1.16/1.55 , X ) ), hAPP( 'c_Suc', Y ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'(
% 1.16/1.55 'tc_nat' ), X ), Y ) ) ],
% 1.16/1.55 [ =( 'c_Nat_Onat_Onat__case'( X, Y, hAPP( 'c_Suc', Z ), T ), hAPP( Y, Z
% 1.16/1.55 ) ) ],
% 1.16/1.55 [ hBOOL( 'c_Orderings_Oorder__class_Omono'( 'c_Suc', 'tc_nat', 'tc_nat'
% 1.16/1.55 ) ) ],
% 1.16/1.55 [ =( 'c_Power_Opower_Opower'( X, Y, Z, hAPP( 'c_Suc', T ), U ), hAPP(
% 1.16/1.55 hAPP( Y, Z ), 'c_Power_Opower_Opower'( X, Y, Z, T, U ) ) ) ],
% 1.16/1.55 [ 'c_Fun_Oinj__on'( 'c_Suc', X, 'tc_nat', 'tc_nat' ) ],
% 1.16/1.55 [ =( 'c_Nat_Onat_Onat__rec'( X, Y, hAPP( 'c_Suc', Z ), T ), hAPP( hAPP(
% 1.16/1.55 Y, Z ), 'c_Nat_Onat_Onat__rec'( X, Y, Z, T ) ) ) ],
% 1.16/1.55 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 1.16/1.55 ,
% 1.16/1.55 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), hAPP( 'c_Suc', X ) ) ) ]
% 1.16/1.55 ,
% 1.16/1.55 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.16/1.55 X ) ), Y ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.16/1.55 'tc_nat' ), X ), Y ) ) ) ],
% 1.16/1.55 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.16/1.55 'c_Suc', Y ) ), hAPP( 'c_Suc', hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.16/1.55 'tc_nat' ), X ), Y ) ) ) ],
% 1.16/1.55 [ =( hAPP( hAPP( 'c_Orderings_Oord__class_Omax'( 'tc_nat' ), hAPP(
% 1.16/1.55 'c_Suc', X ) ), hAPP( 'c_Suc', Y ) ), hAPP( 'c_Suc', hAPP( hAPP(
% 1.16/1.55 'c_Orderings_Oord__class_Omax'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.16/1.55 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( 'c_Suc', X ), Y, 'tc_nat' ),
% 1.16/1.55 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =(
% 1.16/1.55 hAPP( 'c_Suc', 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ]
% 1.16/1.55 ,
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.16/1.55 'c_Nat_Osemiring__1__class_Oof__nat__aux'( Y, hAPP( 'c_Suc', Z ), T, X )
% 1.16/1.55 , 'c_Nat_Osemiring__1__class_Oof__nat__aux'( Y, Z, hAPP( Y, T ), X ) ) ]
% 1.16/1.55 ,
% 1.16/1.55 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( 'c_Suc',
% 1.16/1.55 X ) ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.16/1.55 'c_Suc', Y ) ) ) ],
% 1.16/1.55 [ ~( hBOOL( hAPP( X, 'c_Nat_Onat_Onat__case'( Y, Z, hAPP( 'c_Suc', T ),
% 1.16/1.55 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( Z, T ) ) ) ],
% 1.16/1.55 [ ~( hBOOL( hAPP( X, 'c_Nat_Onat_Onat__case'( Y, Z, hAPP( 'c_Suc', T ),
% 1.16/1.55 't_a' ) ) ) ), hBOOL( hAPP( X, hAPP( Z, T ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP(
% 1.16/1.55 'c_Suc', X ) ), Y ) ), =( hAPP( 'c_Suc', X ), Y ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.16/1.55 [ ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), X ), Y ) ) ), ~(
% 1.16/1.55 hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( 'c_Suc', Y ) ), X )
% 1.16/1.55 ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y
% 1.16/1.55 ) ), hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), Y ), X ) ) ],
% 1.16/1.55 [ =( hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( hAPP(
% 1.16/1.55 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), hAPP( 'c_Suc', X ) ), Y ) ),
% 1.16/1.55 hAPP( 'c_Suc', Z ) ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat'
% 1.16/1.55 ), hAPP( hAPP( 'c_HOL_Ominus__class_Ominus'( 'tc_nat' ), X ), Y ) ), Z )
% 1.16/1.55 ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), hAPP( 'c_Suc', X ) ),
% 1.16/1.55 hAPP( 'c_Suc', X ) ) ) ],
% 1.16/1.55 [ =( 'c_Orderings_Oord__class_Omin'( hAPP( 'c_Suc', X ), hAPP( 'c_Suc',
% 1.16/1.55 Y ), 'tc_nat' ), hAPP( 'c_Suc', 'c_Orderings_Oord__class_Omin'( X, Y,
% 1.16/1.55 'tc_nat' ) ) ) ],
% 1.16/1.55 [ =( X, hAPP( 'c_Suc', Y ) ), hBOOL( hAPP( hAPP( 'c_lessequals'(
% 1.16/1.55 'tc_nat' ), X ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' )
% 1.16/1.55 , X ), hAPP( 'c_Suc', Y ) ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), X ) ),
% 1.16/1.55 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP(
% 1.16/1.55 'c_Suc', X ) ) ) ],
% 1.16/1.55 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y )
% 1.16/1.55 ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ),
% 1.16/1.55 hAPP( 'c_Suc', X ) ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP(
% 1.16/1.55 'c_Suc', Y ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat'
% 1.16/1.55 ), Y ), X ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP(
% 1.16/1.55 'c_Suc', X ) ), hAPP( 'c_Suc', Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.16/1.55 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP(
% 1.16/1.55 'c_Suc', X ) ), hAPP( 'c_Suc', Y ) ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP(
% 1.16/1.55 'c_Suc', X ) ), hAPP( 'c_Suc', Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.16/1.55 [ =( hAPP( hAPP( 'c_Fun_Ofcomp'( X, Y, Z ), 'c_Product__Type_Oscomp'( T
% 1.16/1.55 , U, X, W, V0, Y ) ), V1 ), 'c_Product__Type_Oscomp'( T, hAPP( hAPP(
% 1.16/1.55 'c_COMBC'( W, 'tc_fun'( Y, Z ), 'tc_fun'( V0, Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_COMBB'( 'tc_fun'( V0, Y ), 'tc_fun'( 'tc_fun'( Y, Z ), 'tc_fun'( V0, Z
% 1.16/1.55 ) ), W ), 'c_Fun_Ofcomp'( V0, Y, Z ) ), U ) ), V1 ), X, W, V0, Z ) ) ]
% 1.16/1.55 ,
% 1.16/1.55 [ =( 'c_List_Ofilter'( X, 'c_List_Ofilter'( Y, Z, T ), T ),
% 1.16/1.55 'c_List_Ofilter'( hAPP( hAPP( 'c_COMBS'( T, 'tc_bool', 'tc_bool' ), hAPP(
% 1.16/1.55 hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'( 'tc_bool', 'tc_bool' ), T ),
% 1.16/1.55 'c_and' ), Y ) ), X ), Z, T ) ) ],
% 1.16/1.55 [ hBOOL( 'c_HOL_Oinduct__forall'( hAPP( hAPP( 'c_COMBS'( X, 'tc_bool',
% 1.16/1.55 'tc_bool' ), hAPP( hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'( 'tc_bool',
% 1.16/1.55 'tc_bool' ), X ), 'c_HOL_Oinduct__conj' ), Y ) ), Z ), X ) ), ~( hBOOL(
% 1.16/1.55 hAPP( hAPP( 'c_HOL_Oinduct__conj', 'c_HOL_Oinduct__forall'( Y, X ) ),
% 1.16/1.55 'c_HOL_Oinduct__forall'( Z, X ) ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( 'c_HOL_Oinduct__conj', 'c_HOL_Oinduct__forall'( X,
% 1.16/1.55 Y ) ), 'c_HOL_Oinduct__forall'( Z, Y ) ) ), ~( hBOOL(
% 1.16/1.55 'c_HOL_Oinduct__forall'( hAPP( hAPP( 'c_COMBS'( Y, 'tc_bool', 'tc_bool' )
% 1.16/1.55 , hAPP( hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'( 'tc_bool', 'tc_bool' ), Y )
% 1.16/1.55 , 'c_HOL_Oinduct__conj' ), X ) ), Z ), Y ) ) ) ],
% 1.16/1.55 [ 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( X ), hAPP( hAPP( 'c_COMBS'(
% 1.16/1.55 X, 'tc_bool', 'tc_bool' ), hAPP( hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'(
% 1.16/1.55 'tc_bool', 'tc_bool' ), X ), 'c_or' ), Y ) ), Z ) ), X ), ~(
% 1.16/1.55 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( X ), Z ), X ) ), ~(
% 1.16/1.55 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( X ), Y ), X ) ) ],
% 1.16/1.55 [ 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( X ), Y ), X ), ~(
% 1.16/1.55 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( X ), hAPP( hAPP( 'c_COMBS'( X
% 1.16/1.55 , 'tc_bool', 'tc_bool' ), hAPP( hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'(
% 1.16/1.55 'tc_bool', 'tc_bool' ), X ), 'c_or' ), Z ) ), Y ) ), X ) ) ],
% 1.16/1.55 [ 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( X ), Y ), X ), ~(
% 1.16/1.55 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( X ), hAPP( hAPP( 'c_COMBS'( X
% 1.16/1.55 , 'tc_bool', 'tc_bool' ), hAPP( hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'(
% 1.16/1.55 'tc_bool', 'tc_bool' ), X ), 'c_or' ), Y ) ), Z ) ), X ) ) ],
% 1.16/1.55 [ =( hAPP( 'c_Collect'( X ), hAPP( hAPP( 'c_COMBS'( X, 'tc_bool',
% 1.16/1.55 'tc_bool' ), hAPP( hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'( 'tc_bool',
% 1.16/1.55 'tc_bool' ), X ), 'c_or' ), Y ) ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.16/1.55 , hAPP( 'c_Collect'( X ), Y ) ), hAPP( 'c_Collect'( X ), Z ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y
% 1.16/1.55 , X ), Z ), T ) ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( U, X ), W ), V0 )
% 1.16/1.55 ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( X, X ), 'c_Fun_Oid'( X ) ), hAPP(
% 1.16/1.55 'c_Collect'( X ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( Y, 'tc_bool' ),
% 1.16/1.55 'tc_bool', X ), 'c_Ex'( Y ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( Y,
% 1.16/1.55 'tc_fun'( U, 'tc_bool' ) ), 'tc_fun'( Y, 'tc_bool' ), X ), hAPP(
% 1.16/1.55 'c_COMBB'( 'tc_fun'( U, 'tc_bool' ), 'tc_bool', Y ), 'c_Ex'( U ) ) ),
% 1.16/1.55 hAPP( hAPP( 'c_COMBC'( X, 'tc_fun'( Y, 'tc_fun'( U, 'tc_bool' ) ),
% 1.16/1.55 'tc_fun'( Y, 'tc_fun'( U, 'tc_bool' ) ) ), hAPP( hAPP( 'c_COMBB'(
% 1.16/1.55 'tc_fun'( Y, 'tc_fun'( 'tc_fun'( U, 'tc_bool' ), 'tc_fun'( U, 'tc_bool' )
% 1.16/1.55 ) ), 'tc_fun'( 'tc_fun'( Y, 'tc_fun'( U, 'tc_bool' ) ), 'tc_fun'( Y,
% 1.16/1.55 'tc_fun'( U, 'tc_bool' ) ) ), X ), 'c_COMBS'( Y, 'tc_fun'( U, 'tc_bool' )
% 1.16/1.55 , 'tc_fun'( U, 'tc_bool' ) ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( Y,
% 1.16/1.55 'tc_fun'( U, 'tc_fun'( 'tc_bool', 'tc_bool' ) ) ), 'tc_fun'( Y, 'tc_fun'(
% 1.16/1.55 'tc_fun'( U, 'tc_bool' ), 'tc_fun'( U, 'tc_bool' ) ) ), X ), hAPP(
% 1.16/1.55 'c_COMBB'( 'tc_fun'( U, 'tc_fun'( 'tc_bool', 'tc_bool' ) ), 'tc_fun'(
% 1.16/1.55 'tc_fun'( U, 'tc_bool' ), 'tc_fun'( U, 'tc_bool' ) ), Y ), 'c_COMBS'( U,
% 1.16/1.55 'tc_bool', 'tc_bool' ) ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( Y, 'tc_fun'(
% 1.16/1.55 U, 'tc_bool' ) ), 'tc_fun'( Y, 'tc_fun'( U, 'tc_fun'( 'tc_bool',
% 1.16/1.55 'tc_bool' ) ) ), X ), hAPP( 'c_COMBB'( 'tc_fun'( U, 'tc_bool' ), 'tc_fun'(
% 1.16/1.55 U, 'tc_fun'( 'tc_bool', 'tc_bool' ) ), Y ), hAPP( 'c_COMBB'( 'tc_bool',
% 1.16/1.55 'tc_fun'( 'tc_bool', 'tc_bool' ), U ), 'c_and' ) ) ), hAPP( hAPP(
% 1.16/1.55 'c_COMBC'( X, 'tc_fun'( Y, 'tc_fun'( U, X ) ), 'tc_fun'( Y, 'tc_fun'( U,
% 1.16/1.55 'tc_bool' ) ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 'tc_fun'( U, X ),
% 1.16/1.55 'tc_fun'( U, 'tc_bool' ) ), 'tc_fun'( 'tc_fun'( Y, 'tc_fun'( U, X ) ),
% 1.16/1.55 'tc_fun'( Y, 'tc_fun'( U, 'tc_bool' ) ) ), X ), 'c_COMBB'( 'tc_fun'( U, X
% 1.16/1.55 ), 'tc_fun'( U, 'tc_bool' ), Y ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( X,
% 1.16/1.55 'tc_bool' ), 'tc_fun'( 'tc_fun'( U, X ), 'tc_fun'( U, 'tc_bool' ) ), X )
% 1.16/1.55 , 'c_COMBB'( X, 'tc_bool', U ) ), 'c_fequal'( X ) ) ) ), hAPP( hAPP(
% 1.16/1.55 'c_COMBC'( Y, 'tc_fun'( U, X ), 'tc_fun'( U, X ) ), hAPP( hAPP( 'c_COMBB'(
% 1.16/1.55 'tc_fun'( X, X ), 'tc_fun'( 'tc_fun'( U, X ), 'tc_fun'( U, X ) ), Y ),
% 1.16/1.55 'c_COMBB'( X, X, U ) ), hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'( X, X ), Y ),
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ) ), Z ) ) ), W ) ) ) ) ) ), hAPP( hAPP(
% 1.16/1.55 'c_COMBC'( Y, 'tc_fun'( U, 'tc_bool' ), 'tc_fun'( U, 'tc_bool' ) ), hAPP(
% 1.16/1.55 hAPP( 'c_COMBB'( 'tc_fun'( 'tc_bool', 'tc_bool' ), 'tc_fun'( 'tc_fun'( U
% 1.16/1.55 , 'tc_bool' ), 'tc_fun'( U, 'tc_bool' ) ), Y ), 'c_COMBB'( 'tc_bool',
% 1.16/1.55 'tc_bool', U ) ), hAPP( hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'( 'tc_bool',
% 1.16/1.55 'tc_bool' ), Y ), 'c_and' ), hAPP( hAPP( 'c_COMBC'( Y, 'tc_fun'( Y,
% 1.16/1.55 'tc_bool' ), 'tc_bool' ), 'c_in'( Y ) ), T ) ) ) ), hAPP( hAPP( 'c_COMBC'(
% 1.16/1.55 U, 'tc_fun'( U, 'tc_bool' ), 'tc_bool' ), 'c_in'( U ) ), V0 ) ) ) ) ) ) )
% 1.16/1.55 ), ~( 'c_Fun_Oinj__on'( 'c_split'( hAPP( hAPP( 'c_COMBC'( Y, 'tc_fun'( U
% 1.16/1.55 , X ), 'tc_fun'( U, X ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( X, X ),
% 1.16/1.55 'tc_fun'( 'tc_fun'( U, X ), 'tc_fun'( U, X ) ), Y ), 'c_COMBB'( X, X, U )
% 1.16/1.55 ), hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'( X, X ), Y ),
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ) ), Z ) ) ), W ), Y, U, X ),
% 1.16/1.55 'c_Product__Type_OSigma'( T, hAPP( 'c_COMBK'( 'tc_fun'( U, 'tc_bool' ), Y
% 1.16/1.55 ), V0 ), Y, U ), 'tc_prod'( Y, U ), X ) ) ],
% 1.16/1.55 [ ~( =( 'c_ATP__Linkup_Osko__FunDef__Xfundef__ex1__uniqueness__1__1'( X
% 1.16/1.55 , Y, Z, T, U ), Z ) ), ~( hBOOL( hAPP( hAPP( X, Y ), Z ) ) ), =( hAPP( W
% 1.16/1.55 , Y ), hAPP( hAPP( hAPP( 'c_COMBS'( T, 'tc_fun'( U, 'tc_bool' ), U ),
% 1.16/1.55 hAPP( hAPP( 'c_COMBB'( U, 'tc_fun'( 'tc_fun'( U, 'tc_bool' ), U ), T ),
% 1.16/1.55 'c_FunDef_OTHE__default'( U ) ), V0 ) ), X ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.16/1.55 X, Y ), hAPP( W, Y ) ) ) ) ],
% 1.16/1.55 [ ~( =( 'c_ATP__Linkup_Osko__FunDef__Xfundef__ex1__existence__1__1'( X,
% 1.16/1.55 Y, Z, T, U ), Z ) ), ~( hBOOL( hAPP( hAPP( X, Y ), Z ) ) ), hBOOL( hAPP(
% 1.16/1.55 hAPP( X, Y ), hAPP( hAPP( hAPP( 'c_COMBS'( T, 'tc_fun'( U, 'tc_bool' ), U
% 1.16/1.55 ), hAPP( hAPP( 'c_COMBB'( U, 'tc_fun'( 'tc_fun'( U, 'tc_bool' ), U ), T
% 1.16/1.55 ), 'c_FunDef_OTHE__default'( U ) ), W ) ), X ), Y ) ) ) ],
% 1.16/1.55 [ ~( =( 'c_ATP__Linkup_Osko__FunDef__Xfundef__ex1__iff__1__1'( X, Y, Z,
% 1.16/1.55 T, U ), Z ) ), ~( hBOOL( hAPP( hAPP( X, Y ), Z ) ) ), hBOOL( hAPP( hAPP(
% 1.16/1.55 X, Y ), hAPP( hAPP( hAPP( 'c_COMBS'( T, 'tc_fun'( U, 'tc_bool' ), U ),
% 1.16/1.55 hAPP( hAPP( 'c_COMBB'( U, 'tc_fun'( 'tc_fun'( U, 'tc_bool' ), U ), T ),
% 1.16/1.55 'c_FunDef_OTHE__default'( U ) ), W ) ), X ), Y ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( X, Y ), hAPP( hAPP( hAPP( 'c_COMBS'( Z, 'tc_fun'( T
% 1.16/1.55 , 'tc_bool' ), T ), hAPP( hAPP( 'c_COMBB'( T, 'tc_fun'( 'tc_fun'( T,
% 1.16/1.55 'tc_bool' ), T ), Z ), 'c_FunDef_OTHE__default'( T ) ), U ) ), X ), Y ) )
% 1.16/1.55 ), hBOOL( hAPP( hAPP( X, Y ),
% 1.16/1.55 'c_ATP__Linkup_Osko__FunDef__Xfundef__ex1__existence__1__1'( X, Y, W, Z,
% 1.16/1.55 T ) ) ), ~( hBOOL( hAPP( hAPP( X, Y ), W ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( X, Y ),
% 1.16/1.55 'c_ATP__Linkup_Osko__FunDef__Xfundef__ex1__iff__1__1'( X, Y, Z, T, U ) )
% 1.16/1.55 ), ~( hBOOL( hAPP( hAPP( X, Y ), Z ) ) ), hBOOL( hAPP( hAPP( X, Y ),
% 1.16/1.55 hAPP( hAPP( hAPP( 'c_COMBS'( T, 'tc_fun'( U, 'tc_bool' ), U ), hAPP( hAPP(
% 1.16/1.55 'c_COMBB'( U, 'tc_fun'( 'tc_fun'( U, 'tc_bool' ), U ), T ),
% 1.16/1.55 'c_FunDef_OTHE__default'( U ) ), W ) ), X ), Y ) ) ) ],
% 1.16/1.55 [ =( hAPP( X, Y ), hAPP( hAPP( hAPP( 'c_COMBS'( Z, 'tc_fun'( T,
% 1.16/1.55 'tc_bool' ), T ), hAPP( hAPP( 'c_COMBB'( T, 'tc_fun'( 'tc_fun'( T,
% 1.16/1.55 'tc_bool' ), T ), Z ), 'c_FunDef_OTHE__default'( T ) ), U ) ), W ), Y ) )
% 1.16/1.55 , ~( hBOOL( hAPP( hAPP( W, Y ), hAPP( X, Y ) ) ) ), hBOOL( hAPP( hAPP( W
% 1.16/1.55 , Y ), 'c_ATP__Linkup_Osko__FunDef__Xfundef__ex1__uniqueness__1__1'( W, Y
% 1.16/1.55 , V0, Z, T ) ) ), ~( hBOOL( hAPP( hAPP( W, Y ), V0 ) ) ) ],
% 1.16/1.55 [ ~( =( 'c_ATP__Linkup_Osko__FunDef__Xfundef__ex1__iff__1__1'( X, Y, Z,
% 1.16/1.55 T, U ), Z ) ), ~( hBOOL( hAPP( hAPP( X, Y ), Z ) ) ), =( hAPP( hAPP( hAPP(
% 1.16/1.55 'c_COMBS'( T, 'tc_fun'( U, 'tc_bool' ), U ), hAPP( hAPP( 'c_COMBB'( U,
% 1.16/1.55 'tc_fun'( 'tc_fun'( U, 'tc_bool' ), U ), T ), 'c_FunDef_OTHE__default'( U
% 1.16/1.55 ) ), W ) ), X ), Y ), V0 ), ~( hBOOL( hAPP( hAPP( X, Y ), V0 ) ) ) ]
% 1.16/1.55 ,
% 1.16/1.55 [ =( hAPP( hAPP( hAPP( 'c_COMBS'( X, 'tc_fun'( Y, 'tc_bool' ), Y ), hAPP(
% 1.16/1.55 hAPP( 'c_COMBB'( Y, 'tc_fun'( 'tc_fun'( Y, 'tc_bool' ), Y ), X ),
% 1.16/1.55 'c_FunDef_OTHE__default'( Y ) ), Z ) ), T ), U ), hAPP( Z, U ) ), hBOOL(
% 1.16/1.55 hAPP( W, U ) ), ~( hBOOL( hAPP( W,
% 1.16/1.55 'c_ATP__Linkup_Osko__FunDef__Xfundef__default__value__1__1'( W, T, X, Y )
% 1.16/1.55 ) ) ) ],
% 1.16/1.55 [ =( hAPP( hAPP( hAPP( 'c_COMBS'( X, 'tc_fun'( Y, 'tc_bool' ), Y ), hAPP(
% 1.16/1.55 hAPP( 'c_COMBB'( Y, 'tc_fun'( 'tc_fun'( Y, 'tc_bool' ), Y ), X ),
% 1.16/1.55 'c_FunDef_OTHE__default'( Y ) ), Z ) ), T ), U ), W ), ~( hBOOL( hAPP(
% 1.16/1.55 hAPP( T, U ), W ) ) ), hBOOL( hAPP( hAPP( T, U ),
% 1.16/1.55 'c_ATP__Linkup_Osko__FunDef__Xfundef__ex1__iff__1__1'( T, U, V0, X, Y ) )
% 1.16/1.55 ), ~( hBOOL( hAPP( hAPP( T, U ), V0 ) ) ) ],
% 1.16/1.55 [ =( X, hAPP( 'c_Suc',
% 1.16/1.55 'c_Natural_Osko__Natural__Xevaln__elim__cases__6__1'( Y, X, Z, T ) ) ),
% 1.16/1.55 ~( hBOOL( hAPP( hAPP( hAPP( hAPP( 'c_Natural_Oevaln', 'c_Com_Ocom_OBODY'(
% 1.16/1.55 Y ) ), Z ), X ), T ) ) ) ],
% 1.16/1.55 [ =( hAPP( 'c_Collect'( X ), hAPP( hAPP( 'c_COMBS'( X, 'tc_bool',
% 1.16/1.55 'tc_bool' ), hAPP( hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'( 'tc_bool',
% 1.16/1.55 'tc_bool' ), X ), 'c_implies' ), Y ) ), Z ) ), hAPP( hAPP(
% 1.16/1.55 'c_Lattices_Oupper__semilattice__class_Osup'( 'tc_fun'( X, 'tc_bool' ) )
% 1.16/1.55 , hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ), hAPP(
% 1.16/1.55 'c_Collect'( X ), Y ) ) ), hAPP( 'c_Collect'( X ), Z ) ) ) ],
% 1.16/1.55 [ ~( 'class_HOL_Oord'( X ) ), =( 'c_Hilbert__Choice_OGreatestM'( Y, Z, T
% 1.16/1.55 , X ), 'c_Hilbert__Choice_OEps'( hAPP( hAPP( 'c_COMBS'( T, 'tc_bool',
% 1.16/1.55 'tc_bool' ), hAPP( hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'( 'tc_bool',
% 1.16/1.55 'tc_bool' ), T ), 'c_and' ), Z ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( T,
% 1.16/1.55 'tc_bool' ), 'tc_bool', T ), 'c_All'( T ) ), hAPP( hAPP( 'c_COMBB'(
% 1.16/1.55 'tc_fun'( T, 'tc_bool' ), 'tc_fun'( T, 'tc_bool' ), T ), hAPP( 'c_COMBS'(
% 1.16/1.55 T, 'tc_bool', 'tc_bool' ), hAPP( hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'(
% 1.16/1.55 'tc_bool', 'tc_bool' ), T ), 'c_implies' ), Z ) ) ), hAPP( hAPP(
% 1.16/1.55 'c_COMBB'( X, 'tc_fun'( T, 'tc_bool' ), T ), hAPP( 'c_COMBC'( T, X,
% 1.16/1.55 'tc_bool' ), hAPP( hAPP( 'c_COMBB'( X, 'tc_fun'( X, 'tc_bool' ), T ),
% 1.16/1.55 'c_lessequals'( X ) ), Y ) ) ), Y ) ) ) ), T ) ) ],
% 1.16/1.55 [ =( 'c_Predicate_OPowp'( X, 'v_B', 't_a' ), hAPP( 'c_All'( 't_a' ),
% 1.16/1.55 hAPP( hAPP( 'c_COMBS'( 't_a', 'tc_bool', 'tc_bool' ), hAPP( hAPP(
% 1.16/1.55 'c_COMBB'( 'tc_bool', 'tc_fun'( 'tc_bool', 'tc_bool' ), 't_a' ),
% 1.16/1.55 'c_implies' ), hAPP( hAPP( 'c_COMBC'( 't_a', 'tc_fun'( 't_a', 'tc_bool' )
% 1.16/1.55 , 'tc_bool' ), 'c_in'( 't_a' ) ), 'v_B' ) ) ), X ) ) ) ],
% 1.16/1.55 [ =( 'c_Orderings_Oord_OLeast'( X, 'v_P', 't_a' ), 'c_The'( hAPP( hAPP(
% 1.16/1.55 'c_COMBS'( 't_a', 'tc_bool', 'tc_bool' ), hAPP( hAPP( 'c_COMBB'(
% 1.16/1.55 'tc_bool', 'tc_fun'( 'tc_bool', 'tc_bool' ), 't_a' ), 'c_and' ), 'v_P' )
% 1.16/1.55 ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 't_a', 'tc_bool' ), 'tc_bool', 't_a'
% 1.16/1.55 ), 'c_All'( 't_a' ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 't_a', 'tc_bool'
% 1.16/1.55 ), 'tc_fun'( 't_a', 'tc_bool' ), 't_a' ), hAPP( 'c_COMBS'( 't_a',
% 1.16/1.55 'tc_bool', 'tc_bool' ), hAPP( hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'(
% 1.16/1.55 'tc_bool', 'tc_bool' ), 't_a' ), 'c_implies' ), 'v_P' ) ) ), X ) ) ),
% 1.16/1.55 't_a' ) ) ],
% 1.16/1.55 [ =( hAPP( X, Y ), hAPP( Z, hAPP( 'c_Collect'( T ), hAPP( hAPP(
% 1.16/1.55 'c_COMBB'( 'tc_fun'( T, 'tc_bool' ), 'tc_bool', T ), 'c_All'( T ) ), hAPP(
% 1.16/1.55 hAPP( 'c_COMBB'( 'tc_fun'( T, 'tc_bool' ), 'tc_fun'( T, 'tc_bool' ), T )
% 1.16/1.55 , hAPP( 'c_COMBS'( T, 'tc_bool', 'tc_bool' ), hAPP( hAPP( 'c_COMBB'(
% 1.16/1.55 'tc_bool', 'tc_fun'( 'tc_bool', 'tc_bool' ), T ), 'c_implies' ), hAPP(
% 1.16/1.55 hAPP( 'c_COMBC'( T, 'tc_fun'( T, 'tc_bool' ), 'tc_bool' ), 'c_in'( T ) )
% 1.16/1.55 , Y ) ) ) ), U ) ) ) ) ), ~( 'c_Complete__Lattice_Ocomplete__lattice'( X
% 1.16/1.55 , Z, U, W, V0, V1, V2, V3, T ) ) ],
% 1.16/1.55 [ =( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'v_n' ), hAPP(
% 1.16/1.55 'c_lessequals'( 'tc_nat' ), hAPP( 'c_Suc', 'v_n' ) ) ) ],
% 1.16/1.55 [ =( 'c_lessequals'( 'tc_bool' ), 'c_implies' ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( hAPP( hAPP( 'c_Natural_Oevaln', X ), Y ), Z ), T )
% 1.16/1.55 ), hBOOL( hAPP( hAPP( hAPP( hAPP( 'c_Natural_Oevaln', U ), Y ), Z ), T )
% 1.16/1.55 ), ~( hBOOL( hAPP( hAPP( hAPP( hAPP( 'c_Natural_Oevaln',
% 1.16/1.55 'c_Com_Ocom_OCond'( W, U, X ) ), Y ), Z ), T ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( X, Y ) ), =( Z, Y ), ~( hBOOL( hAPP( hAPP( hAPP( hAPP(
% 1.16/1.55 'c_Natural_Oevaln', 'c_Com_Ocom_OWhile'( X, T ) ), Y ), U ), Z ) ) ) ]
% 1.16/1.55 ,
% 1.16/1.55 [ hBOOL( hAPP( hAPP( hAPP( hAPP( 'c_Natural_Oevaln', X ), Y ), Z ), T )
% 1.16/1.55 ), ~( hBOOL( hAPP( hAPP( 'c_lessequals'( 'tc_nat' ), U ), Z ) ) ), ~(
% 1.16/1.55 hBOOL( hAPP( hAPP( hAPP( hAPP( 'c_Natural_Oevaln', X ), Y ), U ), T ) ) )
% 1.16/1.55 ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( hAPP( hAPP( 'c_Natural_Oevaln', 'c_Com_Ocom_OSKIP'
% 1.16/1.55 ), X ), Y ), X ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( hAPP( hAPP( 'c_Natural_Oevaln', 'c_Com_Ocom_OCond'(
% 1.16/1.55 X, Y, Z ) ), T ), U ), W ) ), ~( hBOOL( hAPP( hAPP( hAPP( hAPP(
% 1.16/1.55 'c_Natural_Oevaln', Z ), T ), U ), W ) ) ), hBOOL( hAPP( X, T ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( hAPP( hAPP( 'c_Natural_Oevaln', X ), Y ), Z ), T )
% 1.16/1.55 ), hBOOL( hAPP( U, Y ) ), ~( hBOOL( hAPP( hAPP( hAPP( hAPP(
% 1.16/1.55 'c_Natural_Oevaln', 'c_Com_Ocom_OCond'( U, W, X ) ), Y ), Z ), T ) ) ) ]
% 1.16/1.55 ,
% 1.16/1.55 [ hBOOL( hAPP( hAPP( hAPP( hAPP( 'c_Natural_Oevaln', X ), Y ),
% 1.16/1.55 'c_Natural_Osko__Natural__Xevaln__max2__1__1'( Z, X, T, Y, U, W ) ), W )
% 1.16/1.55 ), ~( hBOOL( hAPP( hAPP( hAPP( hAPP( 'c_Natural_Oevaln', X ), Y ), V0 )
% 1.16/1.55 , W ) ) ), ~( hBOOL( hAPP( hAPP( hAPP( hAPP( 'c_Natural_Oevaln', Z ), T )
% 1.16/1.55 , V1 ), U ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( hAPP( hAPP( 'c_Natural_Oevaln', X ), Y ),
% 1.16/1.55 'c_Natural_Osko__Natural__Xevaln__max2__1__1'( X, Z, Y, T, U, W ) ), U )
% 1.16/1.55 ), ~( hBOOL( hAPP( hAPP( hAPP( hAPP( 'c_Natural_Oevaln', Z ), T ), V0 )
% 1.16/1.55 , W ) ) ), ~( hBOOL( hAPP( hAPP( hAPP( hAPP( 'c_Natural_Oevaln', X ), Y )
% 1.16/1.55 , V1 ), U ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( hAPP( hAPP( 'c_Natural_Oevaln', 'c_Com_Ocom_OWhile'(
% 1.16/1.55 X, Y ) ), Z ), T ), Z ) ), hBOOL( hAPP( X, Z ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( hAPP( hAPP( 'c_Natural_Oevaln', 'c_Com_Ocom_OCond'(
% 1.16/1.55 X, Y, Z ) ), T ), U ), W ) ), ~( hBOOL( hAPP( hAPP( hAPP( hAPP(
% 1.16/1.55 'c_Natural_Oevaln', Y ), T ), U ), W ) ) ), ~( hBOOL( hAPP( X, T ) ) ) ]
% 1.16/1.55 ,
% 1.16/1.55 [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( hAPP( hAPP( hAPP(
% 1.16/1.55 'c_Natural_Oevaln', Z ), Y ), T ), U ) ), ~( hBOOL( hAPP( hAPP( hAPP(
% 1.16/1.55 hAPP( 'c_Natural_Oevaln', 'c_Com_Ocom_OCond'( X, Z, W ) ), Y ), T ), U )
% 1.16/1.55 ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( hAPP( hAPP( 'c_Natural_Oevaln', 'c_Com_Ocom_OWhile'(
% 1.16/1.55 X, Y ) ), Z ), T ), U ) ), ~( hBOOL( hAPP( hAPP( hAPP( hAPP(
% 1.16/1.55 'c_Natural_Oevaln', 'c_Com_Ocom_OWhile'( X, Y ) ), W ), T ), U ) ) ), ~(
% 1.16/1.55 hBOOL( hAPP( hAPP( hAPP( hAPP( 'c_Natural_Oevaln', Y ), Z ), T ), W ) ) )
% 1.16/1.55 , ~( hBOOL( hAPP( X, Z ) ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( hAPP( hAPP( hAPP( 'c_Natural_Oevaln', 'c_Com_Ocom_OSemi'(
% 1.16/1.55 X, Y ) ), Z ), T ), U ) ), ~( hBOOL( hAPP( hAPP( hAPP( hAPP(
% 1.16/1.55 'c_Natural_Oevaln', Y ), W ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP( hAPP(
% 1.16/1.55 hAPP( 'c_Natural_Oevaln', X ), Z ), T ), W ) ) ) ],
% 1.16/1.55 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( hAPP( hAPP( 'c_Natural_Oevaln',
% 1.16/1.55 'c_Com_Ocom_OSKIP' ), Y ), Z ), X ) ) ) ],
% 1.16/1.55 [ 'c_Natural_Oevalc'( X, Y, Z ), ~( hBOOL( hAPP( hAPP( hAPP( hAPP(
% 1.16/1.55 'c_Natural_Oevaln', X ), Y ), T ), Z ) ) ) ],
% 1.16/1.55 [ 'c_Natural_Oevalc'( X, Y, Z ), ~( hBOOL( hAPP( hAPP( hAPP( hAPP(
% 1.16/1.55 'c_Natural_Oevaln', X ), Y ), T ), Z ) ) ) ],
% 1.16/1.55 [ ~( hBOOL( hAPP( X, hAPP( 'c_Hoare__Mirabelle_Otriple_Otriple__case'( Y
% 1.16/1.55 , 't_b', 't_a' ), 'c_Hoare__Mirabelle_Otriple_Otriple'( Z, T, U, 't_b' )
% 1.16/1.55 ) ) ) ), hBOOL( hAPP( X, hAPP( hAPP( hAPP( Y, Z ), T ), U ) ) ) ],
% 1.16/1.55 [ ~( hBOOL( hAPP( X, hAPP( 'c_Hoare__Mirabelle_Otriple_Otriple__case'( Y
% 1.16/1.55 , 't_b', 't_a' ), 'c_Hoare__Mirabelle_Otriple_Otriple'( Z, T, U, 't_b' )
% 1.16/1.55 ) ) ) ), hBOOL( hAPP( X, hAPP( hAPP( hAPP( Y, Z ), T ), U ) ) ) ],
% 1.16/1.55 [ =( hAPP( 'c_Hoare__Mirabelle_Otriple_Otriple__case'( X, Y, Z ),
% 1.16/1.55 'c_Hoare__Mirabelle_Otriple_Otriple'( T, U, W, Y ) ), hAPP( hAPP( hAPP( X
% 1.16/1.55 , T ), U ), W ) ) ],
% 1.16/1.55 [ =( 'c_Relation_Otrans'( 'v_r', 't_a' ), hAPP( 'c_All'( 't_a' ), hAPP(
% 1.16/1.55 hAPP( 'c_COMBB'( 'tc_fun'( 't_a', 'tc_bool' ), 'tc_bool', 't_a' ),
% 1.16/1.55 'c_All'( 't_a' ) ), hAPP( hAPP( 'c_COMBS'( 't_a', 'tc_fun'( 't_a',
% 1.16/1.55 'tc_bool' ), 'tc_fun'( 't_a', 'tc_bool' ) ), hAPP( hAPP( 'c_COMBB'(
% 1.16/1.55 'tc_fun'( 't_a', 'tc_fun'( 'tc_bool', 'tc_bool' ) ), 'tc_fun'( 'tc_fun'(
% 1.16/1.55 't_a', 'tc_bool' ), 'tc_fun'( 't_a', 'tc_bool' ) ), 't_a' ), 'c_COMBS'(
% 1.16/1.55 't_a', 'tc_bool', 'tc_bool' ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 't_a',
% 1.16/1.55 'tc_bool' ), 'tc_fun'( 't_a', 'tc_fun'( 'tc_bool', 'tc_bool' ) ), 't_a' )
% 1.16/1.55 , hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'( 'tc_bool', 'tc_bool' ), 't_a' ),
% 1.16/1.55 'c_implies' ) ), hAPP( hAPP( 'c_COMBC'( 't_a', 'tc_fun'( 'tc_prod'( 't_a'
% 1.16/1.55 , 't_a' ), 'tc_bool' ), 'tc_fun'( 't_a', 'tc_bool' ) ), hAPP( hAPP(
% 1.16/1.55 'c_COMBB'( 'tc_fun'( 't_a', 'tc_fun'( 'tc_fun'( 'tc_prod'( 't_a', 't_a' )
% 1.16/1.55 , 'tc_bool' ), 'tc_bool' ) ), 'tc_fun'( 'tc_fun'( 'tc_prod'( 't_a', 't_a'
% 1.16/1.55 ), 'tc_bool' ), 'tc_fun'( 't_a', 'tc_bool' ) ), 't_a' ), 'c_COMBC'(
% 1.16/1.55 't_a', 'tc_fun'( 'tc_prod'( 't_a', 't_a' ), 'tc_bool' ), 'tc_bool' ) ),
% 1.16/1.55 hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 't_a', 'tc_prod'( 't_a', 't_a' ) ),
% 1.16/1.55 'tc_fun'( 't_a', 'tc_fun'( 'tc_fun'( 'tc_prod'( 't_a', 't_a' ), 'tc_bool'
% 1.16/1.55 ), 'tc_bool' ) ), 't_a' ), hAPP( 'c_COMBB'( 'tc_prod'( 't_a', 't_a' ),
% 1.16/1.55 'tc_fun'( 'tc_fun'( 'tc_prod'( 't_a', 't_a' ), 'tc_bool' ), 'tc_bool' ),
% 1.16/1.55 't_a' ), 'c_in'( 'tc_prod'( 't_a', 't_a' ) ) ) ), 'c_Pair'( 't_a', 't_a'
% 1.16/1.55 ) ) ) ), 'v_r' ) ) ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.55 't_a', 'tc_bool' ) ), 'tc_fun'( 't_a', 'tc_bool' ), 't_a' ), hAPP(
% 1.16/1.55 'c_COMBB'( 'tc_fun'( 't_a', 'tc_bool' ), 'tc_bool', 't_a' ), 'c_All'(
% 1.16/1.55 't_a' ) ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 't_a', 'tc_bool' ),
% 1.16/1.55 'tc_fun'( 't_a', 'tc_fun'( 't_a', 'tc_bool' ) ), 't_a' ), hAPP( 'c_COMBC'(
% 1.16/1.55 't_a', 'tc_fun'( 't_a', 'tc_bool' ), 'tc_fun'( 't_a', 'tc_bool' ) ), hAPP(
% 1.16/1.55 hAPP( 'c_COMBB'( 'tc_fun'( 't_a', 'tc_fun'( 'tc_bool', 'tc_bool' ) ),
% 1.16/1.55 'tc_fun'( 'tc_fun'( 't_a', 'tc_bool' ), 'tc_fun'( 't_a', 'tc_bool' ) ),
% 1.16/1.55 't_a' ), 'c_COMBS'( 't_a', 'tc_bool', 'tc_bool' ) ), hAPP( hAPP(
% 1.16/1.55 'c_COMBB'( 'tc_fun'( 't_a', 'tc_bool' ), 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.55 'tc_bool', 'tc_bool' ) ), 't_a' ), hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'(
% 1.16/1.55 'tc_bool', 'tc_bool' ), 't_a' ), 'c_implies' ) ), hAPP( hAPP( 'c_COMBC'(
% 1.16/1.55 't_a', 'tc_fun'( 'tc_prod'( 't_a', 't_a' ), 'tc_bool' ), 'tc_fun'( 't_a'
% 1.16/1.55 , 'tc_bool' ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.55 'tc_fun'( 'tc_prod'( 't_a', 't_a' ), 'tc_bool' ), 'tc_bool' ) ), 'tc_fun'(
% 1.16/1.55 'tc_fun'( 'tc_prod'( 't_a', 't_a' ), 'tc_bool' ), 'tc_fun'( 't_a',
% 1.16/1.55 'tc_bool' ) ), 't_a' ), 'c_COMBC'( 't_a', 'tc_fun'( 'tc_prod'( 't_a',
% 1.16/1.55 't_a' ), 'tc_bool' ), 'tc_bool' ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'(
% 1.16/1.55 't_a', 'tc_prod'( 't_a', 't_a' ) ), 'tc_fun'( 't_a', 'tc_fun'( 'tc_fun'(
% 1.16/1.55 'tc_prod'( 't_a', 't_a' ), 'tc_bool' ), 'tc_bool' ) ), 't_a' ), hAPP(
% 1.16/1.55 'c_COMBB'( 'tc_prod'( 't_a', 't_a' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 1.16/1.55 't_a', 't_a' ), 'tc_bool' ), 'tc_bool' ), 't_a' ), 'c_in'( 'tc_prod'(
% 1.16/1.55 't_a', 't_a' ) ) ) ), 'c_Pair'( 't_a', 't_a' ) ) ) ), 'v_r' ) ) ) ) ),
% 1.16/1.55 hAPP( hAPP( 'c_COMBC'( 't_a', 'tc_fun'( 'tc_prod'( 't_a', 't_a' ),
% 1.16/1.55 'tc_bool' ), 'tc_fun'( 't_a', 'tc_bool' ) ), hAPP( hAPP( 'c_COMBB'(
% 1.16/1.55 'tc_fun'( 't_a', 'tc_fun'( 'tc_fun'( 'tc_prod'( 't_a', 't_a' ), 'tc_bool'
% 1.16/1.55 ), 'tc_bool' ) ), 'tc_fun'( 'tc_fun'( 'tc_prod'( 't_a', 't_a' ),
% 1.16/1.55 'tc_bool' ), 'tc_fun'( 't_a', 'tc_bool' ) ), 't_a' ), 'c_COMBC'( 't_a',
% 1.16/1.55 'tc_fun'( 'tc_prod'( 't_a', 't_a' ), 'tc_bool' ), 'tc_bool' ) ), hAPP(
% 1.16/1.55 hAPP( 'c_COMBB'( 'tc_fun'( 't_a', 'tc_prod'( 't_a', 't_a' ) ), 'tc_fun'(
% 1.16/1.55 't_a', 'tc_fun'( 'tc_fun'( 'tc_prod'( 't_a', 't_a' ), 'tc_bool' ),
% 1.16/1.55 'tc_bool' ) ), 't_a' ), hAPP( 'c_COMBB'( 'tc_prod'( 't_a', 't_a' ),
% 1.16/1.55 'tc_fun'( 'tc_fun'( 'tc_prod'( 't_a', 't_a' ), 'tc_bool' ), 'tc_bool' ),
% 1.16/1.55 't_a' ), 'c_in'( 'tc_prod'( 't_a', 't_a' ) ) ) ), 'c_Pair'( 't_a', 't_a'
% 1.16/1.55 ) ) ) ), 'v_r' ) ) ) ) ) ) ) ],
% 1.16/1.55 [ 'c_Recdef_Oadm__wf'( X, hAPP( hAPP( 'c_COMBC'( 'tc_fun'( Y, Z ),
% 1.16/1.55 'tc_fun'( Y, Y ), 'tc_fun'( Y, Z ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( Y
% 1.16/1.55 , 'tc_fun'( Y, Z ) ), 'tc_fun'( 'tc_fun'( Y, Y ), 'tc_fun'( Y, Z ) ),
% 1.16/1.55 'tc_fun'( Y, Z ) ), 'c_COMBS'( Y, Y, Z ) ), hAPP( hAPP( 'c_COMBB'(
% 1.16/1.55 'tc_fun'( Y, 'tc_fun'( Y, Z ) ), 'tc_fun'( Y, 'tc_fun'( Y, Z ) ),
% 1.16/1.55 'tc_fun'( Y, Z ) ), hAPP( 'c_COMBB'( 'tc_fun'( Y, Z ), 'tc_fun'( Y, Z ),
% 1.16/1.55 Y ), T ) ), hAPP( hAPP( 'c_COMBC'( 'tc_fun'( Y, Z ), 'tc_fun'( 'tc_prod'(
% 1.16/1.55 Y, Y ), 'tc_bool' ), 'tc_fun'( Y, 'tc_fun'( Y, Z ) ) ), 'c_Recdef_Ocut'(
% 1.16/1.55 Y, Z ) ), X ) ) ) ), 'c_COMBI'( Y ) ), Y, Z ) ],
% 1.16/1.55 [ =( 'c_Record_Oiso__tuple__update__accessor__cong__assist'( 'v_upd',
% 1.16/1.55 'v_acc', 't_a', 't_b' ), hAPP( hAPP( 'c_and', hAPP( 'c_All'( 'tc_fun'(
% 1.16/1.55 't_a', 't_a' ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 't_b', 'tc_bool' ),
% 1.16/1.55 'tc_bool', 'tc_fun'( 't_a', 't_a' ) ), 'c_All'( 't_b' ) ), hAPP( hAPP(
% 1.16/1.55 'c_COMBS'( 'tc_fun'( 't_a', 't_a' ), 'tc_fun'( 't_b', 't_b' ), 'tc_fun'(
% 1.16/1.55 't_b', 'tc_bool' ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 't_b', 'tc_fun'(
% 1.16/1.55 't_b', 'tc_bool' ) ), 'tc_fun'( 'tc_fun'( 't_b', 't_b' ), 'tc_fun'( 't_b'
% 1.16/1.55 , 'tc_bool' ) ), 'tc_fun'( 't_a', 't_a' ) ), 'c_COMBS'( 't_b', 't_b',
% 1.16/1.55 'tc_bool' ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 't_b', 't_b' ), 'tc_fun'(
% 1.16/1.55 't_b', 'tc_fun'( 't_b', 'tc_bool' ) ), 'tc_fun'( 't_a', 't_a' ) ), hAPP(
% 1.16/1.55 'c_COMBB'( 't_b', 'tc_fun'( 't_b', 'tc_bool' ), 't_b' ), 'c_fequal'(
% 1.16/1.55 't_b' ) ) ), hAPP( hAPP( 'c_COMBC'( 'tc_fun'( 't_a', 't_a' ), 'tc_fun'(
% 1.16/1.55 't_b', 't_b' ), 'tc_fun'( 't_b', 't_b' ) ), hAPP( hAPP( 'c_COMBB'(
% 1.16/1.55 'tc_fun'( 't_b', 'tc_fun'( 't_b', 't_b' ) ), 'tc_fun'( 'tc_fun'( 't_b',
% 1.16/1.55 't_b' ), 'tc_fun'( 't_b', 't_b' ) ), 'tc_fun'( 't_a', 't_a' ) ),
% 1.16/1.55 'c_COMBS'( 't_b', 't_b', 't_b' ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'(
% 1.16/1.55 't_b', 'tc_fun'( 't_a', 't_a' ) ), 'tc_fun'( 't_b', 'tc_fun'( 't_b',
% 1.16/1.55 't_b' ) ), 'tc_fun'( 't_a', 't_a' ) ), hAPP( 'c_COMBB'( 'tc_fun'( 't_a',
% 1.16/1.55 't_a' ), 'tc_fun'( 't_b', 't_b' ), 't_b' ), 'v_upd' ) ), hAPP( hAPP(
% 1.16/1.55 'c_COMBB'( 'tc_fun'( 't_b', 't_a' ), 'tc_fun'( 't_b', 'tc_fun'( 't_a',
% 1.16/1.55 't_a' ) ), 'tc_fun'( 't_a', 't_a' ) ), hAPP( 'c_COMBB'( 't_a', 'tc_fun'(
% 1.16/1.55 't_a', 't_a' ), 't_b' ), 'c_COMBK'( 't_a', 't_a' ) ) ), hAPP( hAPP(
% 1.16/1.55 'c_COMBC'( 'tc_fun'( 't_a', 't_a' ), 'tc_fun'( 't_b', 't_a' ), 'tc_fun'(
% 1.16/1.55 't_b', 't_a' ) ), 'c_COMBB'( 't_a', 't_a', 't_b' ) ), 'v_acc' ) ) ) ) ),
% 1.16/1.55 'c_COMBI'( 't_b' ) ) ) ) ), 'v_upd' ) ) ) ), hAPP( 'c_All'( 't_b' ), hAPP(
% 1.16/1.55 hAPP( 'c_COMBS'( 't_b', 't_b', 'tc_bool' ), hAPP( hAPP( 'c_COMBB'( 't_b'
% 1.16/1.55 , 'tc_fun'( 't_b', 'tc_bool' ), 't_b' ), 'c_fequal'( 't_b' ) ), hAPP(
% 1.16/1.55 'v_upd', 'c_Fun_Oid'( 't_a' ) ) ) ), 'c_COMBI'( 't_b' ) ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_HOL_Oord'( X ) ), =( 'c_Hilbert__Choice_OLeastM'( Y, Z, T, X
% 1.16/1.55 ), 'c_Hilbert__Choice_OEps'( hAPP( hAPP( 'c_COMBS'( T, 'tc_bool',
% 1.16/1.55 'tc_bool' ), hAPP( hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'( 'tc_bool',
% 1.16/1.55 'tc_bool' ), T ), 'c_and' ), Z ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( T,
% 1.16/1.55 'tc_bool' ), 'tc_bool', T ), 'c_All'( T ) ), hAPP( hAPP( 'c_COMBB'(
% 1.16/1.55 'tc_fun'( T, 'tc_bool' ), 'tc_fun'( T, 'tc_bool' ), T ), hAPP( 'c_COMBS'(
% 1.16/1.55 T, 'tc_bool', 'tc_bool' ), hAPP( hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'(
% 1.16/1.55 'tc_bool', 'tc_bool' ), T ), 'c_implies' ), Z ) ) ), hAPP( hAPP(
% 1.16/1.55 'c_COMBC'( T, 'tc_fun'( T, X ), 'tc_fun'( T, 'tc_bool' ) ), hAPP( hAPP(
% 1.16/1.55 'c_COMBB'( 'tc_fun'( X, 'tc_bool' ), 'tc_fun'( 'tc_fun'( T, X ), 'tc_fun'(
% 1.16/1.55 T, 'tc_bool' ) ), T ), 'c_COMBB'( X, 'tc_bool', T ) ), hAPP( hAPP(
% 1.16/1.55 'c_COMBB'( X, 'tc_fun'( X, 'tc_bool' ), T ), 'c_lessequals'( X ) ), Y ) )
% 1.16/1.55 ), Y ) ) ) ), T ) ) ],
% 1.16/1.55 [ ~( =( hAPP( X, hAPP( Y, 'c_List_Osko__List__Xfoldl__apply__inv__1__1'(
% 1.16/1.55 X, Y, Z, T ) ) ), 'c_List_Osko__List__Xfoldl__apply__inv__1__1'( X, Y, Z
% 1.16/1.55 , T ) ) ), =( 'c_List_Ofoldl'( U, hAPP( X, W ), V0, T, V1 ), hAPP( X,
% 1.16/1.55 'c_List_Ofoldl'( hAPP( hAPP( 'c_COMBB'( 'tc_fun'( V1, T ), 'tc_fun'( V1,
% 1.16/1.55 Z ), Z ), hAPP( 'c_COMBB'( T, Z, V1 ), Y ) ), hAPP( hAPP( 'c_COMBB'( T,
% 1.16/1.55 'tc_fun'( V1, T ), Z ), U ), X ) ), W, V0, Z, V1 ) ) ) ],
% 1.16/1.55 [ =( 'c_List_Ofoldl'( X, Y, 'c_List_Omap'( Z, T, U, W ), V0, W ),
% 1.16/1.55 'c_List_Ofoldl'( hAPP( hAPP( 'c_COMBC'( V0, 'tc_fun'( U, W ), 'tc_fun'( U
% 1.16/1.55 , V0 ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( W, V0 ), 'tc_fun'( 'tc_fun'( U
% 1.16/1.55 , W ), 'tc_fun'( U, V0 ) ), V0 ), 'c_COMBB'( W, V0, U ) ), X ) ), Z ), Y
% 1.16/1.55 , T, V0, U ) ) ],
% 1.16/1.55 [ 'c_Lattices_Oboolean__algebra'( hAPP( hAPP( 'c_COMBC'( X, 'tc_fun'( X
% 1.16/1.55 , X ), 'tc_fun'( X, X ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( X, X ),
% 1.16/1.55 'tc_fun'( 'tc_fun'( X, X ), 'tc_fun'( X, X ) ), X ), 'c_COMBB'( X, X, X )
% 1.16/1.55 ), Y ) ), Z ), Z, hAPP( 'c_COMBC'( X, X, 'tc_bool' ), T ), hAPP(
% 1.16/1.55 'c_COMBC'( X, X, 'tc_bool' ), U ), Y, W, V0, V1, X ), ~(
% 1.16/1.55 'c_Lattices_Oboolean__algebra'( V2, Z, T, U, W, Y, V1, V0, X ) ) ],
% 1.16/1.55 [ 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( X ), hAPP( hAPP( 'c_COMBB'(
% 1.16/1.55 'tc_fun'( Y, 'tc_bool' ), 'tc_bool', X ), 'c_Ex'( Y ) ), hAPP( hAPP(
% 1.16/1.55 'c_COMBC'( X, 'tc_fun'( Y, 'tc_bool' ), 'tc_fun'( Y, 'tc_bool' ) ), hAPP(
% 1.16/1.55 hAPP( 'c_COMBB'( 'tc_fun'( Y, 'tc_fun'( 'tc_bool', 'tc_bool' ) ),
% 1.16/1.55 'tc_fun'( 'tc_fun'( Y, 'tc_bool' ), 'tc_fun'( Y, 'tc_bool' ) ), X ),
% 1.16/1.55 'c_COMBS'( Y, 'tc_bool', 'tc_bool' ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'(
% 1.16/1.55 Y, 'tc_bool' ), 'tc_fun'( Y, 'tc_fun'( 'tc_bool', 'tc_bool' ) ), X ),
% 1.16/1.55 hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'( 'tc_bool', 'tc_bool' ), Y ),
% 1.16/1.55 'c_and' ) ), hAPP( hAPP( 'c_COMBC'( X, 'tc_fun'( Y, X ), 'tc_fun'( Y,
% 1.16/1.55 'tc_bool' ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( X, 'tc_bool' ), 'tc_fun'(
% 1.16/1.55 'tc_fun'( Y, X ), 'tc_fun'( Y, 'tc_bool' ) ), X ), 'c_COMBB'( X,
% 1.16/1.55 'tc_bool', Y ) ), 'c_fequal'( X ) ) ), Z ) ) ) ), T ) ) ), X ), ~(
% 1.16/1.55 'c_Finite__Set_Ofinite'( hAPP( 'c_Collect'( Y ), T ), Y ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Oorder'( X ) ), =(
% 1.16/1.55 'c_Orderings_Oorder_Ostrict__mono'( Y, Z, X ), hAPP( hAPP( 'c_COMBB'(
% 1.16/1.55 'tc_fun'( Z, 'tc_bool' ), 'tc_bool', 'tc_fun'( Z, X ) ), 'c_All'( Z ) ),
% 1.16/1.55 hAPP( hAPP( 'c_COMBB'( 'tc_fun'( Z, 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'(
% 1.16/1.55 Z, 'tc_bool' ), 'tc_fun'( Z, X ) ), hAPP( 'c_COMBB'( 'tc_fun'( Z,
% 1.16/1.55 'tc_bool' ), 'tc_bool', Z ), 'c_All'( Z ) ) ), hAPP( hAPP( 'c_COMBB'(
% 1.16/1.55 'tc_fun'( Z, 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_fun'( Z,
% 1.16/1.55 'tc_bool' ) ), 'tc_fun'( Z, X ) ), hAPP( 'c_COMBS'( Z, 'tc_fun'( Z,
% 1.16/1.55 'tc_bool' ), 'tc_fun'( Z, 'tc_bool' ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'(
% 1.16/1.55 Z, 'tc_fun'( 'tc_bool', 'tc_bool' ) ), 'tc_fun'( 'tc_fun'( Z, 'tc_bool' )
% 1.16/1.55 , 'tc_fun'( Z, 'tc_bool' ) ), Z ), 'c_COMBS'( Z, 'tc_bool', 'tc_bool' ) )
% 1.16/1.55 , hAPP( hAPP( 'c_COMBB'( 'tc_fun'( Z, 'tc_bool' ), 'tc_fun'( Z, 'tc_fun'(
% 1.16/1.55 'tc_bool', 'tc_bool' ) ), Z ), hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'(
% 1.16/1.55 'tc_bool', 'tc_bool' ), Z ), 'c_implies' ) ), Y ) ) ) ), hAPP( hAPP(
% 1.16/1.55 'c_COMBS'( 'tc_fun'( Z, X ), 'tc_fun'( Z, X ), 'tc_fun'( Z, 'tc_fun'( Z,
% 1.16/1.55 'tc_bool' ) ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( Z, 'tc_fun'( 'tc_fun'(
% 1.16/1.55 Z, X ), 'tc_fun'( Z, 'tc_bool' ) ) ), 'tc_fun'( 'tc_fun'( Z, X ),
% 1.16/1.55 'tc_fun'( Z, 'tc_fun'( Z, 'tc_bool' ) ) ), 'tc_fun'( Z, X ) ), 'c_COMBC'(
% 1.16/1.55 Z, 'tc_fun'( Z, X ), 'tc_fun'( Z, 'tc_bool' ) ) ), hAPP( hAPP( 'c_COMBB'(
% 1.16/1.55 'tc_fun'( Z, 'tc_fun'( X, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_fun'( 'tc_fun'(
% 1.16/1.55 Z, X ), 'tc_fun'( Z, 'tc_bool' ) ) ), 'tc_fun'( Z, X ) ), hAPP( 'c_COMBB'(
% 1.16/1.55 'tc_fun'( X, 'tc_bool' ), 'tc_fun'( 'tc_fun'( Z, X ), 'tc_fun'( Z,
% 1.16/1.55 'tc_bool' ) ), Z ), 'c_COMBB'( X, 'tc_bool', Z ) ) ), hAPP( 'c_COMBB'( X
% 1.16/1.55 , 'tc_fun'( X, 'tc_bool' ), Z ), 'c_HOL_Oord__class_Oless'( X ) ) ) ) ),
% 1.16/1.55 'c_COMBI'( 'tc_fun'( Z, X ) ) ) ) ) ) ), ~( 'c_Orderings_Oorder'( T, Y, Z
% 1.16/1.55 ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Oorder'( X ) ), =( 'c_Orderings_Oorder_Omono'( Y,
% 1.16/1.55 Z, X ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( Z, 'tc_bool' ), 'tc_bool',
% 1.16/1.55 'tc_fun'( Z, X ) ), 'c_All'( Z ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( Z,
% 1.16/1.55 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ), 'tc_fun'( Z, X ) )
% 1.16/1.55 , hAPP( 'c_COMBB'( 'tc_fun'( Z, 'tc_bool' ), 'tc_bool', Z ), 'c_All'( Z )
% 1.16/1.55 ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( Z, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.16/1.55 'tc_fun'( Z, 'tc_fun'( Z, 'tc_bool' ) ), 'tc_fun'( Z, X ) ), hAPP(
% 1.16/1.55 'c_COMBS'( Z, 'tc_fun'( Z, 'tc_bool' ), 'tc_fun'( Z, 'tc_bool' ) ), hAPP(
% 1.16/1.55 hAPP( 'c_COMBB'( 'tc_fun'( Z, 'tc_fun'( 'tc_bool', 'tc_bool' ) ),
% 1.16/1.55 'tc_fun'( 'tc_fun'( Z, 'tc_bool' ), 'tc_fun'( Z, 'tc_bool' ) ), Z ),
% 1.16/1.55 'c_COMBS'( Z, 'tc_bool', 'tc_bool' ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'(
% 1.16/1.55 Z, 'tc_bool' ), 'tc_fun'( Z, 'tc_fun'( 'tc_bool', 'tc_bool' ) ), Z ),
% 1.16/1.55 hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'( 'tc_bool', 'tc_bool' ), Z ),
% 1.16/1.55 'c_implies' ) ), Y ) ) ) ), hAPP( hAPP( 'c_COMBS'( 'tc_fun'( Z, X ),
% 1.16/1.55 'tc_fun'( Z, X ), 'tc_fun'( Z, 'tc_fun'( Z, 'tc_bool' ) ) ), hAPP( hAPP(
% 1.16/1.55 'c_COMBB'( 'tc_fun'( Z, 'tc_fun'( 'tc_fun'( Z, X ), 'tc_fun'( Z,
% 1.16/1.55 'tc_bool' ) ) ), 'tc_fun'( 'tc_fun'( Z, X ), 'tc_fun'( Z, 'tc_fun'( Z,
% 1.16/1.55 'tc_bool' ) ) ), 'tc_fun'( Z, X ) ), 'c_COMBC'( Z, 'tc_fun'( Z, X ),
% 1.16/1.55 'tc_fun'( Z, 'tc_bool' ) ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( Z,
% 1.16/1.55 'tc_fun'( X, 'tc_bool' ) ), 'tc_fun'( Z, 'tc_fun'( 'tc_fun'( Z, X ),
% 1.16/1.55 'tc_fun'( Z, 'tc_bool' ) ) ), 'tc_fun'( Z, X ) ), hAPP( 'c_COMBB'(
% 1.16/1.55 'tc_fun'( X, 'tc_bool' ), 'tc_fun'( 'tc_fun'( Z, X ), 'tc_fun'( Z,
% 1.16/1.55 'tc_bool' ) ), Z ), 'c_COMBB'( X, 'tc_bool', Z ) ) ), hAPP( 'c_COMBB'( X
% 1.16/1.55 , 'tc_fun'( X, 'tc_bool' ), Z ), 'c_lessequals'( X ) ) ) ) ), 'c_COMBI'(
% 1.16/1.55 'tc_fun'( Z, X ) ) ) ) ) ) ), ~( 'c_Orderings_Oorder'( Y, T, Z ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Oorder'( 't_a' ) ), ~( 'class_Orderings_Oorder'(
% 1.16/1.55 't_b' ) ), =( 'c_Orderings_Oorder__class_Omono'( 'v_f', 't_a', 't_b' ),
% 1.16/1.55 hAPP( 'c_All'( 't_a' ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 't_a', 'tc_bool'
% 1.16/1.55 ), 'tc_bool', 't_a' ), 'c_All'( 't_a' ) ), hAPP( hAPP( 'c_COMBS'( 't_a'
% 1.16/1.55 , 'tc_fun'( 't_a', 'tc_bool' ), 'tc_fun'( 't_a', 'tc_bool' ) ), hAPP(
% 1.16/1.55 hAPP( 'c_COMBB'( 'tc_fun'( 't_a', 'tc_fun'( 'tc_bool', 'tc_bool' ) ),
% 1.16/1.55 'tc_fun'( 'tc_fun'( 't_a', 'tc_bool' ), 'tc_fun'( 't_a', 'tc_bool' ) ),
% 1.16/1.55 't_a' ), 'c_COMBS'( 't_a', 'tc_bool', 'tc_bool' ) ), hAPP( hAPP(
% 1.16/1.55 'c_COMBB'( 'tc_fun'( 't_a', 'tc_bool' ), 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.55 'tc_bool', 'tc_bool' ) ), 't_a' ), hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'(
% 1.16/1.55 'tc_bool', 'tc_bool' ), 't_a' ), 'c_implies' ) ), 'c_lessequals'( 't_a' )
% 1.16/1.55 ) ) ), hAPP( hAPP( 'c_COMBC'( 't_a', 'tc_fun'( 't_a', 't_b' ), 'tc_fun'(
% 1.16/1.55 't_a', 'tc_bool' ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 't_b', 'tc_bool' )
% 1.16/1.55 , 'tc_fun'( 'tc_fun'( 't_a', 't_b' ), 'tc_fun'( 't_a', 'tc_bool' ) ),
% 1.16/1.55 't_a' ), 'c_COMBB'( 't_b', 'tc_bool', 't_a' ) ), hAPP( hAPP( 'c_COMBB'(
% 1.16/1.55 't_b', 'tc_fun'( 't_b', 'tc_bool' ), 't_a' ), 'c_lessequals'( 't_b' ) ),
% 1.16/1.55 'v_f' ) ) ), 'v_f' ) ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_Orderings_Oorder'( 't_a' ) ), ~( 'class_Orderings_Oorder'(
% 1.16/1.55 't_b' ) ), =( 'c_Orderings_Oorder__class_Ostrict__mono'( 'v_f', 't_a',
% 1.16/1.55 't_b' ), hAPP( 'c_All'( 't_a' ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 't_a',
% 1.16/1.55 'tc_bool' ), 'tc_bool', 't_a' ), 'c_All'( 't_a' ) ), hAPP( hAPP(
% 1.16/1.55 'c_COMBS'( 't_a', 'tc_fun'( 't_a', 'tc_bool' ), 'tc_fun'( 't_a',
% 1.16/1.55 'tc_bool' ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.55 'tc_bool', 'tc_bool' ) ), 'tc_fun'( 'tc_fun'( 't_a', 'tc_bool' ),
% 1.16/1.55 'tc_fun'( 't_a', 'tc_bool' ) ), 't_a' ), 'c_COMBS'( 't_a', 'tc_bool',
% 1.16/1.55 'tc_bool' ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 't_a', 'tc_bool' ),
% 1.16/1.55 'tc_fun'( 't_a', 'tc_fun'( 'tc_bool', 'tc_bool' ) ), 't_a' ), hAPP(
% 1.16/1.55 'c_COMBB'( 'tc_bool', 'tc_fun'( 'tc_bool', 'tc_bool' ), 't_a' ),
% 1.16/1.55 'c_implies' ) ), 'c_HOL_Oord__class_Oless'( 't_a' ) ) ) ), hAPP( hAPP(
% 1.16/1.55 'c_COMBC'( 't_a', 'tc_fun'( 't_a', 't_b' ), 'tc_fun'( 't_a', 'tc_bool' )
% 1.16/1.55 ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 't_b', 'tc_bool' ), 'tc_fun'(
% 1.16/1.55 'tc_fun'( 't_a', 't_b' ), 'tc_fun'( 't_a', 'tc_bool' ) ), 't_a' ),
% 1.16/1.55 'c_COMBB'( 't_b', 'tc_bool', 't_a' ) ), hAPP( hAPP( 'c_COMBB'( 't_b',
% 1.16/1.55 'tc_fun'( 't_b', 'tc_bool' ), 't_a' ), 'c_HOL_Oord__class_Oless'( 't_b' )
% 1.16/1.55 ), 'v_f' ) ) ), 'v_f' ) ) ) ) ) ],
% 1.16/1.55 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y
% 1.16/1.55 , X ), Z ), T ) ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( U, X ), W ), V0 )
% 1.16/1.55 ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( Y, X ), hAPP( hAPP( 'c_COMBC'( Y
% 1.16/1.55 , 'tc_fun'( U, 'tc_bool' ), X ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( U, X )
% 1.16/1.55 , 'tc_fun'( 'tc_fun'( U, 'tc_bool' ), X ), Y ), 'c_Finite__Set_Osetsum'(
% 1.16/1.55 U, X ) ), hAPP( hAPP( 'c_COMBC'( Y, 'tc_fun'( U, X ), 'tc_fun'( U, X ) )
% 1.16/1.55 , hAPP( hAPP( 'c_COMBB'( 'tc_fun'( X, X ), 'tc_fun'( 'tc_fun'( U, X ),
% 1.16/1.55 'tc_fun'( U, X ) ), Y ), 'c_COMBB'( X, X, U ) ), hAPP( hAPP( 'c_COMBB'( X
% 1.16/1.55 , 'tc_fun'( X, X ), Y ), 'c_HOL_Otimes__class_Otimes'( X ) ), Z ) ) ), W
% 1.16/1.55 ) ) ), V0 ) ), T ) ) ],
% 1.16/1.55 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.16/1.55 'c_Finite__Set_Osetsum'( Y, X ), hAPP( hAPP( 'c_COMBC'( Y, 'tc_fun'( Z,
% 1.16/1.55 'tc_bool' ), X ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( Z, X ), 'tc_fun'(
% 1.16/1.55 'tc_fun'( Z, 'tc_bool' ), X ), Y ), 'c_Finite__Set_Osetsum'( Z, X ) ), T
% 1.16/1.55 ) ), U ) ), W ), hAPP( hAPP( 'c_Finite__Set_Osetsum'( Z, X ), hAPP( hAPP(
% 1.16/1.55 'c_COMBC'( Z, 'tc_fun'( Y, 'tc_bool' ), X ), hAPP( hAPP( 'c_COMBB'(
% 1.16/1.55 'tc_fun'( Y, X ), 'tc_fun'( 'tc_fun'( Y, 'tc_bool' ), X ), Z ),
% 1.16/1.55 'c_Finite__Set_Osetsum'( Y, X ) ), hAPP( 'c_COMBC'( Y, Z, X ), T ) ) ), W
% 1.16/1.55 ) ), U ) ) ],
% 1.16/1.55 [ hBOOL( hAPP( 'c_Hoare__Mirabelle_Otriple__valid'( X, Y ), Z ) ), ~(
% 1.16/1.55 hBOOL( hAPP( 'c_Hoare__Mirabelle_Otriple_Otriple__case'( hAPP( hAPP(
% 1.16/1.55 'c_COMBB'( 'tc_fun'( 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( Y, 'tc_fun'(
% 1.16/1.55 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( Y, 'tc_bool' ) ) ), 'tc_fun'(
% 1.16/1.55 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.55 'tc_bool' ) ), 'tc_bool' ) ), 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.55 'tc_bool' ) ) ), hAPP( 'c_COMBB'( 'tc_fun'( 'tc_fun'( Y, 'tc_fun'(
% 1.16/1.55 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'(
% 1.16/1.55 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_bool' ),
% 1.16/1.55 'tc_Com_Ocom' ), hAPP( 'c_COMBB'( 'tc_fun'( Y, 'tc_bool' ), 'tc_bool',
% 1.16/1.55 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), 'c_All'( Y ) ) )
% 1.16/1.55 ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( Y
% 1.16/1.55 , 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( Y, 'tc_fun'(
% 1.16/1.55 'tc_Com_Ostate', 'tc_bool' ) ) ) ), 'tc_fun'( 'tc_Com_Ocom', 'tc_fun'(
% 1.16/1.55 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( Y,
% 1.16/1.55 'tc_bool' ) ) ), 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) )
% 1.16/1.55 , hAPP( 'c_COMBB'( 'tc_fun'( 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.55 'tc_bool' ) ), 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ),
% 1.16/1.56 'tc_fun'( 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'(
% 1.16/1.56 Y, 'tc_bool' ) ), 'tc_Com_Ocom' ), hAPP( 'c_COMBB'( 'tc_fun'( Y, 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( Y, 'tc_bool' ), 'tc_fun'( Y,
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), hAPP( 'c_COMBB'( 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ), 'tc_bool', Y ), 'c_All'( 'tc_Com_Ostate' )
% 1.16/1.56 ) ) ) ), hAPP( hAPP( 'c_COMBC'( 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ) ), 'tc_fun'( 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( Y, 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ) ) ) ), 'tc_fun'( 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( Y,
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( Y, 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ) ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'(
% 1.16/1.56 'tc_fun'( 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'(
% 1.16/1.56 Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'( 'tc_fun'( Y,
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( Y, 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ) ), 'tc_fun'( 'tc_fun'( 'tc_Com_Ocom',
% 1.16/1.56 'tc_fun'( 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'(
% 1.16/1.56 Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ) ), 'tc_fun'( 'tc_Com_Ocom'
% 1.16/1.56 , 'tc_fun'( 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ),
% 1.16/1.56 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ) ) ), 'tc_fun'( Y
% 1.16/1.56 , 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), 'c_COMBB'( 'tc_fun'(
% 1.16/1.56 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( Y,
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'( 'tc_fun'( Y,
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( Y, 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_Com_Ocom' ) ), hAPP( hAPP(
% 1.16/1.56 'c_COMBB'( 'tc_fun'( 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' )
% 1.16/1.56 ), 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'(
% 1.16/1.56 'tc_fun'( 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'(
% 1.16/1.56 Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'( 'tc_fun'( Y,
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( Y, 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ) ), 'tc_fun'( Y, 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ), 'c_COMBB'( 'tc_fun'( Y, 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ) ), 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ) )
% 1.16/1.56 , hAPP( hAPP( 'c_COMBB'( 'tc_fun'( Y, 'tc_fun'( 'tc_fun'( 'tc_Com_Ostate'
% 1.16/1.56 , 'tc_bool' ), 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'(
% 1.16/1.56 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( Y,
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'( Y, 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ), 'c_COMBS'( Y, 'tc_fun'( 'tc_Com_Ostate'
% 1.16/1.56 , 'tc_bool' ), 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), hAPP( hAPP(
% 1.16/1.56 'c_COMBB'( 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_bool',
% 1.16/1.56 'tc_bool' ) ) ), 'tc_fun'( Y, 'tc_fun'( 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ), 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'( Y,
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), hAPP( 'c_COMBB'( 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_fun'( 'tc_bool', 'tc_bool' ) ), 'tc_fun'( 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ), 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), Y
% 1.16/1.56 ), 'c_COMBS'( 'tc_Com_Ostate', 'tc_bool', 'tc_bool' ) ) ), hAPP(
% 1.16/1.56 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ), 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_fun'( 'tc_bool', 'tc_bool' ) ), Y ), hAPP( 'c_COMBB'(
% 1.16/1.56 'tc_bool', 'tc_fun'( 'tc_bool', 'tc_bool' ), 'tc_Com_Ostate' ),
% 1.16/1.56 'c_implies' ) ) ) ) ) ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 'tc_fun'( Y,
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( Y, 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ) ), 'tc_fun'(
% 1.16/1.56 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( Y,
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_Com_Ocom' ), hAPP(
% 1.16/1.56 'c_COMBB'( 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate'
% 1.16/1.56 , 'tc_bool' ) ), 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) )
% 1.16/1.56 , hAPP( 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ) ), 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ), Y ), hAPP(
% 1.16/1.56 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ), 'tc_bool',
% 1.16/1.56 'tc_Com_Ostate' ), 'c_All'( 'tc_Com_Ostate' ) ) ) ) ), hAPP( hAPP(
% 1.16/1.56 'c_COMBB'( 'tc_fun'( 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ), 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'(
% 1.16/1.56 'tc_fun'( Y, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( Y,
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ) ),
% 1.16/1.56 'tc_Com_Ocom' ), 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ),
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), Y )
% 1.16/1.56 ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ), 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) )
% 1.16/1.56 , 'tc_fun'( 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ), 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ),
% 1.16/1.56 'tc_Com_Ocom' ), 'c_COMBC'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ), 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), hAPP( hAPP(
% 1.16/1.56 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'(
% 1.16/1.56 'tc_bool', 'tc_bool' ) ) ), 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ), 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) )
% 1.16/1.56 , 'tc_Com_Ocom' ), hAPP( 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'(
% 1.16/1.56 'tc_bool', 'tc_bool' ) ), 'tc_fun'( 'tc_fun'( 'tc_Com_Ostate', 'tc_bool'
% 1.16/1.56 ), 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_Com_Ostate' ),
% 1.16/1.56 'c_COMBS'( 'tc_Com_Ostate', 'tc_bool', 'tc_bool' ) ) ), hAPP( hAPP(
% 1.16/1.56 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ) ), 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_fun'( 'tc_bool', 'tc_bool' ) ) ), 'tc_Com_Ocom' ), hAPP( 'c_COMBB'(
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ), 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_fun'( 'tc_bool', 'tc_bool' ) ), 'tc_Com_Ostate' ), hAPP( 'c_COMBB'(
% 1.16/1.56 'tc_bool', 'tc_fun'( 'tc_bool', 'tc_bool' ), 'tc_Com_Ostate' ),
% 1.16/1.56 'c_implies' ) ) ), hAPP( hAPP( 'c_COMBC'( 'tc_Com_Ocom', 'tc_nat',
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ),
% 1.16/1.56 hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_nat',
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'( 'tc_nat', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ),
% 1.16/1.56 'tc_Com_Ocom' ), 'c_COMBC'( 'tc_Com_Ostate', 'tc_nat', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ), 'c_Natural_Oevaln' ) ), X ) ) ) ) ) ) )
% 1.16/1.56 ) ), Y, 'tc_bool' ), Z ) ) ) ],
% 1.16/1.56 [ hBOOL( hAPP( 'c_Hoare__Mirabelle_Otriple_Otriple__case'( hAPP( hAPP(
% 1.16/1.56 'c_COMBB'( 'tc_fun'( 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( X, 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( X, 'tc_bool' ) ) ), 'tc_fun'(
% 1.16/1.56 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ) ), 'tc_bool' ) ), 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ) ) ), hAPP( 'c_COMBB'( 'tc_fun'( 'tc_fun'( X, 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( X, 'tc_bool' ) ), 'tc_fun'(
% 1.16/1.56 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_bool' ),
% 1.16/1.56 'tc_Com_Ocom' ), hAPP( 'c_COMBB'( 'tc_fun'( X, 'tc_bool' ), 'tc_bool',
% 1.16/1.56 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), 'c_All'( X ) ) )
% 1.16/1.56 ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( X
% 1.16/1.56 , 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( X, 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ) ), 'tc_fun'( 'tc_Com_Ocom', 'tc_fun'(
% 1.16/1.56 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( X,
% 1.16/1.56 'tc_bool' ) ) ), 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) )
% 1.16/1.56 , hAPP( 'c_COMBB'( 'tc_fun'( 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ) ), 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ),
% 1.16/1.56 'tc_fun'( 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'(
% 1.16/1.56 X, 'tc_bool' ) ), 'tc_Com_Ocom' ), hAPP( 'c_COMBB'( 'tc_fun'( X, 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( X, 'tc_bool' ), 'tc_fun'( X,
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), hAPP( 'c_COMBB'( 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ), 'tc_bool', X ), 'c_All'( 'tc_Com_Ostate' )
% 1.16/1.56 ) ) ) ), hAPP( hAPP( 'c_COMBC'( 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ) ), 'tc_fun'( 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( X, 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ) ) ) ), 'tc_fun'( 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( X,
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( X, 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ) ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'(
% 1.16/1.56 'tc_fun'( 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'(
% 1.16/1.56 X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'( 'tc_fun'( X,
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( X, 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ) ), 'tc_fun'( 'tc_fun'( 'tc_Com_Ocom',
% 1.16/1.56 'tc_fun'( 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'(
% 1.16/1.56 X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ) ), 'tc_fun'( 'tc_Com_Ocom'
% 1.16/1.56 , 'tc_fun'( 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ),
% 1.16/1.56 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ) ) ), 'tc_fun'( X
% 1.16/1.56 , 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), 'c_COMBB'( 'tc_fun'(
% 1.16/1.56 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( X,
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'( 'tc_fun'( X,
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( X, 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_Com_Ocom' ) ), hAPP( hAPP(
% 1.16/1.56 'c_COMBB'( 'tc_fun'( 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' )
% 1.16/1.56 ), 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'(
% 1.16/1.56 'tc_fun'( 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'(
% 1.16/1.56 X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'( 'tc_fun'( X,
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( X, 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ) ), 'tc_fun'( X, 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ), 'c_COMBB'( 'tc_fun'( X, 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ) ), 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ) )
% 1.16/1.56 , hAPP( hAPP( 'c_COMBB'( 'tc_fun'( X, 'tc_fun'( 'tc_fun'( 'tc_Com_Ostate'
% 1.16/1.56 , 'tc_bool' ), 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'(
% 1.16/1.56 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( X,
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'( X, 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ), 'c_COMBS'( X, 'tc_fun'( 'tc_Com_Ostate'
% 1.16/1.56 , 'tc_bool' ), 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), hAPP( hAPP(
% 1.16/1.56 'c_COMBB'( 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_bool',
% 1.16/1.56 'tc_bool' ) ) ), 'tc_fun'( X, 'tc_fun'( 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ), 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'( X,
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), hAPP( 'c_COMBB'( 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_fun'( 'tc_bool', 'tc_bool' ) ), 'tc_fun'( 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ), 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), X
% 1.16/1.56 ), 'c_COMBS'( 'tc_Com_Ostate', 'tc_bool', 'tc_bool' ) ) ), hAPP(
% 1.16/1.56 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ), 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_fun'( 'tc_bool', 'tc_bool' ) ), X ), hAPP( 'c_COMBB'(
% 1.16/1.56 'tc_bool', 'tc_fun'( 'tc_bool', 'tc_bool' ), 'tc_Com_Ostate' ),
% 1.16/1.56 'c_implies' ) ) ) ) ) ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 'tc_fun'( X,
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( X, 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ) ), 'tc_fun'(
% 1.16/1.56 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( X,
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_Com_Ocom' ), hAPP(
% 1.16/1.56 'c_COMBB'( 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate'
% 1.16/1.56 , 'tc_bool' ) ), 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) )
% 1.16/1.56 , hAPP( 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ) ), 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ), X ), hAPP(
% 1.16/1.56 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ), 'tc_bool',
% 1.16/1.56 'tc_Com_Ostate' ), 'c_All'( 'tc_Com_Ostate' ) ) ) ) ), hAPP( hAPP(
% 1.16/1.56 'c_COMBB'( 'tc_fun'( 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ), 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'(
% 1.16/1.56 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( X,
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ) ),
% 1.16/1.56 'tc_Com_Ocom' ), 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ),
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), X )
% 1.16/1.56 ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ), 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) )
% 1.16/1.56 , 'tc_fun'( 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ), 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ),
% 1.16/1.56 'tc_Com_Ocom' ), 'c_COMBC'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ), 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), hAPP( hAPP(
% 1.16/1.56 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'(
% 1.16/1.56 'tc_bool', 'tc_bool' ) ) ), 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ), 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) )
% 1.16/1.56 , 'tc_Com_Ocom' ), hAPP( 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'(
% 1.16/1.56 'tc_bool', 'tc_bool' ) ), 'tc_fun'( 'tc_fun'( 'tc_Com_Ostate', 'tc_bool'
% 1.16/1.56 ), 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_Com_Ostate' ),
% 1.16/1.56 'c_COMBS'( 'tc_Com_Ostate', 'tc_bool', 'tc_bool' ) ) ), hAPP( hAPP(
% 1.16/1.56 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ) ), 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_fun'( 'tc_bool', 'tc_bool' ) ) ), 'tc_Com_Ocom' ), hAPP( 'c_COMBB'(
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ), 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_fun'( 'tc_bool', 'tc_bool' ) ), 'tc_Com_Ostate' ), hAPP( 'c_COMBB'(
% 1.16/1.56 'tc_bool', 'tc_fun'( 'tc_bool', 'tc_bool' ), 'tc_Com_Ostate' ),
% 1.16/1.56 'c_implies' ) ) ), hAPP( hAPP( 'c_COMBC'( 'tc_Com_Ocom', 'tc_nat',
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ),
% 1.16/1.56 hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_nat',
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'( 'tc_nat', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ),
% 1.16/1.56 'tc_Com_Ocom' ), 'c_COMBC'( 'tc_Com_Ostate', 'tc_nat', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ), 'c_Natural_Oevaln' ) ), Y ) ) ) ) ) ) )
% 1.16/1.56 ) ), X, 'tc_bool' ), Z ) ), ~( hBOOL( hAPP(
% 1.16/1.56 'c_Hoare__Mirabelle_Otriple__valid'( Y, X ), Z ) ) ) ],
% 1.16/1.56 [ =( 'c_Hoare__Mirabelle_Otriple__valid'( 'v_n', X ),
% 1.16/1.56 'c_Hoare__Mirabelle_Otriple_Otriple__case'( hAPP( hAPP( 'c_COMBB'(
% 1.16/1.56 'tc_fun'( 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate'
% 1.16/1.56 , 'tc_bool' ) ), 'tc_fun'( X, 'tc_bool' ) ) ), 'tc_fun'( 'tc_Com_Ocom',
% 1.16/1.56 'tc_fun'( 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ),
% 1.16/1.56 'tc_bool' ) ), 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ),
% 1.16/1.56 hAPP( 'c_COMBB'( 'tc_fun'( 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ) ), 'tc_fun'( X, 'tc_bool' ) ), 'tc_fun'( 'tc_fun'( X,
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_bool' ), 'tc_Com_Ocom' ),
% 1.16/1.56 hAPP( 'c_COMBB'( 'tc_fun'( X, 'tc_bool' ), 'tc_bool', 'tc_fun'( X,
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), 'c_All'( X ) ) ) ), hAPP(
% 1.16/1.56 hAPP( 'c_COMBB'( 'tc_fun'( 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( X, 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ) ) ) ), 'tc_fun'( 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( X,
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.16/1.56 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), hAPP( 'c_COMBB'(
% 1.16/1.56 'tc_fun'( 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'(
% 1.16/1.56 X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'( 'tc_fun'( X,
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( X, 'tc_bool' ) ),
% 1.16/1.56 'tc_Com_Ocom' ), hAPP( 'c_COMBB'( 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate'
% 1.16/1.56 , 'tc_bool' ) ), 'tc_fun'( X, 'tc_bool' ), 'tc_fun'( X, 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ), hAPP( 'c_COMBB'( 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ), 'tc_bool', X ), 'c_All'( 'tc_Com_Ostate' )
% 1.16/1.56 ) ) ) ), hAPP( hAPP( 'c_COMBC'( 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ) ), 'tc_fun'( 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( X, 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ) ) ) ), 'tc_fun'( 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( X,
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( X, 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ) ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'(
% 1.16/1.56 'tc_fun'( 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'(
% 1.16/1.56 X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'( 'tc_fun'( X,
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( X, 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ) ), 'tc_fun'( 'tc_fun'( 'tc_Com_Ocom',
% 1.16/1.56 'tc_fun'( 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'(
% 1.16/1.56 X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ) ), 'tc_fun'( 'tc_Com_Ocom'
% 1.16/1.56 , 'tc_fun'( 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ),
% 1.16/1.56 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ) ) ), 'tc_fun'( X
% 1.16/1.56 , 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), 'c_COMBB'( 'tc_fun'(
% 1.16/1.56 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( X,
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'( 'tc_fun'( X,
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( X, 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_Com_Ocom' ) ), hAPP( hAPP(
% 1.16/1.56 'c_COMBB'( 'tc_fun'( 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' )
% 1.16/1.56 ), 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'(
% 1.16/1.56 'tc_fun'( 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'(
% 1.16/1.56 X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'( 'tc_fun'( X,
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( X, 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ) ), 'tc_fun'( X, 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ), 'c_COMBB'( 'tc_fun'( X, 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ) ), 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ) )
% 1.16/1.56 , hAPP( hAPP( 'c_COMBB'( 'tc_fun'( X, 'tc_fun'( 'tc_fun'( 'tc_Com_Ostate'
% 1.16/1.56 , 'tc_bool' ), 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'(
% 1.16/1.56 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( X,
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'( X, 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ), 'c_COMBS'( X, 'tc_fun'( 'tc_Com_Ostate'
% 1.16/1.56 , 'tc_bool' ), 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), hAPP( hAPP(
% 1.16/1.56 'c_COMBB'( 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_bool',
% 1.16/1.56 'tc_bool' ) ) ), 'tc_fun'( X, 'tc_fun'( 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ), 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'( X,
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), hAPP( 'c_COMBB'( 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_fun'( 'tc_bool', 'tc_bool' ) ), 'tc_fun'( 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ), 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), X
% 1.16/1.56 ), 'c_COMBS'( 'tc_Com_Ostate', 'tc_bool', 'tc_bool' ) ) ), hAPP(
% 1.16/1.56 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ), 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_fun'( 'tc_bool', 'tc_bool' ) ), X ), hAPP( 'c_COMBB'(
% 1.16/1.56 'tc_bool', 'tc_fun'( 'tc_bool', 'tc_bool' ), 'tc_Com_Ostate' ),
% 1.16/1.56 'c_implies' ) ) ) ) ) ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 'tc_fun'( X,
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( X, 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ) ), 'tc_fun'(
% 1.16/1.56 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( X,
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_Com_Ocom' ), hAPP(
% 1.16/1.56 'c_COMBB'( 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate'
% 1.16/1.56 , 'tc_bool' ) ), 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) )
% 1.16/1.56 , hAPP( 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ) ), 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ), X ), hAPP(
% 1.16/1.56 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ), 'tc_bool',
% 1.16/1.56 'tc_Com_Ostate' ), 'c_All'( 'tc_Com_Ostate' ) ) ) ) ), hAPP( hAPP(
% 1.16/1.56 'c_COMBB'( 'tc_fun'( 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ), 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'(
% 1.16/1.56 'tc_fun'( X, 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( X,
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ) ),
% 1.16/1.56 'tc_Com_Ocom' ), 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ),
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), X )
% 1.16/1.56 ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ), 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) )
% 1.16/1.56 , 'tc_fun'( 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ), 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ),
% 1.16/1.56 'tc_Com_Ocom' ), 'c_COMBC'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ), 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), hAPP( hAPP(
% 1.16/1.56 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'(
% 1.16/1.56 'tc_bool', 'tc_bool' ) ) ), 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ), 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) )
% 1.16/1.56 , 'tc_Com_Ocom' ), hAPP( 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'(
% 1.16/1.56 'tc_bool', 'tc_bool' ) ), 'tc_fun'( 'tc_fun'( 'tc_Com_Ostate', 'tc_bool'
% 1.16/1.56 ), 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_Com_Ostate' ),
% 1.16/1.56 'c_COMBS'( 'tc_Com_Ostate', 'tc_bool', 'tc_bool' ) ) ), hAPP( hAPP(
% 1.16/1.56 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ) ), 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_fun'( 'tc_bool', 'tc_bool' ) ) ), 'tc_Com_Ocom' ), hAPP( 'c_COMBB'(
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ), 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_fun'( 'tc_bool', 'tc_bool' ) ), 'tc_Com_Ostate' ), hAPP( 'c_COMBB'(
% 1.16/1.56 'tc_bool', 'tc_fun'( 'tc_bool', 'tc_bool' ), 'tc_Com_Ostate' ),
% 1.16/1.56 'c_implies' ) ) ), hAPP( hAPP( 'c_COMBC'( 'tc_Com_Ocom', 'tc_nat',
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ),
% 1.16/1.56 hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_nat',
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'( 'tc_nat', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ),
% 1.16/1.56 'tc_Com_Ocom' ), 'c_COMBC'( 'tc_Com_Ostate', 'tc_nat', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ), 'c_Natural_Oevaln' ) ), 'v_n' ) ) ) ) )
% 1.16/1.56 ) ) ) ), X, 'tc_bool' ) ) ],
% 1.16/1.56 [ ~( =( X, hAPP( 'c_Suc', X ) ) ) ],
% 1.16/1.56 [ ~( =( hAPP( 'c_Suc', X ), X ) ) ],
% 1.16/1.56 [ hBOOL( hAPP( hAPP( hAPP( hAPP( 'c_Natural_Oevaln', X ), Y ), hAPP(
% 1.16/1.56 'c_Suc', Z ) ), T ) ), ~( hBOOL( hAPP( hAPP( hAPP( hAPP(
% 1.16/1.56 'c_Natural_Oevaln', X ), Y ), Z ), T ) ) ) ],
% 1.16/1.56 [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X, Y ) ],
% 1.16/1.56 [ ~( =( hAPP( 'c_Suc', X ), hAPP( 'c_Suc', Y ) ) ), =( X, Y ) ],
% 1.16/1.56 [ =( hAPP( hAPP( hAPP( 'c_COMBB'( X, Y, Z ), T ), U ), W ), hAPP( T,
% 1.16/1.56 hAPP( U, W ) ) ) ],
% 1.16/1.56 [ =( hAPP( hAPP( hAPP( 'c_COMBC'( X, Y, Z ), T ), U ), W ), hAPP( hAPP(
% 1.16/1.56 T, W ), U ) ) ],
% 1.16/1.56 [ =( hAPP( hAPP( hAPP( 'c_COMBS'( X, Y, Z ), T ), U ), W ), hAPP( hAPP(
% 1.16/1.56 T, W ), hAPP( U, W ) ) ) ],
% 1.16/1.56 [ hBOOL( hAPP( 'c_Hoare__Mirabelle_Otriple_Otriple__case'( hAPP( hAPP(
% 1.16/1.56 'c_COMBB'( 'tc_fun'( 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( 't_a', 'tc_bool' ) ) ),
% 1.16/1.56 'tc_fun'( 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_bool' ) ), 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ), hAPP( 'c_COMBB'( 'tc_fun'( 'tc_fun'(
% 1.16/1.56 't_a', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( 't_a',
% 1.16/1.56 'tc_bool' ) ), 'tc_fun'( 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ) ), 'tc_bool' ), 'tc_Com_Ocom' ), hAPP( 'c_COMBB'( 'tc_fun'(
% 1.16/1.56 't_a', 'tc_bool' ), 'tc_bool', 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate'
% 1.16/1.56 , 'tc_bool' ) ) ), 'c_All'( 't_a' ) ) ) ), hAPP( hAPP( 'c_COMBB'(
% 1.16/1.56 'tc_fun'( 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ) ), 'tc_fun'( 'tc_Com_Ocom', 'tc_fun'(
% 1.16/1.56 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'(
% 1.16/1.56 't_a', 'tc_bool' ) ) ), 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ) ) ), hAPP( 'c_COMBB'( 'tc_fun'( 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'( 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( 't_a', 'tc_bool' ) ),
% 1.16/1.56 'tc_Com_Ocom' ), hAPP( 'c_COMBB'( 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( 't_a', 'tc_bool' ), 'tc_fun'(
% 1.16/1.56 't_a', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), hAPP( 'c_COMBB'(
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ), 'tc_bool', 't_a' ), 'c_All'(
% 1.16/1.56 'tc_Com_Ostate' ) ) ) ) ), hAPP( hAPP( 'c_COMBC'( 'tc_fun'( 't_a',
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( 'tc_Com_Ocom',
% 1.16/1.56 'tc_fun'( 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ),
% 1.16/1.56 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ) ), 'tc_fun'(
% 1.16/1.56 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ) ), 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) )
% 1.16/1.56 ) ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 'tc_fun'( 'tc_fun'( 't_a',
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'( 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ) ), 'tc_fun'( 'tc_fun'( 'tc_Com_Ocom',
% 1.16/1.56 'tc_fun'( 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ),
% 1.16/1.56 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ) ), 'tc_fun'(
% 1.16/1.56 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ) ), 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) )
% 1.16/1.56 ) ) ), 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ),
% 1.16/1.56 'c_COMBB'( 'tc_fun'( 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ) ), 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) )
% 1.16/1.56 ), 'tc_fun'( 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ),
% 1.16/1.56 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ),
% 1.16/1.56 'tc_Com_Ocom' ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 'tc_fun'( 't_a',
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'( 'tc_fun'( 'tc_fun'( 't_a',
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'( 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ) ), 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ), 'c_COMBB'( 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'(
% 1.16/1.56 't_a', 'tc_fun'( 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ), 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'( 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ), 'c_COMBS'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ), 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) )
% 1.16/1.56 , hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_fun'( 'tc_bool', 'tc_bool' ) ) ), 'tc_fun'( 't_a', 'tc_fun'( 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ), 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) )
% 1.16/1.56 , 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), hAPP(
% 1.16/1.56 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_bool', 'tc_bool' ) )
% 1.16/1.56 , 'tc_fun'( 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ), 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ), 't_a' ), 'c_COMBS'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool', 'tc_bool' ) ) ), hAPP( 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ), 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_bool', 'tc_bool' )
% 1.16/1.56 ), 't_a' ), hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'( 'tc_bool', 'tc_bool' )
% 1.16/1.56 , 'tc_Com_Ostate' ), 'c_implies' ) ) ) ) ) ) ), hAPP( hAPP( 'c_COMBB'(
% 1.16/1.56 'tc_fun'( 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ),
% 1.16/1.56 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ) ) ) ), 'tc_fun'( 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ) ), 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) )
% 1.16/1.56 ), 'tc_Com_Ocom' ), hAPP( 'c_COMBB'( 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'(
% 1.16/1.56 't_a', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( 't_a',
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), hAPP( 'c_COMBB'( 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ), 't_a' ), hAPP( 'c_COMBB'( 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ), 'tc_bool', 'tc_Com_Ostate' ), 'c_All'(
% 1.16/1.56 'tc_Com_Ostate' ) ) ) ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ), 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'( 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ) ),
% 1.16/1.56 'tc_Com_Ocom' ), 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ),
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ),
% 1.16/1.56 't_a' ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'(
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ), 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ) ) ), 'tc_fun'( 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ),
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ),
% 1.16/1.56 'tc_Com_Ocom' ), 'c_COMBC'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ), 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), hAPP( hAPP(
% 1.16/1.56 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'(
% 1.16/1.56 'tc_bool', 'tc_bool' ) ) ), 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ), 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) )
% 1.16/1.56 , 'tc_Com_Ocom' ), hAPP( 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'(
% 1.16/1.56 'tc_bool', 'tc_bool' ) ), 'tc_fun'( 'tc_fun'( 'tc_Com_Ostate', 'tc_bool'
% 1.16/1.56 ), 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_Com_Ostate' ),
% 1.16/1.56 'c_COMBS'( 'tc_Com_Ostate', 'tc_bool', 'tc_bool' ) ) ), hAPP( hAPP(
% 1.16/1.56 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ) ), 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_fun'( 'tc_bool', 'tc_bool' ) ) ), 'tc_Com_Ocom' ), hAPP( 'c_COMBB'(
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ), 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_fun'( 'tc_bool', 'tc_bool' ) ), 'tc_Com_Ostate' ), hAPP( 'c_COMBB'(
% 1.16/1.56 'tc_bool', 'tc_fun'( 'tc_bool', 'tc_bool' ), 'tc_Com_Ostate' ),
% 1.16/1.56 'c_implies' ) ) ), hAPP( hAPP( 'c_COMBC'( 'tc_Com_Ocom', 'tc_nat',
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ),
% 1.16/1.56 hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_nat',
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'( 'tc_nat', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ),
% 1.16/1.56 'tc_Com_Ocom' ), 'c_COMBC'( 'tc_Com_Ostate', 'tc_nat', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ), 'c_Natural_Oevaln' ) ), hAPP( 'c_Suc',
% 1.16/1.56 'v_n' ) ) ) ) ) ) ) ) ) ), 't_a', 'tc_bool' ), 'v_t' ) ) ],
% 1.16/1.56 [ ~( hBOOL( hAPP( 'c_Hoare__Mirabelle_Otriple_Otriple__case'( hAPP( hAPP(
% 1.16/1.56 'c_COMBB'( 'tc_fun'( 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( 't_a', 'tc_bool' ) ) ),
% 1.16/1.56 'tc_fun'( 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_bool' ) ), 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ), hAPP( 'c_COMBB'( 'tc_fun'( 'tc_fun'(
% 1.16/1.56 't_a', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( 't_a',
% 1.16/1.56 'tc_bool' ) ), 'tc_fun'( 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ) ), 'tc_bool' ), 'tc_Com_Ocom' ), hAPP( 'c_COMBB'( 'tc_fun'(
% 1.16/1.56 't_a', 'tc_bool' ), 'tc_bool', 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate'
% 1.16/1.56 , 'tc_bool' ) ) ), 'c_All'( 't_a' ) ) ) ), hAPP( hAPP( 'c_COMBB'(
% 1.16/1.56 'tc_fun'( 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ) ), 'tc_fun'( 'tc_Com_Ocom', 'tc_fun'(
% 1.16/1.56 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'(
% 1.16/1.56 't_a', 'tc_bool' ) ) ), 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ) ) ), hAPP( 'c_COMBB'( 'tc_fun'( 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'( 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( 't_a', 'tc_bool' ) ),
% 1.16/1.56 'tc_Com_Ocom' ), hAPP( 'c_COMBB'( 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( 't_a', 'tc_bool' ), 'tc_fun'(
% 1.16/1.56 't_a', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), hAPP( 'c_COMBB'(
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ), 'tc_bool', 't_a' ), 'c_All'(
% 1.16/1.56 'tc_Com_Ostate' ) ) ) ) ), hAPP( hAPP( 'c_COMBC'( 'tc_fun'( 't_a',
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( 'tc_Com_Ocom',
% 1.16/1.56 'tc_fun'( 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ),
% 1.16/1.56 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ) ), 'tc_fun'(
% 1.16/1.56 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ) ), 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) )
% 1.16/1.56 ) ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 'tc_fun'( 'tc_fun'( 't_a',
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'( 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ) ), 'tc_fun'( 'tc_fun'( 'tc_Com_Ocom',
% 1.16/1.56 'tc_fun'( 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ),
% 1.16/1.56 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ) ), 'tc_fun'(
% 1.16/1.56 'tc_Com_Ocom', 'tc_fun'( 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ) ), 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) )
% 1.16/1.56 ) ) ), 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ),
% 1.16/1.56 'c_COMBB'( 'tc_fun'( 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ) ), 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) )
% 1.16/1.56 ), 'tc_fun'( 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ),
% 1.16/1.56 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ),
% 1.16/1.56 'tc_Com_Ocom' ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 'tc_fun'( 't_a',
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'( 'tc_fun'( 'tc_fun'( 't_a',
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'( 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ) ), 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ), 'c_COMBB'( 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'(
% 1.16/1.56 't_a', 'tc_fun'( 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ), 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'( 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ), 'c_COMBS'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ), 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) )
% 1.16/1.56 , hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_fun'( 'tc_bool', 'tc_bool' ) ) ), 'tc_fun'( 't_a', 'tc_fun'( 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ), 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) )
% 1.16/1.56 , 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), hAPP(
% 1.16/1.56 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_bool', 'tc_bool' ) )
% 1.16/1.56 , 'tc_fun'( 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ), 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ), 't_a' ), 'c_COMBS'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool', 'tc_bool' ) ) ), hAPP( 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ), 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_bool', 'tc_bool' )
% 1.16/1.56 ), 't_a' ), hAPP( 'c_COMBB'( 'tc_bool', 'tc_fun'( 'tc_bool', 'tc_bool' )
% 1.16/1.56 , 'tc_Com_Ostate' ), 'c_implies' ) ) ) ) ) ) ), hAPP( hAPP( 'c_COMBB'(
% 1.16/1.56 'tc_fun'( 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ),
% 1.16/1.56 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ) ) ) ), 'tc_fun'( 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ) ), 'tc_fun'( 't_a', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) )
% 1.16/1.56 ), 'tc_Com_Ocom' ), hAPP( 'c_COMBB'( 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'(
% 1.16/1.56 't_a', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( 't_a',
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), hAPP( 'c_COMBB'( 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ), 't_a' ), hAPP( 'c_COMBB'( 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ), 'tc_bool', 'tc_Com_Ostate' ), 'c_All'(
% 1.16/1.56 'tc_Com_Ostate' ) ) ) ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ), 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'( 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_fun'( 't_a', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ) ),
% 1.16/1.56 'tc_Com_Ocom' ), 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ),
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ),
% 1.16/1.56 't_a' ) ), hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'(
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ), 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ) ) ), 'tc_fun'( 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ),
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ),
% 1.16/1.56 'tc_Com_Ocom' ), 'c_COMBC'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ), 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), hAPP( hAPP(
% 1.16/1.56 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'(
% 1.16/1.56 'tc_bool', 'tc_bool' ) ) ), 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ), 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) )
% 1.16/1.56 , 'tc_Com_Ocom' ), hAPP( 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'(
% 1.16/1.56 'tc_bool', 'tc_bool' ) ), 'tc_fun'( 'tc_fun'( 'tc_Com_Ostate', 'tc_bool'
% 1.16/1.56 ), 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ), 'tc_Com_Ostate' ),
% 1.16/1.56 'c_COMBS'( 'tc_Com_Ostate', 'tc_bool', 'tc_bool' ) ) ), hAPP( hAPP(
% 1.16/1.56 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_bool' ) ), 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_fun'( 'tc_bool', 'tc_bool' ) ) ), 'tc_Com_Ocom' ), hAPP( 'c_COMBB'(
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ), 'tc_fun'( 'tc_Com_Ostate',
% 1.16/1.56 'tc_fun'( 'tc_bool', 'tc_bool' ) ), 'tc_Com_Ostate' ), hAPP( 'c_COMBB'(
% 1.16/1.56 'tc_bool', 'tc_fun'( 'tc_bool', 'tc_bool' ), 'tc_Com_Ostate' ),
% 1.16/1.56 'c_implies' ) ) ), hAPP( hAPP( 'c_COMBC'( 'tc_Com_Ocom', 'tc_nat',
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ),
% 1.16/1.56 hAPP( hAPP( 'c_COMBB'( 'tc_fun'( 'tc_Com_Ostate', 'tc_fun'( 'tc_nat',
% 1.16/1.56 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ), 'tc_fun'( 'tc_nat', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_fun'( 'tc_Com_Ostate', 'tc_bool' ) ) ),
% 1.16/1.56 'tc_Com_Ocom' ), 'c_COMBC'( 'tc_Com_Ostate', 'tc_nat', 'tc_fun'(
% 1.16/1.56 'tc_Com_Ostate', 'tc_bool' ) ) ), 'c_Natural_Oevaln' ) ), 'v_n' ) ) ) ) )
% 1.16/1.56 ) ) ) ), 't_a', 'tc_bool' ), 'v_t' ) ) ) ],
% 1.16/1.56 [ 'class_Finite__Set_Ofinite_Ofinite'( 'tc_prod'( X, Y ) ), ~(
% 1.16/1.56 'class_Finite__Set_Ofinite_Ofinite'( Y ) ), ~(
% 1.16/1.56 'class_Finite__Set_Ofinite_Ofinite'( X ) ) ],
% 1.16/1.56 [ 'class_Lattices_Oupper__semilattice'( 'tc_fun'( X, Y ) ), ~(
% 1.16/1.56 'class_Lattices_Olattice'( Y ) ) ],
% 1.16/1.56 [ 'class_Lattices_Oboolean__algebra'( 'tc_fun'( X, Y ) ), ~(
% 1.16/1.56 'class_Lattices_Oboolean__algebra'( Y ) ) ],
% 1.16/1.56 [ 'class_Finite__Set_Ofinite_Ofinite'( 'tc_fun'( X, Y ) ), ~(
% 1.16/1.56 'class_Finite__Set_Ofinite_Ofinite'( Y ) ), ~(
% 1.16/1.56 'class_Finite__Set_Ofinite_Ofinite'( X ) ) ],
% 1.16/1.56 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 1.16/1.56 'class_Orderings_Opreorder'( Y ) ) ],
% 1.16/1.56 [ 'class_Lattices_Olattice'( 'tc_fun'( X, Y ) ), ~(
% 1.16/1.56 'class_Lattices_Olattice'( Y ) ) ],
% 1.16/1.56 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 1.16/1.56 'class_Orderings_Oorder'( Y ) ) ],
% 1.16/1.56 [ 'class_HOL_Oord'( 'tc_fun'( X, Y ) ), ~( 'class_HOL_Oord'( Y ) ) ]
% 1.16/1.56 ,
% 1.16/1.56 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.16/1.56 ],
% 1.16/1.56 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.16/1.56 ) ],
% 1.16/1.56 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.16/1.56 ],
% 1.16/1.56 [ 'class_Ring__and__Field_Opordered__cancel__semiring'( 'tc_nat' ) ]
% 1.16/1.56 ,
% 1.16/1.56 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.16/1.56 [ 'class_OrderedGroup_Opordered__ab__semigroup__add'( 'tc_nat' ) ],
% 1.16/1.56 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.16/1.56 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.16/1.56 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.16/1.56 [ 'class_Ring__and__Field_Opordered__semiring'( 'tc_nat' ) ],
% 1.16/1.56 [ 'class_Ring__and__Field_Oordered__semiring'( 'tc_nat' ) ],
% 1.16/1.56 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.16/1.56 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.16/1.56 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.16/1.56 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.16/1.56 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.16/1.56 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.16/1.56 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.16/1.56 [ 'class_OrderedGroup_Osemigroup__add'( 'tc_nat' ) ],
% 1.16/1.56 [ 'class_Lattices_Oupper__semilattice'( 'tc_nat' ) ],
% 1.16/1.56 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.16/1.56 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.16/1.56 [ 'class_Ring__and__Field_Omult__mono1'( 'tc_nat' ) ],
% 1.16/1.56 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.16/1.56 [ 'class_Ring__and__Field_Omult__mono'( 'tc_nat' ) ],
% 1.16/1.56 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.16/1.56 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.16/1.56 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 1.16/1.56 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.16/1.56 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.16/1.56 [ 'class_Lattices_Olattice'( 'tc_nat' ) ],
% 1.16/1.56 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.16/1.56 [ 'class_HOL_Oord'( 'tc_nat' ) ],
% 1.16/1.56 [ 'class_Lattices_Oupper__semilattice'( 'tc_bool' ) ],
% 1.16/1.56 [ 'class_Lattices_Oboolean__algebra'( 'tc_bool' ) ],
% 1.16/1.56 [ 'class_Finite__Set_Ofinite_Ofinite'( 'tc_bool' ) ],
% 1.16/1.56 [ 'class_Orderings_Opreorder'( 'tc_bool' ) ],
% 1.16/1.56 [ 'class_Lattices_Olattice'( 'tc_bool' ) ],
% 1.16/1.56 [ 'class_Orderings_Oorder'( 'tc_bool' ) ],
% 1.16/1.56 [ 'class_HOL_Oord'( 'tc_bool' ) ],
% 1.16/1.56 [ =( hAPP( hAPP( hAPP( 'c_COMBS'( X, Y, Z ), T ), U ), W ), hAPP( hAPP(
% 1.16/1.56 T, W ), hAPP( U, W ) ) ) ],
% 1.16/1.56 [ =( hAPP( hAPP( hAPP( 'c_COMBC'( X, Y, Z ), T ), U ), W ), hAPP( hAPP(
% 1.16/1.56 T, W ), U ) ) ],
% 1.16/1.56 [ =( hAPP( hAPP( hAPP( 'c_COMBB'( X, Y, Z ), T ), U ), W ), hAPP( T,
% 1.16/1.56 hAPP( U, W ) ) ) ],
% 1.16/1.56 [ hBOOL( hAPP( hAPP( 'c_fequal'( X ), Y ), Y ) ) ],
% 1.16/1.56 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_fequal'( Z ), X ), Y ) ) ) ]
% 1.16/1.56 ] .
% 1.16/1.56
% 1.16/1.56
% 1.16/1.56 percentage equality = 0.254349, percentage horn = 0.909817
% 1.16/1.56 This is a problem with some equality
% 1.16/1.56
% 1.16/1.56
% 1.16/1.56
% 1.16/1.56 Options Used:
% 1.16/1.56
% 1.16/1.56 useres = 1
% 1.16/1.56 useparamod = 1
% 1.16/1.56 useeqrefl = 1
% 1.16/1.56 useeqfact = 1
% 1.16/1.56 usefactor = 1
% 1.16/1.56 usesimpsplitting = 0
% 1.16/1.56 usesimpdemod = 5
% 1.16/1.56 usesimpres = 3
% 1.16/1.56
% 1.16/1.56 resimpinuse = 1000
% 1.16/1.56 resimpclauses = 20000
% 1.16/1.56 substype = eqrewr
% 1.16/1.56 backwardsubs = 1
% 1.16/1.56 selectoldest = 5
% 1.16/1.56
% 1.16/1.56 litorderings [0] = split
% 1.16/1.56 litorderings [1] = extend the termordering, first sorting on arguments
% 1.16/1.56
% 1.16/1.56 termordering = kbo
% 1.16/1.56
% 1.16/1.56 litapriori = 0
% 1.16/1.56 termapriori = 1
% 1.16/1.56 litaposteriori = 0
% 1.16/1.56 termaposteriori = 0
% 1.16/1.56 demodaposteriori = 0
% 1.16/1.56 ordereqreflfact = 0
% 1.16/1.56
% 1.16/1.56 litselect = negord
% 1.16/1.56
% 1.16/1.56 maxweight = 15
% 1.16/1.56 maxdepth = 30000
% 1.16/1.56 maxlength = 115
% 1.16/1.56 maxnrvars = 195
% 1.16/1.56 excuselevel = 1
% 1.16/1.56 increasemaxweight = 1
% 1.16/1.56
% 1.16/1.56 maxselected = 10000000
% 1.16/1.56 maxnrclauses = 10000000
% 1.16/1.56
% 1.16/1.56 showgenerated = 0
% 1.16/1.56 showkept = 0
% 1.16/1.56 showselected = 0
% 1.16/1.56 showdeleted = 0
% 1.16/1.56 showresimp = 1
% 1.16/1.56 showstatus = 2000
% 1.16/1.56
% 1.16/1.56 prologoutput = 1
% 1.16/1.56 nrgoals = 5000000
% 1.16/1.56 totalproof = 1
% 1.16/1.56
% 1.16/1.56 Symbols occurring in the translation:
% 1.16/1.56
% 1.16/1.56 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.16/1.56 . [1, 2] (w:1, o:211, a:1, s:1, b:0),
% 1.16/1.56 ! [4, 1] (w:0, o:137, a:1, s:1, b:0),
% 1.16/1.56 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.16/1.56 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.16/1.56 'c_Collect' [40, 1] (w:1, o:142, a:1, s:1, b:0),
% 1.16/1.56 hAPP [42, 2] (w:1, o:236, a:1, s:1, b:0),
% 1.16/1.56 'class_Orderings_Olinorder' [43, 1] (w:1, o:143, a:1, s:1, b:0),
% 1.16/1.56 'c_lessequals' [44, 1] (w:1, o:144, a:1, s:1, b:0),
% 1.16/1.56 'c_Orderings_Oord__class_Omax' [46, 1] (w:1, o:145, a:1, s:1, b:0),
% 1.16/1.56 hBOOL [48, 1] (w:1, o:146, a:1, s:1, b:0),
% 1.16/1.56 'c_Com_Ocom_OSemi' [51, 2] (w:1, o:237, a:1, s:1, b:0),
% 1.16/1.56 'class_OrderedGroup_Ocomm__monoid__add' [54, 1] (w:1, o:147, a:1, s:1
% 1.16/1.56 , b:0),
% 1.16/1.56 'c_Finite__Set_Osetsum' [56, 2] (w:1, o:238, a:1, s:1, b:0),
% 1.16/1.56 'c_COMBK' [57, 2] (w:1, o:239, a:1, s:1, b:0),
% 1.16/1.56 'c_HOL_Ozero__class_Ozero' [58, 1] (w:1, o:148, a:1, s:1, b:0),
% 1.16/1.56 'c_Com_Ocom_OWhile' [62, 2] (w:1, o:240, a:1, s:1, b:0),
% 1.16/1.56 'c_Orderings_Oord__class_Omin' [64, 3] (w:1, o:252, a:1, s:1, b:0),
% 1.16/1.56 'c_Com_Ocom_OCond' [65, 3] (w:1, o:253, a:1, s:1, b:0),
% 1.16/1.56 'c_split' [68, 4] (w:1, o:268, a:1, s:1, b:0),
% 1.16/1.56 'c_Pair' [69, 2] (w:1, o:241, a:1, s:1, b:0),
% 1.16/1.56 'c_COMBI' [72, 1] (w:1, o:149, a:1, s:1, b:0),
% 1.16/1.56 'c_Fun_Oinj__on' [73, 4] (w:1, o:269, a:1, s:1, b:0),
% 1.16/1.56 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [74, 1]
% 1.16/1.56 (w:1, o:151, a:1, s:1, b:0),
% 1.16/1.56 'c_HOL_Oplus__class_Oplus' [75, 1] (w:1, o:153, a:1, s:1, b:0),
% 1.16/1.56 'tc_nat' [77, 0] (w:1, o:46, a:1, s:1, b:0),
% 1.16/1.56 'c_Suc' [78, 0] (w:1, o:47, a:1, s:1, b:0),
% 1.16/1.56 'c_HOL_Oord__class_Oless' [81, 1] (w:1, o:152, a:1, s:1, b:0),
% 1.16/1.56 'class_Ring__and__Field_Opordered__ring' [85, 1] (w:1, o:164, a:1, s:
% 1.16/1.56 1, b:0),
% 1.16/1.56 'c_HOL_Otimes__class_Otimes' [86, 1] (w:1, o:165, a:1, s:1, b:0),
% 1.16/1.56 'c_HOL_Ominus__class_Ominus' [89, 1] (w:1, o:166, a:1, s:1, b:0),
% 1.16/1.56 'class_Orderings_Oorder' [91, 1] (w:1, o:167, a:1, s:1, b:0),
% 1.16/1.56 'c_Orderings_Oorder__class_Ostrict__mono' [92, 3] (w:1, o:254, a:1
% 1.16/1.56 , s:1, b:0),
% 1.16/1.56 'class_Ring__and__Field_Oordered__ring__strict' [93, 1] (w:1, o:158
% 1.16/1.56 , a:1, s:1, b:0),
% 1.16/1.56 'class_Divides_Osemiring__div' [94, 1] (w:1, o:169, a:1, s:1, b:0),
% 1.16/1.56 'c_Divides_Odiv__class_Omod' [95, 3] (w:1, o:258, a:1, s:1, b:0),
% 1.16/1.56 'class_Ring__and__Field_Ocomm__semiring__1' [96, 1] (w:1, o:170, a:1
% 1.16/1.56 , s:1, b:0),
% 1.16/1.56 'class_Ring__and__Field_Oring' [97, 1] (w:1, o:171, a:1, s:1, b:0),
% 1.16/1.56 'class_OrderedGroup_Opordered__ab__group__add' [98, 1] (w:1, o:172
% 1.16/1.56 , a:1, s:1, b:0),
% 1.16/1.56 'c_HOL_Ouminus__class_Ouminus' [99, 1] (w:1, o:173, a:1, s:1, b:0),
% 1.16/1.56 'class_Ring__and__Field_Oordered__semiring__strict' [100, 1] (w:1, o:
% 1.16/1.56 159, a:1, s:1, b:0),
% 1.16/1.56 'c_Natural_Oevalc' [102, 3] (w:1, o:251, a:1, s:1, b:0),
% 1.16/1.56 'c_Hoare__Mirabelle_Otriple__valid' [103, 2] (w:1, o:242, a:1, s:1
% 1.16/1.56 , b:0),
% 1.16/1.56 'c_Com_Ocom_OBODY' [105, 1] (w:1, o:174, a:1, s:1, b:0),
% 1.16/1.58 'c_Hoare__Mirabelle_Otriple_Otriple' [107, 4] (w:1, o:270, a:1, s:1
% 1.16/1.58 , b:0),
% 1.16/1.58 'class_OrderedGroup_Olordered__ab__group__add' [110, 1] (w:1, o:175
% 1.16/1.58 , a:1, s:1, b:0),
% 1.16/1.58 'class_OrderedGroup_Oordered__ab__group__add' [111, 1] (w:1, o:150
% 1.16/1.58 , a:1, s:1, b:0),
% 1.16/1.58 'c_Com_Ocom_OSKIP' [112, 0] (w:1, o:75, a:1, s:1, b:0),
% 1.16/1.58 'c_in' [113, 1] (w:1, o:176, a:1, s:1, b:0),
% 1.16/1.58 'tc_bool' [114, 0] (w:1, o:76, a:1, s:1, b:0),
% 1.16/1.58 'tc_fun' [115, 2] (w:1, o:243, a:1, s:1, b:0),
% 1.16/1.58 'c_Product__Type_OSigma' [117, 4] (w:1, o:271, a:1, s:1, b:0),
% 1.16/1.58 't_a' [121, 0] (w:1, o:81, a:1, s:1, b:0),
% 1.16/1.58 'c_Nat_Onat_Onat__case' [122, 4] (w:1, o:272, a:1, s:1, b:0),
% 1.16/1.58 'class_Ring__and__Field_Oidom' [123, 1] (w:1, o:177, a:1, s:1, b:0),
% 1.16/1.58
% 1.16/1.58 'class_Int_Onumber__ring' [124, 1] (w:1, o:179, a:1, s:1, b:0),
% 1.16/1.58 'c_Orderings_Oorder__class_Omono' [125, 3] (w:1, o:259, a:1, s:1, b:0
% 1.16/1.58 ),
% 1.16/1.58 'c_Lattices_Oupper__semilattice__class_Osup' [126, 1] (w:1, o:180, a:
% 1.16/1.58 1, s:1, b:0),
% 1.16/1.58 'class_OrderedGroup_Ogroup__add' [127, 1] (w:1, o:181, a:1, s:1, b:0)
% 1.16/1.58 ,
% 1.16/1.58 'tc_prod' [128, 2] (w:1, o:244, a:1, s:1, b:0),
% 1.16/1.58 'c_COMBB' [129, 3] (w:1, o:255, a:1, s:1, b:0),
% 1.16/1.58 'class_OrderedGroup_Opordered__ab__semigroup__add' [131, 1] (w:1, o:
% 1.16/1.58 182, a:1, s:1, b:0),
% 1.16/1.58 'c_Power_Opower_Opower' [132, 5] (w:1, o:283, a:1, s:1, b:0),
% 1.16/1.58 'class_OrderedGroup_Opordered__comm__monoid__add' [133, 1] (w:1, o:
% 1.16/1.58 183, a:1, s:1, b:0),
% 1.16/1.58 'class_OrderedGroup_Olordered__ab__group__add__join' [134, 1] (w:1
% 1.16/1.58 , o:184, a:1, s:1, b:0),
% 1.16/1.58 'c_Orderings_Oorder' [137, 3] (w:1, o:260, a:1, s:1, b:0),
% 1.16/1.58 'class_Lattices_Oupper__semilattice' [138, 1] (w:1, o:185, a:1, s:1
% 1.16/1.58 , b:0),
% 1.16/1.58 'class_Orderings_Opreorder' [139, 1] (w:1, o:186, a:1, s:1, b:0),
% 1.16/1.58 'c_Hilbert__Choice_OEps' [140, 2] (w:1, o:245, a:1, s:1, b:0),
% 1.16/1.58 'c_Lattices_Oboolean__algebra' [147, 9] (w:1, o:290, a:1, s:1, b:0),
% 1.16/1.58
% 1.16/1.58 'class_OrderedGroup_Oab__group__add' [148, 1] (w:1, o:187, a:1, s:1
% 1.16/1.58 , b:0),
% 1.16/1.58 'class_OrderedGroup_Osemigroup__add' [149, 1] (w:1, o:188, a:1, s:1
% 1.16/1.58 , b:0),
% 1.16/1.58 'c_List_Ofoldl' [151, 5] (w:1, o:284, a:1, s:1, b:0),
% 1.16/1.58 'c_COMBC' [152, 3] (w:1, o:256, a:1, s:1, b:0),
% 1.16/1.58 'c_fequal' [153, 1] (w:1, o:189, a:1, s:1, b:0),
% 1.16/1.58 'c_The' [154, 2] (w:1, o:246, a:1, s:1, b:0),
% 1.16/1.58 'c_Record_Oiso__tuple__update__accessor__cong__assist' [158, 4] (w:1
% 1.16/1.58 , o:273, a:1, s:1, b:0),
% 1.16/1.58 'class_Ring__and__Field_Oordered__semiring' [159, 1] (w:1, o:160, a:1
% 1.16/1.58 , s:1, b:0),
% 1.16/1.58 'class_Divides_Oring__div' [160, 1] (w:1, o:168, a:1, s:1, b:0),
% 1.16/1.58 'c_Finite__Set_Ofinite' [164, 2] (w:1, o:247, a:1, s:1, b:0),
% 1.16/1.58 'c_Ex' [165, 1] (w:1, o:190, a:1, s:1, b:0),
% 1.16/1.58 'c_COMBS' [166, 3] (w:1, o:257, a:1, s:1, b:0),
% 1.16/1.58 'c_and' [167, 0] (w:1, o:99, a:1, s:1, b:0),
% 1.16/1.58 'class_Ring__and__Field_Oring__no__zero__divisors' [168, 1] (w:1, o:
% 1.16/1.58 191, a:1, s:1, b:0),
% 1.16/1.58 'class_Ring__and__Field_Ono__zero__divisors' [169, 1] (w:1, o:157, a:
% 1.16/1.58 1, s:1, b:0),
% 1.16/1.58 'class_Ring__and__Field_Oordered__idom' [171, 1] (w:1, o:161, a:1, s:
% 1.16/1.58 1, b:0),
% 1.16/1.58 'class_OrderedGroup_Omonoid__add' [172, 1] (w:1, o:192, a:1, s:1, b:0
% 1.16/1.58 ),
% 1.16/1.58 'class_OrderedGroup_Oab__semigroup__add' [174, 1] (w:1, o:193, a:1
% 1.16/1.58 , s:1, b:0),
% 1.16/1.58 'c_Fun_Oid' [176, 1] (w:1, o:194, a:1, s:1, b:0),
% 1.16/1.58 'class_Ring__and__Field_Osemiring__0' [188, 1] (w:1, o:195, a:1, s:1
% 1.16/1.58 , b:0),
% 1.16/1.58 'class_Lattices_Olattice' [190, 1] (w:1, o:196, a:1, s:1, b:0),
% 1.16/1.58 'c_Orderings_Oorder_Ostrict__mono' [191, 3] (w:1, o:261, a:1, s:1, b:
% 1.16/1.58 0),
% 1.16/1.58 'class_Ring__and__Field_Omult__zero' [196, 1] (w:1, o:154, a:1, s:1
% 1.16/1.58 , b:0),
% 1.16/1.58 'c_Orderings_Oorder_Omono' [197, 3] (w:1, o:262, a:1, s:1, b:0),
% 1.16/1.58 'c_Product__Type_Oscomp' [198, 6] (w:1, o:288, a:1, s:1, b:0),
% 1.16/1.58 'class_Lattices_Oboolean__algebra' [199, 1] (w:1, o:197, a:1, s:1, b:
% 1.16/1.58 0),
% 1.16/1.58 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [200, 1]
% 1.16/1.58 (w:1, o:198, a:1, s:1, b:0),
% 1.16/1.58 'c_Recdef_Ocut' [201, 2] (w:1, o:248, a:1, s:1, b:0),
% 1.16/1.58 'c_Natural_Oevaln' [205, 0] (w:1, o:110, a:1, s:1, b:0),
% 11.60/11.98 'c_Complete__Lattice_Ocomplete__lattice' [208, 9] (w:1, o:291, a:1
% 11.60/11.98 , s:1, b:0),
% 11.60/11.98 'class_Ring__and__Field_Osemiring' [209, 1] (w:1, o:199, a:1, s:1, b:
% 11.60/11.98 0),
% 11.60/11.98 'class_Ring__and__Field_Opordered__cancel__semiring' [211, 1] (w:1
% 11.60/11.98 , o:200, a:1, s:1, b:0),
% 11.60/11.98 'class_OrderedGroup_Ocancel__ab__semigroup__add' [212, 1] (w:1, o:201
% 11.60/11.98 , a:1, s:1, b:0),
% 11.60/11.98 'class_OrderedGroup_Ocancel__semigroup__add' [213, 1] (w:1, o:202, a:
% 11.60/11.98 1, s:1, b:0),
% 11.60/11.98 'c_HOL_Oinduct__forall' [214, 2] (w:1, o:249, a:1, s:1, b:0),
% 11.60/11.98 'c_Not' [216, 0] (w:1, o:114, a:1, s:1, b:0),
% 11.60/11.98 'v_P' [218, 0] (w:1, o:116, a:1, s:1, b:0),
% 11.60/11.98 'c_Nat_Onat_Onat__rec' [223, 4] (w:1, o:274, a:1, s:1, b:0),
% 11.60/11.98 'class_OrderedGroup_Oab__semigroup__idem__mult' [225, 1] (w:1, o:203
% 11.60/11.98 , a:1, s:1, b:0),
% 11.60/11.98 'c_Fun_Ofcomp' [228, 3] (w:1, o:263, a:1, s:1, b:0),
% 11.60/11.98 'class_Ring__and__Field_Oordered__semidom' [230, 1] (w:1, o:162, a:1
% 11.60/11.98 , s:1, b:0),
% 11.60/11.98 'class_Ring__and__Field_Osemiring__1' [231, 1] (w:1, o:204, a:1, s:1
% 11.60/11.98 , b:0),
% 11.60/11.98 'c_Nat_Osemiring__1__class_Oof__nat__aux' [233, 4] (w:1, o:275, a:1
% 11.60/11.98 , s:1, b:0),
% 11.60/11.98 'class_Ring__and__Field_Omult__mono' [234, 1] (w:1, o:155, a:1, s:1
% 11.60/11.98 , b:0),
% 11.60/11.98 'class_Ring__and__Field_Omult__mono1' [235, 1] (w:1, o:156, a:1, s:1
% 11.60/11.98 , b:0),
% 11.60/11.98 'c_Relation_Otrans' [236, 2] (w:1, o:250, a:1, s:1, b:0),
% 11.60/11.98 'c_or' [237, 0] (w:1, o:118, a:1, s:1, b:0),
% 11.60/11.98 'class_Finite__Set_Ofinite_Ofinite' [240, 1] (w:1, o:205, a:1, s:1
% 11.60/11.98 , b:0),
% 11.60/11.98 'class_Ring__and__Field_Oordered__comm__semiring__strict' [241, 1]
% 11.60/11.98 (w:1, o:163, a:1, s:1, b:0),
% 11.60/11.98 'class_Ring__and__Field_Opordered__semiring' [242, 1] (w:1, o:206, a:
% 11.60/11.98 1, s:1, b:0),
% 11.60/11.98 'c_All' [243, 1] (w:1, o:207, a:1, s:1, b:0),
% 11.60/11.98 'c_implies' [244, 0] (w:1, o:119, a:1, s:1, b:0),
% 11.60/11.98 'class_OrderedGroup_Oab__semigroup__mult' [246, 1] (w:1, o:208, a:1
% 11.60/11.98 , s:1, b:0),
% 11.60/11.98 'class_Ring__and__Field_Ocomm__semiring' [248, 1] (w:1, o:209, a:1
% 11.60/11.98 , s:1, b:0),
% 11.60/11.98 'c_List_Ofilter' [253, 3] (w:1, o:264, a:1, s:1, b:0),
% 11.60/11.98 'c_HOL_Oinduct__conj' [254, 0] (w:1, o:122, a:1, s:1, b:0),
% 11.60/11.98 'c_ATP__Linkup_Osko__FunDef__Xfundef__ex1__uniqueness__1__1' [255, 5
% 11.60/11.98 ] (w:1, o:285, a:1, s:1, b:0),
% 11.60/11.98 'c_FunDef_OTHE__default' [256, 1] (w:1, o:210, a:1, s:1, b:0),
% 11.60/11.98 'c_ATP__Linkup_Osko__FunDef__Xfundef__ex1__existence__1__1' [257, 5]
% 11.60/11.98 (w:1, o:286, a:1, s:1, b:0),
% 11.60/11.98 'c_ATP__Linkup_Osko__FunDef__Xfundef__ex1__iff__1__1' [258, 5] (w:1
% 11.60/11.98 , o:287, a:1, s:1, b:0),
% 11.60/11.98 'c_ATP__Linkup_Osko__FunDef__Xfundef__default__value__1__1' [260, 4]
% 11.60/11.98 (w:1, o:276, a:1, s:1, b:0),
% 11.60/11.98 'c_Natural_Osko__Natural__Xevaln__elim__cases__6__1' [261, 4] (w:1
% 11.60/11.98 , o:277, a:1, s:1, b:0),
% 11.60/11.98 'class_HOL_Oord' [262, 1] (w:1, o:178, a:1, s:1, b:0),
% 11.60/11.98 'c_Hilbert__Choice_OGreatestM' [263, 4] (w:1, o:278, a:1, s:1, b:0),
% 11.60/11.98
% 11.60/11.98 'v_B' [264, 0] (w:1, o:124, a:1, s:1, b:0),
% 11.60/11.98 'c_Predicate_OPowp' [265, 3] (w:1, o:266, a:1, s:1, b:0),
% 11.60/11.98 'c_Orderings_Oord_OLeast' [266, 3] (w:1, o:265, a:1, s:1, b:0),
% 11.60/11.98 'v_n' [267, 0] (w:1, o:125, a:1, s:1, b:0),
% 11.60/11.98 'c_Natural_Osko__Natural__Xevaln__max2__1__1' [270, 6] (w:1, o:289
% 11.60/11.98 , a:1, s:1, b:0),
% 11.60/11.98 't_b' [273, 0] (w:1, o:126, a:1, s:1, b:0),
% 11.60/11.98 'c_Hoare__Mirabelle_Otriple_Otriple__case' [274, 3] (w:1, o:267, a:1
% 11.60/11.98 , s:1, b:0),
% 11.60/11.98 'v_r' [277, 0] (w:1, o:127, a:1, s:1, b:0),
% 11.60/11.98 'c_Recdef_Oadm__wf' [278, 4] (w:1, o:279, a:1, s:1, b:0),
% 11.60/11.98 'v_upd' [279, 0] (w:1, o:129, a:1, s:1, b:0),
% 11.60/11.98 'v_acc' [280, 0] (w:1, o:130, a:1, s:1, b:0),
% 11.60/11.98 'c_Hilbert__Choice_OLeastM' [281, 4] (w:1, o:280, a:1, s:1, b:0),
% 11.60/11.98 'c_List_Osko__List__Xfoldl__apply__inv__1__1' [282, 4] (w:1, o:281
% 11.60/11.98 , a:1, s:1, b:0),
% 11.60/11.98 'c_List_Omap' [283, 4] (w:1, o:282, a:1, s:1, b:0),
% 11.60/11.98 'v_f' [284, 0] (w:1, o:131, a:1, s:1, b:0),
% 11.60/11.98 'tc_Com_Ocom' [285, 0] (w:1, o:132, a:1, s:1, b:0),
% 11.60/11.98 'tc_Com_Ostate' [286, 0] (w:1, o:133, a:1, s:1, b:0),
% 11.60/11.98 'v_t' [287, 0] (w:1, o:128, a:1, s:1, b:0).
% 11.60/11.98
% 11.60/11.98
% 11.60/11.98 Starting Search:
% 11.60/11.98
% 11.60/11.98 Resimplifying inuse:
% 11.60/11.98 Done
% 11.60/11.98
% 11.60/11.98
% 11.60/11.98 Intermediate Status:
% 39.33/39.76 Generated: 4471
% 39.33/39.76 Kept: 2340
% 39.33/39.76 Inuse: 115
% 39.33/39.76 Deleted: 0
% 39.33/39.76 Deletedinuse: 0
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76
% 39.33/39.76 Intermediate Status:
% 39.33/39.76 Generated: 12061
% 39.33/39.76 Kept: 4822
% 39.33/39.76 Inuse: 214
% 39.33/39.76 Deleted: 2
% 39.33/39.76 Deletedinuse: 0
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76
% 39.33/39.76 Intermediate Status:
% 39.33/39.76 Generated: 18307
% 39.33/39.76 Kept: 6883
% 39.33/39.76 Inuse: 304
% 39.33/39.76 Deleted: 3
% 39.33/39.76 Deletedinuse: 1
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76
% 39.33/39.76 Intermediate Status:
% 39.33/39.76 Generated: 28384
% 39.33/39.76 Kept: 9472
% 39.33/39.76 Inuse: 343
% 39.33/39.76 Deleted: 6
% 39.33/39.76 Deletedinuse: 3
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76
% 39.33/39.76 Intermediate Status:
% 39.33/39.76 Generated: 35080
% 39.33/39.76 Kept: 11546
% 39.33/39.76 Inuse: 396
% 39.33/39.76 Deleted: 8
% 39.33/39.76 Deletedinuse: 3
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76
% 39.33/39.76 Intermediate Status:
% 39.33/39.76 Generated: 41973
% 39.33/39.76 Kept: 13574
% 39.33/39.76 Inuse: 458
% 39.33/39.76 Deleted: 11
% 39.33/39.76 Deletedinuse: 3
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76
% 39.33/39.76 Intermediate Status:
% 39.33/39.76 Generated: 48183
% 39.33/39.76 Kept: 15587
% 39.33/39.76 Inuse: 519
% 39.33/39.76 Deleted: 13
% 39.33/39.76 Deletedinuse: 3
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76
% 39.33/39.76 Intermediate Status:
% 39.33/39.76 Generated: 58484
% 39.33/39.76 Kept: 17894
% 39.33/39.76 Inuse: 560
% 39.33/39.76 Deleted: 14
% 39.33/39.76 Deletedinuse: 3
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76
% 39.33/39.76 Intermediate Status:
% 39.33/39.76 Generated: 63466
% 39.33/39.76 Kept: 19949
% 39.33/39.76 Inuse: 594
% 39.33/39.76 Deleted: 15
% 39.33/39.76 Deletedinuse: 3
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76 Resimplifying clauses:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76
% 39.33/39.76 Intermediate Status:
% 39.33/39.76 Generated: 68659
% 39.33/39.76 Kept: 21964
% 39.33/39.76 Inuse: 622
% 39.33/39.76 Deleted: 244
% 39.33/39.76 Deletedinuse: 3
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76
% 39.33/39.76 Intermediate Status:
% 39.33/39.76 Generated: 75475
% 39.33/39.76 Kept: 24653
% 39.33/39.76 Inuse: 639
% 39.33/39.76 Deleted: 245
% 39.33/39.76 Deletedinuse: 4
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76
% 39.33/39.76 Intermediate Status:
% 39.33/39.76 Generated: 80079
% 39.33/39.76 Kept: 26654
% 39.33/39.76 Inuse: 647
% 39.33/39.76 Deleted: 245
% 39.33/39.76 Deletedinuse: 4
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76
% 39.33/39.76 Intermediate Status:
% 39.33/39.76 Generated: 99875
% 39.33/39.76 Kept: 31532
% 39.33/39.76 Inuse: 669
% 39.33/39.76 Deleted: 245
% 39.33/39.76 Deletedinuse: 4
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76
% 39.33/39.76 Intermediate Status:
% 39.33/39.76 Generated: 116323
% 39.33/39.76 Kept: 34596
% 39.33/39.76 Inuse: 684
% 39.33/39.76 Deleted: 246
% 39.33/39.76 Deletedinuse: 5
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76
% 39.33/39.76 Intermediate Status:
% 39.33/39.76 Generated: 126686
% 39.33/39.76 Kept: 36645
% 39.33/39.76 Inuse: 696
% 39.33/39.76 Deleted: 247
% 39.33/39.76 Deletedinuse: 6
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76
% 39.33/39.76 Intermediate Status:
% 39.33/39.76 Generated: 136409
% 39.33/39.76 Kept: 38660
% 39.33/39.76 Inuse: 734
% 39.33/39.76 Deleted: 247
% 39.33/39.76 Deletedinuse: 6
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76
% 39.33/39.76 Intermediate Status:
% 39.33/39.76 Generated: 145403
% 39.33/39.76 Kept: 40781
% 39.33/39.76 Inuse: 759
% 39.33/39.76 Deleted: 250
% 39.33/39.76 Deletedinuse: 9
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76 Resimplifying clauses:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76
% 39.33/39.76 Intermediate Status:
% 39.33/39.76 Generated: 156321
% 39.33/39.76 Kept: 43410
% 39.33/39.76 Inuse: 769
% 39.33/39.76 Deleted: 396
% 39.33/39.76 Deletedinuse: 9
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76
% 39.33/39.76 Intermediate Status:
% 39.33/39.76 Generated: 164285
% 39.33/39.76 Kept: 46108
% 39.33/39.76 Inuse: 774
% 39.33/39.76 Deleted: 396
% 39.33/39.76 Deletedinuse: 9
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76
% 39.33/39.76 Intermediate Status:
% 39.33/39.76 Generated: 174604
% 39.33/39.76 Kept: 48683
% 39.33/39.76 Inuse: 781
% 39.33/39.76 Deleted: 405
% 39.33/39.76 Deletedinuse: 10
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76
% 39.33/39.76 Intermediate Status:
% 39.33/39.76 Generated: 181469
% 39.33/39.76 Kept: 50695
% 39.33/39.76 Inuse: 801
% 39.33/39.76 Deleted: 405
% 39.33/39.76 Deletedinuse: 10
% 39.33/39.76
% 39.33/39.76
% 39.33/39.76 Intermediate Status:
% 39.33/39.76 Generated: 194749
% 39.33/39.76 Kept: 53326
% 39.33/39.76 Inuse: 806
% 39.33/39.76 Deleted: 405
% 39.33/39.76 Deletedinuse: 10
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76
% 39.33/39.76 Intermediate Status:
% 39.33/39.76 Generated: 208593
% 39.33/39.76 Kept: 55977
% 39.33/39.76 Inuse: 811
% 39.33/39.76 Deleted: 405
% 39.33/39.76 Deletedinuse: 10
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76
% 39.33/39.76 Intermediate Status:
% 39.33/39.76 Generated: 230686
% 39.33/39.76 Kept: 60430
% 39.33/39.76 Inuse: 836
% 39.33/39.76 Deleted: 410
% 39.33/39.76 Deletedinuse: 10
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76
% 39.33/39.76 Intermediate Status:
% 39.33/39.76 Generated: 245607
% 39.33/39.76 Kept: 63115
% 39.33/39.76 Inuse: 841
% 39.33/39.76 Deleted: 410
% 39.33/39.76 Deletedinuse: 10
% 39.33/39.76
% 39.33/39.76 Resimplifying inuse:
% 39.33/39.76 Done
% 39.33/39.76
% 39.33/39.76 Resimplifying clauses:
% 39.33/39.76 Done
% 96.39/96.82
% 96.39/96.82 Resimplifying inuse:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82
% 96.39/96.82 Intermediate Status:
% 96.39/96.82 Generated: 253649
% 96.39/96.82 Kept: 65125
% 96.39/96.82 Inuse: 866
% 96.39/96.82 Deleted: 636
% 96.39/96.82 Deletedinuse: 10
% 96.39/96.82
% 96.39/96.82 Resimplifying inuse:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82 Resimplifying inuse:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82
% 96.39/96.82 Intermediate Status:
% 96.39/96.82 Generated: 260312
% 96.39/96.82 Kept: 67245
% 96.39/96.82 Inuse: 891
% 96.39/96.82 Deleted: 636
% 96.39/96.82 Deletedinuse: 10
% 96.39/96.82
% 96.39/96.82 Resimplifying inuse:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82 Resimplifying inuse:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82
% 96.39/96.82 Intermediate Status:
% 96.39/96.82 Generated: 266695
% 96.39/96.82 Kept: 69337
% 96.39/96.82 Inuse: 911
% 96.39/96.82 Deleted: 636
% 96.39/96.82 Deletedinuse: 10
% 96.39/96.82
% 96.39/96.82 Resimplifying inuse:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82
% 96.39/96.82 Intermediate Status:
% 96.39/96.82 Generated: 275721
% 96.39/96.82 Kept: 71918
% 96.39/96.82 Inuse: 926
% 96.39/96.82 Deleted: 636
% 96.39/96.82 Deletedinuse: 10
% 96.39/96.82
% 96.39/96.82 Resimplifying inuse:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82 Resimplifying inuse:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82
% 96.39/96.82 Intermediate Status:
% 96.39/96.82 Generated: 283180
% 96.39/96.82 Kept: 74086
% 96.39/96.82 Inuse: 936
% 96.39/96.82 Deleted: 636
% 96.39/96.82 Deletedinuse: 10
% 96.39/96.82
% 96.39/96.82 Resimplifying inuse:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82
% 96.39/96.82 Intermediate Status:
% 96.39/96.82 Generated: 324123
% 96.39/96.82 Kept: 79250
% 96.39/96.82 Inuse: 950
% 96.39/96.82 Deleted: 643
% 96.39/96.82 Deletedinuse: 16
% 96.39/96.82
% 96.39/96.82 Resimplifying inuse:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82 Resimplifying inuse:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82
% 96.39/96.82 Intermediate Status:
% 96.39/96.82 Generated: 331547
% 96.39/96.82 Kept: 81250
% 96.39/96.82 Inuse: 976
% 96.39/96.82 Deleted: 643
% 96.39/96.82 Deletedinuse: 16
% 96.39/96.82
% 96.39/96.82 Resimplifying inuse:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82
% 96.39/96.82 Intermediate Status:
% 96.39/96.82 Generated: 343063
% 96.39/96.82 Kept: 85837
% 96.39/96.82 Inuse: 982
% 96.39/96.82 Deleted: 643
% 96.39/96.82 Deletedinuse: 16
% 96.39/96.82
% 96.39/96.82 Resimplifying inuse:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82 Resimplifying clauses:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82 Resimplifying inuse:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82
% 96.39/96.82 Intermediate Status:
% 96.39/96.82 Generated: 356677
% 96.39/96.82 Kept: 88579
% 96.39/96.82 Inuse: 1000
% 96.39/96.82 Deleted: 849
% 96.39/96.82 Deletedinuse: 17
% 96.39/96.82
% 96.39/96.82 Resimplifying inuse:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82 Resimplifying inuse:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82
% 96.39/96.82 Intermediate Status:
% 96.39/96.82 Generated: 368146
% 96.39/96.82 Kept: 91630
% 96.39/96.82 Inuse: 1015
% 96.39/96.82 Deleted: 849
% 96.39/96.82 Deletedinuse: 17
% 96.39/96.82
% 96.39/96.82 Resimplifying inuse:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82 Resimplifying inuse:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82
% 96.39/96.82 Intermediate Status:
% 96.39/96.82 Generated: 375491
% 96.39/96.82 Kept: 93735
% 96.39/96.82 Inuse: 1035
% 96.39/96.82 Deleted: 849
% 96.39/96.82 Deletedinuse: 17
% 96.39/96.82
% 96.39/96.82 Resimplifying inuse:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82 Resimplifying inuse:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82
% 96.39/96.82 Intermediate Status:
% 96.39/96.82 Generated: 383545
% 96.39/96.82 Kept: 95759
% 96.39/96.82 Inuse: 1066
% 96.39/96.82 Deleted: 850
% 96.39/96.82 Deletedinuse: 18
% 96.39/96.82
% 96.39/96.82 Resimplifying inuse:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82 Resimplifying inuse:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82
% 96.39/96.82 Intermediate Status:
% 96.39/96.82 Generated: 392470
% 96.39/96.82 Kept: 97947
% 96.39/96.82 Inuse: 1095
% 96.39/96.82 Deleted: 852
% 96.39/96.82 Deletedinuse: 20
% 96.39/96.82
% 96.39/96.82 Resimplifying inuse:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82 Resimplifying inuse:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82
% 96.39/96.82 Intermediate Status:
% 96.39/96.82 Generated: 402382
% 96.39/96.82 Kept: 99983
% 96.39/96.82 Inuse: 1126
% 96.39/96.82 Deleted: 854
% 96.39/96.82 Deletedinuse: 22
% 96.39/96.82
% 96.39/96.82 Resimplifying inuse:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82 Resimplifying inuse:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82
% 96.39/96.82 Intermediate Status:
% 96.39/96.82 Generated: 413301
% 96.39/96.82 Kept: 102463
% 96.39/96.82 Inuse: 1155
% 96.39/96.82 Deleted: 854
% 96.39/96.82 Deletedinuse: 22
% 96.39/96.82
% 96.39/96.82 Resimplifying inuse:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82 Resimplifying inuse:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82
% 96.39/96.82 Intermediate Status:
% 96.39/96.82 Generated: 452646
% 96.39/96.82 Kept: 106279
% 96.39/96.82 Inuse: 1180
% 96.39/96.82 Deleted: 854
% 96.39/96.82 Deletedinuse: 22
% 96.39/96.82
% 96.39/96.82 Resimplifying inuse:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82 Resimplifying clauses:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82
% 96.39/96.82 Intermediate Status:
% 96.39/96.82 Generated: 472368
% 96.39/96.82 Kept: 110188
% 96.39/96.82 Inuse: 1190
% 96.39/96.82 Deleted: 1237
% 96.39/96.82 Deletedinuse: 22
% 96.39/96.82
% 96.39/96.82 Resimplifying inuse:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82
% 96.39/96.82 Intermediate Status:
% 96.39/96.82 Generated: 491042
% 96.39/96.82 Kept: 113904
% 96.39/96.82 Inuse: 1195
% 96.39/96.82 Deleted: 1237
% 96.39/96.82 Deletedinuse: 22
% 96.39/96.82
% 96.39/96.82 Resimplifying inuse:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82 Resimplifying inuse:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82
% 96.39/96.82 Intermediate Status:
% 96.39/96.82 Generated: 498863
% 96.39/96.82 Kept: 116022
% 96.39/96.82 Inuse: 1210
% 96.39/96.82 Deleted: 1237
% 96.39/96.82 Deletedinuse: 22
% 96.39/96.82
% 96.39/96.82 Resimplifying inuse:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82
% 96.39/96.82 Intermediate Status:
% 96.39/96.82 Generated: 508451
% 96.39/96.82 Kept: 118441
% 96.39/96.82 Inuse: 1225
% 96.39/96.82 Deleted: 1237
% 96.39/96.82 Deletedinuse: 22
% 96.39/96.82
% 96.39/96.82 Resimplifying inuse:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82 Resimplifying inuse:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82
% 96.39/96.82 Intermediate Status:
% 96.39/96.82 Generated: 515107
% 96.39/96.82 Kept: 120648
% 96.39/96.82 Inuse: 1239
% 96.39/96.82 Deleted: 1240
% 96.39/96.82 Deletedinuse: 25
% 96.39/96.82
% 96.39/96.82 Resimplifying inuse:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82 Resimplifying inuse:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82
% 96.39/96.82 Intermediate Status:
% 96.39/96.82 Generated: 529268
% 96.39/96.82 Kept: 122854
% 96.39/96.82 Inuse: 1257
% 96.39/96.82 Deleted: 1254
% 96.39/96.82 Deletedinuse: 26
% 96.39/96.82
% 96.39/96.82
% 96.39/96.82 Intermediate Status:
% 96.39/96.82 Generated: 548895
% 96.39/96.82 Kept: 124954
% 96.39/96.82 Inuse: 1260
% 96.39/96.82 Deleted: 1261
% 96.39/96.82 Deletedinuse: 26
% 96.39/96.82
% 96.39/96.82 Resimplifying inuse:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82 Resimplifying inuse:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82 Resimplifying clauses:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82
% 96.39/96.82 Intermediate Status:
% 96.39/96.82 Generated: 569702
% 96.39/96.82 Kept: 129141
% 96.39/96.82 Inuse: 1276
% 96.39/96.82 Deleted: 1897
% 96.39/96.82 Deletedinuse: 26
% 96.39/96.82
% 96.39/96.82 Resimplifying inuse:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82 Resimplifying inuse:
% 96.39/96.82 Done
% 96.39/96.82
% 96.39/96.82
% 96.39/96.82 Intermediate Status:
% 96.39/96.82 Generated: 576331
% 96.39/96.82 Kept: 131232
% 181.88/182.34 Inuse: 1297
% 181.88/182.34 Deleted: 1910
% 181.88/182.34 Deletedinuse: 39
% 181.88/182.34
% 181.88/182.34 Resimplifying inuse:
% 181.88/182.34 Done
% 181.88/182.34
% 181.88/182.34 Resimplifying inuse:
% 181.88/182.34 Done
% 181.88/182.34
% 181.88/182.34
% 181.88/182.34 Intermediate Status:
% 181.88/182.34 Generated: 586806
% 181.88/182.34 Kept: 133514
% 181.88/182.34 Inuse: 1322
% 181.88/182.34 Deleted: 1910
% 181.88/182.34 Deletedinuse: 39
% 181.88/182.34
% 181.88/182.34 Resimplifying inuse:
% 181.88/182.34 Done
% 181.88/182.34
% 181.88/182.34
% 181.88/182.34 Intermediate Status:
% 181.88/182.34 Generated: 601928
% 181.88/182.34 Kept: 137547
% 181.88/182.34 Inuse: 1337
% 181.88/182.34 Deleted: 1910
% 181.88/182.34 Deletedinuse: 39
% 181.88/182.34
% 181.88/182.34 Resimplifying inuse:
% 181.88/182.34 Done
% 181.88/182.34
% 181.88/182.34 Resimplifying inuse:
% 181.88/182.34 Done
% 181.88/182.34
% 181.88/182.34
% 181.88/182.34 Intermediate Status:
% 181.88/182.34 Generated: 614533
% 181.88/182.34 Kept: 140137
% 181.88/182.34 Inuse: 1372
% 181.88/182.34 Deleted: 1910
% 181.88/182.34 Deletedinuse: 39
% 181.88/182.34
% 181.88/182.34 Resimplifying inuse:
% 181.88/182.34 Done
% 181.88/182.34
% 181.88/182.34 Resimplifying inuse:
% 181.88/182.34 Done
% 181.88/182.34
% 181.88/182.34
% 181.88/182.34 Intermediate Status:
% 181.88/182.34 Generated: 624556
% 181.88/182.34 Kept: 142141
% 181.88/182.34 Inuse: 1394
% 181.88/182.34 Deleted: 1910
% 181.88/182.34 Deletedinuse: 39
% 181.88/182.34
% 181.88/182.34 Resimplifying inuse:
% 181.88/182.34 Done
% 181.88/182.34
% 181.88/182.34 Resimplifying inuse:
% 181.88/182.34 Done
% 181.88/182.34
% 181.88/182.34
% 181.88/182.34 Intermediate Status:
% 181.88/182.34 Generated: 633001
% 181.88/182.34 Kept: 144296
% 181.88/182.34 Inuse: 1420
% 181.88/182.34 Deleted: 1914
% 181.88/182.34 Deletedinuse: 41
% 181.88/182.34
% 181.88/182.34
% 181.88/182.34 Intermediate Status:
% 181.88/182.34 Generated: 643666
% 181.88/182.34 Kept: 147276
% 181.88/182.34 Inuse: 1430
% 181.88/182.34 Deleted: 1914
% 181.88/182.34 Deletedinuse: 41
% 181.88/182.34
% 181.88/182.34 Resimplifying inuse:
% 181.88/182.34 Done
% 181.88/182.34
% 181.88/182.34 Resimplifying clauses:
% 181.88/182.34 Done
% 181.88/182.34
% 181.88/182.34 Resimplifying inuse:
% 181.88/182.34 Done
% 181.88/182.34
% 181.88/182.34
% 181.88/182.34 Intermediate Status:
% 181.88/182.34 Generated: 668021
% 181.88/182.34 Kept: 151376
% 181.88/182.34 Inuse: 1449
% 181.88/182.34 Deleted: 2625
% 181.88/182.34 Deletedinuse: 47
% 181.88/182.34
% 181.88/182.34 Resimplifying inuse:
% 181.88/182.34 Done
% 181.88/182.34
% 181.88/182.34
% 181.88/182.34 Intermediate Status:
% 181.88/182.34 Generated: 685095
% 181.88/182.34 Kept: 153711
% 181.88/182.34 Inuse: 1452
% 181.88/182.34 Deleted: 2631
% 181.88/182.34 Deletedinuse: 51
% 181.88/182.34
% 181.88/182.34 Resimplifying inuse:
% 181.88/182.34 Done
% 181.88/182.34
% 181.88/182.34
% 181.88/182.34 Intermediate Status:
% 181.88/182.34 Generated: 703166
% 181.88/182.34 Kept: 156055
% 181.88/182.34 Inuse: 1456
% 181.88/182.34 Deleted: 2632
% 181.88/182.34 Deletedinuse: 51
% 181.88/182.34
% 181.88/182.34 Resimplifying inuse:
% 181.88/182.34 Done
% 181.88/182.34
% 181.88/182.34
% 181.88/182.34 Intermediate Status:
% 181.88/182.34 Generated: 721786
% 181.88/182.34 Kept: 158432
% 181.88/182.34 Inuse: 1461
% 181.88/182.34 Deleted: 2632
% 181.88/182.34 Deletedinuse: 51
% 181.88/182.34
% 181.88/182.34 Resimplifying inuse:
% 181.88/182.34 Done
% 181.88/182.34
% 181.88/182.34
% 181.88/182.34 Intermediate Status:
% 181.88/182.34 Generated: 740754
% 181.88/182.34 Kept: 160813
% 181.88/182.34 Inuse: 1466
% 181.88/182.34 Deleted: 2632
% 181.88/182.34 Deletedinuse: 51
% 181.88/182.34
% 181.88/182.34 Resimplifying inuse:
% 181.88/182.34 Done
% 181.88/182.34
% 181.88/182.34
% 181.88/182.34 Intermediate Status:
% 181.88/182.34 Generated: 760264
% 181.88/182.34 Kept: 163222
% 181.88/182.34 Inuse: 1471
% 181.88/182.34 Deleted: 2632
% 181.88/182.34 Deletedinuse: 51
% 181.88/182.34
% 181.88/182.34 Resimplifying inuse:
% 181.88/182.34 Done
% 181.88/182.34
% 181.88/182.34
% 181.88/182.34 Intermediate Status:
% 181.88/182.34 Generated: 779335
% 181.88/182.34 Kept: 165686
% 181.88/182.34 Inuse: 1475
% 181.88/182.34 Deleted: 2633
% 181.88/182.34 Deletedinuse: 51
% 181.88/182.34
% 181.88/182.34 Resimplifying inuse:
% 181.88/182.34 Done
% 181.88/182.34
% 181.88/182.34
% 181.88/182.34 Intermediate Status:
% 181.88/182.34 Generated: 798052
% 181.88/182.34 Kept: 169159
% 181.88/182.34 Inuse: 1479
% 181.88/182.34 Deleted: 2636
% 181.88/182.34 Deletedinuse: 53
% 181.88/182.34
% 181.88/182.34 Resimplifying inuse:
% 181.88/182.34 Done
% 181.88/182.34
% 181.88/182.34 Resimplifying clauses:
% 181.88/182.34 Done
% 181.88/182.34
% 181.88/182.34
% 181.88/182.34 Intermediate Status:
% 181.88/182.34 Generated: 816495
% 181.88/182.34 Kept: 171490
% 181.88/182.34 Inuse: 1484
% 181.88/182.34 Deleted: 3283
% 181.88/182.34 Deletedinuse: 59
% 181.88/182.34
% 181.88/182.34 Resimplifying inuse:
% 181.88/182.34 Done
% 181.88/182.34
% 181.88/182.34
% 181.88/182.34 Intermediate Status:
% 181.88/182.34 Generated: 836177
% 181.88/182.34 Kept: 173859
% 181.88/182.34 Inuse: 1489
% 181.88/182.34 Deleted: 3283
% 181.88/182.34 Deletedinuse: 59
% 181.88/182.34
% 181.88/182.34 Resimplifying inuse:
% 181.88/182.34 Done
% 181.88/182.34
% 181.88/182.34 Resimplifying inuse:
% 181.88/182.34 Done
% 181.88/182.34
% 181.88/182.34
% 181.88/182.34 Intermediate Status:
% 181.88/182.34 Generated: 848304
% 181.88/182.34 Kept: 175878
% 181.88/182.34 Inuse: 1508
% 181.88/182.34 Deleted: 3283
% 181.88/182.34 Deletedinuse: 59
% 181.88/182.34
% 181.88/182.34 Resimplifying inuse:
% 181.88/182.34 Done
% 181.88/182.34
% 181.88/182.34 Resimplifying inuse:
% 181.88/182.34 Done
% 181.88/182.34
% 181.88/182.34
% 181.88/182.34 Intermediate Status:
% 181.88/182.34 Generated: 858052
% 181.88/182.34 Kept: 177881
% 181.88/182.34 Inuse: 1520
% 181.88/182.34 Deleted: 3283
% 181.88/182.34 Deletedinuse: 59
% 181.88/182.34
% 181.88/182.34 Resimplifying inuse:
% 181.88/182.34 Done
% 181.88/182.34
% 181.88/182.34
% 181.88/182.34 Intermediate Status:
% 181.88/182.34 Generated: 868031
% 181.88/182.34 Kept: 179903
% 181.88/182.34 Inuse: 1539
% 181.88/182.34 Deleted: 3283
% 181.88/182.34 Deletedinuse: 59
% 181.88/182.34
% 181.88/182.34 Resimplifying inuse:
% 181.88/182.34 Done
% 181.88/182.34
% 181.88/182.34 Resimplifying inuse:
% 181.88/182.34 Done
% 181.88/182.34
% 181.88/182.34
% 181.88/182.34 Intermediate Status:
% 181.88/182.34 Generated: 880332
% 181.88/182.34 Kept: 181903
% 181.88/182.34 Inuse: 1563
% 181.88/182.34 Deleted: 3283
% 181.88/182.34 Deletedinuse: 59
% 181.88/182.34
% 181.88/182.34
% 181.88/182.34 Intermediate Status:
% 181.88/182.34 Generated: 889816
% 181.88/182.34 Kept: 184012
% 181.88/182.34 Inuse: 1564
% 181.88/182.34 Deleted: 3283
% 181.88/182.34 Deletedinuse: 59
% 181.88/182.34
% 181.88/182.34 Resimplifying inuse:
% 181.88/182.34 Done
% 181.88/182.34
% 181.88/182.34 Resimplifying inuse:
% 181.88/182.34 Done
% 181.88/182.34
% 181.88/182.34
% 181.88/182.34 Intermediate Status:
% 181.88/182.34 Generated: 901673
% 181.88/182.34 Kept: 186305
% 181.88/182.34 Inuse: 1584
% 181.88/182.34 Deleted: 3283
% 181.88/182.34 Deletedinuse: 59
% 181.88/182.34
% 181.88/182.34 Resimplifying inuse:
% 181.88/182.34 Done
% 181.88/182.34
% 181.88/182.34 Resimplifying inuse:
% 181.88/182.34 Done
% 181.88/182.34
% 181.88/182.34
% 181.88/182.34 Intermediate Status:
% 181.88/182.34 Generated: 911749
% 181.88/182.34 Kept: 188913
% 181.88/182.34 Inuse: 1599
% 181.88/182.34 Deleted: 3283
% 181.88/182.34 Deletedinuse: 59
% 181.88/182.34
% 181.88/182.34 Resimplifying inuse:
% 181.88/182.34 Done
% 181.88/182.34
% 181.88/182.34 Resimplifying clauses:
% 181.88/182.34 Done
% 181.88/182.34
% 181.88/182.34
% 181.88/182.34 Intermediate Status:
% 181.88/182.34 Generated: 922458
% 181.88/182.34 Kept: 191265
% 181.88/182.34 Inuse: 1614
% 181.88/182.34 Deleted: 3451
% 181.88/182.34 Deletedinuse: 59
% 181.88/182.34
% 181.88/182.34 Resimplifying inuse:
% 181.88/182.34 Done
% 181.88/182.34
% 181.88/182.34 Resimplifying inuse:
% 181.88/182.34 Done
% 181.88/182.34
% 181.88/182.34
% 181.88/182.34 Intermediate Status:
% 181.88/182.34 Generated: 936172
% 181.88/182.34 Kept: 194322
% 181.88/182.34 Inuse: 1629
% 181.88/182.34 Deleted: 3451
% 181.88/182.34 Deletedinuse: 59
% 181.88/182.34
% 181.88/182.34 Resimplifying inuse:
% 181.88/182.34 Done
% 181.88/182.34
% 300.06/300.50 Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------