TSTP Solution File: SCT081-1 by Bliksem---1.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SCT081-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n007.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 : Mon Jul 18 21:01:04 EDT 2022
% Result : Timeout 300.04s 301.01s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SCT081-1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % DateTime : Sat Jul 2 00:51:24 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.00/1.34 *** allocated 10000 integers for termspace/termends
% 1.00/1.34 *** allocated 10000 integers for clauses
% 1.00/1.34 *** allocated 10000 integers for justifications
% 1.00/1.34 *** allocated 15000 integers for termspace/termends
% 1.00/1.34 *** allocated 22500 integers for termspace/termends
% 1.00/1.34 Bliksem 1.12
% 1.00/1.34
% 1.00/1.34
% 1.00/1.34 Automatic Strategy Selection
% 1.00/1.34
% 1.00/1.34 Clauses:
% 1.00/1.34 [
% 1.00/1.34 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Orderings_Obot__class_Obot'(
% 1.00/1.34 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ],
% 1.00/1.34 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Orderings_Otop__class_Otop'(
% 1.00/1.34 'tc_fun'( X, 'tc_bool' ) ) ) ) ],
% 1.00/1.34 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP(
% 1.00/1.34 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ), Z ) ) ),
% 1.00/1.34 hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ],
% 1.00/1.34 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.34 'c_in'( X ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X,
% 1.00/1.34 'tc_bool' ) ), Z ) ) ) ) ],
% 1.00/1.34 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.34 'c_in'( X ), Y ), 'c_Lattices_Olower__semilattice__class_Oinf'( T, Z,
% 1.00/1.34 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ],
% 1.00/1.34 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.34 'c_in'( X ), Y ), 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T,
% 1.00/1.34 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ],
% 1.00/1.34 [ ~( hBOOL( hAPP( X, Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), Y ),
% 1.00/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ) ) ],
% 1.00/1.34 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.00/1.34 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.00/1.34 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.00/1.34 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), =( hAPP(
% 1.00/1.34 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.00/1.34 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.00/1.34 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =(
% 1.00/1.34 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.00/1.34 ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.00/1.34 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP(
% 1.00/1.34 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.00/1.34 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.00/1.34 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =(
% 1.00/1.34 'c_HOL_Ozero__class_Ozero'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.00/1.34 ), Y ) ) ), =( 'c_HOL_Ozero__class_Ozero'( X ), Y ) ],
% 1.00/1.34 [ ~( 'class_OrderedGroup_Oordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.00/1.34 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y ) ), =( Y,
% 1.00/1.34 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.00/1.34 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.00/1.34 'c_HOL_Oord__class_Oless'( X ),
% 1.00/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ), T ) ), ~(
% 1.00/1.34 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.00/1.34 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), hBOOL( hAPP( hAPP(
% 1.00/1.34 'c_HOL_Oord__class_Oless'( X ),
% 1.00/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ), T ) ), ~(
% 1.00/1.34 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ],
% 1.00/1.34 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.00/1.34 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.34 'c_HOL_Oord__class_Oless'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X )
% 1.00/1.34 , Z ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ) ) ],
% 1.00/1.34 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.00/1.34 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.00/1.34 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), hAPP(
% 1.00/1.34 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.34 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ],
% 1.00/1.34 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.00/1.34 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP(
% 1.00/1.34 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.34 'c_HOL_Oord__class_Oless'( X ), Z ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.00/1.34 X ), Y ) ) ) ) ],
% 1.00/1.34 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.00/1.34 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP(
% 1.00/1.34 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.34 'c_HOL_Oord__class_Oless'( X ), Z ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.00/1.34 X ), Y ) ) ) ) ],
% 1.00/1.34 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.00/1.34 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.00/1.34 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.34 'c_HOL_Oord__class_Oless'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X )
% 1.00/1.34 , Z ) ), Y ) ) ) ],
% 1.00/1.34 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.00/1.34 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.00/1.34 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.34 'c_HOL_Oord__class_Oless'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X )
% 1.00/1.34 , Z ) ), Y ) ) ) ],
% 1.00/1.34 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Orderings_Obot__class_Obot'(
% 1.00/1.34 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ],
% 1.00/1.34 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), Y ),
% 1.00/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z, 'tc_bool' ) ) ) ) ) ],
% 1.00/1.34 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Orderings_Obot__class_Obot'(
% 1.00/1.34 'tc_fun'( X, 'tc_bool' ) ) ) ) ) ],
% 1.00/1.34 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.00/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, 'tc_fun'( X,
% 1.00/1.34 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~(
% 1.00/1.34 hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ],
% 1.00/1.34 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ),
% 1.00/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, 'tc_fun'( X,
% 1.00/1.34 'tc_bool' ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~(
% 1.00/1.34 hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ) ],
% 1.00/1.34 [ 'c_Finite__Set_Ofinite'( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.00/1.34 X, Y, 'tc_fun'( Z, 'tc_bool' ) ), Z ), ~( 'c_Finite__Set_Ofinite'( X, Z )
% 1.00/1.34 ) ],
% 1.00/1.34 [ 'c_Finite__Set_Ofinite'( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.00/1.34 X, Y, 'tc_fun'( Z, 'tc_bool' ) ), Z ), ~( 'c_Finite__Set_Ofinite'( Y, Z )
% 1.00/1.34 ) ],
% 1.00/1.34 [ =( 'c_Set_Ovimage'( X, 'c_Lattices_Olower__semilattice__class_Oinf'( Y
% 1.00/1.34 , Z, 'tc_fun'( T, 'tc_bool' ) ), U, T ),
% 1.00/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( 'c_Set_Ovimage'( X, Y, U, T
% 1.00/1.34 ), 'c_Set_Ovimage'( X, Z, U, T ), 'tc_fun'( U, 'tc_bool' ) ) ) ],
% 1.00/1.34 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.00/1.34 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.00/1.34 X ), Y ) ), Y ) ],
% 1.00/1.34 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y, hAPP(
% 1.00/1.34 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.00/1.34 X ), Y ) ) ) ],
% 1.00/1.34 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( Y, hAPP(
% 1.00/1.34 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.00/1.34 X ), Y ) ) ) ],
% 1.00/1.34 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =( hAPP(
% 1.00/1.34 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.00/1.34 X ), Y ) ), Y ) ],
% 1.00/1.34 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.00/1.34 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.00/1.34 X ), Y ) ), Y ) ],
% 1.00/1.34 [ =( hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.00/1.34 hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ), Y ) ),
% 1.00/1.34 Y ) ],
% 1.00/1.34 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP(
% 1.00/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 1.00/1.34 'tc_bool' ) ), Y ) ) ) ],
% 1.00/1.34 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP(
% 1.00/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Z, X, 'tc_fun'( T,
% 1.00/1.34 'tc_bool' ) ), Y ) ) ) ],
% 1.00/1.34 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.00/1.34 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.00/1.34 X ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), hAPP( hAPP(
% 1.00/1.34 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.00/1.34 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), =( hAPP( hAPP(
% 1.00/1.34 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.00/1.34 X ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), hAPP( hAPP(
% 1.00/1.34 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ) ],
% 1.00/1.34 [ ~( 'class_Divides_Oring__div'( X ) ), =( 'c_Divides_Odiv__class_Omod'(
% 1.00/1.34 hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ),
% 1.00/1.34 'c_Divides_Odiv__class_Omod'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.00/1.34 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), Z, X ) ) ],
% 1.00/1.34 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.00/1.34 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.00/1.34 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), Z ) ), =( Y, hAPP(
% 1.00/1.34 'c_HOL_Ouminus__class_Ouminus'( X ), T ) ) ],
% 1.00/1.34 [ =( 'c_Set_Ovimage'( X, hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'(
% 1.00/1.34 Y, 'tc_bool' ) ), Z ), T, Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.00/1.34 'tc_fun'( T, 'tc_bool' ) ), 'c_Set_Ovimage'( X, Z, T, Y ) ) ) ],
% 1.00/1.34 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.00/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.00/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Z, Y, X ) ) ],
% 1.00/1.34 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.00/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.00/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Z, Y, X ) ) ],
% 1.00/1.34 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.00/1.34 'tc_bool' ) ), 'c_Lattices_Olower__semilattice__class_Oinf'( Y, X,
% 1.00/1.34 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.00/1.34 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.00/1.34 hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.00/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ), T ),
% 1.00/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 1.00/1.34 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.00/1.34 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.00/1.34 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.00/1.34 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.00/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ) ),
% 1.00/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 1.00/1.34 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.00/1.34 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ],
% 1.00/1.34 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__meet'( X ) ), =(
% 1.00/1.34 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ),
% 1.00/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ), T ),
% 1.00/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 1.00/1.34 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), hAPP( hAPP(
% 1.00/1.34 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ), X ) ) ],
% 1.00/1.34 [ ~( 'class_OrderedGroup_Olordered__ab__group__add__meet'( X ) ), =(
% 1.00/1.34 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.00/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ) ),
% 1.00/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP( hAPP(
% 1.00/1.34 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.00/1.34 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), X ) ) ],
% 1.00/1.34 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =(
% 1.00/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y, hAPP(
% 1.00/1.34 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.34 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.00/1.34 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 1.00/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y, hAPP(
% 1.00/1.34 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), X ),
% 1.00/1.34 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.00/1.34 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =(
% 1.00/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP(
% 1.00/1.34 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Y, X ),
% 1.00/1.34 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.00/1.34 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, hAPP(
% 1.00/1.34 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( Y, 'tc_bool' ) ), X ), 'tc_fun'(
% 1.00/1.34 Y, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool'
% 1.00/1.34 ) ) ) ],
% 1.00/1.34 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( hAPP(
% 1.00/1.34 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ), Y ), Y,
% 1.00/1.34 'tc_fun'( X, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.00/1.34 'tc_bool' ) ) ) ],
% 1.00/1.34 [ =( 'c_Set_Ovimage'( X, 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y,
% 1.00/1.34 'tc_bool' ) ), Z, Y ), 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Z,
% 1.00/1.34 'tc_bool' ) ) ) ],
% 1.00/1.34 [ =( 'c_Relation_OImage'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y
% 1.00/1.34 , 'tc_bool' ) ), Y, Z ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.00/1.34 'tc_bool' ) ) ) ],
% 1.00/1.34 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.00/1.34 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.00/1.34 'c_Orderings_Obot__class_Obot'( X ), X ), 'c_Orderings_Obot__class_Obot'(
% 1.00/1.34 X ) ) ],
% 1.00/1.34 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.00/1.34 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.00/1.34 'c_Orderings_Obot__class_Obot'( X ), Y, X ),
% 1.00/1.34 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.00/1.34 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.00/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 1.00/1.34 X, 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.00/1.34 ) ) ) ],
% 1.00/1.34 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.00/1.34 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 1.00/1.34 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y, 'tc_bool' ) )
% 1.00/1.34 ) ],
% 1.00/1.34 [ 'c_Finite__Set_Ofinite'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.00/1.34 'tc_bool' ) ), X ) ],
% 1.00/1.34 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( =( hAPP( hAPP(
% 1.00/1.34 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), hAPP( hAPP(
% 1.00/1.34 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ), =( Y, hAPP(
% 1.00/1.34 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ), =( Y, Z ) ],
% 1.00/1.34 [ ~( 'class_Divides_Oring__div'( X ) ), ~( =(
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.00/1.35 , Z, X ) ) ), =( 'c_Divides_Odiv__class_Omod'( hAPP(
% 1.00/1.35 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z, X ),
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.00/1.35 T ), Z, X ) ) ],
% 1.00/1.35 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.00/1.35 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.00/1.35 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 1.00/1.35 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.00/1.35 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ],
% 1.00/1.35 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.00/1.35 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.00/1.35 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.00/1.35 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 1.00/1.35 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ],
% 1.00/1.35 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.00/1.35 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.00/1.35 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ),
% 1.00/1.35 'c_Lattices_Olower__semilattice__class_Oinf'( Z,
% 1.00/1.35 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, X ), X ) ) ],
% 1.00/1.35 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.00/1.35 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.00/1.35 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), T, X ),
% 1.00/1.35 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.00/1.35 'c_Lattices_Olower__semilattice__class_Oinf'( Z, T, X ), X ) ) ],
% 1.00/1.35 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.00/1.35 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.00/1.35 'tc_bool' ) ), T, 'tc_fun'( Z, 'tc_bool' ) ),
% 1.00/1.35 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.00/1.35 'c_Lattices_Olower__semilattice__class_Oinf'( Y, T, 'tc_fun'( Z,
% 1.00/1.35 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ) ) ],
% 1.00/1.35 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.00/1.35 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, 'tc_fun'( T,
% 1.00/1.35 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ),
% 1.00/1.35 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.00/1.35 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( T,
% 1.00/1.35 'tc_bool' ) ), 'tc_fun'( T, 'tc_bool' ) ) ) ],
% 1.00/1.35 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =(
% 1.00/1.35 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.00/1.35 'c_Orderings_Otop__class_Otop'( X ) ) ), =( Z,
% 1.00/1.35 'c_Orderings_Otop__class_Otop'( X ) ) ],
% 1.00/1.35 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), ~( =(
% 1.00/1.35 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ),
% 1.00/1.35 'c_Orderings_Otop__class_Otop'( X ) ) ), =( Y,
% 1.00/1.35 'c_Orderings_Otop__class_Otop'( X ) ) ],
% 1.00/1.35 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =( hAPP(
% 1.00/1.35 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_Orderings_Otop__class_Otop'( X )
% 1.00/1.35 ), 'c_Orderings_Obot__class_Obot'( X ) ) ],
% 1.00/1.35 [ =( hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.00/1.35 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.00/1.35 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.00/1.35 [ ~( hBOOL( hAPP( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool'
% 1.00/1.35 ) ), Y ) ) ) ],
% 1.00/1.35 [ ~( =( 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.00/1.35 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ) ) ],
% 1.00/1.35 [ ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_in'( X ), Y ), T ) ) ), ~( =(
% 1.00/1.35 'c_Lattices_Olower__semilattice__class_Oinf'( T, Z, 'tc_fun'( X,
% 1.00/1.35 'tc_bool' ) ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) )
% 1.00/1.35 ) ) ],
% 1.00/1.35 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.00/1.35 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.00/1.35 'c_Orderings_Otop__class_Otop'( X ), X ), Y ) ],
% 1.00/1.35 [ ~( 'class_Lattices_Obounded__lattice'( X ) ), =(
% 1.00/1.35 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.00/1.35 'c_Orderings_Otop__class_Otop'( X ), Y, X ), Y ) ],
% 1.00/1.35 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.00/1.35 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ), Y, 'tc_fun'(
% 1.00/1.35 X, 'tc_bool' ) ), Y ) ],
% 1.00/1.35 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.00/1.35 'c_Orderings_Otop__class_Otop'( 'tc_fun'( Y, 'tc_bool' ) ), 'tc_fun'( Y,
% 1.00/1.35 'tc_bool' ) ), X ) ],
% 1.00/1.35 [ hBOOL( hAPP( 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' )
% 1.00/1.35 ), Y ) ) ],
% 1.00/1.35 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), ~( =( hAPP(
% 1.00/1.35 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.00/1.35 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), =( Y, Z ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP(
% 1.00/1.35 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), hAPP(
% 1.00/1.35 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ), =( Y, Z ) ],
% 1.00/1.35 [ ~( =( hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) )
% 1.00/1.35 , Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.00/1.35 Z ) ) ), =( Y, Z ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.00/1.35 ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), Z ) ]
% 1.00/1.35 ,
% 1.00/1.35 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.00/1.35 ), Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ), Z ) ]
% 1.00/1.35 ,
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP(
% 1.00/1.35 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.00/1.35 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP(
% 1.00/1.35 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.00/1.35 X ), Y ) ), Z ) ) ],
% 1.00/1.35 [ 'c_Finite__Set_Ofinite'( 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X,
% 1.00/1.35 'tc_bool' ) ), X ), ~( 'c_Finite__Set_Ofinite'( hAPP(
% 1.00/1.35 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ), Y ), X ) ),
% 1.00/1.35 ~( 'c_Finite__Set_Ofinite'( Y, X ) ) ],
% 1.00/1.35 [ 'c_Finite__Set_Ofinite'( hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.00/1.35 'tc_fun'( X, 'tc_bool' ) ), Y ), X ), ~( 'c_Finite__Set_Ofinite'(
% 1.00/1.35 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ), X ) ), ~(
% 1.00/1.35 'c_Finite__Set_Ofinite'( Y, X ) ) ],
% 1.00/1.35 [ 'c_Relation_Ototal__on'( 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X,
% 1.00/1.35 'tc_bool' ) ), Y, X ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oring'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.00/1.35 X ), Y ) ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP(
% 1.00/1.35 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.00/1.35 ), Y ) ), Z ) ), Z ) ],
% 1.00/1.35 [ ~( 'class_Lattices_Oboolean__algebra'( X ) ), =( hAPP(
% 1.00/1.35 'c_HOL_Ouminus__class_Ouminus'( X ), 'c_Orderings_Obot__class_Obot'( X )
% 1.00/1.35 ), 'c_Orderings_Otop__class_Otop'( X ) ) ],
% 1.00/1.35 [ =( hAPP( 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( X, 'tc_bool' ) ),
% 1.00/1.35 'c_Orderings_Obot__class_Obot'( 'tc_fun'( X, 'tc_bool' ) ) ),
% 1.00/1.35 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ) ) ],
% 1.00/1.35 [ ~( 'class_Lattices_Olattice'( X ) ), =(
% 1.00/1.35 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.00/1.35 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ),
% 1.00/1.35 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ],
% 1.00/1.35 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.00/1.35 'c_Lattices_Olower__semilattice__class_Oinf'( Y,
% 1.00/1.35 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ), X ),
% 1.00/1.35 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Z, X ) ) ],
% 1.00/1.35 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X,
% 1.00/1.35 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.00/1.35 'tc_bool' ) ), 'tc_fun'( Z, 'tc_bool' ) ),
% 1.00/1.35 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y, 'tc_fun'( Z,
% 1.00/1.35 'tc_bool' ) ) ) ],
% 1.00/1.35 [ ~( 'class_Finite__Set_Ofinite_Ofinite'( X ) ), 'c_Finite__Set_Ofinite'(
% 1.00/1.35 'c_Orderings_Otop__class_Otop'( 'tc_fun'( X, 'tc_bool' ) ), X ) ],
% 1.00/1.35 [ ~( 'class_Lattices_Olower__semilattice'( X ) ), =(
% 1.00/1.35 'c_Lattices_Olower__semilattice__class_Oinf'( Y, Y, X ), Y ) ],
% 1.00/1.35 [ =( 'c_Lattices_Olower__semilattice__class_Oinf'( X, X, 'tc_fun'( Y,
% 1.00/1.35 'tc_bool' ) ), X ) ],
% 1.00/1.35 [ hBOOL( hAPP( 'c_Lattices_Olower__semilattice__class_Oinf'( X, Y,
% 1.00/1.35 'tc_fun'( Z, 'tc_bool' ) ), T ) ), ~( hBOOL( hAPP( Y, T ) ) ), ~( hBOOL(
% 1.00/1.35 hAPP( X, T ) ) ) ],
% 1.00/1.35 [ =( 'c_Set_Ovimage'( X, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Y,
% 1.00/1.35 'tc_bool' ) ), Z, Y ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.00/1.35 'tc_bool' ) ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP(
% 1.00/1.35 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.00/1.35 ), Y ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP(
% 1.00/1.35 'c_HOL_Ouminus__class_Ouminus'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.00/1.35 ), Z ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.00/1.35 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X
% 1.00/1.35 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.00/1.35 Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP(
% 1.00/1.35 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X
% 1.00/1.35 ) ) ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.00/1.35 hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.00/1.35 ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Opordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.00/1.35 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.00/1.35 X ), Y ) ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.00/1.35 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP(
% 1.00/1.35 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.00/1.35 X ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.00/1.35 ), Y ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.00/1.35 ), Y ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP(
% 1.00/1.35 'c_HOL_Ouminus__class_Ouminus'( X ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X
% 1.00/1.35 ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X
% 1.00/1.35 ), Y ) ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.00/1.35 ) ) ), =( Y, hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Z ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Ogroup__add'( X ) ), ~( =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), 'c_HOL_Ozero__class_Ozero'( X
% 1.00/1.35 ) ) ), =( hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ), Y ), Z ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.00/1.35 'c_Finite__Set_Osetsum'( Y, 'c_Orderings_Obot__class_Obot'( 'tc_fun'( Z,
% 1.00/1.35 'tc_bool' ) ), Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =(
% 1.00/1.35 'c_Finite__Set_Osetsum'( 'c_COMBB'( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.00/1.35 Y, X, X, Z ), T, Z, X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'( X ),
% 1.00/1.35 'c_Finite__Set_Osetsum'( Y, T, Z, X ) ) ) ],
% 1.00/1.35 [ =( 'c_Relation_OImage'( 'c_Relation_OId__on'( X, Y ), Z, Y, Y ),
% 1.00/1.35 'c_Lattices_Olower__semilattice__class_Oinf'( X, Z, 'tc_fun'( Y,
% 1.00/1.35 'tc_bool' ) ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.00/1.35 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBS'( 'c_COMBB'( 'c_HOL_OIf'( X
% 1.00/1.35 ), 'c_COMBC'( 'c_in'( Y ), Z, Y, 'tc_fun'( Y, 'tc_bool' ), 'tc_bool' ),
% 1.00/1.35 'tc_bool', 'tc_fun'( X, 'tc_fun'( X, X ) ), Y ), T, Y, X, 'tc_fun'( X, X
% 1.00/1.35 ) ), U, Y, X, X ), W, Y, X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.00/1.35 ), 'c_Finite__Set_Osetsum'( T,
% 1.00/1.35 'c_Lattices_Olower__semilattice__class_Oinf'( W, Z, 'tc_fun'( Y,
% 1.00/1.35 'tc_bool' ) ), Y, X ) ), 'c_Finite__Set_Osetsum'( U,
% 1.00/1.35 'c_Lattices_Olower__semilattice__class_Oinf'( W, hAPP(
% 1.00/1.35 'c_HOL_Ouminus__class_Ouminus'( 'tc_fun'( Y, 'tc_bool' ) ), Z ), 'tc_fun'(
% 1.00/1.35 Y, 'tc_bool' ) ), Y, X ) ) ), ~( 'c_Finite__Set_Ofinite'( W, Y ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.00/1.35 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), ~( =(
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X
% 1.00/1.35 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.00/1.35 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.35 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.00/1.35 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.35 'c_Divides_Odiv__class_Odiv'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), ~( =( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.00/1.35 ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.00/1.35 X ) ), ~( =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) )
% 1.00/1.35 , =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.00/1.35 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( Y, Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.00/1.35 ) ],
% 1.00/1.35 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( X ), X ), Y
% 1.00/1.35 ) ],
% 1.00/1.35 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( 'c_HOL_Ozero__class_Ozero'( X ), Y, X ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), =( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.00/1.35 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.00/1.35 ,
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.00/1.35 Y ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.00/1.35 Y ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.00/1.35 X ) ), =( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.00/1.35 Y ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.00/1.35 Y ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Omonoid__add'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.00/1.35 Y ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.00/1.35 Y ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ),
% 1.00/1.35 Y ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( hBOOL(
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.00/1.35 X ), Y ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z )
% 1.00/1.35 ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ) ), =( Y,
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ) ) ), =( Z,
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( hBOOL(
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.00/1.35 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.00/1.35 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL(
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), T ), Y ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.00/1.35 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.00/1.35 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.00/1.35 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL(
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( X ) )
% 1.00/1.35 , hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.00/1.35 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( X ) ),
% 1.00/1.35 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Z ), U ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.00/1.35 X ), T ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y )
% 1.00/1.35 ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.00/1.35 X ), Z ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.00/1.35 ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.00/1.35 ), 'c_Nat_Ocompow'( 'c_Suc'( T ), U, 'tc_prod'( X, X ), 'tc_bool' ) ) )
% 1.00/1.35 , ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( W, Z, X, X
% 1.00/1.35 ) ), 'c_Nat_Ocompow'( T, U, 'tc_prod'( X, X ), 'tc_bool' ) ) ) ), ~(
% 1.00/1.35 hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, W, X, X ) )
% 1.00/1.35 , U ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.00/1.35 ), 'c_Nat_Ocompow'( 'c_Suc'( T ), U, 'tc_prod'( X, X ), 'tc_bool' ) ) )
% 1.00/1.35 , ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( W, Z, X, X
% 1.00/1.35 ) ), U ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ),
% 1.00/1.35 'c_Pair'( Y, W, X, X ) ), 'c_Nat_Ocompow'( T, U, 'tc_prod'( X, X ),
% 1.00/1.35 'tc_bool' ) ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), 'c_Finite__Set_Osetsum'( Y, Z, T, X )
% 1.00/1.35 ), U ), 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBB'(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y, X, 'tc_fun'( X, X ), T ), U, T, X,
% 1.00/1.35 X ), Z, T, X ) ) ],
% 1.00/1.35 [ ~( hBOOL( hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.00/1.35 'tc_nat' ) ) ) ],
% 1.00/1.35 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Omod'( Y,
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.00/1.35 , Y ) ) ],
% 1.00/1.35 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 'tc_nat' ) ) ) ],
% 1.00/1.35 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 'tc_nat' ) ), Y ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ), ~( hBOOL( hAPP( X
% 1.00/1.35 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.00/1.35 [ ~( hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), hBOOL(
% 1.00/1.35 hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 'tc_nat' ), 'tc_nat' ) ) ) ],
% 1.00/1.35 [ ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Odiv'( Y,
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ), hBOOL( hAPP( X
% 1.00/1.35 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.00/1.35 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.00/1.35 [ ~( =( 'c_Suc'( X ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.00/1.35 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 'tc_nat' ) ) ],
% 1.00/1.35 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 'tc_nat' ) ) ],
% 1.00/1.35 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X,
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.00/1.35 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.00/1.35 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X,
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.00/1.35 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), =( Y
% 1.00/1.35 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, Z ) ],
% 1.00/1.35 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( X
% 1.00/1.35 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y, Z ) ],
% 1.00/1.35 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), =( Y
% 1.00/1.35 , Z ), =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.00/1.35 'c_Finite__Set_Osetsum'( Y, 'c_Lattices_Olower__semilattice__class_Oinf'(
% 1.00/1.35 Z, T, 'tc_fun'( U, 'tc_bool' ) ), U, X ), 'c_Finite__Set_Osetsum'(
% 1.00/1.35 'c_COMBC'( 'c_COMBS'( 'c_COMBB'( 'c_HOL_OIf'( X ), 'c_COMBC'( 'c_in'( U )
% 1.00/1.35 , T, U, 'tc_fun'( U, 'tc_bool' ), 'tc_bool' ), 'tc_bool', 'tc_fun'( X,
% 1.00/1.35 'tc_fun'( X, X ) ), U ), Y, U, X, 'tc_fun'( X, X ) ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ), U, X, X ), Z, U, X ) ), ~(
% 1.00/1.35 'c_Finite__Set_Ofinite'( Z, U ) ) ],
% 1.00/1.35 [ =( 'c_Set_Ovimage'( 'c_COMBC'( 'c_COMBC'( 'c_COMBB'( 'c_HOL_OIf'( X )
% 1.00/1.35 , 'c_COMBC'( 'c_in'( Y ), Z, Y, 'tc_fun'( Y, 'tc_bool' ), 'tc_bool' ),
% 1.00/1.35 'tc_bool', 'tc_fun'( X, 'tc_fun'( X, X ) ), Y ), T, Y, X, 'tc_fun'( X, X
% 1.00/1.35 ) ), U, Y, X, X ), W, Y, X ), hAPP( 'c_HOL_Ouminus__class_Ouminus'(
% 1.00/1.35 'tc_fun'( Y, 'tc_bool' ) ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), U )
% 1.00/1.35 , W ) ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), T ), W ) ) ],
% 1.00/1.35 [ =( 'c_Set_Ovimage'( 'c_COMBC'( 'c_COMBC'( 'c_COMBB'( 'c_HOL_OIf'( X )
% 1.00/1.35 , 'c_COMBC'( 'c_in'( Y ), Z, Y, 'tc_fun'( Y, 'tc_bool' ), 'tc_bool' ),
% 1.00/1.35 'tc_bool', 'tc_fun'( X, 'tc_fun'( X, X ) ), Y ), T, Y, X, 'tc_fun'( X, X
% 1.00/1.35 ) ), U, Y, X, X ), W, Y, X ), 'c_Orderings_Otop__class_Otop'( 'tc_fun'(
% 1.00/1.35 Y, 'tc_bool' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), U ), W ) ) ), ~(
% 1.00/1.35 hBOOL( hAPP( hAPP( 'c_in'( X ), T ), W ) ) ) ],
% 1.00/1.35 [ =( 'c_Set_Ovimage'( 'c_COMBC'( 'c_COMBC'( 'c_COMBB'( 'c_HOL_OIf'( X )
% 1.00/1.35 , 'c_COMBC'( 'c_in'( Y ), Z, Y, 'tc_fun'( Y, 'tc_bool' ), 'tc_bool' ),
% 1.00/1.35 'tc_bool', 'tc_fun'( X, 'tc_fun'( X, X ) ), Y ), T, Y, X, 'tc_fun'( X, X
% 1.00/1.35 ) ), U, Y, X, X ), W, Y, X ), 'c_Orderings_Obot__class_Obot'( 'tc_fun'(
% 1.00/1.35 Y, 'tc_bool' ) ) ), hBOOL( hAPP( hAPP( 'c_in'( X ), U ), W ) ), hBOOL(
% 1.00/1.35 hAPP( hAPP( 'c_in'( X ), T ), W ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~( =( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.00/1.35 ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.00/1.35 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.00/1.35 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 X ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oring__no__zero__divisors'( X ) ), =( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.00/1.35 ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.00/1.35 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Omult__zero'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.00/1.35 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y )
% 1.00/1.35 , 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oring__1__no__zero__divisors'( X ) ), ~(
% 1.00/1.35 =( 'c_Power_Opower__class_Opower'( Y, Z, X ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.00/1.35 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.00/1.35 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.00/1.35 ), ~( =( 'c_Power_Opower__class_Opower'( Y, Z, X ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X
% 1.00/1.35 ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_in'( U ), Z ), 'c_Set_Ovimage'( Y, T, U, X ) ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( X ), hAPP( Y, Z ) ), T ) ), ~( hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_in'( U ), Z ), 'c_Set_Ovimage'( Y, T, U, X ) ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z, T, X, U ) ) )
% 1.00/1.35 , ~( hBOOL( hAPP( hAPP( 'c_in'( U ), hAPP( Z, Y ) ), T ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z, T, X, U ) ) )
% 1.00/1.35 , ~( hBOOL( hAPP( hAPP( 'c_in'( U ), hAPP( Z, Y ) ), T ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Set_Ovimage'( Z, T, X, U ) ) )
% 1.00/1.35 , ~( hBOOL( hAPP( hAPP( 'c_in'( U ), hAPP( Z, Y ) ), T ) ) ) ],
% 1.00/1.35 [ ~( =( 'c_COMBC'( 'c_in'( X ), Y, X, 'tc_fun'( X, 'tc_bool' ),
% 1.00/1.35 'tc_bool' ), 'c_COMBC'( 'c_in'( X ), Z, X, 'tc_fun'( X, 'tc_bool' ),
% 1.00/1.35 'tc_bool' ) ) ), =( Y, Z ) ],
% 1.00/1.35 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y )
% 1.00/1.35 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.35 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.00/1.35 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, X ) ) ],
% 1.00/1.35 [ =( 'c_Divides_Odiv__class_Odiv'( X, 'c_Suc'(
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ), X ) ],
% 1.00/1.35 [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( hBOOL(
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL(
% 1.00/1.35 hAPP( X, Y ) ) ), ~( hBOOL( hAPP( X, 'c_Divides_Odiv__class_Omod'(
% 1.00/1.35 'c_Suc'( 'c_List_Osko__Divides__Xmod__induct__0__1__1'( X, Z ) ), Z,
% 1.00/1.35 'tc_nat' ) ) ) ) ],
% 1.00/1.35 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ) ), hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), 'c_Suc'(
% 1.00/1.35 'c_Divides_Odiv__class_Odiv'( Y, X, 'tc_nat' ) ) ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.00/1.35 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.00/1.35 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.00/1.35 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.00/1.35 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.00/1.35 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.00/1.35 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.00/1.35 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.00/1.35 , 'c_Divides_Odiv__class_Omod'( Y, T, X ) ) ],
% 1.00/1.35 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), Y, 'tc_nat' )
% 1.00/1.35 , 'c_Divides_Odiv__class_Omod'( Z, Y, 'tc_nat' ) ) ],
% 1.00/1.35 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.00/1.35 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), =( X,
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.00/1.35 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.35 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.00/1.35 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.00/1.35 ), 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ), =( Z,
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.00/1.35 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.35 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.00/1.35 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.00/1.35 ), 'c_Divides_Odiv__class_Odiv'( Z, T, X ) ), =( Y,
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.00/1.35 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Divides_Odiv__class_Odiv'( X,
% 1.00/1.35 Z, 'tc_nat' ) ), 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.00/1.35 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.35 'tc_nat' ), 'c_Divides_Odiv__class_Omod'( X, Z, 'tc_nat' ) ),
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z, 'tc_nat' ) ) ) ]
% 1.00/1.35 ,
% 1.00/1.35 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Z ),
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.00/1.35 'tc_nat' ), X ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.00/1.35 ), Y ), Z ), 'tc_nat' ) ) ],
% 1.00/1.35 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ),
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.00/1.35 'tc_nat' ), X ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat'
% 1.00/1.35 ), X ), Z ), 'tc_nat' ) ) ],
% 1.00/1.35 [ ~( 'class_Finite__Set_Ofinite_Ofinite'( X ) ), 'c_Finite__Set_Ofinite'(
% 1.00/1.35 Y, X ) ],
% 1.00/1.35 [ =( 'c_Power_Opower__class_Opower'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 'tc_nat' ) ), X, 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 'tc_nat' ) ) ) ],
% 1.00/1.35 [ =( 'c_Power_Opower__class_Opower'( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 'tc_nat' ) ), X, 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 'tc_nat' ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.35 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ), U ) )
% 1.00/1.35 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ) ],
% 1.00/1.35 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.00/1.35 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.00/1.35 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.00/1.35 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.00/1.35 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.00/1.35 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z,
% 1.00/1.35 T, X ) ), T, X ) ) ],
% 1.00/1.35 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.00/1.35 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.00/1.35 ) ), Z ), T, X ) ) ],
% 1.00/1.35 [ ~( =( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) )
% 1.00/1.35 , =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), T ), Z ) ) ), =( Y, T ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Ocancel__semigroup__add'( X ) ), ~( =( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Ocancel__ab__semigroup__add'( X ) ), ~( =( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.00/1.35 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ), =( Z, T ) ],
% 1.00/1.35 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.00/1.35 ) ],
% 1.00/1.35 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), =( X, Z
% 1.00/1.35 ) ],
% 1.00/1.35 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), =( Y, Z
% 1.00/1.35 ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.00/1.35 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( Z ) ), X ) ), hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( Z ) ), Y ) ) ) )
% 1.00/1.35 ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( X ) ), Y ) ), hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( X ) ), Z ) ) ),
% 1.00/1.35 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), Z ) ) )
% 1.00/1.35 ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Osemiring'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.00/1.35 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), U ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.00/1.35 X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ), U )
% 1.00/1.35 ) ],
% 1.00/1.35 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ), T ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ), T ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.00/1.35 'c_Finite__Set_Osetsum'( 'c_COMBS'( 'c_COMBB'( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.35 X ), Y, X, 'tc_fun'( X, X ), Z ), T, Z, X, X ), U, Z, X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), 'c_Finite__Set_Osetsum'( Y, U, Z, X ) )
% 1.00/1.35 , 'c_Finite__Set_Osetsum'( T, U, Z, X ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Finite__Set_Osetsum'( Z, T, U
% 1.00/1.35 , X ) ), 'c_Finite__Set_Osetsum'( 'c_COMBB'( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z, X, X, U ), T, U, X ) ) ],
% 1.00/1.35 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 1.00/1.35 , Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'(
% 1.00/1.35 Y ) ) ) ],
% 1.00/1.35 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( X, 'c_Suc'(
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.00/1.35 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'(
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.00/1.35 [ =( hAPP( X, hAPP( 'c_Nat_Ocompow'( Y, X, Z, Z ), T ) ), hAPP(
% 1.00/1.35 'c_Nat_Ocompow'( Y, X, Z, Z ), hAPP( X, T ) ) ) ],
% 1.00/1.35 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ]
% 1.00/1.35 ,
% 1.00/1.35 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.00/1.35 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), 'c_Divides_Odiv__class_Omod'( Z, T
% 1.00/1.35 , X ) ), T, X ) ) ],
% 1.00/1.35 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.00/1.35 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.00/1.35 ), Z ), T, X ) ) ],
% 1.00/1.35 [ =( hAPP( 'c_COMBS'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), hAPP( Y
% 1.00/1.35 , W ) ) ) ],
% 1.00/1.35 [ =( 'c_Relation_ODomain'( 'c_Relation_OId__on'( X, Y ), Y, Y ), X ) ]
% 1.00/1.35 ,
% 1.00/1.35 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), ~( =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Z ), U ) ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ), U ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.00/1.35 'c_Power_Opower__class_Opower'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.35 'tc_nat' ), Z ), T ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X )
% 1.00/1.35 , 'c_Power_Opower__class_Opower'( Y, Z, X ) ),
% 1.00/1.35 'c_Power_Opower__class_Opower'( Y, T, X ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.35 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.35 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ), Z ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.35 X ), Y ), Z ) ), T ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Oab__semigroup__add'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.35 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.35 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ),
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ) ],
% 1.00/1.35 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.00/1.35 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Oab__group__add'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Z ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.35 X ), Y ), Z ) ), T ) ) ],
% 1.00/1.35 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.00/1.35 , Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X )
% 1.00/1.35 ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.00/1.35 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.00/1.35 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Power_Opower__class_Opower'( Y
% 1.00/1.35 , Z, X ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.00/1.35 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Power_Opower__class_Opower'( Y
% 1.00/1.35 , Z, X ) ) ) ],
% 1.00/1.35 [ ~( 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'( Y,
% 1.00/1.35 'c_Suc'( Z ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.00/1.35 'c_Power_Opower__class_Opower'( Y, Z, X ) ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.00/1.35 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( Y, Z,
% 1.00/1.35 X ) ), Y ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.00/1.35 'c_Power_Opower__class_Opower'( 'c_Power_Opower__class_Opower'( Y, Z, X )
% 1.00/1.35 , T, X ), 'c_Power_Opower__class_Opower'( Y, hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ), X ) ) ],
% 1.00/1.35 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ), 'c_Suc'(
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ) ), =( 'c_Suc'(
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.00/1.35 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.00/1.35 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.00/1.35 ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.00/1.35 X ) ), =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.00/1.35 X ), Y ), T ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z )
% 1.00/1.35 ) ) ],
% 1.00/1.35 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.00/1.35 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.00/1.35 [ 'c_Relation_Orefl__on'( X, 'c_Relation_OId__on'( X, Y ), Y ) ],
% 1.00/1.35 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.00/1.35 , X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.00/1.35 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 'tc_nat' ) ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.00/1.35 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_Power_Opower__class_Opower'( Y,
% 1.00/1.35 Z, 'tc_nat' ), X ), 'c_Power_Opower__class_Opower'(
% 1.00/1.35 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ), Z, X ) ) ],
% 1.00/1.35 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.00/1.35 ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.00/1.35 ), Y ), T ), Z, X ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.00/1.35 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ), 'c_Suc'( Y ), X ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.00/1.35 [ =( 'c_Power_Opower__class_Opower'( X, 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 'tc_nat' ), 'tc_nat' ), 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) )
% 1.00/1.35 ) ],
% 1.00/1.35 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), 'c_Suc'( Y
% 1.00/1.35 ) ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y
% 1.00/1.35 ) ) ) ],
% 1.00/1.35 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'( X ) )
% 1.00/1.35 , Y ), 'c_Suc'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.00/1.35 Y ) ) ) ],
% 1.00/1.35 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.35 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.00/1.35 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ), 'c_Divides_Odiv__class_Omod'(
% 1.00/1.35 Z, Y, X ) ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ), T )
% 1.00/1.35 ) ],
% 1.00/1.35 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.35 X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.00/1.35 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ), T ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), T ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), 'c_Suc'(
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ) ) ],
% 1.00/1.35 [ ~( =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y )
% 1.00/1.35 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.00/1.35 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), X
% 1.00/1.35 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.00/1.35 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.00/1.35 [ ~( =( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'c_Suc'( X ) ) ) ],
% 1.00/1.35 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( X,
% 1.00/1.35 'c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1'( X ) ) ) ), ~( hBOOL(
% 1.00/1.35 hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.00/1.35 [ =( X, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.00/1.35 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ), X ) ],
% 1.00/1.35 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), ~( hBOOL(
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_Suc'(
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_Suc'(
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ) ), ~( hBOOL(
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_Suc'(
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_Suc'(
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X ) ) ) ],
% 1.00/1.35 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ), 'tc_nat' ),
% 1.00/1.35 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 'tc_nat' ) ), X ) ) ) ],
% 1.00/1.35 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ), Y ),
% 1.00/1.35 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ) ) ],
% 1.00/1.35 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Y, 'tc_nat' ), X ),
% 1.00/1.35 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_Suc'(
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_Suc'(
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_Suc'(
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), Y ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), 'c_Suc'(
% 1.00/1.35 Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X )
% 1.00/1.35 , Y ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.00/1.35 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_Suc'( X )
% 1.00/1.35 ), Y ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.00/1.35 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), X ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.00/1.35 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Y ) ) ) ],
% 1.00/1.35 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), X ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.00/1.35 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.00/1.35 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_Suc'( X )
% 1.00/1.35 ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Z
% 1.00/1.35 ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.00/1.35 , X ), Z ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), 'c_Suc'(
% 1.00/1.35 X ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), 'c_Suc'(
% 1.00/1.35 X ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~( hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), T ) ) ), ~( hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.00/1.35 [ =( 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ), X ), ~( hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.00/1.35 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.00/1.35 , X ), 'c_Suc'( Y ) ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.00/1.35 'tc_nat' ), X ), Y ) ) ],
% 1.00/1.35 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' )
% 1.00/1.35 , Y ), 'c_Suc'( X ) ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.00/1.35 'tc_nat' ), Y ), X ) ) ],
% 1.00/1.35 [ =( X, Y ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X
% 1.00/1.35 ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X
% 1.00/1.35 ), 'c_Suc'( Y ) ) ) ) ],
% 1.00/1.35 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Z ), T ) ) ), ~(
% 1.00/1.35 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Z ), Y ) ) ),
% 1.00/1.35 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), T ) ) ]
% 1.00/1.35 ,
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL(
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL(
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.00/1.35 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Z ) ), Y ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL(
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL(
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_Suc'( X )
% 1.00/1.35 ), Y ) ), =( 'c_Suc'( X ), Y ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), X ) ),
% 1.00/1.35 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), 'c_Suc'( X
% 1.00/1.35 ) ) ) ],
% 1.00/1.35 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y )
% 1.00/1.35 ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ),
% 1.00/1.35 'c_Suc'( X ) ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), 'c_Suc'(
% 1.00/1.35 Y ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), X
% 1.00/1.35 ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_Suc'( X )
% 1.00/1.35 ), 'c_Suc'( Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.00/1.35 'tc_nat' ), X ), Y ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.00/1.35 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_Suc'( X )
% 1.00/1.35 ), 'c_Suc'( Y ) ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_Suc'( X )
% 1.00/1.35 ), 'c_Suc'( Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.00/1.35 'tc_nat' ), X ), Y ) ) ) ],
% 1.00/1.35 [ ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.00/1.35 , 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_in'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'c_Pair'( Y, X,
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.00/1.35 , Z ) ) ), =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_fun'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.00/1.35 'tc_bool' ) ), Z ), 'c_Arrow__Order__Mirabelle_OLin' ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.00/1.35 , 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ) ), Z ) ), hBOOL( hAPP( hAPP( 'c_in'(
% 1.00/1.35 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'c_Pair'( Y, X,
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.00/1.35 , Z ) ), =( Y, X ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_fun'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.00/1.35 'tc_bool' ) ), Z ), 'c_Arrow__Order__Mirabelle_OLin' ) ) ) ],
% 1.00/1.35 [ ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.00/1.35 , 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_in'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'c_Pair'( Y, X,
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.00/1.35 , Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_fun'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.00/1.35 'tc_bool' ) ), Z ), 'c_Arrow__Order__Mirabelle_OLin' ) ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.00/1.35 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBS'( 'c_COMBB'( 'c_HOL_OIf'( X
% 1.00/1.35 ), hAPP( 'c_fequal'( Y ), Z ), 'tc_bool', 'tc_fun'( X, 'tc_fun'( X, X )
% 1.00/1.35 ), Y ), T, Y, X, 'tc_fun'( X, X ) ), 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.00/1.35 , X, X ), U, Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_in'( Y ), Z ), U ) ), ~( 'c_Finite__Set_Ofinite'( U, Y ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.00/1.35 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBS'( 'c_COMBB'( 'c_HOL_OIf'( X
% 1.00/1.35 ), hAPP( 'c_fequal'( Y ), Z ), 'tc_bool', 'tc_fun'( X, 'tc_fun'( X, X )
% 1.00/1.35 ), Y ), T, Y, X, 'tc_fun'( X, X ) ), 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.00/1.35 , X, X ), U, Y, X ), hAPP( T, Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Y ), Z
% 1.00/1.35 ), U ) ) ), ~( 'c_Finite__Set_Ofinite'( U, Y ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.00/1.35 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.00/1.35 ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ),
% 1.00/1.35 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), T ) )
% 1.00/1.35 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.00/1.35 ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ),
% 1.00/1.35 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), T ), Y ) ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.00/1.35 ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.00/1.35 ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.00/1.35 ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.00/1.35 ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.00/1.35 ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.00/1.35 ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.00/1.35 'c_Power_Opower__class_Opower'( Y, Z, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.00/1.35 ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~( hBOOL(
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.00/1.35 ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.00/1.35 ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ), ~(
% 1.00/1.35 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.00/1.35 ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.00/1.35 ) ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), Y ) ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X
% 1.00/1.35 ) ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X
% 1.00/1.35 ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.00/1.35 ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.00/1.35 , ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 X ) ) ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.00/1.35 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 X ) ) ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Opordered__comm__monoid__add'( X ) ), hBOOL(
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ) ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.00/1.35 ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( hBOOL(
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 X ) ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), ~( hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.00/1.35 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.00/1.35 ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.00/1.35 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.00/1.35 ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X
% 1.00/1.35 ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.00/1.35 X ), Z ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y )
% 1.00/1.35 ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.00/1.35 X ), T ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Y )
% 1.00/1.35 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ) ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.00/1.35 ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.00/1.35 X ), T ), Y ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.00/1.35 ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ) ), T ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.00/1.35 ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.00/1.35 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ) ]
% 1.00/1.35 ,
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.00/1.35 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ]
% 1.00/1.35 ,
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.00/1.35 ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Y ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.00/1.35 ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.00/1.35 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), T ), Y ) ) ) ]
% 1.00/1.35 ,
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__semiring__strict'( X ) ), hBOOL(
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.00/1.35 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ]
% 1.00/1.35 ,
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z ) )
% 1.00/1.35 ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), T ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Z ), 'c_HOL_Ozero__class_Ozero'( X ) ) )
% 1.00/1.35 ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__comm__semiring__strict'( X ) ),
% 1.00/1.35 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ) )
% 1.00/1.35 ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ), Z ), T ) ) ) ]
% 1.00/1.35 ,
% 1.00/1.35 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.00/1.35 Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.35 X ), Y ), Y ) ) ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Olordered__ab__group__add'( X ) ), hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), Y ) ) ), ~( hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.00/1.35 Y ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.00/1.35 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.00/1.35 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.00/1.35 ), =( 'c_Power_Opower__class_Opower'( 'c_HOL_Ozero__class_Ozero'( X ), Y
% 1.00/1.35 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ), =( Y,
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Osemiring__0'( X ) ), ~(
% 1.00/1.35 'class_Power_Opower'( X ) ), =( 'c_Power_Opower__class_Opower'(
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X )
% 1.00/1.35 ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Ozero__neq__one'( X ) ), ~(
% 1.00/1.35 'class_Ring__and__Field_Ono__zero__divisors'( X ) ), ~(
% 1.00/1.35 'class_Ring__and__Field_Omult__zero'( X ) ), ~( 'class_Power_Opower'( X )
% 1.00/1.35 ), ~( =( 'c_Power_Opower__class_Opower'( Y, 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.00/1.35 'c_Nat_Osemiring__1__class_Oof__nat'( 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 'tc_nat' ), X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.00/1.35 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) ), 'c_Pair'(
% 1.00/1.35 X, Y, Z, Z ) ), 'c_Relation_OId__on'( T, Z ) ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), Z ) ), ~( hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.00/1.35 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ),
% 1.00/1.35 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( X ),
% 1.00/1.35 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ),
% 1.00/1.35 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( hBOOL(
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL(
% 1.00/1.35 hAPP( X, Y ) ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat'
% 1.00/1.35 ), 'c_List_Osko__Divides__Xmod__induct__0__1__1'( X, Z ) ), Z ) ) ],
% 1.00/1.35 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 'tc_nat' ) ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.00/1.35 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.00/1.35 'c_Power_Opower__class_Opower'( Y, X, 'tc_nat' ) ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Power_Opower__class_Opower'(
% 1.00/1.35 X, Y, 'tc_nat' ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.00/1.35 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 'tc_nat' ) ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.00/1.35 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), 'c_Suc'(
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), 'c_Suc'(
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.00/1.35 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ), hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), Z ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Z ), Y ) ) ],
% 1.00/1.35 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.00/1.35 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.00/1.35 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.00/1.35 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.00/1.35 [ ~( 'class_Nat_Osemiring__char__0'( X ) ), ~( =(
% 1.00/1.35 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ),
% 1.00/1.35 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ), =( Y, Z ) ],
% 1.00/1.35 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.35 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Omod'( Y, Z, X ), Z
% 1.00/1.35 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.00/1.35 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.00/1.35 ), Y ), Z ), T, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), 'c_Divides_Odiv__class_Omod'( Y, T, X
% 1.00/1.35 ) ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( Y, Z,
% 1.00/1.35 X ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.00/1.35 'c_Power_Opower__class_Opower'( Y, Z, X ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( Y, Z,
% 1.00/1.35 X ) ), 'c_Power_Opower__class_Opower'( Y, T, X ) ),
% 1.00/1.35 'c_Power_Opower__class_Opower'( Y, hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.35 'tc_nat' ), Z ), T ), X ) ) ],
% 1.00/1.35 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.35 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.00/1.35 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), Z, X )
% 1.00/1.35 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), T ),
% 1.00/1.35 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ) ), =( Z,
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.00/1.35 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.35 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.00/1.35 , Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), T, X )
% 1.00/1.35 , hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Z ),
% 1.00/1.35 'c_Divides_Odiv__class_Odiv'( Y, T, X ) ) ), =( T,
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.00/1.35 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.00/1.35 [ ~( =( 'c_Suc'( X ), 'c_Suc'( Y ) ) ), =( X, Y ) ],
% 1.00/1.35 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.00/1.35 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.00/1.35 , U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), W ), T ), Z, X ) ) ],
% 1.00/1.35 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( Y, 'c_Suc'(
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.00/1.35 [ ~( =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), =( X,
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.00/1.35 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), 'c_Suc'(
% 1.00/1.35 Y ) ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.00/1.35 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( X )
% 1.00/1.35 ), Y ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.00/1.35 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y )
% 1.00/1.35 ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( Z,
% 1.00/1.35 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.35 'tc_nat' ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T
% 1.00/1.35 ) ), X ), Y, 'tc_nat' ) ) ) ), hBOOL( hAPP( Z, T ) ) ],
% 1.00/1.35 [ =( 'c_Relation_ORange'( 'c_Relation_OId__on'( X, Y ), Y, Y ), X ) ]
% 1.00/1.35 ,
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.00/1.35 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.00/1.35 Y, X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ],
% 1.00/1.35 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ) ), Y, 'tc_nat'
% 1.00/1.35 ), 'c_Divides_Odiv__class_Omod'( 'c_Suc'( Z ), Y, 'tc_nat' ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.00/1.35 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.00/1.35 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.00/1.35 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.00/1.35 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.00/1.35 X ), Y ), U ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z )
% 1.00/1.35 ) ) ), =( Z, U ), =( Y, T ) ],
% 1.00/1.35 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.00/1.35 , Z ) ],
% 1.00/1.35 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), T ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), =( Y, T ), =( X
% 1.00/1.35 , Z ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.00/1.35 'c_Finite__Set_Osetsum'( Y, Z, T, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.00/1.35 , 'c_Finite__Set_Ofinite'( Z, T ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.00/1.35 'c_Finite__Set_Osetsum'( Y, Z, T, X ), 'c_HOL_Ozero__class_Ozero'( X ) )
% 1.00/1.35 , 'c_Finite__Set_Ofinite'( Z, T ) ],
% 1.00/1.35 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.35 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.00/1.35 ), Y ), Z ), Z, X ), Y ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.00/1.35 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.35 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.00/1.35 ), Y ), Z ), Y, X ), Z ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.00/1.35 [ ~( 'class_Divides_Osemiring__div'( X ) ), ~( =(
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( Y, Z, X ), 'c_Divides_Odiv__class_Omod'( T
% 1.00/1.35 , Z, X ) ) ), ~( =( 'c_Divides_Odiv__class_Omod'( U, Z, X ),
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( W, Z, X ) ) ), =(
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.00/1.35 ), U ), Y ), Z, X ), 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), W ), T ), Z, X ) ) ],
% 1.00/1.35 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'(
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), T ), U ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), T ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), U ) ) ) ],
% 1.00/1.35 [ =( 'c_Divides_Odiv__class_Omod'( X, 'c_Suc'(
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'tc_nat' ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.00/1.35 [ 'c_Relation_Orefl__on'( X, Y, Z ), ~( 'c_Equiv__Relations_Oequiv'( X,
% 1.00/1.35 Y, Z ) ) ],
% 1.00/1.35 [ =( 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), 'c_Suc'(
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 'tc_nat' ) ) ) ],
% 1.00/1.35 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), Z, 'tc_nat' ), hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.00/1.35 'c_Divides_Odiv__class_Odiv'( Y, Z, 'tc_nat' ) ) ),
% 1.00/1.35 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.00/1.35 'tc_nat' ), X ), 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ), Z,
% 1.00/1.35 'tc_nat' ) ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ) ],
% 1.00/1.35 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), T ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), U ) ) ) ), =(
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ),
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( T, Y, 'tc_nat' ) ) ],
% 1.00/1.35 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.35 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.00/1.35 ), 'c_HOL_Ozero__class_Ozero'( X ) ), Y ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ), Z )
% 1.00/1.35 , X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.00/1.35 [ =( 'c_Divides_Odiv__class_Odiv'( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 'tc_nat' ) ), X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), Y ), 'tc_nat' ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), 'c_Power_Opower__class_Opower'( Y
% 1.00/1.35 , Z, X ) ), 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), 'c_Power_Opower__class_Opower'( Y, Z,
% 1.00/1.35 X ) ), Y ), 'c_Power_Opower__class_Opower'( Y, 'c_Suc'( Z ), X ) ) ],
% 1.00/1.35 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.00/1.35 , Y ), Z ), Z, X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ],
% 1.00/1.35 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.00/1.35 , Y ), Z ), Y, X ), 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ) ],
% 1.00/1.35 [ =( 'c_Divides_Odiv__class_Omod'( X, hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ), hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ),
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.00/1.35 'tc_nat' ), Z, 'tc_nat' ) ) ), 'c_Divides_Odiv__class_Omod'( X, Y,
% 1.00/1.35 'tc_nat' ) ) ) ],
% 1.00/1.35 [ =( 'c_Divides_Odiv__class_Odiv'( X, hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ), 'tc_nat' ),
% 1.00/1.35 'c_Divides_Odiv__class_Odiv'( 'c_Divides_Odiv__class_Odiv'( X, Y,
% 1.00/1.35 'tc_nat' ), Z, 'tc_nat' ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( Y, Z, 'tc_nat' ) ) ), T ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), T ), X ) ) ), ~( hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 'tc_nat' ) ), Z ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oidom'( X ) ), ~( 'class_Int_Onumber__ring'(
% 1.00/1.35 X ) ), ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Y ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Z ), U ) ) ) ), =( T, U ), =( Z,
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.00/1.35 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), T ) ) ) ), =( Z, T ), =( Y
% 1.00/1.35 , 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 X ) ) ), =( Z, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), ~( =( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Z ), Z ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 X ) ) ), =( Y, 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.00/1.35 [ ~( =( 'c_Power_Opower__class_Opower'( X, Y, 'tc_nat' ), 'c_Suc'(
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X, 'c_Suc'(
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( Y,
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.00/1.35 [ ~( =( 'c_Suc'( X ), X ) ) ],
% 1.00/1.35 [ ~( =( X, 'c_Suc'( X ) ) ) ],
% 1.00/1.35 [ =( 'c_Divides_Odiv__class_Omod'( 'c_Suc'( X ), Y, 'tc_nat' ),
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( 'c_Suc'( 'c_Divides_Odiv__class_Omod'( X, Y
% 1.00/1.35 , 'tc_nat' ) ), Y, 'tc_nat' ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_fun'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.00/1.35 'tc_bool' ) ), 'c_Arrow__Order__Mirabelle_Omkbot'( X, Y ) ),
% 1.00/1.35 'c_Arrow__Order__Mirabelle_OLin' ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.00/1.35 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ), X ),
% 1.00/1.35 'c_Arrow__Order__Mirabelle_OLin' ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_fun'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.00/1.35 'tc_bool' ) ), 'c_Arrow__Order__Mirabelle_Omktop'( X, Y ) ),
% 1.00/1.35 'c_Arrow__Order__Mirabelle_OLin' ) ), ~( hBOOL( hAPP( hAPP( 'c_in'(
% 1.00/1.35 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ), X ),
% 1.00/1.35 'c_Arrow__Order__Mirabelle_OLin' ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_fun'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.00/1.35 'tc_bool' ) ), 'v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1'( X, Y
% 1.00/1.35 ) ), 'c_Arrow__Order__Mirabelle_OLin' ) ), =( X, Y ) ],
% 1.00/1.35 [ =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'(
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), 'c_Suc'(
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Oab__semigroup__idem__mult'( X ) ), =( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), Y ), Y ) ],
% 1.00/1.35 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.00/1.35 ), Y ), Z ), Z, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.00/1.35 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.00/1.35 ), Y ), Z ), Y, X ), 'c_HOL_Ozero__class_Ozero'( X ) ) ],
% 1.00/1.35 [ =( 'c_Divides_Odiv__class_Omod'( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ), X, 'tc_nat' ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.00/1.35 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), 'c_Divides_Odiv__class_Omod'( Y, Z, X )
% 1.00/1.35 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.00/1.35 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ), Y ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__ring__strict'( X ) ), =( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ) ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ) ) ), 'c_HOL_Ozero__class_Ozero'( X ) ) ]
% 1.00/1.35 ,
% 1.00/1.35 [ hBOOL( hAPP( X, hAPP( Y, Z ) ) ), ~( hBOOL( hAPP( 'c_Set_Ovimage'( Y,
% 1.00/1.35 X, T, U ), Z ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( 'c_Set_Ovimage'( X, Y, Z, T ), U ) ), ~( hBOOL( hAPP( Y,
% 1.00/1.35 hAPP( X, U ) ) ) ) ],
% 1.00/1.35 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'( X
% 1.00/1.35 ) ), Y ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), 'c_Suc'(
% 1.00/1.35 X ) ), Z ) ) ), =( Y, Z ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Osemiring__1'( X ) ), =(
% 1.00/1.35 'c_Nat_Osemiring__1__class_Oof__nat'( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ), X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), 'c_Nat_Osemiring__1__class_Oof__nat'( Y
% 1.00/1.35 , X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'( Z, X ) ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Ocomm__monoid__mult'( X ) ), =(
% 1.00/1.35 'c_Power_Opower__class_Opower'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.00/1.35 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.00/1.35 'c_Power_Opower__class_Opower'( Y, T, X ) ),
% 1.00/1.35 'c_Power_Opower__class_Opower'( Z, T, X ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =(
% 1.00/1.35 'c_Power_Opower__class_Opower'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.00/1.35 X ), Y ), Z ), T, X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.00/1.35 'c_Power_Opower__class_Opower'( Y, T, X ) ),
% 1.00/1.35 'c_Power_Opower__class_Opower'( Z, T, X ) ) ) ],
% 1.00/1.35 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.00/1.35 , 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), T ), Z, X ),
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.00/1.35 , Y ), T ), Z, X ) ) ],
% 1.00/1.35 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.00/1.35 , Y ), 'c_Divides_Odiv__class_Omod'( Z, T, X ) ), T, X ),
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X )
% 1.00/1.35 , Y ), Z ), T, X ) ) ],
% 1.00/1.35 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.00/1.35 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( Y, 'c_Suc'(
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), =( X, 'c_Suc'(
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ],
% 1.00/1.35 [ ~( =( hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ),
% 1.00/1.35 'c_Suc'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ), =( X,
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), =( Y,
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Omonoid__mult'( X ) ), =(
% 1.00/1.35 'c_Power_Opower__class_Opower'( Y, hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), T ), X ),
% 1.00/1.35 'c_Power_Opower__class_Opower'( 'c_Power_Opower__class_Opower'( Y, Z, X )
% 1.00/1.35 , T, X ) ) ],
% 1.00/1.35 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.00/1.35 X ), Y ), 'c_Divides_Odiv__class_Odiv'( Z, Y, X ) ) ),
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( Z, Y, X ) ), Z ) ],
% 1.00/1.35 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.00/1.35 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ), Y ) ],
% 1.00/1.35 [ ~( 'class_Divides_Osemiring__div'( X ) ), =( Y, hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.00/1.35 X ), 'c_Divides_Odiv__class_Odiv'( Y, Z, X ) ), Z ) ),
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( Y, Z, X ) ) ) ],
% 1.00/1.35 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.00/1.35 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), T ), Z ), X
% 1.00/1.35 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ),
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( Y, T, X ) ), Z ) ) ],
% 1.00/1.35 [ ~( 'class_Divides_Osemiring__div'( X ) ), =(
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X
% 1.00/1.35 ), Y ), Z ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ), X
% 1.00/1.35 ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ),
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( Z, T, X ) ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Oab__semigroup__mult'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), Z ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Z ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ) ) ],
% 1.00/1.35 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), Z ) ), T ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.35 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Ocomm__semiring'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'(
% 1.00/1.35 X ), Y ), Z ) ), T ), hAPP( hAPP( 'c_HOL_Oplus__class_Oplus'( X ), hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Z ), T ) ) ) ],
% 1.00/1.35 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ), Z ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), Z ) ) ) ],
% 1.00/1.35 [ =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), Z ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Ocomm__semiring__1'( X ) ), =( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( X ), Y ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), Z ), T ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( X ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'(
% 1.00/1.35 X ), Y ), Z ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( X ), Y ), T )
% 1.00/1.35 ) ) ],
% 1.00/1.35 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 'tc_nat' ) ), Y ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ), ~( hBOOL(
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL(
% 1.00/1.35 hAPP( X, Y ) ) ), hBOOL( hAPP( X,
% 1.00/1.35 'c_List_Osko__Divides__Xmod__induct__0__1__1'( X, Z ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( X, Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Z ),
% 1.00/1.35 'c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1'( X ) ) ) ), ~( hBOOL(
% 1.00/1.35 hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.00/1.35 [ =( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), 'c_Suc'(
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ), hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 'tc_nat' ) ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.00/1.35 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), Y ), X ) ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.00/1.35 'c_Divides_Odiv__class_Omod'( X, Y, 'tc_nat' ) ), Y ) ), ~( hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 'tc_nat' ) ), Y ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( X, Y ) ), hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.00/1.35 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ),
% 1.00/1.35 'c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1'( X ) ) ), ~( hBOOL(
% 1.00/1.35 hAPP( X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.00/1.35 [ ~( =( hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ),
% 1.00/1.35 hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~(
% 1.00/1.35 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ) ), =( Y, Z ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ), X ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ) ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'( X ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Suc'( X ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Y ),
% 1.00/1.35 X ) ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 'tc_nat' ) ), hAPP( hAPP( 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ),
% 1.00/1.35 Y ) ) ) ) ],
% 1.00/1.35 [ =( 'c_Divides_Odiv__class_Odiv'( X, Y, 'tc_nat' ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 'tc_nat' ) ), Y ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 'tc_nat' ) ), X ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 'tc_nat' ) ), X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.00/1.35 'tc_nat' ), Y ), Z ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ), ~( hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 'tc_nat' ) ), Y ) ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'(
% 1.00/1.35 'tc_nat' ), X ), Z ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.00/1.35 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), X ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), Z ), Y ) ) ) ), ~( hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 'tc_nat' ) ), Z ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Y ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Otimes__class_Otimes'( 'tc_nat' ), X ), Z ) ) ), ~( hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), Z ) ) ), ~( hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 'tc_nat' ) ), X ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.00/1.35 ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.00/1.35 'c_Power_Opower__class_Opower'( Z, X, 'tc_nat' ) ),
% 1.00/1.35 'c_Power_Opower__class_Opower'( Z, Y, 'tc_nat' ) ) ) ), ~( hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 'tc_nat' ) ), Z ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_Power_Opower__class_Opower'(
% 1.00/1.35 X, 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), 'tc_nat' ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 'tc_nat' ) ), Y ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oplus__class_Oplus'( 'tc_nat' ), X ), Y ) ) ), ~( hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 'tc_nat' ) ), X ) ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.00/1.35 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBS'( 'c_COMBB'( 'c_HOL_OIf'( X
% 1.00/1.35 ), 'c_COMBC'( 'c_fequal'( Y ), Z, Y, Y, 'tc_bool' ), 'tc_bool', 'tc_fun'(
% 1.00/1.35 X, 'tc_fun'( X, X ) ), Y ), T, Y, X, 'tc_fun'( X, X ) ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ), Y, X, X ), U, Y, X ), hAPP( T, Z ) ),
% 1.00/1.35 ~( hBOOL( hAPP( hAPP( 'c_in'( Y ), Z ), U ) ) ), ~(
% 1.00/1.35 'c_Finite__Set_Ofinite'( U, Y ) ) ],
% 1.00/1.35 [ ~( 'class_OrderedGroup_Ocomm__monoid__add'( X ) ), =(
% 1.00/1.35 'c_Finite__Set_Osetsum'( 'c_COMBC'( 'c_COMBS'( 'c_COMBB'( 'c_HOL_OIf'( X
% 1.00/1.35 ), 'c_COMBC'( 'c_fequal'( Y ), Z, Y, Y, 'tc_bool' ), 'tc_bool', 'tc_fun'(
% 1.00/1.35 X, 'tc_fun'( X, X ) ), Y ), T, Y, X, 'tc_fun'( X, X ) ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ), Y, X, X ), U, Y, X ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( X ) ), hBOOL( hAPP( hAPP( 'c_in'( Y ), Z ), U
% 1.00/1.35 ) ), ~( 'c_Finite__Set_Ofinite'( U, Y ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.00/1.35 , 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'c_Arrow__Order__Mirabelle_Omktop'(
% 1.00/1.35 Z, T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.00/1.35 , 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ) ), Z ) ) ), =( X, Y ), =( X, T ) ]
% 1.00/1.35 ,
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.00/1.35 , 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'c_Arrow__Order__Mirabelle_Omktop'(
% 1.00/1.35 Z, T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.00/1.35 , 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ) ), Z ) ) ), =( Y, T ), =( X, T ) ]
% 1.00/1.35 ,
% 1.00/1.35 [ ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.00/1.35 , 'c_Pair'( X, X, 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'c_Arrow__Order__Mirabelle_Omktop'(
% 1.00/1.35 Y, X ) ) ) ) ],
% 1.00/1.35 [ ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.00/1.35 , 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'c_Arrow__Order__Mirabelle_Omktop'(
% 1.00/1.35 Z, X ) ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.00/1.35 , 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ) ), Z ) ), =( Y, T ), ~( hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_in'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'c_Pair'( X, Y,
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.00/1.35 , 'c_Arrow__Order__Mirabelle_Omktop'( Z, T ) ) ) ) ],
% 1.00/1.35 [ =( X, Y ), =( Y, X ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.00/1.35 , 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'c_Arrow__Order__Mirabelle_Omkbot'(
% 1.00/1.35 Z, X ) ) ) ],
% 1.00/1.35 [ ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.00/1.35 , 'c_Pair'( X, X, 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'c_Arrow__Order__Mirabelle_Omkbot'(
% 1.00/1.35 Y, X ) ) ) ) ],
% 1.00/1.35 [ ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.00/1.35 , 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'c_Arrow__Order__Mirabelle_Omkbot'(
% 1.00/1.35 Z, Y ) ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.00/1.35 , 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'c_Arrow__Order__Mirabelle_Omkbot'(
% 1.00/1.35 Z, T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.00/1.35 , 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ) ), Z ) ) ), =( X, Y ), =( Y, T ) ]
% 1.00/1.35 ,
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.00/1.35 , 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'c_Arrow__Order__Mirabelle_Omkbot'(
% 1.00/1.35 Z, T ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.00/1.35 , 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ) ), Z ) ) ), =( X, T ), =( Y, T ) ]
% 1.00/1.35 ,
% 1.00/1.35 [ =( X, Y ), =( X, Y ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.00/1.35 , 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'c_Arrow__Order__Mirabelle_Omktop'(
% 1.00/1.35 Z, Y ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.00/1.35 , 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ) ), Z ) ), =( X, T ), ~( hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_in'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'c_Pair'( X, Y,
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.00/1.35 , 'c_Arrow__Order__Mirabelle_Omkbot'( Z, T ) ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.00/1.35 , 'c_Pair'( X, Y, 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ) ),
% 1.00/1.35 'v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1'( X, Y ) ) ), =( X, Y
% 1.00/1.35 ) ],
% 1.00/1.35 [ =( 'c_Set_Ovimage'( 'c_COMBC'( 'c_COMBC'( 'c_COMBB'( 'c_HOL_OIf'( X )
% 1.00/1.35 , 'c_COMBC'( 'c_in'( Y ), Z, Y, 'tc_fun'( Y, 'tc_bool' ), 'tc_bool' ),
% 1.00/1.35 'tc_bool', 'tc_fun'( X, 'tc_fun'( X, X ) ), Y ), T, Y, X, 'tc_fun'( X, X
% 1.00/1.35 ) ), U, Y, X, X ), W, Y, X ), Z ), hBOOL( hAPP( hAPP( 'c_in'( X ), U ),
% 1.00/1.35 W ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), T ), W ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'( Z, T, X, Y )
% 1.00/1.35 ), 'c_Product__Type_OSigma'( U, W, X, Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_in'( Y ), T ), hAPP( W, Z ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.00/1.35 Z ), U ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, Y ) ), 'c_Pair'( Z, T, X, Y )
% 1.00/1.35 ), 'c_Product__Type_OSigma'( U, W, X, Y ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_in'( Y ), T ), hAPP( W, Z ) ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.00/1.35 Z ), U ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Wellfounded_Oacc'( Z, X ) ) )
% 1.00/1.35 , ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, T, X, X
% 1.00/1.35 ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), T ),
% 1.00/1.35 'c_Wellfounded_Oacc'( Z, X ) ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Wellfounded_Oacc'( Z, X ) ) )
% 1.00/1.35 , ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, T, X, X
% 1.00/1.35 ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), T ),
% 1.00/1.35 'c_Wellfounded_Oacc'( Z, X ) ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Relation_OImage'( Z, T, U, X )
% 1.00/1.35 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( U, X ) ), 'c_Pair'( W, Y,
% 1.00/1.35 U, X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), W ), T ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Relation_OImage'( Z, T, U, X )
% 1.00/1.35 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( U, X ) ), 'c_Pair'( W, Y,
% 1.00/1.35 U, X ) ), Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( U ), W ), T ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, T, X, X ) ),
% 1.00/1.35 'c_Relation_OId__on'( Z, X ) ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Y, X, X )
% 1.00/1.35 ), 'c_Relation_OId__on'( Z, X ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ),
% 1.00/1.35 Y ), Z ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( T, Y, X, X ) ), U ) ) ), ~(
% 1.00/1.35 'c_Equiv__Relations_Oequiv'( Z, U, X ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, T, X, X ) ), U ) ) ), ~(
% 1.00/1.35 'c_Equiv__Relations_Oequiv'( Z, U, X ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Relation_ORange'( Z, T, X ) )
% 1.00/1.35 ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( T, X ) ), 'c_Pair'( U, Y, T
% 1.00/1.35 , X ) ), Z ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Relation_ORange'( Z, T, X ) )
% 1.00/1.35 ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( T, X ) ), 'c_Pair'( U, Y, T
% 1.00/1.35 , X ) ), Z ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Relation_ODomain'( Z, X, T ) )
% 1.00/1.35 ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, T ) ), 'c_Pair'( Y, U, X
% 1.00/1.35 , T ) ), Z ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), 'c_Relation_ODomain'( Z, X, T ) )
% 1.00/1.35 ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, T ) ), 'c_Pair'( Y, U, X
% 1.00/1.35 , T ) ), Z ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), hAPP( Z, T ) ) ), ~( hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_in'( 'tc_prod'( U, X ) ), 'c_Pair'( T, Y, U, X ) ),
% 1.00/1.35 'c_Product__Type_OSigma'( W, Z, U, X ) ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_in'( 'tc_prod'( X, T ) ), 'c_Pair'( Y, U, X, T ) ),
% 1.00/1.35 'c_Product__Type_OSigma'( Z, W, X, T ) ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.00/1.35 ), T ) ), hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Z, Y
% 1.00/1.35 , X, X ) ), T ) ), =( Z, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), U )
% 1.00/1.35 ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Z ), U ) ) ), ~(
% 1.00/1.35 'c_Relation_Ototal__on'( U, T, X ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Y, X, X )
% 1.00/1.35 ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~(
% 1.00/1.35 'c_Relation_Orefl__on'( T, Z, X ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( T, Y, X, X ) ), U ) ) ), ~(
% 1.00/1.35 'c_Relation_Orefl__on'( Z, U, X ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, T, X, X ) ), U ) ) ), ~(
% 1.00/1.35 'c_Relation_Orefl__on'( Z, U, X ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Y, X, X )
% 1.00/1.35 ), Z ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), T ) ) ), ~(
% 1.00/1.35 'c_Relation_Orefl__on'( T, Z, X ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Y, X, X )
% 1.00/1.35 ), 'c_Nat_Ocompow'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ), Z, 'tc_prod'(
% 1.00/1.35 X, X ), 'tc_bool' ) ) ) ],
% 1.00/1.35 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( Z, Z ) ), 'c_Pair'(
% 1.00/1.35 X, Y, Z, Z ) ), 'c_Nat_Ocompow'( 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ),
% 1.00/1.35 T, 'tc_prod'( Z, Z ), 'tc_bool' ) ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.00/1.35 ), 'c_Wellfounded_Omlex__prod'( T, U, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( T, Y ) ), hAPP( T, Z ) ) ) )
% 1.00/1.35 ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( X, X ) ), 'c_Pair'( Y, Z, X, X )
% 1.00/1.35 ), 'c_Wellfounded_Omeasure'( T, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( T, Y ) ), hAPP( T, Z ) ) ) )
% 1.00/1.35 ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), hAPP( X, Y )
% 1.00/1.35 ), hAPP( X, Z ) ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'( T, T ) ),
% 1.00/1.35 'c_Pair'( Y, Z, T, T ) ), 'c_Wellfounded_Omeasure'( X, T ) ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 'tc_nat' ) ), Y ) ), ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( X )
% 1.00/1.35 , 'c_HOL_Ozero__class_Ozero'( X ) ), 'c_Nat_Osemiring__1__class_Oof__nat'(
% 1.00/1.35 Y, X ) ) ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__semidom'( X ) ), hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( X ), 'c_HOL_Ozero__class_Ozero'( X ) ),
% 1.00/1.35 'c_Nat_Osemiring__1__class_Oof__nat'( Y, X ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 'tc_nat' ) ), Y ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_fun'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.00/1.35 'tc_bool' ) ) ), 'c_COMBC'( 'c_COMBC'( 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'(
% 1.00/1.35 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ), 'c_COMBC'( 'c_COMBB'(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'v_h____', 'tc_nat', 'tc_fun'(
% 1.00/1.35 'tc_nat', 'tc_bool' ), 'tc_Arrow__Order__Mirabelle_Oindi' ), X,
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_nat', 'tc_bool' ), 'tc_bool',
% 1.00/1.35 'tc_fun'( 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 1.00/1.35 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.00/1.35 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_Lab____',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.00/1.35 'tc_bool' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.00/1.35 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'v_Lba____',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.00/1.35 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ),
% 1.00/1.35 'c_Arrow__Order__Mirabelle_OProf' ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_fun'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.00/1.35 'tc_bool' ) ), hAPP( 'v_F', 'c_COMBC'( 'c_COMBC'( 'c_COMBB'( 'c_HOL_OIf'(
% 1.00/1.35 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ), 'c_COMBC'( 'c_COMBB'(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( 'tc_nat' ), 'v_h____', 'tc_nat', 'tc_fun'(
% 1.00/1.35 'tc_nat', 'tc_bool' ), 'tc_Arrow__Order__Mirabelle_Oindi' ), X,
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_nat', 'tc_bool' ), 'tc_bool',
% 1.00/1.35 'tc_fun'( 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_fun'(
% 1.00/1.35 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ), 'tc_fun'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.00/1.35 'tc_bool' ) ) ), 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_Lab____',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.00/1.35 'tc_bool' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.00/1.35 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'v_Lba____',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.00/1.35 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ) ),
% 1.00/1.35 'c_Arrow__Order__Mirabelle_OLin' ) ) ],
% 1.00/1.35 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ],
% 1.00/1.35 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ],
% 1.00/1.35 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ],
% 1.00/1.35 [ ~( 'class_Orderings_Oorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ) ],
% 1.00/1.35 [ ~( =( 'c_Pair'( X, Y, Z, T ), 'c_Pair'( U, W, Z, T ) ) ), =( Y, W ) ]
% 1.00/1.35 ,
% 1.00/1.35 [ ~( =( 'c_Pair'( X, Y, Z, T ), 'c_Pair'( U, W, Z, T ) ) ), =( X, U ) ]
% 1.00/1.35 ,
% 1.00/1.35 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 'tc_nat' ) ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ), X ) ), =( X,
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ],
% 1.00/1.35 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ],
% 1.00/1.35 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), =( Z, Y ), hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ) ],
% 1.00/1.35 [ ~( 'class_Orderings_Olinorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ), =( Z, Y ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.00/1.35 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), X ) ), =(
% 1.00/1.35 Y, X ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), Z ) ), =( Z, Y ), hBOOL( hAPP(
% 1.00/1.35 hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Z ), Y ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), Y ) ),
% 1.00/1.35 hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), Y ), X ) ), =(
% 1.00/1.35 Y, X ) ],
% 1.00/1.35 [ ~( 'class_Orderings_Olinorder'( X ) ), =( Y, Z ), hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ), hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ) ],
% 1.00/1.35 [ ~( 'class_Ring__and__Field_Oordered__idom'( X ) ), hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Z ), Y ) ), =( Z, Y ) ],
% 1.00/1.35 [ ~( 'class_Orderings_Opreorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Y ), Y ) ) ) ],
% 1.00/1.35 [ ~( 'class_Orderings_Olinorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Y ), Y ) ) ) ],
% 1.00/1.35 [ ~( 'class_Orderings_Oorder'( X ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Y ), Y ) ) ) ],
% 1.00/1.35 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), X )
% 1.00/1.35 ) ) ],
% 1.00/1.35 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ), X )
% 1.00/1.35 ) ) ],
% 1.00/1.35 [ ~( 'class_Orderings_Opreorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ) ],
% 1.00/1.35 [ ~( 'class_Orderings_Oorder'( X ) ), hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Y ), Z ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), Y ), T ) ) ), ~( hBOOL( hAPP( hAPP(
% 1.00/1.35 'c_HOL_Oord__class_Oless'( X ), T ), Z ) ) ) ],
% 1.00/1.35 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.00/1.35 [ ~( hBOOL( hAPP( hAPP( 'c_HOL_Oord__class_Oless'( 'tc_nat' ), X ),
% 1.00/1.35 'c_HOL_Ozero__class_Ozero'( 'tc_nat' ) ) ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( X ), Y ), Z ) ), ~( hBOOL( hAPP( Z, Y ) ) )
% 1.00/1.35 ],
% 1.00/1.35 [ hBOOL( hAPP( X, Y ) ), ~( hBOOL( hAPP( hAPP( 'c_in'( Z ), Y ), X ) ) )
% 1.00/1.35 ],
% 1.00/1.35 [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 1.00/1.35 ,
% 1.00/1.35 [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), Y ) ) ]
% 1.00/1.35 ,
% 1.00/1.35 [ ~( =( 'v_a____', 'v_b____' ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_fun'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.00/1.35 'tc_bool' ) ), 'v_Lba____' ), 'c_Arrow__Order__Mirabelle_OLin' ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_fun'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.00/1.35 'tc_bool' ) ), 'v_Lba____' ), 'c_Arrow__Order__Mirabelle_OLin' ) ) ],
% 1.00/1.35 [ ~( hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.00/1.35 , 'c_Pair'( 'v_a____', 'v_b____', 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ) ), 'v_Lba____' ) ) ) ],
% 1.00/1.35 [ 'c_Arrow__Order__Mirabelle_Ounanimity'( 'v_F' ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_fun'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.00/1.35 'tc_bool' ) ), hAPP( 'v_F', 'c_COMBK'( 'v_Lba____', 'tc_fun'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.00/1.35 'tc_bool' ), 'tc_Arrow__Order__Mirabelle_Oindi' ) ) ),
% 1.00/1.35 'c_Arrow__Order__Mirabelle_OLin' ) ) ],
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_in'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ) )
% 1.00/1.35 , 'c_Pair'( 'v_a____', 'v_b____', 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ) ), hAPP( 'v_F', 'c_COMBC'( 'c_COMBC'(
% 1.00/1.35 'c_COMBB'( 'c_HOL_OIf'( 'tc_fun'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.00/1.35 'tc_bool' ) ), 'c_COMBC'( 'c_COMBB'( 'c_HOL_Oord__class_Oless'( 'tc_nat'
% 1.00/1.35 ), 'v_h____', 'tc_nat', 'tc_fun'( 'tc_nat', 'tc_bool' ),
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oindi' ), 'c_HOL_Ozero__class_Ozero'(
% 1.00/1.35 'tc_nat' ), 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_nat', 'tc_bool' ),
% 1.00/1.35 'tc_bool', 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.00/1.35 'tc_bool' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.00/1.35 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ),
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oindi' ), 'v_Lab____',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.00/1.35 'tc_bool' ), 'tc_fun'( 'tc_fun'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.00/1.35 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ), 'v_Lba____',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oindi', 'tc_fun'( 'tc_prod'(
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt', 'tc_Arrow__Order__Mirabelle_Oalt' ),
% 1.00/1.35 'tc_bool' ), 'tc_fun'( 'tc_prod'( 'tc_Arrow__Order__Mirabelle_Oalt',
% 1.00/1.35 'tc_Arrow__Order__Mirabelle_Oalt' ), 'tc_bool' ) ) ) ) ) ],
% 1.00/1.35 [ 'class_Finite__Set_Ofinite_Ofinite'( 'tc_prod'( X, Y ) ), ~(
% 1.00/1.35 'class_Finite__Set_Ofinite_Ofinite'( Y ) ), ~(
% 1.00/1.35 'class_Finite__Set_Ofinite_Ofinite'( X ) ) ],
% 1.00/1.35 [ 'class_Lattices_Olower__semilattice'( 'tc_fun'( X, Y ) ), ~(
% 1.00/1.35 'class_Lattices_Olattice'( Y ) ) ],
% 1.00/1.35 [ 'class_Lattices_Obounded__lattice'( 'tc_fun'( X, Y ) ), ~(
% 1.00/1.35 'class_Lattices_Obounded__lattice'( Y ) ) ],
% 1.00/1.35 [ 'class_Lattices_Oboolean__algebra'( 'tc_fun'( X, Y ) ), ~(
% 1.00/1.35 'class_Lattices_Oboolean__algebra'( Y ) ) ],
% 1.00/1.35 [ 'class_Finite__Set_Ofinite_Ofinite'( 'tc_fun'( X, Y ) ), ~(
% 1.00/1.35 'class_Finite__Set_Ofinite_Ofinite'( Y ) ), ~(
% 1.00/1.35 'class_Finite__Set_Ofinite_Ofinite'( X ) ) ],
% 1.00/1.35 [ 'class_Orderings_Opreorder'( 'tc_fun'( X, Y ) ), ~(
% 1.00/1.35 'class_Orderings_Opreorder'( Y ) ) ],
% 1.00/1.35 [ 'class_Lattices_Olattice'( 'tc_fun'( X, Y ) ), ~(
% 1.00/1.35 'class_Lattices_Olattice'( Y ) ) ],
% 1.00/1.35 [ 'class_Orderings_Oorder'( 'tc_fun'( X, Y ) ), ~(
% 1.00/1.35 'class_Orderings_Oorder'( Y ) ) ],
% 1.00/1.35 [ 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add'( 'tc_nat' )
% 1.00/1.35 ],
% 1.00/1.35 [ 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le'( 'tc_nat'
% 1.00/1.35 ) ],
% 1.00/1.35 [ 'class_Ring__and__Field_Oordered__comm__semiring__strict'( 'tc_nat' )
% 1.00/1.35 ],
% 1.00/1.35 [ 'class_Ring__and__Field_Oordered__semiring__strict'( 'tc_nat' ) ],
% 1.00/1.35 [ 'class_OrderedGroup_Opordered__comm__monoid__add'( 'tc_nat' ) ],
% 1.00/1.35 [ 'class_OrderedGroup_Ocancel__ab__semigroup__add'( 'tc_nat' ) ],
% 1.00/1.35 [ 'class_OrderedGroup_Ocancel__semigroup__add'( 'tc_nat' ) ],
% 1.00/1.35 [ 'class_Ring__and__Field_Ono__zero__divisors'( 'tc_nat' ) ],
% 1.00/1.35 [ 'class_Ring__and__Field_Oordered__semidom'( 'tc_nat' ) ],
% 1.00/1.35 [ 'class_Ring__and__Field_Ocomm__semiring__1'( 'tc_nat' ) ],
% 1.00/1.35 [ 'class_OrderedGroup_Oab__semigroup__mult'( 'tc_nat' ) ],
% 1.00/1.35 [ 'class_OrderedGroup_Ocomm__monoid__mult'( 'tc_nat' ) ],
% 1.00/1.35 [ 'class_OrderedGroup_Oab__semigroup__add'( 'tc_nat' ) ],
% 1.00/1.35 [ 'class_Ring__and__Field_Ocomm__semiring'( 'tc_nat' ) ],
% 1.00/1.35 [ 'class_OrderedGroup_Ocomm__monoid__add'( 'tc_nat' ) ],
% 1.00/1.35 [ 'class_Ring__and__Field_Ozero__neq__one'( 'tc_nat' ) ],
% 1.00/1.35 [ 'class_Lattices_Olower__semilattice'( 'tc_nat' ) ],
% 1.00/1.35 [ 'class_Ring__and__Field_Osemiring__1'( 'tc_nat' ) ],
% 1.00/1.35 [ 'class_Ring__and__Field_Osemiring__0'( 'tc_nat' ) ],
% 1.00/1.35 [ 'class_Ring__and__Field_Omult__zero'( 'tc_nat' ) ],
% 1.00/1.35 [ 'class_OrderedGroup_Omonoid__mult'( 'tc_nat' ) ],
% 1.00/1.35 [ 'class_Ring__and__Field_Osemiring'( 'tc_nat' ) ],
% 1.00/1.35 [ 'class_OrderedGroup_Omonoid__add'( 'tc_nat' ) ],
% 1.00/1.35 [ 'class_Divides_Osemiring__div'( 'tc_nat' ) ],
% 1.00/1.35 [ 'class_Nat_Osemiring__char__0'( 'tc_nat' ) ],
% 1.00/1.35 [ 'class_Orderings_Opreorder'( 'tc_nat' ) ],
% 1.00/1.35 [ 'class_Orderings_Olinorder'( 'tc_nat' ) ],
% 1.00/1.35 [ 'class_Lattices_Olattice'( 'tc_nat' ) ],
% 1.00/1.35 [ 'class_Orderings_Oorder'( 'tc_nat' ) ],
% 1.00/1.35 [ 'class_Power_Opower'( 'tc_nat' ) ],
% 1.00/1.35 [ 'class_Lattices_Olower__semilattice'( 'tc_bool' ) ],
% 1.00/1.35 [ 'class_Lattices_Obounded__lattice'( 'tc_bool' ) ],
% 1.00/1.35 [ 'class_Lattices_Oboolean__algebra'( 'tc_bool' ) ],
% 1.00/1.35 [ 'class_Finite__Set_Ofinite_Ofinite'( 'tc_bool' ) ],
% 1.00/1.35 [ 'class_Orderings_Opreorder'( 'tc_bool' ) ],
% 1.00/1.35 [ 'class_Lattices_Olattice'( 'tc_bool' ) ],
% 1.00/1.35 [ 'class_Orderings_Oorder'( 'tc_bool' ) ],
% 1.00/1.35 [ =( hAPP( 'c_COMBC'( X, Y, Z, T, U ), W ), hAPP( hAPP( X, W ), Y ) ) ]
% 1.00/1.35 ,
% 1.00/1.35 [ =( hAPP( 'c_COMBB'( X, Y, Z, T, U ), W ), hAPP( X, hAPP( Y, W ) ) ) ]
% 1.00/1.35 ,
% 1.00/1.35 [ hBOOL( hAPP( hAPP( 'c_fequal'( X ), Y ), Y ) ) ],
% 1.00/1.35 [ =( X, Y ), ~( hBOOL( hAPP( hAPP( 'c_fequal'( Z ), X ), Y ) ) ) ]
% 1.00/1.35 ] .
% 1.00/1.35
% 1.00/1.35
% 1.00/1.35 percentage equality = 0.345968, percentage horn = 0.867857
% 1.00/1.35 This is a problem with some equality
% 1.00/1.35
% 1.00/1.35
% 1.00/1.35
% 1.00/1.35 Options Used:
% 1.00/1.35
% 1.00/1.35 useres = 1
% 1.00/1.35 useparamod = 1
% 1.00/1.35 useeqrefl = 1
% 1.00/1.35 useeqfact = 1
% 1.00/1.35 usefactor = 1
% 1.00/1.35 usesimpsplitting = 0
% 1.00/1.35 usesimpdemod = 5
% 1.00/1.35 usesimpres = 3
% 1.00/1.35
% 1.00/1.35 resimpinuse = 1000
% 1.00/1.35 resimpclauses = 20000
% 1.00/1.35 substype = eqrewr
% 1.00/1.35 backwardsubs = 1
% 1.00/1.35 selectoldest = 5
% 1.00/1.35
% 1.00/1.35 litorderings [0] = split
% 1.00/1.35 litorderings [1] = extend the termordering, first sorting on arguments
% 1.00/1.35
% 1.00/1.35 termordering = kbo
% 1.00/1.35
% 1.00/1.35 litapriori = 0
% 1.00/1.35 termapriori = 1
% 1.00/1.35 litaposteriori = 0
% 1.00/1.35 termaposteriori = 0
% 1.00/1.35 demodaposteriori = 0
% 1.00/1.35 ordereqreflfact = 0
% 1.00/1.35
% 1.00/1.35 litselect = negord
% 1.00/1.35
% 1.00/1.35 maxweight = 15
% 1.00/1.35 maxdepth = 30000
% 1.00/1.35 maxlength = 115
% 1.00/1.35 maxnrvars = 195
% 1.00/1.35 excuselevel = 1
% 1.00/1.35 increasemaxweight = 1
% 1.00/1.35
% 1.00/1.35 maxselected = 10000000
% 1.00/1.35 maxnrclauses = 10000000
% 1.00/1.35
% 1.00/1.35 showgenerated = 0
% 1.00/1.35 showkept = 0
% 1.00/1.35 showselected = 0
% 1.00/1.35 showdeleted = 0
% 1.00/1.35 showresimp = 1
% 1.00/1.35 showstatus = 2000
% 1.00/1.35
% 1.00/1.35 prologoutput = 1
% 1.00/1.35 nrgoals = 5000000
% 1.00/1.35 totalproof = 1
% 1.00/1.35
% 1.00/1.35 Symbols occurring in the translation:
% 1.00/1.35
% 1.00/1.35 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.00/1.35 . [1, 2] (w:1, o:136, a:1, s:1, b:0),
% 1.00/1.35 ! [4, 1] (w:0, o:69, a:1, s:1, b:0),
% 1.00/1.35 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.00/1.35 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.00/1.35 'c_in' [40, 1] (w:1, o:74, a:1, s:1, b:0),
% 1.00/1.35 hAPP [42, 2] (w:1, o:161, a:1, s:1, b:0),
% 1.00/1.35 'tc_bool' [43, 0] (w:1, o:11, a:1, s:1, b:0),
% 1.00/1.35 'tc_fun' [44, 2] (w:1, o:162, a:1, s:1, b:0),
% 1.00/1.35 'c_Orderings_Obot__class_Obot' [45, 1] (w:1, o:75, a:1, s:1, b:0),
% 1.00/1.35 hBOOL [46, 1] (w:1, o:76, a:1, s:1, b:0),
% 1.00/1.35 'c_Orderings_Otop__class_Otop' [48, 1] (w:1, o:77, a:1, s:1, b:0),
% 1.00/1.35 'c_HOL_Ouminus__class_Ouminus' [50, 1] (w:1, o:79, a:1, s:1, b:0),
% 1.00/1.35 'c_Lattices_Olower__semilattice__class_Oinf' [53, 3] (w:1, o:173, a:1
% 1.00/1.35 , s:1, b:0),
% 1.00/1.35 'class_OrderedGroup_Ogroup__add' [55, 1] (w:1, o:81, a:1, s:1, b:0),
% 1.00/1.35
% 1.00/1.35 'c_HOL_Ozero__class_Ozero' [56, 1] (w:1, o:82, a:1, s:1, b:0),
% 1.00/1.35 'class_OrderedGroup_Oordered__ab__group__add' [57, 1] (w:1, o:83, a:1
% 1.00/1.35 , s:1, b:0),
% 1.00/1.35 'class_Lattices_Olower__semilattice' [58, 1] (w:1, o:84, a:1, s:1, b:
% 1.00/1.35 0),
% 1.00/1.35 'c_HOL_Oord__class_Oless' [59, 1] (w:1, o:85, a:1, s:1, b:0),
% 1.00/1.35 'class_OrderedGroup_Opordered__ab__group__add' [61, 1] (w:1, o:86, a:
% 1.00/1.35 1, s:1, b:0),
% 1.00/1.35 'c_Finite__Set_Ofinite' [64, 2] (w:1, o:163, a:1, s:1, b:0),
% 1.00/1.35 'c_Set_Ovimage' [67, 4] (w:1, o:185, a:1, s:1, b:0),
% 1.00/1.35 'class_Lattices_Oboolean__algebra' [68, 1] (w:1, o:87, a:1, s:1, b:0)
% 1.00/1.35 ,
% 1.00/1.35 'class_Ring__and__Field_Oring' [69, 1] (w:1, o:88, a:1, s:1, b:0),
% 1.00/1.35 'c_HOL_Otimes__class_Otimes' [70, 1] (w:1, o:78, a:1, s:1, b:0),
% 1.00/1.35 'class_Ring__and__Field_Oidom' [71, 1] (w:1, o:89, a:1, s:1, b:0),
% 1.00/1.35 'class_Divides_Oring__div' [72, 1] (w:1, o:90, a:1, s:1, b:0),
% 1.00/1.35 'c_Divides_Odiv__class_Omod' [73, 3] (w:1, o:175, a:1, s:1, b:0),
% 1.00/1.35 'class_OrderedGroup_Oab__group__add' [74, 1] (w:1, o:91, a:1, s:1, b:
% 1.00/1.35 0),
% 1.00/1.35 'c_HOL_Oplus__class_Oplus' [75, 1] (w:1, o:92, a:1, s:1, b:0),
% 1.00/1.35 'class_Lattices_Olattice' [78, 1] (w:1, o:93, a:1, s:1, b:0),
% 1.00/1.35 'class_OrderedGroup_Olordered__ab__group__add' [79, 1] (w:1, o:94, a:
% 1.00/1.35 1, s:1, b:0),
% 1.00/1.35 'class_OrderedGroup_Olordered__ab__group__add__meet' [80, 1] (w:1, o:
% 1.00/1.35 95, a:1, s:1, b:0),
% 1.00/1.35 'c_Relation_OImage' [82, 4] (w:1, o:184, a:1, s:1, b:0),
% 1.00/1.35 'class_Lattices_Obounded__lattice' [83, 1] (w:1, o:96, a:1, s:1, b:0)
% 1.00/1.35 ,
% 1.00/1.35 'c_Relation_Ototal__on' [87, 3] (w:1, o:176, a:1, s:1, b:0),
% 1.00/1.35 'class_Finite__Set_Ofinite_Ofinite' [88, 1] (w:1, o:97, a:1, s:1, b:0
% 6.06/6.43 ),
% 6.06/6.43 'class_Ring__and__Field_Oordered__idom' [89, 1] (w:1, o:100, a:1, s:1
% 6.06/6.43 , b:0),
% 6.06/6.43 'class_OrderedGroup_Ocomm__monoid__add' [90, 1] (w:1, o:101, a:1, s:1
% 6.06/6.43 , b:0),
% 6.06/6.43 'c_Finite__Set_Osetsum' [91, 4] (w:1, o:186, a:1, s:1, b:0),
% 6.06/6.43 'c_COMBB' [92, 5] (w:1, o:190, a:1, s:1, b:0),
% 6.06/6.43 'c_Relation_OId__on' [93, 2] (w:1, o:164, a:1, s:1, b:0),
% 6.06/6.43 'c_HOL_OIf' [94, 1] (w:1, o:102, a:1, s:1, b:0),
% 6.06/6.43 'c_COMBC' [95, 5] (w:1, o:191, a:1, s:1, b:0),
% 6.06/6.43 'c_COMBS' [96, 5] (w:1, o:192, a:1, s:1, b:0),
% 6.06/6.43 'class_Ring__and__Field_Ono__zero__divisors' [98, 1] (w:1, o:99, a:1
% 6.06/6.43 , s:1, b:0),
% 6.06/6.43 'class_Ring__and__Field_Oring__no__zero__divisors' [99, 1] (w:1, o:
% 6.06/6.43 103, a:1, s:1, b:0),
% 6.06/6.43 'class_Divides_Osemiring__div' [100, 1] (w:1, o:104, a:1, s:1, b:0),
% 6.06/6.43
% 6.06/6.43 'c_Divides_Odiv__class_Odiv' [101, 3] (w:1, o:177, a:1, s:1, b:0),
% 6.06/6.43 'class_Int_Onumber__ring' [102, 1] (w:1, o:105, a:1, s:1, b:0),
% 6.06/6.43 'class_Ring__and__Field_Ocomm__semiring__1' [103, 1] (w:1, o:106, a:1
% 6.06/6.43 , s:1, b:0),
% 6.06/6.43 'class_OrderedGroup_Omonoid__add' [104, 1] (w:1, o:107, a:1, s:1, b:0
% 6.06/6.43 ),
% 6.06/6.43 'class_Ring__and__Field_Oordered__ring__strict' [105, 1] (w:1, o:108
% 6.06/6.43 , a:1, s:1, b:0),
% 6.06/6.43 'class_OrderedGroup_Opordered__ab__semigroup__add__imp__le' [106, 1]
% 6.06/6.43 (w:1, o:109, a:1, s:1, b:0),
% 6.06/6.43 'class_OrderedGroup_Opordered__cancel__ab__semigroup__add' [107, 1]
% 6.06/6.43 (w:1, o:110, a:1, s:1, b:0),
% 6.06/6.43 'tc_prod' [109, 2] (w:1, o:165, a:1, s:1, b:0),
% 6.06/6.43 'c_Pair' [110, 4] (w:1, o:187, a:1, s:1, b:0),
% 6.06/6.43 'c_Suc' [112, 1] (w:1, o:111, a:1, s:1, b:0),
% 6.06/6.43 'c_Nat_Ocompow' [113, 4] (w:1, o:188, a:1, s:1, b:0),
% 6.06/6.43 'class_Ring__and__Field_Osemiring__0' [114, 1] (w:1, o:113, a:1, s:1
% 6.06/6.43 , b:0),
% 6.06/6.43 'tc_nat' [115, 0] (w:1, o:42, a:1, s:1, b:0),
% 6.06/6.43 'class_Ring__and__Field_Omult__zero' [119, 1] (w:1, o:98, a:1, s:1
% 6.06/6.43 , b:0),
% 6.06/6.43 'class_Ring__and__Field_Oring__1__no__zero__divisors' [120, 1] (w:1
% 6.06/6.43 , o:112, a:1, s:1, b:0),
% 6.06/6.43 'c_Power_Opower__class_Opower' [121, 3] (w:1, o:178, a:1, s:1, b:0),
% 6.06/6.43
% 6.06/6.43 'class_Ring__and__Field_Ozero__neq__one' [122, 1] (w:1, o:114, a:1
% 6.06/6.43 , s:1, b:0),
% 6.06/6.43 'class_Power_Opower' [123, 1] (w:1, o:126, a:1, s:1, b:0),
% 6.06/6.43 'c_List_Osko__Divides__Xmod__induct__0__1__1' [128, 2] (w:1, o:166
% 6.06/6.43 , a:1, s:1, b:0),
% 6.06/6.43 'class_OrderedGroup_Ocancel__semigroup__add' [129, 1] (w:1, o:115, a:
% 6.06/6.43 1, s:1, b:0),
% 6.06/6.43 'class_OrderedGroup_Ocancel__ab__semigroup__add' [130, 1] (w:1, o:116
% 6.06/6.43 , a:1, s:1, b:0),
% 6.06/6.43 'class_Ring__and__Field_Osemiring' [131, 1] (w:1, o:127, a:1, s:1, b:
% 6.06/6.43 0),
% 6.06/6.43 'c_Relation_ODomain' [136, 3] (w:1, o:179, a:1, s:1, b:0),
% 6.06/6.43 'class_OrderedGroup_Omonoid__mult' [137, 1] (w:1, o:117, a:1, s:1, b:
% 6.06/6.43 0),
% 6.06/6.43 'class_OrderedGroup_Oab__semigroup__add' [138, 1] (w:1, o:118, a:1
% 6.06/6.43 , s:1, b:0),
% 6.06/6.43 'c_Relation_Orefl__on' [140, 3] (w:1, o:180, a:1, s:1, b:0),
% 6.06/6.43 'class_Ring__and__Field_Osemiring__1' [141, 1] (w:1, o:128, a:1, s:1
% 6.06/6.43 , b:0),
% 6.06/6.43 'c_Nat_Osemiring__1__class_Oof__nat' [142, 2] (w:1, o:167, a:1, s:1
% 6.06/6.43 , b:0),
% 6.06/6.43 'c_ATP__Linkup_Osko__Nat__Xinfinite__descent0__1__1' [143, 1] (w:1
% 6.06/6.43 , o:129, a:1, s:1, b:0),
% 6.06/6.43 'tc_Arrow__Order__Mirabelle_Oalt' [145, 0] (w:1, o:51, a:1, s:1, b:0)
% 6.06/6.43 ,
% 6.06/6.43 'c_Arrow__Order__Mirabelle_OLin' [147, 0] (w:1, o:53, a:1, s:1, b:0)
% 6.06/6.43 ,
% 6.06/6.43 'c_fequal' [148, 1] (w:1, o:130, a:1, s:1, b:0),
% 6.06/6.43 'class_Ring__and__Field_Oordered__semidom' [149, 1] (w:1, o:131, a:1
% 6.06/6.43 , s:1, b:0),
% 6.06/6.43 'class_Ring__and__Field_Oordered__semiring__strict' [150, 1] (w:1, o:
% 6.06/6.43 132, a:1, s:1, b:0),
% 6.06/6.43 'class_OrderedGroup_Opordered__comm__monoid__add' [151, 1] (w:1, o:
% 6.06/6.43 119, a:1, s:1, b:0),
% 6.06/6.43 'class_Ring__and__Field_Oordered__comm__semiring__strict' [152, 1]
% 6.06/6.43 (w:1, o:133, a:1, s:1, b:0),
% 6.06/6.43 'class_Nat_Osemiring__char__0' [153, 1] (w:1, o:80, a:1, s:1, b:0),
% 6.06/6.43 'c_Relation_ORange' [156, 3] (w:1, o:181, a:1, s:1, b:0),
% 6.06/6.43 'c_Equiv__Relations_Oequiv' [162, 3] (w:1, o:182, a:1, s:1, b:0),
% 6.06/6.43 'class_OrderedGroup_Oab__semigroup__idem__mult' [163, 1] (w:1, o:120
% 6.06/6.43 , a:1, s:1, b:0),
% 28.29/28.65 'c_Arrow__Order__Mirabelle_Omkbot' [166, 2] (w:1, o:168, a:1, s:1, b:
% 28.29/28.65 0),
% 28.29/28.65 'c_Arrow__Order__Mirabelle_Omktop' [167, 2] (w:1, o:169, a:1, s:1, b:
% 28.29/28.65 0),
% 28.29/28.65 'v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1' [168, 2] (w:1, o:
% 28.29/28.65 170, a:1, s:1, b:0),
% 28.29/28.65 'class_OrderedGroup_Ocomm__monoid__mult' [169, 1] (w:1, o:121, a:1
% 28.29/28.65 , s:1, b:0),
% 28.29/28.65 'class_OrderedGroup_Oab__semigroup__mult' [170, 1] (w:1, o:122, a:1
% 28.29/28.65 , s:1, b:0),
% 28.29/28.65 'class_Ring__and__Field_Ocomm__semiring' [171, 1] (w:1, o:134, a:1
% 28.29/28.65 , s:1, b:0),
% 28.29/28.65 'c_Product__Type_OSigma' [172, 4] (w:1, o:189, a:1, s:1, b:0),
% 28.29/28.65 'c_Wellfounded_Oacc' [173, 2] (w:1, o:171, a:1, s:1, b:0),
% 28.29/28.65 'c_Wellfounded_Omlex__prod' [174, 3] (w:1, o:183, a:1, s:1, b:0),
% 28.29/28.65 'c_Wellfounded_Omeasure' [175, 2] (w:1, o:172, a:1, s:1, b:0),
% 28.29/28.65 'tc_Arrow__Order__Mirabelle_Oindi' [176, 0] (w:1, o:57, a:1, s:1, b:0
% 28.29/28.65 ),
% 28.29/28.65 'v_h____' [177, 0] (w:1, o:58, a:1, s:1, b:0),
% 28.29/28.65 'v_Lab____' [178, 0] (w:1, o:59, a:1, s:1, b:0),
% 28.29/28.65 'v_Lba____' [179, 0] (w:1, o:60, a:1, s:1, b:0),
% 28.29/28.65 'c_Arrow__Order__Mirabelle_OProf' [180, 0] (w:1, o:61, a:1, s:1, b:0)
% 28.29/28.65 ,
% 28.29/28.65 'v_F' [181, 0] (w:1, o:62, a:1, s:1, b:0),
% 28.29/28.65 'class_Orderings_Opreorder' [182, 1] (w:1, o:124, a:1, s:1, b:0),
% 28.29/28.65 'class_Orderings_Olinorder' [183, 1] (w:1, o:125, a:1, s:1, b:0),
% 28.29/28.65 'class_Orderings_Oorder' [184, 1] (w:1, o:123, a:1, s:1, b:0),
% 28.29/28.65 'v_a____' [185, 0] (w:1, o:63, a:1, s:1, b:0),
% 28.29/28.65 'v_b____' [186, 0] (w:1, o:64, a:1, s:1, b:0),
% 28.29/28.65 'c_Arrow__Order__Mirabelle_Ounanimity' [187, 1] (w:1, o:135, a:1, s:1
% 28.29/28.65 , b:0),
% 28.29/28.65 'c_COMBK' [188, 3] (w:1, o:174, a:1, s:1, b:0).
% 28.29/28.65
% 28.29/28.65
% 28.29/28.65 Starting Search:
% 28.29/28.65
% 28.29/28.65 Resimplifying inuse:
% 28.29/28.65 Done
% 28.29/28.65
% 28.29/28.65
% 28.29/28.65 Intermediate Status:
% 28.29/28.65 Generated: 4649
% 28.29/28.65 Kept: 2016
% 28.29/28.65 Inuse: 185
% 28.29/28.65 Deleted: 1
% 28.29/28.65 Deletedinuse: 0
% 28.29/28.65
% 28.29/28.65 Resimplifying inuse:
% 28.29/28.65 Done
% 28.29/28.65
% 28.29/28.65 Resimplifying inuse:
% 28.29/28.65 Done
% 28.29/28.65
% 28.29/28.65
% 28.29/28.65 Intermediate Status:
% 28.29/28.65 Generated: 13932
% 28.29/28.65 Kept: 4290
% 28.29/28.65 Inuse: 251
% 28.29/28.65 Deleted: 1
% 28.29/28.65 Deletedinuse: 0
% 28.29/28.65
% 28.29/28.65 Resimplifying inuse:
% 28.29/28.65 Done
% 28.29/28.65
% 28.29/28.65 Resimplifying inuse:
% 28.29/28.65 Done
% 28.29/28.65
% 28.29/28.65
% 28.29/28.65 Intermediate Status:
% 28.29/28.65 Generated: 24445
% 28.29/28.65 Kept: 6550
% 28.29/28.65 Inuse: 332
% 28.29/28.65 Deleted: 4
% 28.29/28.65 Deletedinuse: 0
% 28.29/28.65
% 28.29/28.65 Resimplifying inuse:
% 28.29/28.65 Done
% 28.29/28.65
% 28.29/28.65 Resimplifying inuse:
% 28.29/28.65 Done
% 28.29/28.65
% 28.29/28.65
% 28.29/28.65 Intermediate Status:
% 28.29/28.65 Generated: 35328
% 28.29/28.65 Kept: 8577
% 28.29/28.65 Inuse: 379
% 28.29/28.65 Deleted: 7
% 28.29/28.65 Deletedinuse: 1
% 28.29/28.65
% 28.29/28.65 Resimplifying inuse:
% 28.29/28.65 Done
% 28.29/28.65
% 28.29/28.65 Resimplifying inuse:
% 28.29/28.65 Done
% 28.29/28.65
% 28.29/28.65
% 28.29/28.65 Intermediate Status:
% 28.29/28.65 Generated: 41115
% 28.29/28.65 Kept: 10669
% 28.29/28.65 Inuse: 411
% 28.29/28.65 Deleted: 10
% 28.29/28.65 Deletedinuse: 1
% 28.29/28.65
% 28.29/28.65 Resimplifying inuse:
% 28.29/28.65 Done
% 28.29/28.65
% 28.29/28.65 Resimplifying inuse:
% 28.29/28.65 Done
% 28.29/28.65
% 28.29/28.65
% 28.29/28.65 Intermediate Status:
% 28.29/28.65 Generated: 46572
% 28.29/28.65 Kept: 12744
% 28.29/28.65 Inuse: 436
% 28.29/28.65 Deleted: 10
% 28.29/28.65 Deletedinuse: 1
% 28.29/28.65
% 28.29/28.65 Resimplifying inuse:
% 28.29/28.65 Done
% 28.29/28.65
% 28.29/28.65 Resimplifying inuse:
% 28.29/28.65 Done
% 28.29/28.65
% 28.29/28.65
% 28.29/28.65 Intermediate Status:
% 28.29/28.65 Generated: 54139
% 28.29/28.65 Kept: 15118
% 28.29/28.65 Inuse: 472
% 28.29/28.65 Deleted: 10
% 28.29/28.65 Deletedinuse: 1
% 28.29/28.65
% 28.29/28.65 Resimplifying inuse:
% 28.29/28.65 Done
% 28.29/28.65
% 28.29/28.65 Resimplifying inuse:
% 28.29/28.65 Done
% 28.29/28.65
% 28.29/28.65
% 28.29/28.65 Intermediate Status:
% 28.29/28.65 Generated: 69854
% 28.29/28.65 Kept: 18127
% 28.29/28.65 Inuse: 502
% 28.29/28.65 Deleted: 10
% 28.29/28.65 Deletedinuse: 1
% 28.29/28.65
% 28.29/28.65 Resimplifying inuse:
% 28.29/28.65 Done
% 28.29/28.65
% 28.29/28.65 Resimplifying inuse:
% 28.29/28.65 Done
% 28.29/28.65
% 28.29/28.65
% 28.29/28.65 Intermediate Status:
% 28.29/28.65 Generated: 82691
% 28.29/28.65 Kept: 20262
% 28.29/28.65 Inuse: 522
% 28.29/28.65 Deleted: 10
% 28.29/28.65 Deletedinuse: 1
% 28.29/28.65
% 28.29/28.65 Resimplifying clauses:
% 28.29/28.65 Done
% 28.29/28.65
% 28.29/28.65 Resimplifying inuse:
% 28.29/28.65 Done
% 28.29/28.65
% 28.29/28.65 Resimplifying inuse:
% 28.29/28.65 Done
% 28.29/28.65
% 28.29/28.65
% 28.29/28.65 Intermediate Status:
% 28.29/28.65 Generated: 94413
% 28.29/28.65 Kept: 22289
% 28.29/28.65 Inuse: 569
% 28.29/28.65 Deleted: 165
% 28.29/28.65 Deletedinuse: 2
% 28.29/28.65
% 28.29/28.65 Resimplifying inuse:
% 28.29/28.65 Done
% 28.29/28.65
% 28.29/28.65 Resimplifying inuse:
% 28.29/28.65 Done
% 28.29/28.65
% 28.29/28.65
% 28.29/28.65 Intermediate Status:
% 28.29/28.65 Generated: 105177
% 28.29/28.65 Kept: 25081
% 28.29/28.65 Inuse: 584
% 28.29/28.65 Deleted: 165
% 28.29/28.65 Deletedinuse: 2
% 28.29/28.65
% 28.29/28.65 Resimplifying inuse:
% 28.29/28.65 Done
% 28.29/28.65
% 28.29/28.65 Resimplifying inuse:
% 28.29/28.65 Done
% 28.29/28.65
% 28.29/28.65
% 28.29/28.65 Intermediate Status:
% 28.29/28.65 Generated: 109673
% 28.29/28.65 Kept: 27170
% 28.29/28.65 Inuse: 598
% 28.29/28.65 Deleted: 165
% 28.29/28.65 Deletedinuse: 2
% 28.29/28.65
% 28.29/28.65 Resimplifying inuse:
% 28.29/28.65 Done
% 28.29/28.65
% 28.29/28.65 Resimplifying inuse:
% 28.29/28.65 Done
% 28.29/28.65
% 28.29/28.65
% 28.29/28.65 Intermediate Status:
% 28.29/28.65 Generated: 115114
% 28.29/28.65 Kept: 29329
% 28.29/28.65 Inuse: 609
% 28.29/28.65 Deleted: 165
% 28.29/28.65 Deletedinuse: 2
% 28.29/28.65
% 28.29/28.65 Resimplifying inuse:
% 28.29/28.65 Done
% 28.29/28.65
% 28.29/28.65 Resimplifying inuse:
% 28.29/28.65 Done
% 28.29/28.65
% 28.29/28.65
% 28.29/28.65 Intermediate Status:
% 28.29/28.65 Generated: 123222
% 28.29/28.65 Kept: 31537
% 28.29/28.65 Inuse: 639
% 28.29/28.65 Deleted: 165
% 28.29/28.65 Deletedinuse: 2
% 28.29/28.65
% 28.29/28.65 Resimplifying inuse:
% 28.29/28.65 Done
% 28.29/28.65
% 28.29/28.65 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52
% 68.09/68.52 Intermediate Status:
% 68.09/68.52 Generated: 140540
% 68.09/68.52 Kept: 34945
% 68.09/68.52 Inuse: 667
% 68.09/68.52 Deleted: 167
% 68.09/68.52 Deletedinuse: 2
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52
% 68.09/68.52 Intermediate Status:
% 68.09/68.52 Generated: 153931
% 68.09/68.52 Kept: 37075
% 68.09/68.52 Inuse: 677
% 68.09/68.52 Deleted: 167
% 68.09/68.52 Deletedinuse: 2
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52
% 68.09/68.52 Intermediate Status:
% 68.09/68.52 Generated: 188157
% 68.09/68.52 Kept: 40343
% 68.09/68.52 Inuse: 685
% 68.09/68.52 Deleted: 171
% 68.09/68.52 Deletedinuse: 4
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52 Resimplifying clauses:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52
% 68.09/68.52 Intermediate Status:
% 68.09/68.52 Generated: 196437
% 68.09/68.52 Kept: 42538
% 68.09/68.52 Inuse: 700
% 68.09/68.52 Deleted: 387
% 68.09/68.52 Deletedinuse: 4
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52
% 68.09/68.52 Intermediate Status:
% 68.09/68.52 Generated: 203340
% 68.09/68.52 Kept: 44648
% 68.09/68.52 Inuse: 716
% 68.09/68.52 Deleted: 387
% 68.09/68.52 Deletedinuse: 4
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52
% 68.09/68.52 Intermediate Status:
% 68.09/68.52 Generated: 213048
% 68.09/68.52 Kept: 46793
% 68.09/68.52 Inuse: 740
% 68.09/68.52 Deleted: 387
% 68.09/68.52 Deletedinuse: 4
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52
% 68.09/68.52 Intermediate Status:
% 68.09/68.52 Generated: 221392
% 68.09/68.52 Kept: 48848
% 68.09/68.52 Inuse: 755
% 68.09/68.52 Deleted: 387
% 68.09/68.52 Deletedinuse: 4
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52
% 68.09/68.52 Intermediate Status:
% 68.09/68.52 Generated: 239494
% 68.09/68.52 Kept: 51523
% 68.09/68.52 Inuse: 765
% 68.09/68.52 Deleted: 387
% 68.09/68.52 Deletedinuse: 4
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52
% 68.09/68.52 Intermediate Status:
% 68.09/68.52 Generated: 248350
% 68.09/68.52 Kept: 53757
% 68.09/68.52 Inuse: 780
% 68.09/68.52 Deleted: 387
% 68.09/68.52 Deletedinuse: 4
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52
% 68.09/68.52 Intermediate Status:
% 68.09/68.52 Generated: 257197
% 68.09/68.52 Kept: 55819
% 68.09/68.52 Inuse: 798
% 68.09/68.52 Deleted: 387
% 68.09/68.52 Deletedinuse: 4
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52
% 68.09/68.52 Intermediate Status:
% 68.09/68.52 Generated: 270731
% 68.09/68.52 Kept: 58515
% 68.09/68.52 Inuse: 805
% 68.09/68.52 Deleted: 387
% 68.09/68.52 Deletedinuse: 4
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52 Resimplifying clauses:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52
% 68.09/68.52 Intermediate Status:
% 68.09/68.52 Generated: 279906
% 68.09/68.52 Kept: 60578
% 68.09/68.52 Inuse: 822
% 68.09/68.52 Deleted: 881
% 68.09/68.52 Deletedinuse: 4
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52
% 68.09/68.52 Intermediate Status:
% 68.09/68.52 Generated: 294382
% 68.09/68.52 Kept: 63258
% 68.09/68.52 Inuse: 830
% 68.09/68.52 Deleted: 881
% 68.09/68.52 Deletedinuse: 4
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52
% 68.09/68.52 Intermediate Status:
% 68.09/68.52 Generated: 307259
% 68.09/68.52 Kept: 65346
% 68.09/68.52 Inuse: 835
% 68.09/68.52 Deleted: 881
% 68.09/68.52 Deletedinuse: 4
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52
% 68.09/68.52 Intermediate Status:
% 68.09/68.52 Generated: 333650
% 68.09/68.52 Kept: 68188
% 68.09/68.52 Inuse: 860
% 68.09/68.52 Deleted: 881
% 68.09/68.52 Deletedinuse: 4
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52
% 68.09/68.52 Intermediate Status:
% 68.09/68.52 Generated: 355852
% 68.09/68.52 Kept: 70495
% 68.09/68.52 Inuse: 870
% 68.09/68.52 Deleted: 881
% 68.09/68.52 Deletedinuse: 4
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52
% 68.09/68.52 Intermediate Status:
% 68.09/68.52 Generated: 379722
% 68.09/68.52 Kept: 73230
% 68.09/68.52 Inuse: 880
% 68.09/68.52 Deleted: 881
% 68.09/68.52 Deletedinuse: 4
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52
% 68.09/68.52 Intermediate Status:
% 68.09/68.52 Generated: 393444
% 68.09/68.52 Kept: 75443
% 68.09/68.52 Inuse: 905
% 68.09/68.52 Deleted: 881
% 68.09/68.52 Deletedinuse: 4
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52
% 68.09/68.52 Intermediate Status:
% 68.09/68.52 Generated: 409779
% 68.09/68.52 Kept: 77915
% 68.09/68.52 Inuse: 925
% 68.09/68.52 Deleted: 881
% 68.09/68.52 Deletedinuse: 4
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52
% 68.09/68.52 Intermediate Status:
% 68.09/68.52 Generated: 420120
% 68.09/68.52 Kept: 80165
% 68.09/68.52 Inuse: 945
% 68.09/68.52 Deleted: 881
% 68.09/68.52 Deletedinuse: 4
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52 Resimplifying clauses:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52
% 68.09/68.52 Intermediate Status:
% 68.09/68.52 Generated: 438813
% 68.09/68.52 Kept: 82174
% 68.09/68.52 Inuse: 986
% 68.09/68.52 Deleted: 1023
% 68.09/68.52 Deletedinuse: 4
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52
% 68.09/68.52 Intermediate Status:
% 68.09/68.52 Generated: 445458
% 68.09/68.52 Kept: 84205
% 68.09/68.52 Inuse: 996
% 68.09/68.52 Deleted: 1024
% 68.09/68.52 Deletedinuse: 5
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52
% 68.09/68.52 Intermediate Status:
% 68.09/68.52 Generated: 460187
% 68.09/68.52 Kept: 86205
% 68.09/68.52 Inuse: 1039
% 68.09/68.52 Deleted: 1024
% 68.09/68.52 Deletedinuse: 5
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52
% 68.09/68.52 Intermediate Status:
% 68.09/68.52 Generated: 468109
% 68.09/68.52 Kept: 88210
% 68.09/68.52 Inuse: 1045
% 68.09/68.52 Deleted: 1024
% 68.09/68.52 Deletedinuse: 5
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52 Resimplifying inuse:
% 68.09/68.52 Done
% 68.09/68.52
% 68.09/68.52
% 68.09/68.52 Intermediate Status:
% 68.09/68.52 Generated: 480203
% 68.09/68.52 Kept: 90498
% 234.16/234.89 Inuse: 1065
% 234.16/234.89 Deleted: 1024
% 234.16/234.89 Deletedinuse: 5
% 234.16/234.89
% 234.16/234.89 Resimplifying inuse:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89
% 234.16/234.89 Intermediate Status:
% 234.16/234.89 Generated: 491298
% 234.16/234.89 Kept: 92720
% 234.16/234.89 Inuse: 1080
% 234.16/234.89 Deleted: 1024
% 234.16/234.89 Deletedinuse: 5
% 234.16/234.89
% 234.16/234.89 Resimplifying inuse:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89 Resimplifying inuse:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89
% 234.16/234.89 Intermediate Status:
% 234.16/234.89 Generated: 501376
% 234.16/234.89 Kept: 94968
% 234.16/234.89 Inuse: 1100
% 234.16/234.89 Deleted: 1024
% 234.16/234.89 Deletedinuse: 5
% 234.16/234.89
% 234.16/234.89 Resimplifying inuse:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89 Resimplifying inuse:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89
% 234.16/234.89 Intermediate Status:
% 234.16/234.89 Generated: 510371
% 234.16/234.89 Kept: 96980
% 234.16/234.89 Inuse: 1120
% 234.16/234.89 Deleted: 1024
% 234.16/234.89 Deletedinuse: 5
% 234.16/234.89
% 234.16/234.89 Resimplifying inuse:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89
% 234.16/234.89 Intermediate Status:
% 234.16/234.89 Generated: 530609
% 234.16/234.89 Kept: 101011
% 234.16/234.89 Inuse: 1135
% 234.16/234.89 Deleted: 1024
% 234.16/234.89 Deletedinuse: 5
% 234.16/234.89
% 234.16/234.89 Resimplifying inuse:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89 Resimplifying clauses:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89 Resimplifying inuse:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89
% 234.16/234.89 Intermediate Status:
% 234.16/234.89 Generated: 541174
% 234.16/234.89 Kept: 103170
% 234.16/234.89 Inuse: 1155
% 234.16/234.89 Deleted: 1749
% 234.16/234.89 Deletedinuse: 5
% 234.16/234.89
% 234.16/234.89 Resimplifying inuse:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89 Resimplifying inuse:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89
% 234.16/234.89 Intermediate Status:
% 234.16/234.89 Generated: 552844
% 234.16/234.89 Kept: 105283
% 234.16/234.89 Inuse: 1165
% 234.16/234.89 Deleted: 1752
% 234.16/234.89 Deletedinuse: 8
% 234.16/234.89
% 234.16/234.89 Resimplifying inuse:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89
% 234.16/234.89 Intermediate Status:
% 234.16/234.89 Generated: 577907
% 234.16/234.89 Kept: 108687
% 234.16/234.89 Inuse: 1185
% 234.16/234.89 Deleted: 1752
% 234.16/234.89 Deletedinuse: 8
% 234.16/234.89
% 234.16/234.89 Resimplifying inuse:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89 Resimplifying inuse:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89
% 234.16/234.89 Intermediate Status:
% 234.16/234.89 Generated: 588202
% 234.16/234.89 Kept: 110905
% 234.16/234.89 Inuse: 1200
% 234.16/234.89 Deleted: 1752
% 234.16/234.89 Deletedinuse: 8
% 234.16/234.89
% 234.16/234.89 Resimplifying inuse:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89
% 234.16/234.89 Intermediate Status:
% 234.16/234.89 Generated: 598562
% 234.16/234.89 Kept: 113288
% 234.16/234.89 Inuse: 1215
% 234.16/234.89 Deleted: 1752
% 234.16/234.89 Deletedinuse: 8
% 234.16/234.89
% 234.16/234.89 Resimplifying inuse:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89 Resimplifying inuse:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89
% 234.16/234.89 Intermediate Status:
% 234.16/234.89 Generated: 609363
% 234.16/234.89 Kept: 115748
% 234.16/234.89 Inuse: 1230
% 234.16/234.89 Deleted: 1752
% 234.16/234.89 Deletedinuse: 8
% 234.16/234.89
% 234.16/234.89 Resimplifying inuse:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89 Resimplifying inuse:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89
% 234.16/234.89 Intermediate Status:
% 234.16/234.89 Generated: 619609
% 234.16/234.89 Kept: 117775
% 234.16/234.89 Inuse: 1244
% 234.16/234.89 Deleted: 1752
% 234.16/234.89 Deletedinuse: 8
% 234.16/234.89
% 234.16/234.89 Resimplifying inuse:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89 Resimplifying inuse:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89
% 234.16/234.89 Intermediate Status:
% 234.16/234.89 Generated: 630656
% 234.16/234.89 Kept: 120234
% 234.16/234.89 Inuse: 1260
% 234.16/234.89 Deleted: 1754
% 234.16/234.89 Deletedinuse: 10
% 234.16/234.89
% 234.16/234.89 Resimplifying inuse:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89 Resimplifying clauses:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89 Resimplifying inuse:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89
% 234.16/234.89 Intermediate Status:
% 234.16/234.89 Generated: 640573
% 234.16/234.89 Kept: 122694
% 234.16/234.89 Inuse: 1279
% 234.16/234.89 Deleted: 2023
% 234.16/234.89 Deletedinuse: 11
% 234.16/234.89
% 234.16/234.89 Resimplifying inuse:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89 Resimplifying inuse:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89
% 234.16/234.89 Intermediate Status:
% 234.16/234.89 Generated: 650414
% 234.16/234.89 Kept: 124840
% 234.16/234.89 Inuse: 1299
% 234.16/234.89 Deleted: 2023
% 234.16/234.89 Deletedinuse: 11
% 234.16/234.89
% 234.16/234.89 Resimplifying inuse:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89
% 234.16/234.89 Intermediate Status:
% 234.16/234.89 Generated: 660821
% 234.16/234.89 Kept: 127330
% 234.16/234.89 Inuse: 1314
% 234.16/234.89 Deleted: 2023
% 234.16/234.89 Deletedinuse: 11
% 234.16/234.89
% 234.16/234.89 Resimplifying inuse:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89 Resimplifying inuse:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89
% 234.16/234.89 Intermediate Status:
% 234.16/234.89 Generated: 671059
% 234.16/234.89 Kept: 129805
% 234.16/234.89 Inuse: 1329
% 234.16/234.89 Deleted: 2023
% 234.16/234.89 Deletedinuse: 11
% 234.16/234.89
% 234.16/234.89 Resimplifying inuse:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89
% 234.16/234.89 Intermediate Status:
% 234.16/234.89 Generated: 681834
% 234.16/234.89 Kept: 132348
% 234.16/234.89 Inuse: 1344
% 234.16/234.89 Deleted: 2023
% 234.16/234.89 Deletedinuse: 11
% 234.16/234.89
% 234.16/234.89 Resimplifying inuse:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89 Resimplifying inuse:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89
% 234.16/234.89 Intermediate Status:
% 234.16/234.89 Generated: 691929
% 234.16/234.89 Kept: 134480
% 234.16/234.89 Inuse: 1359
% 234.16/234.89 Deleted: 2023
% 234.16/234.89 Deletedinuse: 11
% 234.16/234.89
% 234.16/234.89 Resimplifying inuse:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89
% 234.16/234.89 Intermediate Status:
% 234.16/234.89 Generated: 705165
% 234.16/234.89 Kept: 137047
% 234.16/234.89 Inuse: 1369
% 234.16/234.89 Deleted: 2023
% 234.16/234.89 Deletedinuse: 11
% 234.16/234.89
% 234.16/234.89 Resimplifying inuse:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89
% 234.16/234.89 Intermediate Status:
% 234.16/234.89 Generated: 715161
% 234.16/234.89 Kept: 139053
% 234.16/234.89 Inuse: 1374
% 234.16/234.89 Deleted: 2023
% 234.16/234.89 Deletedinuse: 11
% 234.16/234.89
% 234.16/234.89 Resimplifying inuse:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89
% 234.16/234.89 Intermediate Status:
% 234.16/234.89 Generated: 734932
% 234.16/234.89 Kept: 143138
% 234.16/234.89 Inuse: 1384
% 234.16/234.89 Deleted: 2023
% 234.16/234.89 Deletedinuse: 11
% 234.16/234.89
% 234.16/234.89 Resimplifying inuse:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89 Resimplifying clauses:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89 Resimplifying inuse:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89
% 234.16/234.89 Intermediate Status:
% 234.16/234.89 Generated: 743773
% 234.16/234.89 Kept: 145486
% 234.16/234.89 Inuse: 1398
% 234.16/234.89 Deleted: 2278
% 234.16/234.89 Deletedinuse: 11
% 234.16/234.89
% 234.16/234.89 Resimplifying inuse:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89
% 234.16/234.89 Intermediate Status:
% 234.16/234.89 Generated: 756178
% 234.16/234.89 Kept: 147781
% 234.16/234.89 Inuse: 1403
% 234.16/234.89 Deleted: 2278
% 234.16/234.89 Deletedinuse: 11
% 234.16/234.89
% 234.16/234.89 Resimplifying inuse:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89 Resimplifying inuse:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89
% 234.16/234.89 Intermediate Status:
% 234.16/234.89 Generated: 778054
% 234.16/234.89 Kept: 151347
% 234.16/234.89 Inuse: 1428
% 234.16/234.89 Deleted: 2279
% 234.16/234.89 Deletedinuse: 12
% 234.16/234.89
% 234.16/234.89 Resimplifying inuse:
% 234.16/234.89 Done
% 234.16/234.89
% 234.16/234.89
% 234.16/234.89 Intermediate Status:
% 234.16/234.89 GCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------