TSTP Solution File: SWV595-1 by Refute---2015
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%------------------------------------------------------------------------------
% File : Refute---2015
% Problem : SWV595-1 : TPTP v6.4.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : isabelle tptp_refute %d %s
% Computer : n133.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32218.75MB
% OS : Linux 3.10.0-327.10.1.el7.x86_64
% CPULimit : 300s
% DateTime : Thu Apr 14 05:29:47 EDT 2016
% Result : Timeout 300.10s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV595-1 : TPTP v6.4.0. Released v4.1.0.
% 0.00/0.04 % Command : isabelle tptp_refute %d %s
% 0.02/0.23 % Computer : n133.star.cs.uiowa.edu
% 0.02/0.23 % Model : x86_64 x86_64
% 0.02/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/0.23 % Memory : 32218.75MB
% 0.02/0.23 % OS : Linux 3.10.0-327.10.1.el7.x86_64
% 0.02/0.23 % CPULimit : 300
% 0.02/0.23 % DateTime : Fri Apr 8 17:32:09 CDT 2016
% 0.02/0.23 % CPUTime :
% 6.30/7.04 > val it = (): unit
% 7.01/7.73 Trying to find a model that refutes: True
% 18.72/19.46 Unfolded term: [| bnd_class_Power_Opower bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_Int_Onumber__ring bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_Orderings_Oorder bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_Orderings_Olinorder bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_Orderings_Opreorder bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_Ring__and__Field_Odvd bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_Ring__and__Field_Oidom bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_Ring__and__Field_Oring bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_Ring__and__Field_Ofield bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_Ring__and__Field_Oring__1 bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_Ring__and__Field_Osgn__if bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_OrderedGroup_Ogroup__add bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_RealVector_Oreal__vector bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_RealVector_Oreal__algebra bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_OrderedGroup_Omonoid__mult bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_Ring__and__Field_Omult__mono bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_Ring__and__Field_Omult__zero bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_RealVector_Oreal__algebra__1 bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_Ring__and__Field_Omult__mono1 bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_Ring__and__Field_Osemiring__1 bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_Ring__and__Field_Ocomm__ring__1 bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_Ring__and__Field_Oordered__idom bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_Ring__and__Field_Ozero__neq__one bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_RealVector_Oreal__normed__field bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_Ring__and__Field_Odivision__ring bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_Ring__and__Field_Olordered__ring bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_Ring__and__Field_Oordered__field bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_Ring__and__Field_Opordered__ring bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_OrderedGroup_Ocomm__monoid__mult bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_RealVector_Oreal__normed__vector bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_OrderedGroup_Oab__semigroup__mult bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_RealVector_Oreal__normed__algebra bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_Ring__and__Field_Ocomm__semiring__1 bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_Ring__and__Field_Oordered__semidom bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_Ring__and__Field_Odivision__by__zero bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_Ring__and__Field_Ono__zero__divisors bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_RealVector_Oreal__normed__algebra__1 bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_Ring__and__Field_Opordered__ring__abs bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_Ring__and__Field_Opordered__semiring bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_OrderedGroup_Oordered__ab__group__add bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_OrderedGroup_Olordered__ab__group__add bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_OrderedGroup_Opordered__ab__group__add bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_RealVector_Oreal__normed__div__algebra bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_Ring__and__Field_Oordered__ring__strict bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_Ring__and__Field_Oring__no__zero__divisors
% 18.72/19.46 bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_OrderedGroup_Opordered__ab__group__add__abs
% 18.72/19.46 bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_Ring__and__Field_Oring__1__no__zero__divisors
% 18.72/19.46 bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_class_Ring__and__Field_Opordered__cancel__semiring
% 18.72/19.46 bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_c_Transcendental_Ocos bnd_v_x =
% 18.72/19.46 bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_v_x = bnd_c_Transcendental_Opi;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 ~ bnd_class_Divides_Osemiring__div T_a |
% 18.72/19.46 bnd_c_Divides_Odiv__class_Odiv V_a (bnd_c_HOL_Oone__class_Oone T_a)
% 18.72/19.46 T_a =
% 18.72/19.46 V_a;
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal)
% 18.72/19.46 (bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal) bnd_tc_RealDef_Oreal =
% 18.72/19.46 bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_x.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 ~ bnd_c_HOL_Oinverse__class_Oinverse V_x T_a =
% 18.72/19.46 bnd_c_HOL_Oone__class_Oone T_a) |
% 18.72/19.46 V_x = bnd_c_HOL_Oone__class_Oone T_a;
% 18.72/19.46 !!T_a.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__normed__algebra__1 T_a |
% 18.72/19.46 bnd_c_HOL_Osgn__class_Osgn (bnd_c_HOL_Oone__class_Oone T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Oone__class_Oone T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Ocomm__semiring__1 T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes (bnd_c_HOL_Oone__class_Oone T_a) V_a
% 18.72/19.46 T_a =
% 18.72/19.46 V_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Ocomm__semiring__1 T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_a (bnd_c_HOL_Oone__class_Oone T_a)
% 18.72/19.46 T_a =
% 18.72/19.46 V_a;
% 18.72/19.46 !!V_z.
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal) V_z
% 18.72/19.46 bnd_tc_RealDef_Oreal =
% 18.72/19.46 V_z;
% 18.72/19.46 !!T_a V_x.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Ocomm__semiring__1 T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes (bnd_c_HOL_Oone__class_Oone T_a) V_x
% 18.72/19.46 T_a =
% 18.72/19.46 V_x;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 ~ bnd_class_OrderedGroup_Ocomm__monoid__mult T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes (bnd_c_HOL_Oone__class_Oone T_a) V_a
% 18.72/19.46 T_a =
% 18.72/19.46 V_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 ~ bnd_class_OrderedGroup_Omonoid__mult T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes (bnd_c_HOL_Oone__class_Oone T_a) V_a
% 18.72/19.46 T_a =
% 18.72/19.46 V_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 ~ bnd_class_OrderedGroup_Omonoid__mult T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_a (bnd_c_HOL_Oone__class_Oone T_a)
% 18.72/19.46 T_a =
% 18.72/19.46 V_a;
% 18.72/19.46 !!V_x.
% 18.72/19.46 ~ bnd_c_NthRoot_Osqrt V_x =
% 18.72/19.46 bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal |
% 18.72/19.46 V_x = bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Ozero__neq__one T_a |
% 18.72/19.46 ~ bnd_c_HOL_Oone__class_Oone T_a = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 bnd_c_Fun_Oid bnd_v_x bnd_t_a = bnd_v_x;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Ocomm__semiring__1 T_a |
% 18.72/19.46 bnd_c_Ring__and__Field_Odvd__class_Odvd
% 18.72/19.46 (bnd_c_HOL_Oone__class_Oone T_a) V_a T_a;
% 18.72/19.46 !!V_x.
% 18.72/19.46 bnd_c_lessequals (bnd_c_Transcendental_Ocos V_x)
% 18.72/19.46 (bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal)
% 18.72/19.46 bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_x.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__vector T_a |
% 18.72/19.46 bnd_c_RealVector_OscaleR__class_OscaleR
% 18.72/19.46 (bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal) V_x T_a =
% 18.72/19.46 V_x;
% 18.72/19.46 !!V_x.
% 18.72/19.46 bnd_c_lessequals
% 18.72/19.46 (bnd_c_HOL_Oabs__class_Oabs (bnd_c_Transcendental_Ocos V_x)
% 18.72/19.46 bnd_tc_RealDef_Oreal)
% 18.72/19.46 (bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal)
% 18.72/19.46 bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Oordered__idom T_a |
% 18.72/19.46 bnd_c_HOL_Oabs__class_Oabs (bnd_c_HOL_Oone__class_Oone T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Oone__class_Oone T_a;
% 18.72/19.46 !!T_a.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__algebra__1 T_a |
% 18.72/19.46 bnd_c_RealVector_Oof__real
% 18.72/19.46 (bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal) T_a =
% 18.72/19.46 bnd_c_HOL_Oone__class_Oone T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide V_a (bnd_c_HOL_Oone__class_Oone T_a)
% 18.72/19.46 T_a =
% 18.72/19.46 V_a;
% 18.72/19.46 !!T_a.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__normed__algebra__1 T_a |
% 18.72/19.46 bnd_c_RealVector_Onorm__class_Onorm (bnd_c_HOL_Oone__class_Oone T_a)
% 18.72/19.46 T_a =
% 18.72/19.46 bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_c_Transcendental_Ocos
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal) =
% 18.72/19.46 bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal;
% 18.72/19.46 ~ bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal =
% 18.72/19.46 bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Ozero__neq__one T_a |
% 18.72/19.46 ~ bnd_c_HOL_Ozero__class_Ozero T_a = bnd_c_HOL_Oone__class_Oone T_a;
% 18.72/19.46 !!T_a V_n.
% 18.72/19.46 ~ bnd_class_OrderedGroup_Omonoid__mult T_a |
% 18.72/19.46 bnd_c_Power_Opower__class_Opower (bnd_c_HOL_Oone__class_Oone T_a) V_n
% 18.72/19.46 T_a =
% 18.72/19.46 bnd_c_HOL_Oone__class_Oone T_a;
% 18.72/19.46 !!V_x.
% 18.72/19.46 ~ bnd_c_Transcendental_Ocos V_x =
% 18.72/19.46 bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal |
% 18.72/19.46 bnd_c_Transcendental_Osin V_x =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Oinverse (bnd_c_HOL_Oone__class_Oone T_a)
% 18.72/19.46 T_a =
% 18.72/19.46 bnd_c_HOL_Oone__class_Oone T_a;
% 18.72/19.46 !!T_a.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__ring T_a |
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Oinverse (bnd_c_HOL_Oone__class_Oone T_a)
% 18.72/19.46 T_a =
% 18.72/19.46 bnd_c_HOL_Oone__class_Oone T_a;
% 18.72/19.46 !!V_x.
% 18.72/19.46 bnd_c_Transcendental_Ocos
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_x bnd_tc_RealDef_Oreal) =
% 18.72/19.46 bnd_c_Transcendental_Ocos V_x;
% 18.72/19.46 bnd_c_NthRoot_Osqrt (bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal) =
% 18.72/19.46 bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!V_a.
% 18.72/19.46 bnd_c_Log_Opowr (bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal)
% 18.72/19.46 V_a =
% 18.72/19.46 bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Osemiring__1 T_a |
% 18.72/19.46 ~ bnd_c_Int_Oiszero (bnd_c_HOL_Oone__class_Oone T_a) T_a;
% 18.72/19.46 !!V_w V_z.
% 18.72/19.46 bnd_c_lessequals V_w V_z bnd_tc_RealDef_Oreal |
% 18.72/19.46 bnd_c_lessequals V_z V_w bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_y V_x.
% 18.72/19.46 (~ bnd_class_Orderings_Olinorder T_a | bnd_c_lessequals V_y V_x T_a) |
% 18.72/19.46 bnd_c_lessequals V_x V_y T_a;
% 18.72/19.46 !!T_a V_l V_k.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Oordered__idom T_a |
% 18.72/19.46 ~ bnd_c_HOL_Oabs__class_Oabs V_l T_a =
% 18.72/19.46 bnd_c_HOL_Oabs__class_Oabs V_k T_a) |
% 18.72/19.46 bnd_c_Ring__and__Field_Odvd__class_Odvd V_l V_k T_a;
% 18.72/19.46 !!T_a V_c.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 V_c T_a)
% 18.72/19.46 V_c T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 ~ bnd_class_OrderedGroup_Opordered__ab__group__add__abs T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 (bnd_c_HOL_Oabs__class_Oabs V_a T_a) T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Oordered__idom T_a |
% 18.72/19.46 bnd_c_HOL_Osgn__class_Osgn
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes (bnd_c_HOL_Osgn__class_Osgn V_a T_a)
% 18.72/19.46 (bnd_c_HOL_Osgn__class_Osgn V_b T_a) T_a;
% 18.72/19.46 !!T_a V_x V_y.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__normed__div__algebra T_a |
% 18.72/19.46 bnd_c_HOL_Osgn__class_Osgn
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_x V_y T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes (bnd_c_HOL_Osgn__class_Osgn V_x T_a)
% 18.72/19.46 (bnd_c_HOL_Osgn__class_Osgn V_y T_a) T_a;
% 18.72/19.46 !!T_a.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__normed__vector T_a |
% 18.72/19.46 bnd_c_RealVector_Onorm__class_Onorm
% 18.72/19.46 (bnd_c_HOL_Osgn__class_Osgn (bnd_c_HOL_Ozero__class_Ozero T_a) T_a)
% 18.72/19.46 T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_x V_z V_w V_y.
% 18.72/19.46 (((~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 ~ bnd_c_HOL_Otimes__class_Otimes V_x V_z T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_w V_y T_a) |
% 18.72/19.46 V_z = bnd_c_HOL_Ozero__class_Ozero T_a) |
% 18.72/19.46 V_y = bnd_c_HOL_Ozero__class_Ozero T_a) |
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide V_x V_y T_a =
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide V_w V_z T_a;
% 18.72/19.46 !!T_a V_x V_y V_w V_z.
% 18.72/19.46 (((~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 ~ bnd_c_HOL_Oinverse__class_Odivide V_x V_y T_a =
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide V_w V_z T_a) |
% 18.72/19.46 V_z = bnd_c_HOL_Ozero__class_Ozero T_a) |
% 18.72/19.46 V_y = bnd_c_HOL_Ozero__class_Ozero T_a) |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_x V_z T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_w V_y T_a;
% 18.72/19.46 !!T_a V_b.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a =
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide V_b
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero T_a) T_a;
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus
% 18.72/19.46 (bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal)
% 18.72/19.46 bnd_tc_RealDef_Oreal)
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus
% 18.72/19.46 (bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal)
% 18.72/19.46 bnd_tc_RealDef_Oreal)
% 18.72/19.46 bnd_tc_RealDef_Oreal =
% 18.72/19.46 bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_a V_x V_b.
% 18.72/19.46 ((~ bnd_class_RealVector_Oreal__vector T_a |
% 18.72/19.46 ~ bnd_c_RealVector_OscaleR__class_OscaleR V_a V_x T_a =
% 18.72/19.46 bnd_c_RealVector_OscaleR__class_OscaleR V_b V_x T_a) |
% 18.72/19.46 V_x = bnd_c_HOL_Ozero__class_Ozero T_a) |
% 18.72/19.46 V_a = V_b;
% 18.72/19.46 !!T_a V_a V_x V_y.
% 18.72/19.46 ((~ bnd_class_RealVector_Oreal__vector T_a |
% 18.72/19.46 ~ bnd_c_RealVector_OscaleR__class_OscaleR V_a V_x T_a =
% 18.72/19.46 bnd_c_RealVector_OscaleR__class_OscaleR V_a V_y T_a) |
% 18.72/19.46 V_a = bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal) |
% 18.72/19.46 V_x = V_y;
% 18.72/19.46 !!T_a V_x V_c V_y.
% 18.72/19.46 ((~ bnd_class_RealVector_Oreal__normed__vector T_a |
% 18.72/19.46 V_x = bnd_c_HOL_Ozero__class_Ozero T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_RealVector_Onorm__class_Onorm V_x T_a)
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_c
% 18.72/19.46 (bnd_c_RealVector_Onorm__class_Onorm V_y T_a)
% 18.72/19.46 bnd_tc_RealDef_Oreal)
% 18.72/19.46 bnd_tc_RealDef_Oreal) |
% 18.72/19.46 ~ bnd_c_lessequals V_c
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal)
% 18.72/19.46 bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__vector T_a |
% 18.72/19.46 bnd_c_RealVector_OscaleR__class_OscaleR V_a
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero T_a) T_a =
% 18.72/19.46 bnd_c_RealVector_OscaleR__class_OscaleR V_b
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero T_a) T_a;
% 18.72/19.46 !!T_a V_x V_y.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__vector T_a |
% 18.72/19.46 bnd_c_RealVector_OscaleR__class_OscaleR
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal) V_x T_a =
% 18.72/19.46 bnd_c_RealVector_OscaleR__class_OscaleR
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal) V_y T_a;
% 18.72/19.46 !!T_a V_z V_x V_y.
% 18.72/19.46 ((~ bnd_class_Orderings_Oorder T_a | bnd_c_lessequals V_z V_x T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_z V_y T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_y V_x T_a;
% 18.72/19.46 !!T_a V_x V_z V_y.
% 18.72/19.46 ((~ bnd_class_Orderings_Opreorder T_a |
% 18.72/19.46 bnd_c_lessequals V_x V_z T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_y V_z T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_x V_y T_a;
% 18.72/19.46 !!V_w. bnd_c_lessequals V_w V_w bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!V_i V_k V_j.
% 18.72/19.46 (bnd_c_lessequals V_i V_k bnd_tc_RealDef_Oreal |
% 18.72/19.46 ~ bnd_c_lessequals V_j V_k bnd_tc_RealDef_Oreal) |
% 18.72/19.46 ~ bnd_c_lessequals V_i V_j bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_x.
% 18.72/19.46 ~ bnd_class_Orderings_Oorder T_a | bnd_c_lessequals V_x V_x T_a;
% 18.72/19.46 !!T_a V_x.
% 18.72/19.46 ~ bnd_class_Orderings_Opreorder T_a | bnd_c_lessequals V_x V_x T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 (~ bnd_class_OrderedGroup_Opordered__ab__group__add__abs T_a |
% 18.72/19.46 ~ bnd_c_HOL_Oabs__class_Oabs V_a T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a) |
% 18.72/19.46 V_a = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_a V_c V_b V_d.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Ocomm__semiring__1 T_a |
% 18.72/19.46 bnd_c_Ring__and__Field_Odvd__class_Odvd
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_c T_a)
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) |
% 18.72/19.46 ~ bnd_c_Ring__and__Field_Odvd__class_Odvd V_c V_d T_a) |
% 18.72/19.46 ~ bnd_c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a;
% 18.72/19.46 !!T_a V_a V_b V_n.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 bnd_c_Power_Opower__class_Opower
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Odivide V_a V_b T_a) V_n T_a =
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide
% 18.72/19.46 (bnd_c_Power_Opower__class_Opower V_a V_n T_a)
% 18.72/19.46 (bnd_c_Power_Opower__class_Opower V_b V_n T_a) T_a) |
% 18.72/19.46 V_b = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!V_x.
% 18.72/19.46 bnd_c_NthRoot_Osqrt
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_x V_x bnd_tc_RealDef_Oreal) =
% 18.72/19.46 bnd_c_HOL_Oabs__class_Oabs V_x bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Osemiring__1 T_a |
% 18.72/19.46 bnd_c_Int_Oiszero (bnd_c_HOL_Ozero__class_Ozero T_a) T_a;
% 18.72/19.46 !!T_a V_x V_y.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 ~ bnd_class_Int_Onumber__ring T_a) |
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide V_x V_y T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_x
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Oinverse V_y T_a) T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide V_a V_b T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_a
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Oinverse V_b T_a) T_a;
% 18.72/19.46 !!T_a.
% 18.72/19.46 ~ bnd_class_OrderedGroup_Oordered__ab__group__add T_a |
% 18.72/19.46 bnd_c_HOL_Ouminus__class_Ouminus (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a.
% 18.72/19.46 ~ bnd_class_OrderedGroup_Ogroup__add T_a |
% 18.72/19.46 bnd_c_HOL_Ouminus__class_Ouminus (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Oring T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_a
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_b T_a) T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Odivision__ring T_a |
% 18.72/19.46 ~ bnd_c_HOL_Oinverse__class_Oinverse V_a T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a) |
% 18.72/19.46 V_a = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Odivision__ring T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 ~ bnd_c_HOL_Oinverse__class_Oinverse V_a T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a) |
% 18.72/19.46 V_a = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a.
% 18.72/19.46 ~ bnd_class_OrderedGroup_Ogroup__add T_a |
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a =
% 18.72/19.46 bnd_c_HOL_Ouminus__class_Ouminus (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 T_a;
% 18.72/19.46 !!T_a.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Oordered__idom T_a |
% 18.72/19.46 bnd_c_HOL_Osgn__class_Osgn (bnd_c_HOL_Ozero__class_Ozero T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Osgn__if T_a |
% 18.72/19.46 bnd_c_HOL_Osgn__class_Osgn (bnd_c_HOL_Ozero__class_Ozero T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__normed__vector T_a |
% 18.72/19.46 bnd_c_HOL_Osgn__class_Osgn (bnd_c_HOL_Ozero__class_Ozero T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!V_x V_y.
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal)
% 18.72/19.46 (bnd_c_Log_Opowr V_x V_y) bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 (((~ bnd_class_Ring__and__Field_Oordered__field T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_b (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_a (bnd_c_HOL_Ozero__class_Ozero T_a) T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 (((~ bnd_class_Ring__and__Field_Oordered__field T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_b T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_a T_a;
% 18.72/19.46 !!T_a.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Oordered__semidom T_a |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Oone__class_Oone T_a)
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero T_a) T_a;
% 18.72/19.46 !!T_a V_m V_k.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Oordered__idom T_a |
% 18.72/19.46 bnd_c_Ring__and__Field_Odvd__class_Odvd V_m
% 18.72/19.46 (bnd_c_HOL_Oabs__class_Oabs V_k T_a) T_a) |
% 18.72/19.46 ~ bnd_c_Ring__and__Field_Odvd__class_Odvd V_m V_k T_a;
% 18.72/19.46 !!T_a V_m V_k.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Oordered__idom T_a |
% 18.72/19.46 bnd_c_Ring__and__Field_Odvd__class_Odvd V_m V_k T_a) |
% 18.72/19.46 ~ bnd_c_Ring__and__Field_Odvd__class_Odvd V_m
% 18.72/19.46 (bnd_c_HOL_Oabs__class_Oabs V_k T_a) T_a;
% 18.72/19.46 !!T_a V_m V_k.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Oordered__idom T_a |
% 18.72/19.46 bnd_c_Ring__and__Field_Odvd__class_Odvd
% 18.72/19.46 (bnd_c_HOL_Oabs__class_Oabs V_m T_a) V_k T_a) |
% 18.72/19.46 ~ bnd_c_Ring__and__Field_Odvd__class_Odvd V_m V_k T_a;
% 18.72/19.46 !!T_a V_m V_k.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Oordered__idom T_a |
% 18.72/19.46 bnd_c_Ring__and__Field_Odvd__class_Odvd V_m V_k T_a) |
% 18.72/19.46 ~ bnd_c_Ring__and__Field_Odvd__class_Odvd
% 18.72/19.46 (bnd_c_HOL_Oabs__class_Oabs V_m T_a) V_k T_a;
% 18.72/19.46 !!T_a V_x.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Oordered__field T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_lessequals V_x (bnd_c_HOL_Oone__class_Oone T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Oone__class_Oone T_a)
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Oinverse V_x T_a) T_a;
% 18.72/19.46 !!T_a V_y V_x.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Oordered__idom T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes (bnd_c_HOL_Oabs__class_Oabs V_y T_a)
% 18.72/19.46 V_x T_a =
% 18.72/19.46 bnd_c_HOL_Oabs__class_Oabs
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_y V_x T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_x T_a;
% 18.72/19.46 !!T_a V_z.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Osemiring__1 T_a |
% 18.72/19.46 V_z = bnd_c_HOL_Ozero__class_Ozero T_a) |
% 18.72/19.46 ~ bnd_c_Int_Oiszero V_z T_a;
% 18.72/19.46 !!V_x V_a V_b.
% 18.72/19.46 bnd_c_Log_Opowr (bnd_c_Log_Opowr V_x V_a) V_b =
% 18.72/19.46 bnd_c_Log_Opowr V_x
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_b bnd_tc_RealDef_Oreal);
% 18.72/19.46 !!T_a V_a V_n.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Oordered__idom T_a |
% 18.72/19.46 bnd_c_HOL_Oabs__class_Oabs
% 18.72/19.46 (bnd_c_Power_Opower__class_Opower
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_a T_a) V_n T_a)
% 18.72/19.46 T_a =
% 18.72/19.46 bnd_c_HOL_Oabs__class_Oabs
% 18.72/19.46 (bnd_c_Power_Opower__class_Opower V_a V_n T_a) T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Oring__no__zero__divisors T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_a (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_b.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Oring__no__zero__divisors T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes (bnd_c_HOL_Ozero__class_Ozero T_a) V_b
% 18.72/19.46 T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Omult__zero T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_a (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Omult__zero T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes (bnd_c_HOL_Ozero__class_Ozero T_a) V_a
% 18.72/19.46 T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_x.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Ocomm__semiring__1 T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes (bnd_c_HOL_Ozero__class_Ozero T_a) V_x
% 18.72/19.46 T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_x.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__normed__algebra T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_x (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__normed__algebra T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_a (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_b.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__normed__algebra T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes (bnd_c_HOL_Ozero__class_Ozero T_a) V_b
% 18.72/19.46 T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_y.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__normed__algebra T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes (bnd_c_HOL_Ozero__class_Ozero T_a) V_y
% 18.72/19.46 T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Ocomm__semiring__1 T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_a (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Ocomm__semiring__1 T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes (bnd_c_HOL_Ozero__class_Ozero T_a) V_a
% 18.72/19.46 T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Oordered__semidom T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 (bnd_c_HOL_Oone__class_Oone T_a) T_a;
% 18.72/19.46 !!T_a V_b V_c.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_c T_a =
% 18.72/19.46 V_b) |
% 18.72/19.46 V_c = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_b V_c.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 V_b =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Odivide V_b V_c T_a) V_c T_a) |
% 18.72/19.46 V_c = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!V_x.
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal)
% 18.72/19.46 (bnd_c_NthRoot_Osqrt V_x) bnd_tc_RealDef_Oreal |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal)
% 18.72/19.46 V_x bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!V_y.
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal) V_y
% 18.72/19.46 bnd_tc_RealDef_Oreal |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal)
% 18.72/19.46 (bnd_c_NthRoot_Osqrt V_y) bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!V_y.
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal)
% 18.72/19.46 (bnd_c_NthRoot_Osqrt V_y) bnd_tc_RealDef_Oreal |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal)
% 18.72/19.46 V_y bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Ocomm__semiring__1 T_a |
% 18.72/19.46 bnd_c_Ring__and__Field_Odvd__class_Odvd V_a
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero T_a) T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Odivision__ring T_a |
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Oinverse
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_a T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Ouminus__class_Ouminus
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) |
% 18.72/19.46 V_a = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_a V_n.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Odivision__ring T_a |
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Oinverse
% 18.72/19.46 (bnd_c_Power_Opower__class_Opower V_a V_n T_a) T_a =
% 18.72/19.46 bnd_c_Power_Opower__class_Opower
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Oinverse V_a T_a) V_n T_a) |
% 18.72/19.46 V_a = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Oordered__idom T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes (bnd_c_HOL_Oabs__class_Oabs V_a T_a)
% 18.72/19.46 (bnd_c_HOL_Oabs__class_Oabs V_a T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_a V_a T_a;
% 18.72/19.46 !!T_a V_x V_y V_n.
% 18.72/19.46 (~ bnd_class_Divides_Osemiring__div T_a |
% 18.72/19.46 bnd_c_Power_Opower__class_Opower
% 18.72/19.46 (bnd_c_Divides_Odiv__class_Odiv V_x V_y T_a) V_n T_a =
% 18.72/19.46 bnd_c_Divides_Odiv__class_Odiv
% 18.72/19.46 (bnd_c_Power_Opower__class_Opower V_x V_n T_a)
% 18.72/19.46 (bnd_c_Power_Opower__class_Opower V_y V_n T_a) T_a) |
% 18.72/19.46 ~ bnd_c_Ring__and__Field_Odvd__class_Odvd V_y V_x T_a;
% 18.72/19.46 !!V_x V_a.
% 18.72/19.46 ~ bnd_c_Log_Opowr V_x V_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_c.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a =
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 V_c T_a)
% 18.72/19.46 V_c T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 ~ bnd_class_OrderedGroup_Opordered__ab__group__add__abs T_a |
% 18.72/19.46 bnd_c_lessequals V_a (bnd_c_HOL_Oabs__class_Oabs V_a T_a) T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 ~ bnd_class_OrderedGroup_Opordered__ab__group__add__abs T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ouminus__class_Ouminus V_a T_a)
% 18.72/19.46 (bnd_c_HOL_Oabs__class_Oabs V_a T_a) T_a;
% 18.72/19.46 !!T_a V_x.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Oordered__field T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Oinverse__class_Oinverse V_x T_a)
% 18.72/19.46 (bnd_c_HOL_Oone__class_Oone T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Oone__class_Oone T_a) V_x T_a;
% 18.72/19.46 !!V_a V_c V_b.
% 18.72/19.46 (~ bnd_c_HOL_Otimes__class_Otimes V_a V_c bnd_tc_RealDef_Oreal =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_b V_c bnd_tc_RealDef_Oreal |
% 18.72/19.46 V_c = bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal) |
% 18.72/19.46 V_a = V_b;
% 18.72/19.46 !!V_c V_a V_b.
% 18.72/19.46 (~ bnd_c_HOL_Otimes__class_Otimes V_c V_a bnd_tc_RealDef_Oreal =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_c V_b bnd_tc_RealDef_Oreal |
% 18.72/19.46 V_c = bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal) |
% 18.72/19.46 V_a = V_b;
% 18.72/19.46 !!V_x.
% 18.72/19.46 bnd_c_Log_Opowr V_x
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal) =
% 18.72/19.46 bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_a V_n.
% 18.72/19.46 ~ bnd_class_OrderedGroup_Omonoid__mult T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_Power_Opower__class_Opower V_a V_n T_a) V_a T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_a
% 18.72/19.46 (bnd_c_Power_Opower__class_Opower V_a V_n T_a) T_a;
% 18.72/19.46 !!T_a V_x V_y.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__normed__div__algebra T_a |
% 18.72/19.46 bnd_c_RealVector_Onorm__class_Onorm
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_x V_y T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_RealVector_Onorm__class_Onorm V_x T_a)
% 18.72/19.46 (bnd_c_RealVector_Onorm__class_Onorm V_y T_a) bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_a V_n.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Oring__1 T_a |
% 18.72/19.46 bnd_c_Power_Opower__class_Opower
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_a T_a) V_n T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_Power_Opower__class_Opower
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus (bnd_c_HOL_Oone__class_Oone T_a)
% 18.72/19.46 T_a)
% 18.72/19.46 V_n T_a)
% 18.72/19.46 (bnd_c_Power_Opower__class_Opower V_a V_n T_a) T_a;
% 18.72/19.46 !!T_a.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__normed__vector T_a |
% 18.72/19.46 bnd_c_RealVector_Onorm__class_Onorm (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_b V_a.
% 18.72/19.46 (((~ bnd_class_Ring__and__Field_Oordered__field T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_b T_a) |
% 18.72/19.46 bnd_c_lessequals V_b (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Oinverse__class_Odivide V_a V_b T_a)
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero T_a) T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 (((~ bnd_class_Ring__and__Field_Oordered__field T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_lessequals V_a (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 bnd_c_lessequals V_b (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Oinverse__class_Odivide V_a V_b T_a)
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero T_a) T_a;
% 18.72/19.46 !!T_a V_b V_a.
% 18.72/19.46 (((~ bnd_class_Ring__and__Field_Oordered__field T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_b T_a) |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_a T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Oinverse__class_Odivide V_a V_b T_a)
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero T_a) T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 (((~ bnd_class_Ring__and__Field_Oordered__field T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_lessequals V_a (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_a T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Oinverse__class_Odivide V_a V_b T_a)
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero T_a) T_a;
% 18.72/19.46 !!T_a V_ra V_r V_x.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__normed__vector T_a |
% 18.72/19.46 bnd_c_RealVector_OscaleR__class_OscaleR V_ra
% 18.72/19.46 (bnd_c_RealVector_OscaleR__class_OscaleR V_r V_x T_a) T_a =
% 18.72/19.46 bnd_c_RealVector_OscaleR__class_OscaleR V_r
% 18.72/19.46 (bnd_c_RealVector_OscaleR__class_OscaleR V_ra V_x T_a) T_a;
% 18.72/19.46 !!T_a V_a V_b V_x.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__vector T_a |
% 18.72/19.46 bnd_c_RealVector_OscaleR__class_OscaleR V_a
% 18.72/19.46 (bnd_c_RealVector_OscaleR__class_OscaleR V_b V_x T_a) T_a =
% 18.72/19.46 bnd_c_RealVector_OscaleR__class_OscaleR V_b
% 18.72/19.46 (bnd_c_RealVector_OscaleR__class_OscaleR V_a V_x T_a) T_a;
% 18.72/19.46 !!T_a V_a V_r V_b.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__normed__vector T_a |
% 18.72/19.46 bnd_c_RealVector_OscaleR__class_OscaleR V_a
% 18.72/19.46 (bnd_c_RealVector_OscaleR__class_OscaleR V_r V_b T_a) T_a =
% 18.72/19.46 bnd_c_RealVector_OscaleR__class_OscaleR V_r
% 18.72/19.46 (bnd_c_RealVector_OscaleR__class_OscaleR V_a V_b T_a) T_a;
% 18.72/19.46 !!V_x.
% 18.72/19.46 bnd_c_NthRoot_Osqrt
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_x bnd_tc_RealDef_Oreal) =
% 18.72/19.46 bnd_c_HOL_Ouminus__class_Ouminus (bnd_c_NthRoot_Osqrt V_x)
% 18.72/19.46 bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_x.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__normed__vector T_a |
% 18.72/19.46 bnd_c_RealVector_Onorm__class_Onorm
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_x T_a) T_a =
% 18.72/19.46 bnd_c_RealVector_Onorm__class_Onorm V_x T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 ~ bnd_class_OrderedGroup_Opordered__ab__group__add__abs T_a |
% 18.72/19.46 bnd_c_HOL_Oabs__class_Oabs (bnd_c_HOL_Oabs__class_Oabs V_a T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Oabs__class_Oabs V_a T_a;
% 18.72/19.46 !!T_a V_a V_n.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Oordered__semidom T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Oone__class_Oone T_a)
% 18.72/19.46 (bnd_c_Power_Opower__class_Opower V_a V_n T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Oone__class_Oone T_a) V_a T_a;
% 18.72/19.46 !!T_a V_a V_c V_b.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Oidom T_a |
% 18.72/19.46 bnd_c_Ring__and__Field_Odvd__class_Odvd
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_c T_a)
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) |
% 18.72/19.46 ~ bnd_c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a;
% 18.72/19.46 !!T_a V_c V_a V_b.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Oidom T_a |
% 18.72/19.46 bnd_c_Ring__and__Field_Odvd__class_Odvd
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_c V_a T_a)
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) |
% 18.72/19.46 ~ bnd_c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a;
% 18.72/19.46 !!V_x.
% 18.72/19.46 ~ bnd_c_Transcendental_Osin V_x =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal |
% 18.72/19.46 bnd_c_HOL_Oabs__class_Oabs (bnd_c_Transcendental_Ocos V_x)
% 18.72/19.46 bnd_tc_RealDef_Oreal =
% 18.72/19.46 bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_b V_a.
% 18.72/19.46 (~ bnd_class_OrderedGroup_Opordered__ab__group__add T_a |
% 18.72/19.46 bnd_c_lessequals V_b (bnd_c_HOL_Ouminus__class_Ouminus V_a T_a)
% 18.72/19.46 T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_a (bnd_c_HOL_Ouminus__class_Ouminus V_b T_a) T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 (~ bnd_class_OrderedGroup_Opordered__ab__group__add T_a |
% 18.72/19.46 bnd_c_lessequals V_a (bnd_c_HOL_Ouminus__class_Ouminus V_b T_a)
% 18.72/19.46 T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_b (bnd_c_HOL_Ouminus__class_Ouminus V_a T_a) T_a;
% 18.72/19.46 !!T_a V_b V_a.
% 18.72/19.46 (~ bnd_class_OrderedGroup_Opordered__ab__group__add T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ouminus__class_Ouminus V_b T_a) V_a
% 18.72/19.46 T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 (~ bnd_class_OrderedGroup_Opordered__ab__group__add T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ouminus__class_Ouminus V_a T_a) V_b
% 18.72/19.46 T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ouminus__class_Ouminus V_b T_a) V_a T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 ~ bnd_class_OrderedGroup_Ogroup__add T_a |
% 18.72/19.46 bnd_c_HOL_Ouminus__class_Ouminus
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_a T_a) T_a =
% 18.72/19.46 V_a;
% 18.72/19.46 !!T_a V_x.
% 18.72/19.46 ~ bnd_class_Lattices_Oboolean__algebra T_a |
% 18.72/19.46 bnd_c_HOL_Ouminus__class_Ouminus
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_x T_a) T_a =
% 18.72/19.46 V_x;
% 18.72/19.46 !!T_a V_b.
% 18.72/19.46 ~ bnd_class_OrderedGroup_Ogroup__add T_a |
% 18.72/19.46 V_b =
% 18.72/19.46 bnd_c_HOL_Ouminus__class_Ouminus
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_b T_a) T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 ~ bnd_class_OrderedGroup_Ogroup__add T_a |
% 18.72/19.46 V_a =
% 18.72/19.46 bnd_c_HOL_Ouminus__class_Ouminus
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_a T_a) T_a;
% 18.72/19.46 !!T_a V_b.
% 18.72/19.46 ~ bnd_class_OrderedGroup_Ogroup__add T_a |
% 18.72/19.46 bnd_c_HOL_Ouminus__class_Ouminus
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_b T_a) T_a =
% 18.72/19.46 V_b;
% 18.72/19.46 !!V_x T_a. bnd_c_Fun_Oid V_x T_a = V_x;
% 18.72/19.46 !!T_a V_b V_c V_a.
% 18.72/19.46 ((((~ bnd_class_Ring__and__Field_Oordered__field T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Oinverse__class_Odivide V_b V_c T_a)
% 18.72/19.46 V_a T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_a T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b
% 18.72/19.46 T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_b (bnd_c_HOL_Otimes__class_Otimes V_a V_c T_a)
% 18.72/19.46 T_a;
% 18.72/19.46 !!T_a V_a V_b V_c.
% 18.72/19.46 ((((~ bnd_class_Ring__and__Field_Oordered__field T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_lessequals V_a
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_a (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_b (bnd_c_HOL_Otimes__class_Otimes V_a V_c T_a)
% 18.72/19.46 T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Otimes__class_Otimes V_a V_c T_a) V_b
% 18.72/19.46 T_a;
% 18.72/19.46 !!T_a V_a V_b V_c.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Oidom T_a |
% 18.72/19.46 bnd_c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a) |
% 18.72/19.46 V_c = bnd_c_HOL_Ozero__class_Ozero T_a) |
% 18.72/19.46 ~ bnd_c_Ring__and__Field_Odvd__class_Odvd
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_c V_a T_a)
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a;
% 18.72/19.46 !!T_a V_a V_b V_c.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Oidom T_a |
% 18.72/19.46 bnd_c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a) |
% 18.72/19.46 V_c = bnd_c_HOL_Ozero__class_Ozero T_a) |
% 18.72/19.46 ~ bnd_c_Ring__and__Field_Odvd__class_Odvd
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_c T_a)
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 (~ bnd_class_OrderedGroup_Opordered__ab__group__add__abs T_a |
% 18.72/19.46 bnd_c_HOL_Oabs__class_Oabs V_a T_a =
% 18.72/19.46 bnd_c_HOL_Ouminus__class_Ouminus V_a T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_a (bnd_c_HOL_Ozero__class_Ozero T_a) T_a;
% 18.72/19.46 !!T_a V_b V_a.
% 18.72/19.46 (~ bnd_class_Divides_Osemiring__div T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_Divides_Odiv__class_Odiv V_b V_a T_a) V_a T_a =
% 18.72/19.46 V_b) |
% 18.72/19.46 ~ bnd_c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 (~ bnd_class_Divides_Osemiring__div T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_a
% 18.72/19.46 (bnd_c_Divides_Odiv__class_Odiv V_b V_a T_a) T_a =
% 18.72/19.46 V_b) |
% 18.72/19.46 ~ bnd_c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a;
% 18.72/19.46 !!T_a V_x V_y V_z.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Odivide V_x V_y T_a) V_z T_a =
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_x V_z T_a) V_y T_a;
% 18.72/19.46 !!T_a V_c V_a V_b.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_c V_a T_a)
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide V_a V_b T_a) |
% 18.72/19.46 V_c = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_a V_c V_b.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_c T_a)
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide V_a V_b T_a) |
% 18.72/19.46 V_c = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!V_u V_x.
% 18.72/19.46 bnd_c_lessequals
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_u V_u bnd_tc_RealDef_Oreal)
% 18.72/19.46 bnd_tc_RealDef_Oreal)
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_x V_x bnd_tc_RealDef_Oreal)
% 18.72/19.46 bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_x.
% 18.72/19.46 (~ bnd_class_RealVector_Oreal__normed__vector T_a |
% 18.72/19.46 ~ bnd_c_HOL_Osgn__class_Osgn V_x T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a) |
% 18.72/19.46 V_x = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Oordered__idom T_a |
% 18.72/19.46 ~ bnd_c_HOL_Osgn__class_Osgn V_a T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a) |
% 18.72/19.46 V_a = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Oordered__field T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_HOL_Oabs__class_Oabs
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide (bnd_c_HOL_Oabs__class_Oabs V_a T_a)
% 18.72/19.46 (bnd_c_HOL_Oabs__class_Oabs V_b T_a) T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Oordered__field T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_HOL_Oabs__class_Oabs
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Oinverse V_a T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Oinverse
% 18.72/19.46 (bnd_c_HOL_Oabs__class_Oabs V_a T_a) T_a;
% 18.72/19.46 !!T_a V_x V_n V_y.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Ocomm__semiring__1 T_a |
% 18.72/19.46 bnd_c_Ring__and__Field_Odvd__class_Odvd
% 18.72/19.46 (bnd_c_Power_Opower__class_Opower V_x V_n T_a)
% 18.72/19.46 (bnd_c_Power_Opower__class_Opower V_y V_n T_a) T_a) |
% 18.72/19.46 ~ bnd_c_Ring__and__Field_Odvd__class_Odvd V_x V_y T_a;
% 18.72/19.46 !!T_a V_a V_n.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Oordered__idom T_a |
% 18.72/19.46 bnd_c_HOL_Oabs__class_Oabs
% 18.72/19.46 (bnd_c_Power_Opower__class_Opower V_a V_n T_a) T_a =
% 18.72/19.46 bnd_c_Power_Opower__class_Opower (bnd_c_HOL_Oabs__class_Oabs V_a T_a)
% 18.72/19.46 V_n T_a;
% 18.72/19.46 !!V_x.
% 18.72/19.46 bnd_c_lessequals (bnd_c_NthRoot_Osqrt V_x)
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal)
% 18.72/19.46 bnd_tc_RealDef_Oreal |
% 18.72/19.46 ~ bnd_c_lessequals V_x
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal)
% 18.72/19.46 bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!V_x.
% 18.72/19.46 bnd_c_lessequals V_x
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal)
% 18.72/19.46 bnd_tc_RealDef_Oreal |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_NthRoot_Osqrt V_x)
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal)
% 18.72/19.46 bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_b V_a V_c.
% 18.72/19.46 (~ bnd_class_Divides_Osemiring__div T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_Divides_Odiv__class_Odiv V_b V_a T_a) V_c T_a =
% 18.72/19.46 bnd_c_Divides_Odiv__class_Odiv
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_b V_c T_a) V_a T_a) |
% 18.72/19.46 ~ bnd_c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Oordered__field T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_lessequals V_a (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Oinverse__class_Oinverse V_a T_a)
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero T_a) T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Oordered__field T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Oinverse__class_Oinverse V_a T_a)
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_a (bnd_c_HOL_Ozero__class_Ozero T_a) T_a;
% 18.72/19.46 !!V_x V_y.
% 18.72/19.46 bnd_c_NthRoot_Osqrt
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_x V_y bnd_tc_RealDef_Oreal) =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes (bnd_c_NthRoot_Osqrt V_x)
% 18.72/19.46 (bnd_c_NthRoot_Osqrt V_y) bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_y.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__normed__field T_a |
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 V_y T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide V_a
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_b.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide V_b
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 V_a T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_x.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__vector T_a |
% 18.72/19.46 bnd_c_RealVector_OscaleR__class_OscaleR
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal) V_x T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__vector T_a |
% 18.72/19.46 bnd_c_RealVector_OscaleR__class_OscaleR V_a
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_b.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__normed__vector T_a |
% 18.72/19.46 bnd_c_RealVector_OscaleR__class_OscaleR
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal) V_b T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__normed__vector T_a |
% 18.72/19.46 bnd_c_RealVector_OscaleR__class_OscaleR V_a
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_a V_b V_x.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__vector T_a |
% 18.72/19.46 bnd_c_RealVector_OscaleR__class_OscaleR V_a
% 18.72/19.46 (bnd_c_RealVector_OscaleR__class_OscaleR V_b V_x T_a) T_a =
% 18.72/19.46 bnd_c_RealVector_OscaleR__class_OscaleR
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_b bnd_tc_RealDef_Oreal) V_x
% 18.72/19.46 T_a;
% 18.72/19.46 !!T_a V_x V_y.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__normed__field T_a |
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_x T_a) V_y T_a =
% 18.72/19.46 bnd_c_HOL_Ouminus__class_Ouminus
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_a T_a)
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_b T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide V_a V_b T_a;
% 18.72/19.46 !!T_a V_x V_n.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Oordered__idom T_a |
% 18.72/19.46 V_x = bnd_c_HOL_Ozero__class_Ozero T_a) |
% 18.72/19.46 bnd_c_lessequals V_x (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_Power_Opower__class_Opower V_x V_n T_a)
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero T_a) T_a;
% 18.72/19.46 !!T_a V_x.
% 18.72/19.46 (((~ bnd_class_Ring__and__Field_Oordered__field T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Oone__class_Oone T_a) V_x T_a) |
% 18.72/19.46 bnd_c_lessequals V_x (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Oinverse__class_Oinverse V_x T_a)
% 18.72/19.46 (bnd_c_HOL_Oone__class_Oone T_a) T_a;
% 18.72/19.46 !!T_a V_a V_n V_b.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Oordered__semidom T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_Power_Opower__class_Opower V_a V_n T_a)
% 18.72/19.46 (bnd_c_Power_Opower__class_Opower V_b V_n T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_a T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_a V_b T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 (((~ bnd_class_Ring__and__Field_Oordered__field T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_lessequals V_a (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_a T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a;
% 18.72/19.46 !!T_a V_b V_a.
% 18.72/19.46 (((~ bnd_class_Ring__and__Field_Oordered__field T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_lessequals V_b (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_a T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 (((~ bnd_class_Ring__and__Field_Oordered__field T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_lessequals V_a (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_b T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a;
% 18.72/19.46 !!T_a V_b V_a.
% 18.72/19.46 (((~ bnd_class_Ring__and__Field_Oordered__field T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_lessequals V_b (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_b T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide V_a V_a T_a =
% 18.72/19.46 bnd_c_HOL_Oone__class_Oone T_a) |
% 18.72/19.46 V_a = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide V_a V_a T_a =
% 18.72/19.46 bnd_c_HOL_Oone__class_Oone T_a) |
% 18.72/19.46 V_a = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_x.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 V_x = bnd_c_HOL_Ozero__class_Ozero T_a) |
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide V_x V_x T_a =
% 18.72/19.46 bnd_c_HOL_Oone__class_Oone T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 (~ bnd_class_OrderedGroup_Ogroup__add T_a |
% 18.72/19.46 ~ bnd_c_HOL_Ozero__class_Ozero T_a =
% 18.72/19.46 bnd_c_HOL_Ouminus__class_Ouminus V_a T_a) |
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a = V_a;
% 18.72/19.46 !!T_a V_r V_x.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__algebra__1 T_a |
% 18.72/19.46 bnd_c_RealVector_OscaleR__class_OscaleR V_r V_x T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes (bnd_c_RealVector_Oof__real V_r T_a)
% 18.72/19.46 V_x T_a;
% 18.72/19.46 !!T_a.
% 18.72/19.46 ~ bnd_class_OrderedGroup_Opordered__ab__group__add__abs T_a |
% 18.72/19.46 bnd_c_HOL_Oabs__class_Oabs (bnd_c_HOL_Ozero__class_Ozero T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Ocomm__semiring__1 T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_b V_a T_a;
% 18.72/19.46 !!V_z V_w.
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_z V_w bnd_tc_RealDef_Oreal =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_w V_z bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_x V_y.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Ocomm__semiring__1 T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_x V_y T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_y V_x T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Odivision__ring T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Oinverse
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Oinverse V_a T_a) T_a =
% 18.72/19.46 V_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 bnd_c_HOL_Ouminus__class_Ouminus
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide V_a
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_b T_a) T_a) |
% 18.72/19.46 V_b = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_a V_n.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide (bnd_c_HOL_Oone__class_Oone T_a)
% 18.72/19.46 (bnd_c_Power_Opower__class_Opower V_a V_n T_a) T_a =
% 18.72/19.46 bnd_c_Power_Opower__class_Opower
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Odivide (bnd_c_HOL_Oone__class_Oone T_a)
% 18.72/19.46 V_a T_a)
% 18.72/19.46 V_n T_a;
% 18.72/19.46 !!T_a V_b V_k.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odvd T_a |
% 18.72/19.46 bnd_c_Ring__and__Field_Odvd__class_Odvd V_b
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_b V_k T_a) T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Ocomm__semiring__1 T_a |
% 18.72/19.46 bnd_c_Ring__and__Field_Odvd__class_Odvd V_a
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Ocomm__semiring__1 T_a |
% 18.72/19.46 bnd_c_Ring__and__Field_Odvd__class_Odvd V_a
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_b V_a T_a) T_a;
% 18.72/19.46 !!T_a V_x.
% 18.72/19.46 (~ bnd_class_RealVector_Oreal__normed__vector T_a |
% 18.72/19.46 V_x = bnd_c_HOL_Ozero__class_Ozero T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_RealVector_Onorm__class_Onorm V_x T_a)
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal)
% 18.72/19.46 bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_x.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 ~ bnd_class_Int_Onumber__ring T_a) |
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Oinverse V_x T_a =
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide (bnd_c_HOL_Oone__class_Oone T_a) V_x
% 18.72/19.46 T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Oinverse V_a T_a =
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide (bnd_c_HOL_Oone__class_Oone T_a) V_a
% 18.72/19.46 T_a;
% 18.72/19.46 !!V_x V_r.
% 18.72/19.46 bnd_c_lessequals V_x V_r bnd_tc_RealDef_Oreal |
% 18.72/19.46 ~ bnd_c_lessequals
% 18.72/19.46 (bnd_c_HOL_Oabs__class_Oabs V_x bnd_tc_RealDef_Oreal) V_r
% 18.72/19.46 bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 (~ bnd_class_OrderedGroup_Opordered__ab__group__add__abs T_a |
% 18.72/19.46 bnd_c_lessequals V_a V_b T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Oabs__class_Oabs V_a T_a) V_b T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Olordered__ring T_a |
% 18.72/19.46 bnd_c_lessequals
% 18.72/19.46 (bnd_c_HOL_Oabs__class_Oabs
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a)
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes (bnd_c_HOL_Oabs__class_Oabs V_a T_a)
% 18.72/19.46 (bnd_c_HOL_Oabs__class_Oabs V_b T_a) T_a)
% 18.72/19.46 T_a;
% 18.72/19.46 !!T_a V_b V_a.
% 18.72/19.46 (~ bnd_class_OrderedGroup_Opordered__ab__group__add T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ouminus__class_Ouminus V_b T_a)
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_a V_b T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 (~ bnd_class_OrderedGroup_Opordered__ab__group__add T_a |
% 18.72/19.46 bnd_c_lessequals V_a V_b T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ouminus__class_Ouminus V_b T_a)
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_a T_a) T_a;
% 18.72/19.46 !!T_a.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__normed__vector T_a |
% 18.72/19.46 bnd_c_lessequals
% 18.72/19.46 (bnd_c_RealVector_Onorm__class_Onorm
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero T_a) T_a)
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal)
% 18.72/19.46 bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_x V_y.
% 18.72/19.46 (~ bnd_class_RealVector_Oreal__algebra__1 T_a |
% 18.72/19.46 ~ bnd_c_RealVector_Oof__real V_x T_a =
% 18.72/19.46 bnd_c_RealVector_Oof__real V_y T_a) |
% 18.72/19.46 V_x = V_y;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 ~ bnd_class_OrderedGroup_Opordered__ab__group__add__abs T_a |
% 18.72/19.46 bnd_c_lessequals
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus
% 18.72/19.46 (bnd_c_HOL_Oabs__class_Oabs V_a T_a) T_a)
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero T_a) T_a;
% 18.72/19.46 !!T_a V_x.
% 18.72/19.46 (~ bnd_class_RealVector_Oreal__normed__vector T_a |
% 18.72/19.46 ~ bnd_c_RealVector_Onorm__class_Onorm V_x T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal) |
% 18.72/19.46 V_x = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__normed__vector T_a |
% 18.72/19.46 bnd_c_RealVector_OscaleR__class_OscaleR
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_a bnd_tc_RealDef_Oreal) V_b T_a =
% 18.72/19.46 bnd_c_HOL_Ouminus__class_Ouminus
% 18.72/19.46 (bnd_c_RealVector_OscaleR__class_OscaleR V_a V_b T_a) T_a;
% 18.72/19.46 !!T_a V_x V_xa.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__vector T_a |
% 18.72/19.46 bnd_c_RealVector_OscaleR__class_OscaleR
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_x bnd_tc_RealDef_Oreal) V_xa
% 18.72/19.46 T_a =
% 18.72/19.46 bnd_c_HOL_Ouminus__class_Ouminus
% 18.72/19.46 (bnd_c_RealVector_OscaleR__class_OscaleR V_x V_xa T_a) T_a;
% 18.72/19.46 !!T_a V_a V_x.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__vector T_a |
% 18.72/19.46 bnd_c_RealVector_OscaleR__class_OscaleR
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_a bnd_tc_RealDef_Oreal) V_x T_a =
% 18.72/19.46 bnd_c_HOL_Ouminus__class_Ouminus
% 18.72/19.46 (bnd_c_RealVector_OscaleR__class_OscaleR V_a V_x T_a) T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__normed__vector T_a |
% 18.72/19.46 bnd_c_RealVector_OscaleR__class_OscaleR V_a
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_b T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Ouminus__class_Ouminus
% 18.72/19.46 (bnd_c_RealVector_OscaleR__class_OscaleR V_a V_b T_a) T_a;
% 18.72/19.46 !!T_a V_a V_x.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__vector T_a |
% 18.72/19.46 bnd_c_RealVector_OscaleR__class_OscaleR V_a
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_x T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Ouminus__class_Ouminus
% 18.72/19.46 (bnd_c_RealVector_OscaleR__class_OscaleR V_a V_x T_a) T_a;
% 18.72/19.46 !!V_x V_a V_b.
% 18.72/19.46 bnd_c_Log_Opowr (bnd_c_Log_Opowr V_x V_a) V_b =
% 18.72/19.46 bnd_c_Log_Opowr (bnd_c_Log_Opowr V_x V_b) V_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 (((~ bnd_class_Ring__and__Field_Oordered__field T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Oinverse__class_Odivide V_a V_b T_a)
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_b (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_a T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 (((~ bnd_class_Ring__and__Field_Oordered__field T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Oinverse__class_Odivide V_a V_b T_a)
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_b T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_a (bnd_c_HOL_Ozero__class_Ozero T_a) T_a;
% 18.72/19.46 !!T_a V_b.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Oordered__field T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_b T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Odivide (bnd_c_HOL_Oone__class_Oone T_a)
% 18.72/19.46 V_b T_a)
% 18.72/19.46 T_a;
% 18.72/19.46 !!T_a V_b.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Oordered__field T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Odivide (bnd_c_HOL_Oone__class_Oone T_a)
% 18.72/19.46 V_b T_a)
% 18.72/19.46 T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_b T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__normed__vector T_a |
% 18.72/19.46 bnd_c_HOL_Oabs__class_Oabs
% 18.72/19.46 (bnd_c_RealVector_Onorm__class_Onorm V_a T_a) bnd_tc_RealDef_Oreal =
% 18.72/19.46 bnd_c_RealVector_Onorm__class_Onorm V_a T_a;
% 18.72/19.46 !!T_a V_x V_y.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__normed__algebra T_a |
% 18.72/19.46 bnd_c_lessequals
% 18.72/19.46 (bnd_c_RealVector_Onorm__class_Onorm
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_x V_y T_a) T_a)
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_RealVector_Onorm__class_Onorm V_x T_a)
% 18.72/19.46 (bnd_c_RealVector_Onorm__class_Onorm V_y T_a) bnd_tc_RealDef_Oreal)
% 18.72/19.46 bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_x.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Oordered__field T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Oinverse__class_Oinverse V_x T_a)
% 18.72/19.46 (bnd_c_HOL_Oone__class_Oone T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_x (bnd_c_HOL_Ozero__class_Ozero T_a) T_a;
% 18.72/19.46 !!T_a V_x.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Oordered__idom T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes (bnd_c_HOL_Osgn__class_Osgn V_x T_a)
% 18.72/19.46 (bnd_c_HOL_Oabs__class_Oabs V_x T_a) T_a =
% 18.72/19.46 V_x;
% 18.72/19.46 !!T_a V_n.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Ocomm__semiring__1 T_a |
% 18.72/19.46 bnd_c_Ring__and__Field_Odvd__class_Odvd
% 18.72/19.46 (bnd_c_HOL_Oone__class_Oone T_a)
% 18.72/19.46 (bnd_c_Power_Opower__class_Opower (bnd_c_HOL_Oone__class_Oone T_a)
% 18.72/19.46 V_n T_a)
% 18.72/19.46 T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Oidom T_a |
% 18.72/19.46 ~ bnd_c_HOL_Otimes__class_Otimes V_a V_a T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_b V_b T_a) |
% 18.72/19.46 V_a = bnd_c_HOL_Ouminus__class_Ouminus V_b T_a) |
% 18.72/19.46 V_a = V_b;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 ~ bnd_class_Divides_Osemiring__div T_a |
% 18.72/19.46 bnd_c_Divides_Odiv__class_Odiv (bnd_c_HOL_Ozero__class_Ozero T_a) V_a
% 18.72/19.46 T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 ~ bnd_class_Divides_Osemiring__div T_a |
% 18.72/19.46 bnd_c_Divides_Odiv__class_Odiv V_a (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Ono__zero__divisors T_a |
% 18.72/19.46 ~ bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a) |
% 18.72/19.46 V_a = bnd_c_HOL_Ozero__class_Ozero T_a) |
% 18.72/19.46 V_b = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Ono__zero__divisors T_a |
% 18.72/19.46 ~ bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a) |
% 18.72/19.46 V_b = bnd_c_HOL_Ozero__class_Ozero T_a) |
% 18.72/19.46 V_a = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Oring__no__zero__divisors T_a |
% 18.72/19.46 ~ bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a) |
% 18.72/19.46 V_b = bnd_c_HOL_Ozero__class_Ozero T_a) |
% 18.72/19.46 V_a = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_b V_a.
% 18.72/19.46 (~ bnd_class_Divides_Osemiring__div T_a |
% 18.72/19.46 bnd_c_Divides_Odiv__class_Odiv
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_b V_a T_a) V_b T_a =
% 18.72/19.46 V_a) |
% 18.72/19.46 V_b = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_r.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__normed__algebra__1 T_a |
% 18.72/19.46 bnd_c_RealVector_Onorm__class_Onorm
% 18.72/19.46 (bnd_c_RealVector_Oof__real V_r T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Oabs__class_Oabs V_r bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 (~ bnd_class_OrderedGroup_Oordered__ab__group__add T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ouminus__class_Ouminus V_a T_a) V_a
% 18.72/19.46 T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_a T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 (~ bnd_class_OrderedGroup_Oordered__ab__group__add T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_a T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 (~ bnd_class_OrderedGroup_Oordered__ab__group__add T_a |
% 18.72/19.46 bnd_c_lessequals V_a (bnd_c_HOL_Ouminus__class_Ouminus V_a T_a)
% 18.72/19.46 T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_a (bnd_c_HOL_Ozero__class_Ozero T_a) T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 (~ bnd_class_OrderedGroup_Oordered__ab__group__add T_a |
% 18.72/19.46 bnd_c_lessequals V_a (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_a (bnd_c_HOL_Ouminus__class_Ouminus V_a T_a) T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 (~ bnd_class_OrderedGroup_Olordered__ab__group__add T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ouminus__class_Ouminus V_a T_a) V_a
% 18.72/19.46 T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_a T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 (~ bnd_class_OrderedGroup_Olordered__ab__group__add T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_a T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ouminus__class_Ouminus V_a T_a) V_a T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 (~ bnd_class_OrderedGroup_Olordered__ab__group__add T_a |
% 18.72/19.46 bnd_c_lessequals V_a (bnd_c_HOL_Ouminus__class_Ouminus V_a T_a)
% 18.72/19.46 T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_a (bnd_c_HOL_Ozero__class_Ozero T_a) T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 (~ bnd_class_OrderedGroup_Olordered__ab__group__add T_a |
% 18.72/19.46 bnd_c_lessequals V_a (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_a (bnd_c_HOL_Ouminus__class_Ouminus V_a T_a) T_a;
% 18.72/19.46 !!T_a V_a V_n.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Oordered__semidom T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 (bnd_c_Power_Opower__class_Opower V_a V_n T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_a T_a;
% 18.72/19.46 !!T_a V_a V_n.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Oordered__idom T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 (bnd_c_Power_Opower__class_Opower V_a V_n T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_a T_a;
% 18.72/19.46 !!V_x.
% 18.72/19.46 ~ bnd_c_NthRoot_Osqrt V_x =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal |
% 18.72/19.46 V_x = bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 (~ bnd_class_Divides_Osemiring__div T_a |
% 18.72/19.46 bnd_c_Divides_Odiv__class_Odiv V_a V_a T_a =
% 18.72/19.46 bnd_c_HOL_Oone__class_Oone T_a) |
% 18.72/19.46 V_a = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Oordered__field T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_a T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Oordered__field T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_a T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Oinverse V_a T_a) T_a;
% 18.72/19.46 !!V_x V_c V_y.
% 18.72/19.46 (V_x = bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal |
% 18.72/19.46 ~ bnd_c_lessequals
% 18.72/19.46 (bnd_c_HOL_Oabs__class_Oabs V_x bnd_tc_RealDef_Oreal)
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_c
% 18.72/19.46 (bnd_c_HOL_Oabs__class_Oabs V_y bnd_tc_RealDef_Oreal)
% 18.72/19.46 bnd_tc_RealDef_Oreal)
% 18.72/19.46 bnd_tc_RealDef_Oreal) |
% 18.72/19.46 ~ bnd_c_lessequals V_c
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal)
% 18.72/19.46 bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_r V_x V_y.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__normed__field T_a |
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide
% 18.72/19.46 (bnd_c_RealVector_OscaleR__class_OscaleR V_r V_x T_a) V_y T_a =
% 18.72/19.46 bnd_c_RealVector_OscaleR__class_OscaleR V_r
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Odivide V_x V_y T_a) T_a;
% 18.72/19.46 !!V_x V_y.
% 18.72/19.46 bnd_c_lessequals V_x V_y bnd_tc_RealDef_Oreal |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_NthRoot_Osqrt V_x) (bnd_c_NthRoot_Osqrt V_y)
% 18.72/19.46 bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!V_x V_y.
% 18.72/19.46 bnd_c_lessequals (bnd_c_NthRoot_Osqrt V_x) (bnd_c_NthRoot_Osqrt V_y)
% 18.72/19.46 bnd_tc_RealDef_Oreal |
% 18.72/19.46 ~ bnd_c_lessequals V_x V_y bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_a V_n.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Oordered__idom T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 (bnd_c_Power_Opower__class_Opower
% 18.72/19.46 (bnd_c_HOL_Oabs__class_Oabs V_a T_a) V_n T_a)
% 18.72/19.46 T_a;
% 18.72/19.46 !!V_x.
% 18.72/19.46 (~ bnd_c_NthRoot_Osqrt V_x =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal |
% 18.72/19.46 ~ bnd_c_lessequals
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal) V_x
% 18.72/19.46 bnd_tc_RealDef_Oreal) |
% 18.72/19.46 V_x = bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Oordered__field T_a |
% 18.72/19.46 bnd_c_HOL_Oabs__class_Oabs
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide
% 18.72/19.46 (bnd_c_HOL_Oabs__class_Oabs V_a T_a)
% 18.72/19.46 (bnd_c_HOL_Oabs__class_Oabs V_b T_a) T_a) |
% 18.72/19.46 V_b = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Oordered__field T_a |
% 18.72/19.46 bnd_c_HOL_Oabs__class_Oabs
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Oinverse V_a T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Oinverse
% 18.72/19.46 (bnd_c_HOL_Oabs__class_Oabs V_a T_a) T_a) |
% 18.72/19.46 V_a = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_a V_x.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__normed__vector T_a |
% 18.72/19.46 bnd_c_RealVector_Onorm__class_Onorm
% 18.72/19.46 (bnd_c_RealVector_OscaleR__class_OscaleR V_a V_x T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_HOL_Oabs__class_Oabs V_a bnd_tc_RealDef_Oreal)
% 18.72/19.46 (bnd_c_RealVector_Onorm__class_Onorm V_x T_a) bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_x V_a V_y.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__algebra T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_x
% 18.72/19.46 (bnd_c_RealVector_OscaleR__class_OscaleR V_a V_y T_a) T_a =
% 18.72/19.46 bnd_c_RealVector_OscaleR__class_OscaleR V_a
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_x V_y T_a) T_a;
% 18.72/19.46 !!T_a V_a V_x V_y.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__algebra T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_RealVector_OscaleR__class_OscaleR V_a V_x T_a) V_y T_a =
% 18.72/19.46 bnd_c_RealVector_OscaleR__class_OscaleR V_a
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_x V_y T_a) T_a;
% 18.72/19.46 !!T_a V_xa V_r V_x.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__normed__algebra T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_xa
% 18.72/19.46 (bnd_c_RealVector_OscaleR__class_OscaleR V_r V_x T_a) T_a =
% 18.72/19.46 bnd_c_RealVector_OscaleR__class_OscaleR V_r
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_xa V_x T_a) T_a;
% 18.72/19.46 !!T_a V_a V_r V_b.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__normed__algebra T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_a
% 18.72/19.46 (bnd_c_RealVector_OscaleR__class_OscaleR V_r V_b T_a) T_a =
% 18.72/19.46 bnd_c_RealVector_OscaleR__class_OscaleR V_r
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a;
% 18.72/19.46 !!T_a V_r V_x V_y.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__normed__algebra T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_RealVector_OscaleR__class_OscaleR V_r V_x T_a) V_y T_a =
% 18.72/19.46 bnd_c_RealVector_OscaleR__class_OscaleR V_r
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_x V_y T_a) T_a;
% 18.72/19.46 !!T_a V_r V_a V_b.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__normed__algebra T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_RealVector_OscaleR__class_OscaleR V_r V_a T_a) V_b T_a =
% 18.72/19.46 bnd_c_RealVector_OscaleR__class_OscaleR V_r
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a;
% 18.72/19.46 !!T_a V_a V_x.
% 18.72/19.46 ((~ bnd_class_RealVector_Oreal__vector T_a |
% 18.72/19.46 ~ bnd_c_RealVector_OscaleR__class_OscaleR V_a V_x T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a) |
% 18.72/19.46 V_x = bnd_c_HOL_Ozero__class_Ozero T_a) |
% 18.72/19.46 V_a = bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 (~ bnd_class_OrderedGroup_Opordered__ab__group__add T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_a T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_a (bnd_c_HOL_Ozero__class_Ozero T_a) T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 (~ bnd_class_OrderedGroup_Opordered__ab__group__add T_a |
% 18.72/19.46 bnd_c_lessequals V_a (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_a T_a) T_a;
% 18.72/19.46 !!V_x.
% 18.72/19.46 bnd_c_lessequals
% 18.72/19.46 (bnd_c_HOL_Oabs__class_Oabs (bnd_c_Transcendental_Osin V_x)
% 18.72/19.46 bnd_tc_RealDef_Oreal)
% 18.72/19.46 (bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal)
% 18.72/19.46 bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Odivision__ring T_a |
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Oinverse
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Oinverse V_a T_a) T_a =
% 18.72/19.46 V_a) |
% 18.72/19.46 V_a = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Ocomm__semiring__1 T_a |
% 18.72/19.46 V_a = bnd_c_HOL_Ozero__class_Ozero T_a) |
% 18.72/19.46 ~ bnd_c_Ring__and__Field_Odvd__class_Odvd
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero T_a) V_a T_a;
% 18.72/19.46 !!T_a.
% 18.72/19.46 ~ bnd_class_OrderedGroup_Opordered__ab__group__add__abs T_a |
% 18.72/19.46 bnd_c_lessequals
% 18.72/19.46 (bnd_c_HOL_Oabs__class_Oabs (bnd_c_HOL_Ozero__class_Ozero T_a) T_a)
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero T_a) T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Odivision__ring T_a |
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Oinverse
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Oinverse V_b T_a)
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Oinverse V_a T_a) T_a) |
% 18.72/19.46 V_b = bnd_c_HOL_Ozero__class_Ozero T_a) |
% 18.72/19.46 V_a = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Oinverse
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Oinverse V_a T_a)
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Oinverse V_b T_a) T_a;
% 18.72/19.46 !!T_a V_b V_a.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Opordered__cancel__semiring T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Otimes__class_Otimes V_b V_a T_a)
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_b (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_a T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Opordered__cancel__semiring T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a)
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_b T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_a (bnd_c_HOL_Ozero__class_Ozero T_a) T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Opordered__cancel__semiring T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a)
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_b (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_a T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Opordered__cancel__semiring T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a)
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_b T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_a (bnd_c_HOL_Ozero__class_Ozero T_a) T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Opordered__cancel__semiring T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a)
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_b (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_a T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Oordered__ring__strict T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a)
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_b T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_a (bnd_c_HOL_Ozero__class_Ozero T_a) T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Oordered__ring__strict T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a)
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_b (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_a T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 ~ bnd_class_OrderedGroup_Opordered__ab__group__add__abs T_a |
% 18.72/19.46 bnd_c_HOL_Oabs__class_Oabs (bnd_c_HOL_Ouminus__class_Ouminus V_a T_a)
% 18.72/19.46 T_a =
% 18.72/19.46 bnd_c_HOL_Oabs__class_Oabs V_a T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ((~ bnd_class_OrderedGroup_Opordered__ab__group__add__abs T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Oabs__class_Oabs V_a T_a) V_b T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ouminus__class_Ouminus V_a T_a) V_b
% 18.72/19.46 T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_a V_b T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ((~ bnd_class_OrderedGroup_Opordered__ab__group__add__abs T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Oabs__class_Oabs V_a T_a) V_b T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ouminus__class_Ouminus V_a T_a) V_b
% 18.72/19.46 T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_a V_b T_a;
% 18.72/19.46 !!V_x V_r.
% 18.72/19.46 (bnd_c_lessequals
% 18.72/19.46 (bnd_c_HOL_Oabs__class_Oabs V_x bnd_tc_RealDef_Oreal) V_r
% 18.72/19.46 bnd_tc_RealDef_Oreal |
% 18.72/19.46 ~ bnd_c_lessequals V_x V_r bnd_tc_RealDef_Oreal) |
% 18.72/19.46 ~ bnd_c_lessequals
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_r bnd_tc_RealDef_Oreal) V_x
% 18.72/19.46 bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!V_x V_a V_b.
% 18.72/19.46 (bnd_c_lessequals (bnd_c_Log_Opowr V_x V_a) (bnd_c_Log_Opowr V_x V_b)
% 18.72/19.46 bnd_tc_RealDef_Oreal |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal)
% 18.72/19.46 V_x bnd_tc_RealDef_Oreal) |
% 18.72/19.46 ~ bnd_c_lessequals V_a V_b bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_x V_y.
% 18.72/19.46 (((~ bnd_class_Ring__and__Field_Oordered__idom T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Otimes__class_Otimes V_x V_y T_a) V_x
% 18.72/19.46 T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_y (bnd_c_HOL_Oone__class_Oone T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_y T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_x T_a;
% 18.72/19.46 !!T_a V_y V_x.
% 18.72/19.46 (((~ bnd_class_Ring__and__Field_Oordered__idom T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Otimes__class_Otimes V_y V_x T_a) V_x
% 18.72/19.46 T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_y (bnd_c_HOL_Oone__class_Oone T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_y T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_x T_a;
% 18.72/19.46 !!V_x.
% 18.72/19.46 bnd_c_Transcendental_Osin
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_x bnd_tc_RealDef_Oreal) =
% 18.72/19.46 bnd_c_HOL_Ouminus__class_Ouminus (bnd_c_Transcendental_Osin V_x)
% 18.72/19.46 bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_x V_y.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Ocomm__ring__1 T_a |
% 18.72/19.46 bnd_c_Ring__and__Field_Odvd__class_Odvd
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_x T_a) V_y T_a) |
% 18.72/19.46 ~ bnd_c_Ring__and__Field_Odvd__class_Odvd V_x V_y T_a;
% 18.72/19.46 !!T_a V_x V_y.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Ocomm__ring__1 T_a |
% 18.72/19.46 bnd_c_Ring__and__Field_Odvd__class_Odvd V_x V_y T_a) |
% 18.72/19.46 ~ bnd_c_Ring__and__Field_Odvd__class_Odvd
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_x T_a) V_y T_a;
% 18.72/19.46 !!T_a V_x V_y.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Ocomm__ring__1 T_a |
% 18.72/19.46 bnd_c_Ring__and__Field_Odvd__class_Odvd V_x
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_y T_a) T_a) |
% 18.72/19.46 ~ bnd_c_Ring__and__Field_Odvd__class_Odvd V_x V_y T_a;
% 18.72/19.46 !!T_a V_x V_y.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Ocomm__ring__1 T_a |
% 18.72/19.46 bnd_c_Ring__and__Field_Odvd__class_Odvd V_x V_y T_a) |
% 18.72/19.46 ~ bnd_c_Ring__and__Field_Odvd__class_Odvd V_x
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_y T_a) T_a;
% 18.72/19.46 !!T_a V_b V_a V_c.
% 18.72/19.46 (((~ bnd_class_Divides_Osemiring__div T_a |
% 18.72/19.46 bnd_c_Ring__and__Field_Odvd__class_Odvd
% 18.72/19.46 (bnd_c_Divides_Odiv__class_Odiv V_b V_a T_a)
% 18.72/19.46 (bnd_c_Divides_Odiv__class_Odiv V_c V_a T_a) T_a) |
% 18.72/19.46 ~ bnd_c_Ring__and__Field_Odvd__class_Odvd V_b V_c T_a) |
% 18.72/19.46 ~ bnd_c_Ring__and__Field_Odvd__class_Odvd V_a V_c T_a) |
% 18.72/19.46 ~ bnd_c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a;
% 18.72/19.46 !!T_a V_b V_c V_a.
% 18.72/19.46 (((~ bnd_class_Divides_Osemiring__div T_a |
% 18.72/19.46 bnd_c_Ring__and__Field_Odvd__class_Odvd V_b V_c T_a) |
% 18.72/19.46 ~ bnd_c_Ring__and__Field_Odvd__class_Odvd
% 18.72/19.46 (bnd_c_Divides_Odiv__class_Odiv V_b V_a T_a)
% 18.72/19.46 (bnd_c_Divides_Odiv__class_Odiv V_c V_a T_a) T_a) |
% 18.72/19.46 ~ bnd_c_Ring__and__Field_Odvd__class_Odvd V_a V_c T_a) |
% 18.72/19.46 ~ bnd_c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_a T_a)
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_b T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide V_a V_b T_a) |
% 18.72/19.46 V_b = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!V_x V_y.
% 18.72/19.46 ~ bnd_c_HOL_Otimes__class_Otimes V_x V_x bnd_tc_RealDef_Oreal =
% 18.72/19.46 bnd_c_HOL_Ouminus__class_Ouminus
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_y V_y bnd_tc_RealDef_Oreal)
% 18.72/19.46 bnd_tc_RealDef_Oreal |
% 18.72/19.46 V_y = bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!V_x V_y.
% 18.72/19.46 ~ bnd_c_HOL_Otimes__class_Otimes V_x V_x bnd_tc_RealDef_Oreal =
% 18.72/19.46 bnd_c_HOL_Ouminus__class_Ouminus
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_y V_y bnd_tc_RealDef_Oreal)
% 18.72/19.46 bnd_tc_RealDef_Oreal |
% 18.72/19.46 V_x = bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_k.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Oordered__idom T_a |
% 18.72/19.46 bnd_c_HOL_Oabs__class_Oabs V_k T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_k
% 18.72/19.46 (bnd_c_HOL_Osgn__class_Osgn V_k T_a) T_a;
% 18.72/19.46 !!V_x.
% 18.72/19.46 bnd_c_lessequals V_x (bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal)
% 18.72/19.46 bnd_tc_RealDef_Oreal |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_NthRoot_Osqrt V_x)
% 18.72/19.46 (bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal)
% 18.72/19.46 bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!V_x.
% 18.72/19.46 bnd_c_lessequals (bnd_c_NthRoot_Osqrt V_x)
% 18.72/19.46 (bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal)
% 18.72/19.46 bnd_tc_RealDef_Oreal |
% 18.72/19.46 ~ bnd_c_lessequals V_x
% 18.72/19.46 (bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal)
% 18.72/19.46 bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_c_NthRoot_Osqrt (bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal) =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal;
% 18.72/19.46 bnd_c_Transcendental_Osin
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal) =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_x.
% 18.72/19.46 (~ bnd_class_RealVector_Oreal__normed__vector T_a |
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__algebra__1 T_a) |
% 18.72/19.46 bnd_c_RealVector_Oof__real
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_x bnd_tc_RealDef_Oreal) T_a =
% 18.72/19.46 bnd_c_HOL_Ouminus__class_Ouminus (bnd_c_RealVector_Oof__real V_x T_a)
% 18.72/19.46 T_a;
% 18.72/19.46 !!T_a V_x.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__algebra__1 T_a |
% 18.72/19.46 bnd_c_RealVector_Oof__real
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_x bnd_tc_RealDef_Oreal) T_a =
% 18.72/19.46 bnd_c_HOL_Ouminus__class_Ouminus (bnd_c_RealVector_Oof__real V_x T_a)
% 18.72/19.46 T_a;
% 18.72/19.46 !!T_a V_x.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__normed__vector T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal)
% 18.72/19.46 (bnd_c_RealVector_Onorm__class_Onorm V_x T_a) bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Oordered__idom T_a |
% 18.72/19.46 bnd_c_HOL_Osgn__class_Osgn (bnd_c_HOL_Osgn__class_Osgn V_a T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Osgn__class_Osgn V_a T_a;
% 18.72/19.46 !!T_a V_a V_c V_b.
% 18.72/19.46 (~ bnd_class_Divides_Osemiring__div T_a |
% 18.72/19.46 bnd_c_Divides_Odiv__class_Odiv
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_c T_a)
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a =
% 18.72/19.46 bnd_c_Divides_Odiv__class_Odiv V_a V_b T_a) |
% 18.72/19.46 V_c = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_c V_a V_b.
% 18.72/19.46 (~ bnd_class_Divides_Osemiring__div T_a |
% 18.72/19.46 bnd_c_Divides_Odiv__class_Odiv
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_c V_a T_a)
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a =
% 18.72/19.46 bnd_c_Divides_Odiv__class_Odiv V_a V_b T_a) |
% 18.72/19.46 V_c = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_a V_c V_b V_d.
% 18.72/19.46 ((((~ bnd_class_Ring__and__Field_Opordered__semiring T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Otimes__class_Otimes V_a V_c T_a)
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_c T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_a T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_c V_d T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_a V_b T_a;
% 18.72/19.46 !!T_a V_a V_c V_b V_d.
% 18.72/19.46 ((((~ bnd_class_Ring__and__Field_Opordered__semiring T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Otimes__class_Otimes V_a V_c T_a)
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_b V_d T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_c T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_b T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_c V_d T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_a V_b T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Odivision__ring T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_a
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Oinverse V_a T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Oone__class_Oone T_a) |
% 18.72/19.46 V_a = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Odivision__ring T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Oinverse V_a T_a) V_a T_a =
% 18.72/19.46 bnd_c_HOL_Oone__class_Oone T_a) |
% 18.72/19.46 V_a = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Oinverse V_a T_a) V_a T_a =
% 18.72/19.46 bnd_c_HOL_Oone__class_Oone T_a) |
% 18.72/19.46 V_a = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Oring T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_a T_a)
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_b T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a;
% 18.72/19.46 !!T_a V_b.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Oidom T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_b T_a)
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_b T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_b V_b T_a;
% 18.72/19.46 !!T_a V_xa V_x.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__normed__algebra T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_xa
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_x T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Ouminus__class_Ouminus
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_xa V_x T_a) T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__normed__algebra T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_a
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_b T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Ouminus__class_Ouminus
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a;
% 18.72/19.46 !!T_a V_x V_y.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__normed__algebra T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_x T_a) V_y T_a =
% 18.72/19.46 bnd_c_HOL_Ouminus__class_Ouminus
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_x V_y T_a) T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__normed__algebra T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a =
% 18.72/19.46 bnd_c_HOL_Ouminus__class_Ouminus
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Oinverse V_a T_a =
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide (bnd_c_HOL_Oone__class_Oone T_a)
% 18.72/19.46 V_a T_a) |
% 18.72/19.46 V_a = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!V_x.
% 18.72/19.46 bnd_c_lessequals (bnd_c_Transcendental_Osin V_x)
% 18.72/19.46 (bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal)
% 18.72/19.46 bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 (~ bnd_class_OrderedGroup_Oordered__ab__group__add T_a |
% 18.72/19.46 ~ bnd_c_HOL_Ouminus__class_Ouminus V_a T_a = V_a) |
% 18.72/19.46 V_a = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_b V_a.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Oordered__ring__strict T_a |
% 18.72/19.46 bnd_c_lessequals V_b (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_b T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Oordered__ring__strict T_a |
% 18.72/19.46 bnd_c_lessequals V_a (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_b T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a;
% 18.72/19.46 !!T_a V_b V_a.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Oordered__ring__strict T_a |
% 18.72/19.46 bnd_c_lessequals V_b (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_a T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Oordered__ring__strict T_a |
% 18.72/19.46 bnd_c_lessequals V_a (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_a T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 bnd_c_HOL_Ouminus__class_Ouminus
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_HOL_Ouminus__class_Ouminus
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide V_a
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_b T_a) T_a;
% 18.72/19.46 !!T_a V_x V_y V_z.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Ocomm__semiring__1 T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_x
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_y V_z T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_x V_y T_a) V_z T_a;
% 18.72/19.46 !!V_z1 V_z2 V_z3.
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_z1 V_z2 bnd_tc_RealDef_Oreal) V_z3
% 18.72/19.46 bnd_tc_RealDef_Oreal =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_z1
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_z2 V_z3 bnd_tc_RealDef_Oreal)
% 18.72/19.46 bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_lx V_rx V_ry.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Ocomm__semiring__1 T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_lx
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_rx V_ry T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_rx
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_lx V_ry T_a) T_a;
% 18.72/19.46 !!T_a V_lx V_rx V_ry.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Ocomm__semiring__1 T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_lx
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_rx V_ry T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_lx V_rx T_a) V_ry T_a;
% 18.72/19.46 !!T_a V_lx V_ly V_rx.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Ocomm__semiring__1 T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_lx V_ly T_a) V_rx T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_lx
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_ly V_rx T_a) T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 (~ bnd_class_Divides_Osemiring__div T_a |
% 18.72/19.46 bnd_c_Divides_Odiv__class_Odiv
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a) V_b T_a =
% 18.72/19.46 V_a) |
% 18.72/19.46 V_b = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a.
% 18.72/19.46 (~ bnd_class_RealVector_Oreal__normed__vector T_a |
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__algebra__1 T_a) |
% 18.72/19.46 bnd_c_RealVector_Oof__real
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal) T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__algebra__1 T_a |
% 18.72/19.46 bnd_c_RealVector_Oof__real
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal) T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 (~ bnd_class_OrderedGroup_Ogroup__add T_a |
% 18.72/19.46 ~ bnd_c_HOL_Ouminus__class_Ouminus V_a T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a) |
% 18.72/19.46 V_a = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_lx V_ly V_rx V_ry.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Ocomm__semiring__1 T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_lx V_ly T_a)
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_rx V_ry T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_lx V_rx T_a)
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_ly V_ry T_a) T_a;
% 18.72/19.46 !!T_a V_lx V_ly V_rx V_ry.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Ocomm__semiring__1 T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_lx V_ly T_a)
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_rx V_ry T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_lx
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_ly
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_rx V_ry T_a) T_a)
% 18.72/19.46 T_a;
% 18.72/19.46 !!T_a V_lx V_ly V_rx V_ry.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Ocomm__semiring__1 T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_lx V_ly T_a)
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_rx V_ry T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_rx
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_lx V_ly T_a) V_ry T_a)
% 18.72/19.46 T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 (~ bnd_class_OrderedGroup_Opordered__ab__group__add__abs T_a |
% 18.72/19.46 V_a = bnd_c_HOL_Ozero__class_Ozero T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Oabs__class_Oabs V_a T_a)
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero T_a) T_a;
% 18.72/19.46 !!T_a V_b.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Oordered__field T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_lessequals V_b (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Odivide (bnd_c_HOL_Oone__class_Oone T_a)
% 18.72/19.46 V_b T_a)
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero T_a) T_a;
% 18.72/19.46 !!T_a V_b.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Oordered__field T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_lessequals
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Odivide (bnd_c_HOL_Oone__class_Oone T_a)
% 18.72/19.46 V_b T_a)
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_b (bnd_c_HOL_Ozero__class_Ozero T_a) T_a;
% 18.72/19.46 !!T_a V_a V_c.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_c T_a) V_c T_a =
% 18.72/19.46 V_a) |
% 18.72/19.46 V_c = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_a V_c.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 V_a =
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_c T_a) V_c T_a) |
% 18.72/19.46 V_c = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_c V_a.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 V_c = bnd_c_HOL_Ozero__class_Ozero T_a) |
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_c T_a) V_c T_a =
% 18.72/19.46 V_a;
% 18.72/19.46 !!T_a V_c V_a.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 V_c = bnd_c_HOL_Ozero__class_Ozero T_a) |
% 18.72/19.46 V_a =
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_c T_a) V_c T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 (~ bnd_class_OrderedGroup_Ogroup__add T_a |
% 18.72/19.46 ~ bnd_c_HOL_Ouminus__class_Ouminus V_a T_a =
% 18.72/19.46 bnd_c_HOL_Ouminus__class_Ouminus V_b T_a) |
% 18.72/19.46 V_a = V_b;
% 18.72/19.46 !!T_a V_x V_y.
% 18.72/19.46 (~ bnd_class_Lattices_Oboolean__algebra T_a |
% 18.72/19.46 ~ bnd_c_HOL_Ouminus__class_Ouminus V_x T_a =
% 18.72/19.46 bnd_c_HOL_Ouminus__class_Ouminus V_y T_a) |
% 18.72/19.46 V_x = V_y;
% 18.72/19.46 !!T_a V_a V_b V_n.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_Power_Opower__class_Opower
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Odivide V_a V_b T_a) V_n T_a =
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide
% 18.72/19.46 (bnd_c_Power_Opower__class_Opower V_a V_n T_a)
% 18.72/19.46 (bnd_c_Power_Opower__class_Opower V_b V_n T_a) T_a;
% 18.72/19.46 !!V_z V_w.
% 18.72/19.46 (V_z = V_w | ~ bnd_c_lessequals V_w V_z bnd_tc_RealDef_Oreal) |
% 18.72/19.46 ~ bnd_c_lessequals V_z V_w bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_x V_y.
% 18.72/19.46 ((~ bnd_class_Orderings_Oorder T_a | V_x = V_y) |
% 18.72/19.46 ~ bnd_c_lessequals V_y V_x T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_x V_y T_a;
% 18.72/19.46 !!T_a V_x V_y.
% 18.72/19.46 ((~ bnd_class_Orderings_Oorder T_a | V_x = V_y) |
% 18.72/19.46 ~ bnd_c_lessequals V_y V_x T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_x V_y T_a;
% 18.72/19.46 !!T_a V_x V_y.
% 18.72/19.46 ((~ bnd_class_Orderings_Oorder T_a | V_x = V_y) |
% 18.72/19.46 ~ bnd_c_lessequals V_x V_y T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_y V_x T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 (~ bnd_class_OrderedGroup_Opordered__ab__group__add__abs T_a |
% 18.72/19.46 bnd_c_HOL_Oabs__class_Oabs V_a T_a = V_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_a T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Ocomm__semiring__1 T_a |
% 18.72/19.46 bnd_c_Ring__and__Field_Odvd__class_Odvd V_a V_a T_a;
% 18.72/19.46 !!T_a V_a V_c V_b.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Ocomm__semiring__1 T_a |
% 18.72/19.46 bnd_c_Ring__and__Field_Odvd__class_Odvd V_a V_c T_a) |
% 18.72/19.46 ~ bnd_c_Ring__and__Field_Odvd__class_Odvd V_b V_c T_a) |
% 18.72/19.46 ~ bnd_c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Oidom T_a |
% 18.72/19.46 bnd_c_Ring__and__Field_Odvd__class_Odvd
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 V_a T_a)
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 V_b T_a)
% 18.72/19.46 T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Oidom T_a |
% 18.72/19.46 bnd_c_Ring__and__Field_Odvd__class_Odvd
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero T_a) T_a)
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_b
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero T_a) T_a)
% 18.72/19.46 T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Oordered__idom T_a |
% 18.72/19.46 bnd_c_HOL_Oabs__class_Oabs
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes (bnd_c_HOL_Oabs__class_Oabs V_a T_a)
% 18.72/19.46 (bnd_c_HOL_Oabs__class_Oabs V_b T_a) T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Opordered__ring__abs T_a |
% 18.72/19.46 bnd_c_HOL_Oabs__class_Oabs
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes (bnd_c_HOL_Oabs__class_Oabs V_a T_a)
% 18.72/19.46 (bnd_c_HOL_Oabs__class_Oabs V_b T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_b T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_a T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Opordered__ring__abs T_a |
% 18.72/19.46 bnd_c_HOL_Oabs__class_Oabs
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes (bnd_c_HOL_Oabs__class_Oabs V_a T_a)
% 18.72/19.46 (bnd_c_HOL_Oabs__class_Oabs V_b T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_b (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_a T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Opordered__ring__abs T_a |
% 18.72/19.46 bnd_c_HOL_Oabs__class_Oabs
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes (bnd_c_HOL_Oabs__class_Oabs V_a T_a)
% 18.72/19.46 (bnd_c_HOL_Oabs__class_Oabs V_b T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_b T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_a (bnd_c_HOL_Ozero__class_Ozero T_a) T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Opordered__ring__abs T_a |
% 18.72/19.46 bnd_c_HOL_Oabs__class_Oabs
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes (bnd_c_HOL_Oabs__class_Oabs V_a T_a)
% 18.72/19.46 (bnd_c_HOL_Oabs__class_Oabs V_b T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_b (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_a (bnd_c_HOL_Ozero__class_Ozero T_a) T_a;
% 18.72/19.46 !!T_a V_x V_y V_z V_w.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Odivide V_x V_y T_a)
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Odivide V_z V_w T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_x V_z T_a)
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_y V_w T_a) T_a;
% 18.72/19.46 !!T_a V_x.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__normed__vector T_a |
% 18.72/19.46 bnd_c_HOL_Osgn__class_Osgn (bnd_c_HOL_Ouminus__class_Ouminus V_x T_a)
% 18.72/19.46 T_a =
% 18.72/19.46 bnd_c_HOL_Ouminus__class_Ouminus (bnd_c_HOL_Osgn__class_Osgn V_x T_a)
% 18.72/19.46 T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Oring T_a |
% 18.72/19.46 bnd_c_HOL_Ouminus__class_Ouminus
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_a T_a) V_b T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Oring T_a |
% 18.72/19.46 bnd_c_HOL_Ouminus__class_Ouminus
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_a
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_b T_a) T_a;
% 18.72/19.46 !!T_a V_x V_y.
% 18.72/19.46 ~ bnd_class_OrderedGroup_Oab__semigroup__idem__mult T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_x
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_x V_y T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_x V_y T_a;
% 18.72/19.46 !!T_a V_a V_n.
% 18.72/19.46 ((((~ bnd_class_Ring__and__Field_Ozero__neq__one T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Ono__zero__divisors T_a) |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Omult__zero T_a) |
% 18.72/19.46 ~ bnd_class_Power_Opower T_a) |
% 18.72/19.46 ~ bnd_c_Power_Opower__class_Opower V_a V_n T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a) |
% 18.72/19.46 V_a = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_a V_n.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Oring__1__no__zero__divisors T_a |
% 18.72/19.46 ~ bnd_c_Power_Opower__class_Opower V_a V_n T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a) |
% 18.72/19.46 V_a = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_x V_y V_w V_z.
% 18.72/19.46 ((~ bnd_class_Divides_Osemiring__div T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_Divides_Odiv__class_Odiv V_x V_y T_a)
% 18.72/19.46 (bnd_c_Divides_Odiv__class_Odiv V_w V_z T_a) T_a =
% 18.72/19.46 bnd_c_Divides_Odiv__class_Odiv
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_x V_w T_a)
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_y V_z T_a) T_a) |
% 18.72/19.46 ~ bnd_c_Ring__and__Field_Odvd__class_Odvd V_z V_w T_a) |
% 18.72/19.46 ~ bnd_c_Ring__and__Field_Odvd__class_Odvd V_y V_x T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 (~ bnd_class_OrderedGroup_Opordered__ab__group__add T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_a T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ouminus__class_Ouminus V_a T_a)
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero T_a) T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 (~ bnd_class_OrderedGroup_Opordered__ab__group__add T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ouminus__class_Ouminus V_a T_a)
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_a T_a;
% 18.72/19.46 !!V_x.
% 18.72/19.46 (~ bnd_c_HOL_Otimes__class_Otimes V_x V_x bnd_tc_RealDef_Oreal =
% 18.72/19.46 bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal |
% 18.72/19.46 V_x =
% 18.72/19.46 bnd_c_HOL_Ouminus__class_Ouminus
% 18.72/19.46 (bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal)
% 18.72/19.46 bnd_tc_RealDef_Oreal) |
% 18.72/19.46 V_x = bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ~ bnd_class_Divides_Osemiring__div T_a |
% 18.72/19.46 bnd_c_Divides_Odiv__class_Odiv
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 V_a T_a)
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 V_b T_a)
% 18.72/19.46 T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Oordered__ring__strict T_a |
% 18.72/19.46 bnd_c_lessequals V_a (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_a T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a)
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero T_a) T_a;
% 18.72/19.46 !!T_a V_b V_a.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Oordered__ring__strict T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_b T_a) |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_a T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a)
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero T_a) T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Oordered__ring__strict T_a |
% 18.72/19.46 bnd_c_lessequals V_a (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 bnd_c_lessequals V_b (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a)
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero T_a) T_a;
% 18.72/19.46 !!T_a V_b V_a.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Oordered__ring__strict T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_b T_a) |
% 18.72/19.46 bnd_c_lessequals V_b (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a)
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero T_a) T_a;
% 18.72/19.46 !!V_r V_x.
% 18.72/19.46 bnd_c_lessequals
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_r bnd_tc_RealDef_Oreal) V_x
% 18.72/19.46 bnd_tc_RealDef_Oreal |
% 18.72/19.46 ~ bnd_c_lessequals
% 18.72/19.46 (bnd_c_HOL_Oabs__class_Oabs V_x bnd_tc_RealDef_Oreal) V_r
% 18.72/19.46 bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 (~ bnd_class_OrderedGroup_Opordered__ab__group__add__abs T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ouminus__class_Ouminus V_a T_a) V_b
% 18.72/19.46 T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Oabs__class_Oabs V_a T_a) V_b T_a;
% 18.72/19.46 !!V_y.
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal)
% 18.72/19.46 (bnd_c_NthRoot_Osqrt V_y) bnd_tc_RealDef_Oreal |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal)
% 18.72/19.46 V_y bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!V_y.
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal)
% 18.72/19.46 V_y bnd_tc_RealDef_Oreal |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal)
% 18.72/19.46 (bnd_c_NthRoot_Osqrt V_y) bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!V_x.
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal)
% 18.72/19.46 (bnd_c_NthRoot_Osqrt V_x) bnd_tc_RealDef_Oreal |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal)
% 18.72/19.46 V_x bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_a V_b V_c.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Ocomm__semiring__1 T_a |
% 18.72/19.46 bnd_c_Ring__and__Field_Odvd__class_Odvd V_a
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) |
% 18.72/19.46 ~ bnd_c_Ring__and__Field_Odvd__class_Odvd V_a V_c T_a;
% 18.72/19.46 !!T_a V_a V_b V_c.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Ocomm__semiring__1 T_a |
% 18.72/19.46 bnd_c_Ring__and__Field_Odvd__class_Odvd V_a
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) |
% 18.72/19.46 ~ bnd_c_Ring__and__Field_Odvd__class_Odvd V_a V_b T_a;
% 18.72/19.46 !!T_a V_a V_c V_b.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Ocomm__semiring__1 T_a |
% 18.72/19.46 bnd_c_Ring__and__Field_Odvd__class_Odvd V_a V_c T_a) |
% 18.72/19.46 ~ bnd_c_Ring__and__Field_Odvd__class_Odvd
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a;
% 18.72/19.46 !!T_a V_b V_c V_a.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Ocomm__semiring__1 T_a |
% 18.72/19.46 bnd_c_Ring__and__Field_Odvd__class_Odvd V_b V_c T_a) |
% 18.72/19.46 ~ bnd_c_Ring__and__Field_Odvd__class_Odvd
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a;
% 18.72/19.46 !!V_x V_y.
% 18.72/19.46 ~ bnd_c_NthRoot_Osqrt V_x = bnd_c_NthRoot_Osqrt V_y | V_x = V_y;
% 18.72/19.46 !!T_a V_x.
% 18.72/19.46 (~ bnd_class_RealVector_Oreal__normed__vector T_a |
% 18.72/19.46 bnd_c_RealVector_Onorm__class_Onorm
% 18.72/19.46 (bnd_c_HOL_Osgn__class_Osgn V_x T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal) |
% 18.72/19.46 V_x = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Oinverse
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Odivide V_a V_b T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Odivide V_b V_a T_a;
% 18.72/19.46 !!T_a V_c V_a V_b.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Omult__mono1 T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Otimes__class_Otimes V_c V_a T_a)
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_c T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_a V_b T_a;
% 18.72/19.46 !!T_a V_c V_a V_b.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Omult__mono T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Otimes__class_Otimes V_c V_a T_a)
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_c T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_a V_b T_a;
% 18.72/19.46 !!T_a V_a V_c V_b.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Omult__mono T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Otimes__class_Otimes V_a V_c T_a)
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_c T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_a V_b T_a;
% 18.72/19.46 !!T_a V_c V_a V_b.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Opordered__ring T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Otimes__class_Otimes V_c V_a T_a)
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_c V_b T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_c (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_b V_a T_a;
% 18.72/19.46 !!T_a V_a V_c V_b.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Opordered__ring T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Otimes__class_Otimes V_a V_c T_a)
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_c (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_b V_a T_a;
% 18.72/19.46 !!V_x V_a.
% 18.72/19.46 (bnd_c_lessequals (bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal)
% 18.72/19.46 (bnd_c_Log_Opowr V_x V_a) bnd_tc_RealDef_Oreal |
% 18.72/19.46 ~ bnd_c_lessequals
% 18.72/19.46 (bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal) V_a
% 18.72/19.46 bnd_tc_RealDef_Oreal) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Oone__class_Oone bnd_tc_RealDef_Oreal)
% 18.72/19.46 V_x bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Odivision__ring T_a |
% 18.72/19.46 ~ bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a =
% 18.72/19.46 bnd_c_HOL_Oone__class_Oone T_a) |
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Oinverse V_a T_a = V_b;
% 18.72/19.46 !!T_a V_x.
% 18.72/19.46 ~ bnd_class_OrderedGroup_Oab__semigroup__idem__mult T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_x V_x T_a = V_x;
% 18.72/19.46 !!T_a V_x.
% 18.72/19.46 (~ bnd_class_RealVector_Oreal__algebra__1 T_a |
% 18.72/19.46 ~ bnd_c_RealVector_Oof__real V_x T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a) |
% 18.72/19.46 V_x = bnd_c_HOL_Ozero__class_Ozero bnd_tc_RealDef_Oreal;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Odivision__ring T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 ~ bnd_c_HOL_Oinverse__class_Oinverse V_a T_a =
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Oinverse V_b T_a) |
% 18.72/19.46 V_a = V_b;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 (((~ bnd_class_Ring__and__Field_Odivision__ring T_a |
% 18.72/19.46 ~ bnd_c_HOL_Oinverse__class_Oinverse V_a T_a =
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Oinverse V_b T_a) |
% 18.72/19.46 V_a = V_b) |
% 18.72/19.46 V_b = bnd_c_HOL_Ozero__class_Ozero T_a) |
% 18.72/19.46 V_a = bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Odivision__ring T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Oinverse (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a |
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Oinverse (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 T_a =
% 18.72/19.46 bnd_c_HOL_Ozero__class_Ozero T_a;
% 18.72/19.46 !!T_a V_x V_y.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__algebra__1 T_a |
% 18.72/19.46 bnd_c_RealVector_Oof__real
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_x V_y bnd_tc_RealDef_Oreal) T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes (bnd_c_RealVector_Oof__real V_x T_a)
% 18.72/19.46 (bnd_c_RealVector_Oof__real V_y T_a) T_a;
% 18.72/19.46 !!T_a V_x V_y V_q.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Ocomm__semiring__1 T_a |
% 18.72/19.46 bnd_c_Power_Opower__class_Opower
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_x V_y T_a) V_q T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_Power_Opower__class_Opower V_x V_q T_a)
% 18.72/19.46 (bnd_c_Power_Opower__class_Opower V_y V_q T_a) T_a;
% 18.72/19.46 !!T_a V_a V_b V_n.
% 18.72/19.46 ~ bnd_class_OrderedGroup_Ocomm__monoid__mult T_a |
% 18.72/19.46 bnd_c_Power_Opower__class_Opower
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a) V_n T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_Power_Opower__class_Opower V_a V_n T_a)
% 18.72/19.46 (bnd_c_Power_Opower__class_Opower V_b V_n T_a) T_a;
% 18.72/19.46 !!T_a V_a V_c V_b.
% 18.72/19.46 (((~ bnd_class_Ring__and__Field_Oordered__field T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Oinverse__class_Odivide V_a V_c T_a)
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Odivide V_b V_c T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_c T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_a V_b T_a;
% 18.72/19.46 !!T_a V_b V_c V_a.
% 18.72/19.46 (((~ bnd_class_Ring__and__Field_Oordered__field T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Oinverse__class_Odivide V_b V_c T_a)
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Odivide V_a V_c T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_c (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_a V_b T_a;
% 18.72/19.46 !!T_a V_a V_n.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Odivision__ring T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Oinverse
% 18.72/19.46 (bnd_c_Power_Opower__class_Opower V_a V_n T_a) T_a =
% 18.72/19.46 bnd_c_Power_Opower__class_Opower
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Oinverse V_a T_a) V_n T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 (~ bnd_class_Ring__and__Field_Odivision__ring T_a |
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Odivision__by__zero T_a) |
% 18.72/19.46 bnd_c_HOL_Oinverse__class_Oinverse
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_a T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Ouminus__class_Ouminus
% 18.72/19.46 (bnd_c_HOL_Oinverse__class_Oinverse V_a T_a) T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Opordered__ring T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_b T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_a T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Opordered__ring T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_b (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_a (bnd_c_HOL_Ozero__class_Ozero T_a) T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Opordered__ring T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_b (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_a (bnd_c_HOL_Ozero__class_Ozero T_a) T_a;
% 18.72/19.46 !!T_a V_a.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Oordered__ring__strict T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_a T_a) T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Oordered__ring__strict T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_b T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_a T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Oordered__ring__strict T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_b (bnd_c_HOL_Ozero__class_Ozero T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals V_a (bnd_c_HOL_Ozero__class_Ozero T_a) T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Opordered__cancel__semiring T_a |
% 18.72/19.46 bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a)
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a) T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_b T_a) |
% 18.72/19.46 ~ bnd_c_lessequals (bnd_c_HOL_Ozero__class_Ozero T_a) V_a T_a;
% 18.72/19.46 !!T_a V_a V_b.
% 18.72/19.46 ((~ bnd_class_Ring__and__Field_Ofield T_a |
% 18.72/19.46 ~ bnd_c_HOL_Oinverse__class_Odivide V_a V_b T_a =
% 18.72/19.46 bnd_c_HOL_Oone__class_Oone T_a) |
% 18.72/19.46 V_b = bnd_c_HOL_Ozero__class_Ozero T_a) |
% 18.72/19.46 V_a = V_b;
% 18.72/19.46 !!T_a V_x.
% 18.72/19.46 ~ bnd_class_Int_Onumber__ring T_a |
% 18.72/19.46 bnd_c_HOL_Ouminus__class_Ouminus V_x T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus (bnd_c_HOL_Oone__class_Oone T_a)
% 18.72/19.46 T_a)
% 18.72/19.46 V_x T_a;
% 18.72/19.46 !!T_a V_r.
% 18.72/19.46 ~ bnd_class_RealVector_Oreal__algebra__1 T_a |
% 18.72/19.46 bnd_c_RealVector_Oof__real V_r T_a =
% 18.72/19.46 bnd_c_RealVector_OscaleR__class_OscaleR V_r
% 18.72/19.46 (bnd_c_HOL_Oone__class_Oone T_a) T_a;
% 18.72/19.46 !!T_a V_x V_y.
% 18.72/19.46 (~ bnd_class_Divides_Oring__div T_a |
% 18.72/19.46 bnd_c_Divides_Odiv__class_Odiv V_x
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_y T_a) T_a =
% 18.72/19.46 bnd_c_HOL_Ouminus__class_Ouminus
% 18.72/19.46 (bnd_c_Divides_Odiv__class_Odiv V_x V_y T_a) T_a) |
% 18.72/19.46 ~ bnd_c_Ring__and__Field_Odvd__class_Odvd V_y V_x T_a;
% 18.72/19.46 !!T_a V_x V_y.
% 18.72/19.46 (~ bnd_class_Divides_Oring__div T_a |
% 18.72/19.46 bnd_c_Divides_Odiv__class_Odiv
% 18.72/19.46 (bnd_c_HOL_Ouminus__class_Ouminus V_x T_a) V_y T_a =
% 18.72/19.46 bnd_c_HOL_Ouminus__class_Ouminus
% 18.72/19.46 (bnd_c_Divides_Odiv__class_Odiv V_x V_y T_a) T_a) |
% 18.72/19.46 ~ bnd_c_Ring__and__Field_Odvd__class_Odvd V_y V_x T_a;
% 18.72/19.46 !!T_a V_a V_b V_c.
% 18.72/19.46 ~ bnd_class_OrderedGroup_Oab__semigroup__mult T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_a V_b T_a) V_c T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes V_a
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_b V_c T_a) T_a;
% 18.72/19.46 !!T_a V_lx V_ly V_rx.
% 18.72/19.46 ~ bnd_class_Ring__and__Field_Ocomm__semiring__1 T_a |
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_lx V_ly T_a) V_rx T_a =
% 18.72/19.46 bnd_c_HOL_Otimes__class_Otimes
% 18.72/19.46 (bnd_c_HOL_Otimes__class_Otimes V_lx V_rx T_a) V_ly T_a |]
% 18.72/19.46 ==> True
% 18.72/19.46 Adding axioms...
% 18.72/19.47 Typedef.type_definition_def
% 88.63/89.22 ...done.
% 88.74/89.33 Ground types: ?'b, TPTP_Interpret.ind
% 88.74/89.33 Translating term (sizes: 1, 1) ...
% 137.46/137.96 Invoking SAT solver...
% 137.46/137.96 No model exists.
% 137.46/137.96 Translating term (sizes: 2, 1) ...
% 187.06/187.37 Invoking SAT solver...
% 187.06/187.37 No model exists.
% 187.06/187.37 Translating term (sizes: 1, 2) ...
% 300.10/299.72 /export/starexec/sandbox/solver/lib/scripts/run-polyml-5.5.2: line 82: 33452 CPU time limit exceeded (core dumped) "$ISABELLE_HOME/lib/scripts/feeder" -p -h "$MLTEXT" -t "$MLEXIT" $FEEDER_OPTS
% 300.10/299.72 33453 (core dumped) | { read FPID; "$POLY" -q -i $ML_OPTIONS; RC="$?"; kill -TERM "$FPID"; exit "$RC"; }
% 300.10/299.73 /export/starexec/sandbox/solver/src/HOL/TPTP/lib/Tools/tptp_refute: line 26: 33398 Exit 152 "$ISABELLE_PROCESS" -q -e "use_thy \"/tmp/$SCRATCH\"; exit 1;" HOL-TPTP
% 300.10/299.73 33399 CPU time limit exceeded (core dumped) | grep --line-buffered -v "^###\|^PROOF FAILED for depth\|^Failure node\|inferences so far. Searching to depth\|^val \|^Loading theory\|^Warning-The type of\|^ monotype.$"
%------------------------------------------------------------------------------