TSTP Solution File: SWW192+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW192+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 23:21:09 EDT 2022
% Result : Timeout 300.04s 300.44s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW192+1 : TPTP v8.1.0. Released v5.2.0.
% 0.14/0.13 % Command : bliksem %s
% 0.14/0.34 % Computer : n025.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % DateTime : Sun Jun 5 12:21:02 EDT 2022
% 0.14/0.34 % CPUTime :
% 1.28/1.65 *** allocated 10000 integers for termspace/termends
% 1.28/1.65 *** allocated 10000 integers for clauses
% 1.28/1.65 *** allocated 10000 integers for justifications
% 1.28/1.65 *** allocated 15000 integers for termspace/termends
% 1.28/1.65 *** allocated 22500 integers for termspace/termends
% 1.28/1.65 *** allocated 33750 integers for termspace/termends
% 1.28/1.65 Bliksem 1.12
% 1.28/1.65
% 1.28/1.65
% 1.28/1.65 Automatic Strategy Selection
% 1.28/1.65
% 1.28/1.65 *** allocated 50625 integers for termspace/termends
% 1.28/1.65 *** allocated 75937 integers for termspace/termends
% 1.28/1.65 *** allocated 113905 integers for termspace/termends
% 1.28/1.65
% 1.28/1.65 Clauses:
% 1.28/1.65
% 1.28/1.65 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 1.28/1.65 { c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, v_z ) =
% 1.28/1.65 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.28/1.65 { v_z = c_Complex_Ocomplex_OComplex( v_x____, v_y____ ) }.
% 1.28/1.65 { ! class_Rings_Osemiring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 1.28/1.65 ( X ), c_Groups_Oone__class_Oone( X ) ), c_Int_Onumber__class_Onumber__of
% 1.28/1.65 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 1.28/1.65 c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) =
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1( c_Int_OPls
% 1.28/1.65 ) ) ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 c_Groups_Oone__class_Oone( X ), c_Int_Onumber__class_Onumber__of( X, Y )
% 1.28/1.65 ) = c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Int_Oint, c_Int_OBit1( c_Int_OPls ), Y ) ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Oone__class_Oone( X )
% 1.28/1.65 ) = c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Int_Oint, Y, c_Int_OBit1( c_Int_OPls ) ) ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), c_Groups_Oone__class_Oone( X ) =
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit1( c_Int_OPls ) ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.28/1.65 c_Int_OBit1( c_Int_OPls ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.28/1.65 c_Int_OBit1( Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( X, c_Int_OPls ) ) = Y }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( X, c_Int_OPls ), Y ) = Y }.
% 1.28/1.65 { c_Int_OBit0( c_Int_OPls ) = c_Int_OPls }.
% 1.28/1.65 { ! c_Int_OPls = c_Int_OBit0( X ), c_Int_OPls = X }.
% 1.28/1.65 { ! c_Int_OPls = X, c_Int_OPls = c_Int_OBit0( X ) }.
% 1.28/1.65 { ! c_Int_OBit0( X ) = c_Int_OPls, X = c_Int_OPls }.
% 1.28/1.65 { ! X = c_Int_OPls, c_Int_OBit0( X ) = c_Int_OPls }.
% 1.28/1.65 { c_Int_OBit1( X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oone__class_Oone(
% 1.28/1.65 tc_Int_Oint ), X ), X ) }.
% 1.28/1.65 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 1.28/1.65 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 1.28/1.65 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 1.28/1.65 { c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 1.28/1.65 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 1.28/1.65 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Int_OPls ) = X }.
% 1.28/1.65 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OPls, X ) = X }.
% 1.28/1.65 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit0(
% 1.28/1.65 X ) ) = c_Int_OBit0( c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }
% 1.28/1.65 .
% 1.28/1.65 { c_Int_OBit0( X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, X ) }.
% 1.28/1.65 { c_Groups_Oone__class_Oone( tc_Int_Oint ) =
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit1( c_Int_OPls )
% 1.28/1.65 ) }.
% 1.28/1.65 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit0(
% 1.28/1.65 X ) ) = c_Int_OBit1( c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }
% 1.28/1.65 .
% 1.28/1.65 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit1(
% 1.28/1.65 X ) ) = c_Int_OBit1( c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }
% 1.28/1.65 .
% 1.28/1.65 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.28/1.65 tc_Nat_Onat ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) =
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ) ) }.
% 1.28/1.65 { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OPls )
% 1.28/1.65 ) = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.28/1.65 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) =
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OPls )
% 1.28/1.65 ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), ! class_Int_Oring__char__0( X ), !
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( X, Z ) =
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( X, Y ), Z = Y }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), ! class_Int_Oring__char__0( X ), ! Z = Y
% 1.28/1.65 , c_Int_Onumber__class_Onumber__of( X, Z ) =
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( X, Y ) }.
% 1.28/1.65 { ! class_Int_Onumber( X ), ! c_Int_Onumber__class_Onumber__of( X, Z ) = Y
% 1.28/1.65 , Y = c_Int_Onumber__class_Onumber__of( X, Z ) }.
% 1.28/1.65 { ! class_Int_Onumber( X ), ! Y = c_Int_Onumber__class_Onumber__of( X, Z )
% 1.28/1.65 , c_Int_Onumber__class_Onumber__of( X, Z ) = Y }.
% 1.28/1.65 { ! c_Int_OBit1( Y ) = c_Int_OBit1( X ), Y = X }.
% 1.28/1.65 { ! Y = X, c_Int_OBit1( Y ) = c_Int_OBit1( X ) }.
% 1.28/1.65 { ! c_Int_OBit0( Y ) = c_Int_OBit0( X ), Y = X }.
% 1.28/1.65 { ! Y = X, c_Int_OBit0( Y ) = c_Int_OBit0( X ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( X, T ), c_Groups_Oplus__class_Oplus( X
% 1.28/1.65 , c_Int_Onumber__class_Onumber__of( X, Z ), Y ) ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, c_Int_Onumber__class_Onumber__of( X,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, T, Z ) ), Y ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( X, Z ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Int_Oint, Z, Y ) ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, c_Int_Onumber__class_Onumber__of( X, Z )
% 1.28/1.65 , c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 1.28/1.65 { ! c_Int_OBit1( X ) = c_Int_OPls }.
% 1.28/1.65 { ! c_Int_OPls = c_Int_OBit1( X ) }.
% 1.28/1.65 { ! c_Int_OBit1( Y ) = c_Int_OBit0( X ) }.
% 1.28/1.65 { ! c_Int_OBit0( Y ) = c_Int_OBit1( X ) }.
% 1.28/1.65 { v_z = c_Complex_Ocomplex_OComplex( skol2, skol11 ) }.
% 1.28/1.65 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 1.28/1.65 c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt( X ) ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ) ) ) = X }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 1.28/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.28/1.65 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 1.28/1.65 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oone__class_Oone( X ) ) =
% 1.28/1.65 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.28/1.65 { c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 1.28/1.65 c_Complex_Ocomplex_OComplex( T, Z ), c_Complex_Ocomplex_OComplex( Y, X )
% 1.28/1.65 ) = c_Complex_Ocomplex_OComplex( c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_RealDef_Oreal, T, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.28/1.65 Z, X ) ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 1.28/1.65 ( X ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ) ) ) = c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Power_Opower__class_Opower
% 1.28/1.65 ( X ), Z ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 1.28/1.65 c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower
% 1.28/1.65 ( X ), Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 1.28/1.65 c_Int_OBit1( c_Int_OPls ) ) ) ) ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.28/1.65 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), Z ) ), Y ) ) }.
% 1.28/1.65 { c_Groups_Oone__class_Oone( tc_Code__Numeral_Ocode__numeral ) =
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Code__Numeral_Ocode__numeral,
% 1.28/1.65 c_Int_OBit1( c_Int_OPls ) ) }.
% 1.28/1.65 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.28/1.65 = c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ) ) ) ) = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), ! c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ) ) ) ) = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__idom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.28/1.65 X ), ! Y = c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus
% 1.28/1.65 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ) ) ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_Groups_Omonoid__mult( X ), ! class_Int_Onumber( X ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), c_Int_Onumber__class_Onumber__of( X, Y
% 1.28/1.65 ) ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 1.28/1.65 c_Int_OBit1( c_Int_OPls ) ) ) ) = hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.28/1.65 Y ) ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 1.28/1.65 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 1.28/1.65 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 1.28/1.65 c_Groups_Oone__class_Oone( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 1.28/1.65 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 1.28/1.65 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 1.28/1.65 ( X ), Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 1.28/1.65 c_Int_OBit1( c_Int_OPls ) ) ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.65 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 1.28/1.65 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ) ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.65 { c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.28/1.65 c_Complex_Ocomplex_OComplex( Y, X ) ) = c_NthRoot_Osqrt(
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.28/1.65 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 1.28/1.65 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) }.
% 1.28/1.65 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 1.28/1.65 ( tc_Int_Oint ) }.
% 1.28/1.65 { c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) =
% 1.28/1.65 c_Complex_Ocomplex_OComplex( c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_RealDef_Oreal ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.28/1.65 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.28/1.65 { c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) = X }.
% 1.28/1.65 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.28/1.65 { c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex,
% 1.28/1.65 c_Complex_Ocomplex_OComplex( Y, X ) ) = c_Complex_Ocomplex_OComplex(
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 1.28/1.65 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.28/1.65 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 1.28/1.65 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.28/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.28/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 1.28/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 1.28/1.65 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 1.28/1.65 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.28/1.65 c_RealVector_Onorm__class_Onorm( X, Y ) = c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_RealDef_Oreal ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X, Y )
% 1.28/1.65 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.28/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ) ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) =
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( X, Z ) ) ), Y ) = hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Z ) ) ), Y ) }.
% 1.28/1.65 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.28/1.65 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.28/1.65 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.28/1.65 .
% 1.28/1.65 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.28/1.65 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.28/1.65 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Nat_Onat ) }.
% 1.28/1.65 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.28/1.65 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.28/1.65 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 1.28/1.65 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Complex_Ocomplex ), Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 1.28/1.65 ) }.
% 1.28/1.65 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Complex_Ocomplex ), X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 1.28/1.65 ) }.
% 1.28/1.65 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.28/1.65 c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Complex_Ocomplex ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.28/1.65 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.28/1.65 ) ), Y ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.28/1.65 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.28/1.65 ( X, Y ) ) = c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.28/1.65 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.28/1.65 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) =
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( X, c_Int_Onumber__class_Onumber__of( X,
% 1.28/1.65 Y ) ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( X, c_Groups_Ouminus__class_Ouminus(
% 1.28/1.65 tc_Int_Oint, Y ) ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), c_Int_Onumber__class_Onumber__of( X, T ) ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.28/1.65 Z ) ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), T ), Z ) ) ), Y ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), c_Int_Onumber__class_Onumber__of( X, Z ) ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X, hAPP
% 1.28/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ) = hAPP(
% 1.28/1.65 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( X, Z ) ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.28/1.65 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 1.28/1.65 ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.28/1.65 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 1.28/1.65 ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ouminus__class_Ouminus
% 1.28/1.65 ( tc_Int_Oint, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.28/1.65 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.28/1.65 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.65 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.28/1.65 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.28/1.65 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.28/1.65 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.28/1.65 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.28/1.65 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ouminus__class_Ouminus( X, Y
% 1.28/1.65 ) ) = c_RealVector_Onorm__class_Onorm( X, Y ) }.
% 1.28/1.65 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 1.28/1.65 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( X ) }.
% 1.28/1.65 { c_Groups_Ozero__class_Ozero( tc_Code__Numeral_Ocode__numeral ) =
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Code__Numeral_Ocode__numeral,
% 1.28/1.65 c_Int_OPls ) }.
% 1.28/1.65 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.28/1.65 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.65 c_Groups_Oone__class_Oone( X ) ) ), Y ) ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.28/1.65 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.28/1.65 ) = c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.65 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.28/1.65 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! c_Complex_Ocomplex_OComplex( Z, Y ) = c_Int_Onumber__class_Onumber__of
% 1.28/1.65 ( tc_Complex_Ocomplex, X ), Z = c_Int_Onumber__class_Onumber__of(
% 1.28/1.65 tc_RealDef_Oreal, X ) }.
% 1.28/1.65 { ! c_Complex_Ocomplex_OComplex( Z, Y ) = c_Int_Onumber__class_Onumber__of
% 1.28/1.65 ( tc_Complex_Ocomplex, X ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_RealDef_Oreal ) }.
% 1.28/1.65 { ! Z = c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, X ), ! Y =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.28/1.65 c_Complex_Ocomplex_OComplex( Z, Y ) = c_Int_Onumber__class_Onumber__of(
% 1.28/1.65 tc_Complex_Ocomplex, X ) }.
% 1.28/1.65 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Int_OPls ) = c_Int_OPls }
% 1.28/1.65 .
% 1.28/1.65 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Int_OBit0( X ) ) =
% 1.28/1.65 c_Int_OBit0( c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.28/1.65 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.28/1.65 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ),
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.28/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Int_OPls ), X
% 1.28/1.65 ) = c_Int_OPls }.
% 1.28/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Int_OBit0( Y
% 1.28/1.65 ) ), X ) = c_Int_OBit0( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.65 tc_Int_Oint ), Y ), X ) ) }.
% 1.28/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.28/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.28/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.28/1.65 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { c_Int_OPls = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.28/1.65 { c_Groups_Ozero__class_Ozero( tc_Int_Oint ) =
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OPls ) }.
% 1.28/1.65 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Int_Oint ) ) = X }.
% 1.28/1.65 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Int_Oint ), X ) = X }.
% 1.28/1.65 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.28/1.65 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.28/1.65 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.28/1.65 c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.65 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Oone__class_Oone(
% 1.28/1.65 tc_Complex_Ocomplex ), Y = c_Groups_Oone__class_Oone( tc_RealDef_Oreal )
% 1.28/1.65 }.
% 1.28/1.65 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Oone__class_Oone(
% 1.28/1.65 tc_Complex_Ocomplex ), X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 1.28/1.65 ) }.
% 1.28/1.65 { ! Y = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), ! X =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.28/1.65 c_Complex_Ocomplex_OComplex( Y, X ) = c_Groups_Oone__class_Oone(
% 1.28/1.65 tc_Complex_Ocomplex ) }.
% 1.28/1.65 { c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) =
% 1.28/1.65 c_Complex_Ocomplex_OComplex( c_Groups_Oone__class_Oone( tc_RealDef_Oreal
% 1.28/1.65 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.28/1.65 { ! class_Int_Onumber( X ), ! class_Rings_Osemiring( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.28/1.65 T ) ), c_Groups_Oplus__class_Oplus( X, Z, Y ) ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), c_Int_Onumber__class_Onumber__of( X, T ) ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.28/1.65 T ) ), Y ) ) }.
% 1.28/1.65 { ! class_Int_Onumber( X ), ! class_Rings_Osemiring( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.28/1.65 ) ), c_Int_Onumber__class_Onumber__of( X, Y ) ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), T ), c_Int_Onumber__class_Onumber__of( X, Y ) ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), c_Int_Onumber__class_Onumber__of
% 1.28/1.65 ( X, Y ) ) ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), c_Groups_Ozero__class_Ozero( X ) =
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( X, c_Int_OPls ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.28/1.65 c_Int_OPls ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) =
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OPls ) }.
% 1.28/1.65 { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OPls ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.65 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.28/1.65 ), c_Groups_Ouminus__class_Ouminus( X, Z ) ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ) ) ), Y ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.28/1.65 , Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ) ) ), Y ) ) }.
% 1.28/1.65 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.28/1.65 ), c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 1.28/1.65 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ) ) ), Y ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), Y ), c_Int_Onumber__class_Onumber__of( X, c_Int_OBit1( c_Int_OPls
% 1.28/1.65 ) ) ) = Y }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), c_Int_Onumber__class_Onumber__of( X, c_Int_OBit1( c_Int_OPls ) ) )
% 1.28/1.65 , Y ) = Y }.
% 1.28/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Int_OBit1( Y
% 1.28/1.65 ) ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Int_OBit0( hAPP(
% 1.28/1.65 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ), X ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.28/1.65 c_Int_OBit0( Y ) ) = c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 1.28/1.65 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.28/1.65 tc_Nat_Onat ) ) = Y }.
% 1.28/1.65 { ! c_Complex_Ocomplex_OComplex( T, Z ) = c_Complex_Ocomplex_OComplex( Y, X
% 1.28/1.65 ), T = Y }.
% 1.28/1.65 { ! c_Complex_Ocomplex_OComplex( T, Z ) = c_Complex_Ocomplex_OComplex( Y, X
% 1.28/1.65 ), Z = X }.
% 1.28/1.65 { ! T = Y, ! Z = X, c_Complex_Ocomplex_OComplex( T, Z ) =
% 1.28/1.65 c_Complex_Ocomplex_OComplex( Y, X ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.28/1.65 c_Groups_Oone__class_Oone( X ) ) ), c_Int_Onumber__class_Onumber__of( X,
% 1.28/1.65 Y ) ) = c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( Y ) ) }.
% 1.28/1.65 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 1.28/1.65 ( tc_Nat_Onat, c_Int_OBit1( c_Int_OBit1( c_Int_OPls ) ) ) ) = hAPP( hAPP
% 1.28/1.65 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ), Y ) }.
% 1.28/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ) ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, X ) }.
% 1.28/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ) ) ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, X
% 1.28/1.65 ) }.
% 1.28/1.65 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ) ) ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.28/1.65 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 1.28/1.65 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 1.28/1.65 c_Int_OBit1( c_Int_OPls ) ) ) ), Y ) ), X ) ) }.
% 1.28/1.65 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.28/1.65 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ) ) ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), Y ), c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1
% 1.28/1.65 ( c_Int_OPls ) ) ) ) = c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ) ) ), Y ) = c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 1.28/1.65 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 1.28/1.65 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) = hAPP( hAPP
% 1.28/1.65 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.28/1.65 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ) ) ), Y ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.28/1.65 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ) ) ) }.
% 1.28/1.65 { ! class_Rings_Osemiring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 1.28/1.65 ( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ) ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 1.28/1.65 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 1.28/1.65 .
% 1.28/1.65 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 1.28/1.65 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.28/1.65 c_NthRoot_Osqrt( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.65 tc_RealDef_Oreal ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP(
% 1.28/1.65 hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), T ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.28/1.65 tc_RealDef_Oreal ), Z ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 1.28/1.65 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ),
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.28/1.65 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 1.28/1.65 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) ) ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ) ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.65 tc_RealDef_Oreal ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP(
% 1.28/1.65 hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), T ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.28/1.65 tc_RealDef_Oreal ), Z ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 1.28/1.65 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ),
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.28/1.65 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 1.28/1.65 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) }.
% 1.28/1.65 { ! c_NthRoot_Osqrt( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP(
% 1.28/1.65 hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.28/1.65 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 1.28/1.65 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) = Y, X =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.28/1.65 { ! c_NthRoot_Osqrt( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP(
% 1.28/1.65 hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), X ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.28/1.65 tc_RealDef_Oreal ), Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 1.28/1.65 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) = Y, X =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.28/1.65 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.28/1.65 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 1.28/1.65 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.28/1.65 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.28/1.65 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 1.28/1.65 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.28/1.65 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.28/1.65 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 1.28/1.65 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ) ) ), Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.28/1.65 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP
% 1.28/1.65 ( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 1.28/1.65 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) }.
% 1.28/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 1.28/1.65 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), X ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ) ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.28/1.65 tc_RealDef_Oreal ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.65 tc_RealDef_Oreal ), c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal,
% 1.28/1.65 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), X ) ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ) ) ) }.
% 1.28/1.65 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), !
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 1.28/1.65 c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.65 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Nat_Onat, Z, Y ) ) }.
% 1.28/1.65 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.28/1.65 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.28/1.65 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.28/1.65 .
% 1.28/1.65 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.28/1.65 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.28/1.65 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), ! c_Int_Onumber__class_Onumber__of(
% 1.28/1.65 tc_Nat_Onat, Y ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.65 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.28/1.65 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.28/1.65 , ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), Z ), c_Int_Onumber__class_Onumber__of
% 1.28/1.65 ( tc_Nat_Onat, Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__ring__1( X ), c_Groups_Ouminus__class_Ouminus( X, Y
% 1.28/1.65 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) ), Y
% 1.28/1.65 ) }.
% 1.28/1.65 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.28/1.65 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) = X }.
% 1.28/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 1.28/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 1.28/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ), X ) =
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.28/1.65 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.28/1.65 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 1.28/1.65 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.28/1.65 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP
% 1.28/1.65 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 1.28/1.65 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 1.28/1.65 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP(
% 1.28/1.65 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) }.
% 1.28/1.65 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP
% 1.28/1.65 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 1.28/1.65 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 1.28/1.65 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP(
% 1.28/1.65 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) }.
% 1.28/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 1.28/1.65 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ), X ) =
% 1.28/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP
% 1.28/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.28/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) =
% 1.28/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y )
% 1.28/1.65 }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.28/1.65 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 1.28/1.65 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.28/1.65 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.28/1.65 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 1.28/1.65 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 1.28/1.65 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 1.28/1.65 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 1.28/1.65 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 1.28/1.65 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.28/1.65 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 1.28/1.65 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.28/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.28/1.65 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) = X }.
% 1.28/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ), X ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.28/1.65 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.28/1.65 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.28/1.65 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.28/1.65 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y = X }.
% 1.28/1.65 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y,
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.28/1.65 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) }.
% 1.28/1.65 { ! X = c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ),
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.28/1.65 { c_NthRoot_Osqrt( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.28/1.65 { c_NthRoot_Osqrt( c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, X ) )
% 1.28/1.65 = c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, c_NthRoot_Osqrt( X
% 1.28/1.65 ) ) }.
% 1.28/1.65 { c_NthRoot_Osqrt( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.65 tc_RealDef_Oreal ), Y ), X ) ) = hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_NthRoot_Osqrt( Y ) )
% 1.28/1.65 , c_NthRoot_Osqrt( X ) ) }.
% 1.28/1.65 { ! c_NthRoot_Osqrt( X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 1.28/1.65 , X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.28/1.65 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X
% 1.28/1.65 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.28/1.65 { ! c_NthRoot_Osqrt( Y ) = c_NthRoot_Osqrt( X ), Y = X }.
% 1.28/1.65 { ! Y = X, c_NthRoot_Osqrt( Y ) = c_NthRoot_Osqrt( X ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.28/1.65 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.28/1.65 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.28/1.65 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.28/1.65 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.28/1.65 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.28/1.65 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.28/1.65 ), U = Z, T = Y }.
% 1.28/1.65 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.28/1.65 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.28/1.65 ) }.
% 1.28/1.65 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.28/1.65 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.28/1.65 ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 1.28/1.65 ) ), Z ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.28/1.65 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.65 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.28/1.65 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.28/1.65 ) }.
% 1.28/1.65 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.28/1.65 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.28/1.65 ), ! U = T }.
% 1.28/1.65 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.28/1.65 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.28/1.65 ), ! Z = Y }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.28/1.65 = Y }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.28/1.65 = Y }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.28/1.65 tc_Nat_Onat ) ) = Y }.
% 1.28/1.65 { c_NthRoot_Osqrt( hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.28/1.65 tc_RealDef_Oreal ), Y ), X ) ) = hAPP( hAPP( c_Power_Opower__class_Opower
% 1.28/1.65 ( tc_RealDef_Oreal ), c_NthRoot_Osqrt( Y ) ), X ) }.
% 1.28/1.65 { ! c_NthRoot_Osqrt( X ) = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X
% 1.28/1.65 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.28/1.65 { ! X = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X )
% 1.28/1.65 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.28/1.65 { c_NthRoot_Osqrt( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 1.28/1.65 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.28/1.65 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.28/1.65 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.65 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.28/1.65 = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus
% 1.28/1.65 ( X, Z ) }.
% 1.28/1.65 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.65 , Z ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 1.28/1.65 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 1.28/1.65 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 1.28/1.65 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 1.28/1.65 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.28/1.65 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.28/1.65 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.28/1.65 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.28/1.65 { c_Complex_Ocomplex_Ocomplex__size( c_Complex_Ocomplex_OComplex( Y, X ) )
% 1.28/1.65 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.65 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 1.28/1.65 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.65 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) = c_Groups_Oone__class_Oone
% 1.28/1.65 ( X ), Y = c_Groups_Oone__class_Oone( X ), Y =
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ) }.
% 1.28/1.65 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 1.28/1.65 c_Groups_Oone__class_Oone( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), Y ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.65 { ! class_Rings_Oring__1__no__zero__divisors( X ), ! Y =
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) ),
% 1.28/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) =
% 1.28/1.65 c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.65 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.28/1.65 = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.65 Z ) = Y }.
% 1.28/1.65 { ! class_Groups_Oab__group__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ), Y ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.65 , Y ), c_Groups_Oplus__class_Oplus( X, Z, Y ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Oplus__class_Oplus( X, Z, Y )
% 1.28/1.65 = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ouminus__class_Ouminus
% 1.28/1.65 ( X, Y ) }.
% 1.28/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = c_Groups_Ozero__class_Ozero(
% 1.28/1.65 X ) }.
% 1.28/1.65 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 1.28/1.65 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.65 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.28/1.65 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.28/1.65 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 T, Y ), Z = Y }.
% 1.28/1.65 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 T, Y ) }.
% 1.28/1.65 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 Y, Z ), T = Y }.
% 1.28/1.65 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 Y, Z ) }.
% 1.28/1.65 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 T, Y ), Z = Y }.
% 1.28/1.65 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 T, Y ), Z = Y }.
% 1.28/1.65 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 Y, T ), Z = Y }.
% 1.28/1.65 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 1.28/1.65 c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.65 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 1.28/1.65 c_Groups_Oone__class_Oone( X ) = Y }.
% 1.28/1.65 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 1.28/1.65 ) = c_Groups_Ouminus__class_Ouminus( X, Y ), Z = Y }.
% 1.28/1.65 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ouminus__class_Ouminus
% 1.28/1.65 ( X, Z ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.28/1.65 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Z
% 1.28/1.65 ) = Y, c_Groups_Ouminus__class_Ouminus( X, Y ) = Z }.
% 1.28/1.65 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 1.28/1.65 ) = Z, c_Groups_Ouminus__class_Ouminus( X, Z ) = Y }.
% 1.28/1.65 { ! class_Groups_Ogroup__add( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.65 , Y ), Y = c_Groups_Ouminus__class_Ouminus( X, Z ) }.
% 1.28/1.65 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.65 , Z ), Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.28/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = Y }.
% 1.28/1.65 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 1.28/1.65 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 1.28/1.65 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.28/1.65 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.28/1.65 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 1.28/1.65 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 1.28/1.65 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 1.28/1.65 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 1.28/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 1.28/1.65 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.28/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 1.28/1.65 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.65 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.65 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.28/1.65 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.65 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.28/1.65 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.28/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.28/1.65 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 1.28/1.65 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.28/1.65 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.28/1.65 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.28/1.65 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.28/1.65 c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.65 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.28/1.65 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.65 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 1.28/1.65 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.65 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 1.28/1.65 ) ), T ), Y ) }.
% 1.28/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) = Y, Y =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.28/1.65 = Y }.
% 1.28/1.65 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ouminus__class_Ouminus( X, Y
% 1.28/1.65 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 1.28/1.65 ) }.
% 1.28/1.65 { ! class_Groups_Ogroup__add( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.28/1.65 ) }.
% 1.28/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ), Y = c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( X ) }.
% 1.28/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.65 , Y ) }.
% 1.28/1.65 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ), c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 = Y }.
% 1.28/1.65 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Ouminus__class_Ouminus( X, Y
% 1.28/1.65 ) }.
% 1.28/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.28/1.65 = Y }.
% 1.28/1.65 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.28/1.65 = Y }.
% 1.28/1.65 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.28/1.65 = Y }.
% 1.28/1.65 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.28/1.65 = Y }.
% 1.28/1.65 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.28/1.65 ), Z ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 1.28/1.65 Z = Y, Z = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.28/1.65 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.28/1.65 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.28/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) = hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.28/1.65 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.28/1.65 , c_Groups_Ouminus__class_Ouminus( X, Z ) ),
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) = hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.28/1.65 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.28/1.65 , c_Groups_Ouminus__class_Ouminus( X, Z ) ), Y ) = hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.28/1.65 ( X, Y ) ) }.
% 1.28/1.65 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 1.28/1.65 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ouminus__class_Ouminus( X, Z
% 1.28/1.65 ) ), Y ) }.
% 1.28/1.65 { ! class_Rings_Oring( X ), c_Groups_Ouminus__class_Ouminus( X, hAPP( hAPP
% 1.28/1.65 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), c_Groups_Ouminus__class_Ouminus
% 1.28/1.65 ( X, Y ) ) }.
% 1.28/1.65 { ! class_Groups_Oab__group__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 1.28/1.65 , c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.28/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus( X
% 1.28/1.65 , c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.28/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X, Z,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.28/1.65 Y ) ) = Y }.
% 1.28/1.65 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 Z, Y ) ) = Y }.
% 1.28/1.65 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Nat_Onat ), X ) = X }.
% 1.28/1.65 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( tc_Nat_Onat ) ) = X }.
% 1.28/1.65 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.65 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.65 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.65 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.65 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.65 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.65 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.65 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.28/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 1.28/1.65 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.65 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.28/1.65 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.28/1.65 .
% 1.28/1.65 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.28/1.65 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.28/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 1.28/1.65 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.65 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.28/1.65 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 1.28/1.65 .
% 1.28/1.65 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.28/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.28/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 1.28/1.65 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 1.28/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.28/1.65 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 1.28/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.28/1.65 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.28/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 1.28/1.65 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.28/1.65 , Y ), X ) }.
% 1.28/1.65 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.28/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.28/1.65 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.28/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 1.28/1.65 tc_Nat_Onat ) }.
% 1.28/1.65 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.28/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 1.28/1.65 tc_Nat_Onat ) }.
% 1.28/1.65 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.28/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.28/1.65 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), ! c_Groups_Oone__class_Oone( X ) =
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( X, Y ), c_Int_Oiszero( X,
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Int_Oint, c_Int_OBit1( c_Int_OPls ), c_Groups_Ouminus__class_Ouminus(
% 1.28/1.65 tc_Int_Oint, Y ) ) ) ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), ! c_Int_Oiszero( X,
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Int_Oint, c_Int_OBit1( c_Int_OPls ), c_Groups_Ouminus__class_Ouminus(
% 1.28/1.65 tc_Int_Oint, Y ) ) ) ), c_Groups_Oone__class_Oone( X ) =
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( X, Y ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), ! c_Int_Onumber__class_Onumber__of( X, Y
% 1.28/1.65 ) = c_Groups_Oone__class_Oone( X ), c_Int_Oiszero( X,
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Int_OBit1
% 1.28/1.65 ( c_Int_OPls ) ) ) ) ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), ! c_Int_Oiszero( X,
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Int_OBit1
% 1.28/1.65 ( c_Int_OPls ) ) ) ) ), c_Int_Onumber__class_Onumber__of( X, Y ) =
% 1.28/1.65 c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.65 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( hAPP(
% 1.28/1.65 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), T ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.28/1.65 tc_RealDef_Oreal ), Z ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 1.28/1.65 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ),
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.28/1.65 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 1.28/1.65 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) ) ) }.
% 1.28/1.65 { c_Nat_Osize__class_Osize( tc_Complex_Ocomplex,
% 1.28/1.65 c_Complex_Ocomplex_OComplex( Y, X ) ) = c_Groups_Ozero__class_Ozero(
% 1.28/1.65 tc_Nat_Onat ) }.
% 1.28/1.65 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt(
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.28/1.65 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 1.28/1.65 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), ! c_Int_Onumber__class_Onumber__of( X, Y
% 1.28/1.65 ) = c_Groups_Ozero__class_Ozero( X ), c_Int_Oiszero( X,
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Int_OPls
% 1.28/1.65 ) ) ) ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), ! c_Int_Oiszero( X,
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Int_Oint, Y, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Int_OPls
% 1.28/1.65 ) ) ) ), c_Int_Onumber__class_Onumber__of( X, Y ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( X, Y ), c_Int_Oiszero( X,
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Int_Oint, c_Int_OPls, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y
% 1.28/1.65 ) ) ) ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), ! c_Int_Oiszero( X,
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 1.28/1.65 tc_Int_Oint, c_Int_OPls, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y
% 1.28/1.65 ) ) ) ), c_Groups_Ozero__class_Ozero( X ) =
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( X, Y ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 1.28/1.65 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, Y ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z, Y ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 1.28/1.65 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ), Y = X }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Z ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, Z ) }.
% 1.28/1.65 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ) }.
% 1.28/1.65 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, X ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__semidom( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 1.28/1.65 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.28/1.65 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.28/1.65 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.28/1.65 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.28/1.65 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.28/1.65 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.28/1.65 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.28/1.65 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.28/1.65 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.28/1.65 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.65 , Y ), c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.65 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.65 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.65 , Z ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ), Z ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.65 , Y ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ), Y ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ouminus__class_Ouminus
% 1.28/1.65 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 1.28/1.65 ( X, Z ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ),
% 1.28/1.65 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y
% 1.28/1.65 ), c_NthRoot_Osqrt( X ) ), c_Orderings_Oord__class_Oless__eq(
% 1.28/1.65 tc_RealDef_Oreal, Y, X ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y )
% 1.28/1.65 , c_NthRoot_Osqrt( X ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y )
% 1.28/1.65 , c_NthRoot_Osqrt( X ) ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 1.28/1.65 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 1.28/1.65 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, Y ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, Y ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__semidom( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.28/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 1.28/1.65 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.65 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.28/1.65 { ! class_Rings_Osemiring__1( X ), ! c_Int_Oiszero( X, Y ), Y =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_Rings_Osemiring__1( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.65 c_Int_Oiszero( X, Y ) }.
% 1.28/1.65 { ! class_Rings_Osemiring__1( X ), c_Int_Oiszero( X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 1.28/1.65 , Y ), c_Groups_Oone__class_Oone( X ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OBit1(
% 1.28/1.65 c_Int_OPls ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Oone__class_Oone( X )
% 1.28/1.65 ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.28/1.65 c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( c_Int_OPls )
% 1.28/1.65 , Y ) }.
% 1.28/1.65 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( c_Int_OPls )
% 1.28/1.65 , Y ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X
% 1.28/1.65 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 1.28/1.65 { ! class_Rings_Osemiring__1( X ), ! c_Int_Oiszero( X,
% 1.28/1.65 c_Groups_Oone__class_Oone( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 1.28/1.65 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha1( X, Y
% 1.28/1.65 , Z ), alpha34( X, Y, Z ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha1( X, Y, Z ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha34( X, Y, Z ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.65 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.65 { ! alpha34( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.65 { ! alpha34( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.28/1.65 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ), alpha34( X, Y, Z ) }.
% 1.28/1.65 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.28/1.65 { ! alpha1( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), Y ), alpha1( X, Y, Z ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( X ) ), alpha2( X, Y, Z ), alpha35( X, Y, Z ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha35( X, Y, Z ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( X ) ) }.
% 1.28/1.65 { ! alpha35( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.65 { ! alpha35( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.28/1.65 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( X ), Y ), alpha35( X, Y, Z ) }.
% 1.28/1.65 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.28/1.65 { ! alpha2( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.65 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ), alpha2( X, Y, Z ) }.
% 1.28/1.65 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.65 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.65 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.65 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.65 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.65 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( X ) ) }.
% 1.28/1.65 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.65 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.28/1.65 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.65 { ! class_Rings_Oordered__semiring( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.28/1.65 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.28/1.65 { ! class_Rings_Oordered__semiring( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.28/1.65 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.65 { ! class_Rings_Oordered__comm__semiring( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.28/1.65 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.65 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.65 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.65 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.28/1.65 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.65 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.65 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.28/1.65 { ! class_Rings_Oordered__semiring( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.28/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.28/1.65 { ! class_Rings_Oordered__semiring( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.28/1.65 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.65 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.65 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.28/1.65 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.65 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.65 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.28/1.65 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.65 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.28/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.65 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.65 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.65 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.28/1.65 ( X ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.65 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 1.28/1.65 ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 Z, Y ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 1.28/1.65 Y, Z ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 1.28/1.65 .
% 1.28/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.28/1.65 .
% 1.28/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 1.28/1.65 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.65 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.65 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.65 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 1.28/1.65 ) }.
% 1.28/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 1.28/1.65 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 ) }.
% 1.28/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 1.28/1.65 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.65 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.65 ) }.
% 1.28/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.65 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.28/1.65 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__semidom( X ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.65 c_Groups_Oone__class_Oone( X ) ) }.
% 1.28/1.65 { ! class_Rings_Olinordered__semidom( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.28/1.65 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.28/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ouminus__class_Ouminus
% 1.28/1.65 ( X, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.65 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.65 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.65 ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.65 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.28/1.65 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.65 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.65 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.66 ) }.
% 1.28/1.66 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.66 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 1.28/1.66 ( X, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.66 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.66 , Y ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.66 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.66 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ouminus__class_Ouminus
% 1.28/1.66 ( X, Y ), Y ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semidom( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.28/1.66 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semidom( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.66 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.28/1.66 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semidom( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 1.28/1.66 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.28/1.66 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.28/1.66 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.28/1.66 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }
% 1.28/1.66 .
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( X
% 1.28/1.66 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( X )
% 1.28/1.66 , c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }
% 1.28/1.66 .
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! c_NthRoot_Osqrt(
% 1.28/1.66 X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ), hAPP( hAPP
% 1.28/1.66 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( X
% 1.28/1.66 ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.28/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.28/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt( X )
% 1.28/1.66 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal,
% 1.28/1.66 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ),
% 1.28/1.66 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.28/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.66 }.
% 1.28/1.66 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.28/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.66 }.
% 1.28/1.66 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.66 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.28/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 1.28/1.66 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 1.28/1.66 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.28/1.66 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.28/1.66 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 1.28/1.66 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.28/1.66 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.28/1.66 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 1.28/1.66 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 1.28/1.66 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 1.28/1.66 tc_RealDef_Oreal ) ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.66 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 1.28/1.66 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ),
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.28/1.66 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.28/1.66 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 1.28/1.66 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 1.28/1.66 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 1.28/1.66 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.28/1.66 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.28/1.66 ( X, Y ) ) ) }.
% 1.28/1.66 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.28/1.66 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.28/1.66 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.28/1.66 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_NthRoot_Osqrt(
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) ) ) }.
% 1.28/1.66 { ! class_Int_Onumber__ring( X ), ! class_Int_Oring__char__0( X ), !
% 1.28/1.66 c_Int_Oiszero( X, c_Int_Onumber__class_Onumber__of( X, c_Int_OBit1( Y ) )
% 1.28/1.66 ) }.
% 1.28/1.66 { ! class_Int_Onumber__ring( X ), c_Int_Oiszero( X,
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( X, c_Int_OPls ) ) }.
% 1.28/1.66 { ! class_Int_Onumber__ring( X ), ! class_Int_Oring__char__0( X ), !
% 1.28/1.66 c_Int_Oiszero( X, c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( Y ) )
% 1.28/1.66 ), c_Int_Oiszero( X, c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 1.28/1.66 { ! class_Int_Onumber__ring( X ), ! class_Int_Oring__char__0( X ), !
% 1.28/1.66 c_Int_Oiszero( X, c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 1.28/1.66 c_Int_Oiszero( X, c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( Y ) )
% 1.28/1.66 ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ),
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.28/1.66 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 1.28/1.66 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semiring__1( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.28/1.66 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.66 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 1.28/1.66 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.66 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 1.28/1.66 ), Y ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt(
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) ) ) }.
% 1.28/1.66 { ! class_Int_Onumber__ring( X ), ! c_Int_Oiszero( X,
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit1( c_Int_OPls ) ) ) }.
% 1.28/1.66 { ! class_Int_Onumber__ring( X ), ! c_Int_Onumber__class_Onumber__of( X, Z
% 1.28/1.66 ) = c_Int_Onumber__class_Onumber__of( X, Y ), c_Int_Oiszero( X,
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 1.28/1.66 tc_Int_Oint, Z, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) ) ) }
% 1.28/1.66 .
% 1.28/1.66 { ! class_Int_Onumber__ring( X ), ! c_Int_Oiszero( X,
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( X, c_Groups_Oplus__class_Oplus(
% 1.28/1.66 tc_Int_Oint, Z, c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, Y ) ) ) ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( X, Z ) =
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( X, Y ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Z ), c_Int_Onumber__class_Onumber__of
% 1.28/1.66 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) = hAPP( hAPP
% 1.28/1.66 ( c_Power_Opower__class_Opower( X ), Y ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.66 c_Int_OPls ) ) ) ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.66 ), Z = Y }.
% 1.28/1.66 { ! class_Rings_Olinordered__semidom( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Z ), c_Int_Onumber__class_Onumber__of
% 1.28/1.66 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 1.28/1.66 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.66 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 1.28/1.66 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 1.28/1.66 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 1.28/1.66 c_Int_OBit1( c_Int_OPls ) ) ) ), X ) ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt(
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 1.28/1.66 c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.66 c_Int_OPls ) ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.28/1.66 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 1.28/1.66 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.28/1.66 ( X, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Z ), c_Int_Onumber__class_Onumber__of
% 1.28/1.66 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 1.28/1.66 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ),
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.66 }.
% 1.28/1.66 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.28/1.66 ( X, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Z ), c_Int_Onumber__class_Onumber__of
% 1.28/1.66 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 1.28/1.66 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ),
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.66 }.
% 1.28/1.66 { ! class_Rings_Olinordered__idom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.28/1.66 X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.28/1.66 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.66 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.66 c_Int_OPls ) ) ) ) ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 1.28/1.66 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 1.28/1.66 ( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.66 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.66 c_Int_OPls ) ) ) ) ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.28/1.66 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.66 c_Int_OPls ) ) ) ), Z ) ), c_Groups_Ozero__class_Ozero( X ) ), Y =
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 1.28/1.66 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Z ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.66 c_Int_OPls ) ) ) ), Y ) ) ) }.
% 1.28/1.66 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.66 c_Int_OPls ) ) ) ) = X, ! c_Orderings_Oord__class_Oless__eq(
% 1.28/1.66 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.28/1.66 c_NthRoot_Osqrt( X ) = Y }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) )
% 1.28/1.66 , c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1
% 1.28/1.66 ( c_Int_OPls ) ) ) ) = X }.
% 1.28/1.66 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.28/1.66 c_NthRoot_Osqrt( X ) ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 1.28/1.66 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) = X,
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) )
% 1.28/1.66 , c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1
% 1.28/1.66 ( c_Int_OPls ) ) ) ) = X }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_NthRoot_Osqrt(
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, T, Z ) ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.66 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.28/1.66 tc_RealDef_Oreal ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X )
% 1.28/1.66 ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 1.28/1.66 c_Int_OBit1( c_Int_OPls ) ) ) ) ) ), c_Groups_Oplus__class_Oplus(
% 1.28/1.66 tc_RealDef_Oreal, c_NthRoot_Osqrt( c_Groups_Oplus__class_Oplus(
% 1.28/1.66 tc_RealDef_Oreal, hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.28/1.66 tc_RealDef_Oreal ), T ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 1.28/1.66 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.66 c_Int_OPls ) ) ) ) ) ), c_NthRoot_Osqrt( c_Groups_Oplus__class_Oplus(
% 1.28/1.66 tc_RealDef_Oreal, hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.28/1.66 tc_RealDef_Oreal ), Z ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 1.28/1.66 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), X ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.66 c_Int_OPls ) ) ) ) ) ) ) ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_NthRoot_Osqrt(
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), X ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.66 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.28/1.66 tc_RealDef_Oreal ), Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 1.28/1.66 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_NthRoot_Osqrt(
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.66 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.28/1.66 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 1.28/1.66 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) ) }.
% 1.28/1.66 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_RealVector_Onorm__class_Onorm( X, Z ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 1.28/1.66 c_RealVector_Onorm__class_Onorm( X, T ) ) ), Z =
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.66 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 1.28/1.66 , Y ) }.
% 1.28/1.66 { c_Complex_Ocomplex_Ocomplex__rec( T, Z, c_Complex_Ocomplex_OComplex( Y, X
% 1.28/1.66 ) ) = hAPP( hAPP( Z, Y ), X ) }.
% 1.28/1.66 { c_Complex_Ocomplex_Ocomplex__case( T, Z, c_Complex_Ocomplex_OComplex( Y,
% 1.28/1.66 X ) ) = hAPP( hAPP( Z, Y ), X ) }.
% 1.28/1.66 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.28/1.66 ), c_Groups_Ouminus__class_Ouminus( X, c_Groups_Oone__class_Oone( X ) )
% 1.28/1.66 ), c_Nat_OSuc( hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.28/1.66 , c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1
% 1.28/1.66 ( c_Int_OPls ) ) ) ), Y ) ) ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.66 c_Groups_Oone__class_Oone( X ) ) }.
% 1.28/1.66 { c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ), X =
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.66 c_Int_OPls ) ) ) ), skol3( X ) ), c_Groups_Oone__class_Oone( tc_Int_Oint
% 1.28/1.66 ) ) }.
% 1.28/1.66 { ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.66 c_Int_OPls ) ) ) ), Y ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ), !
% 1.28/1.66 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.28/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.28/1.66 ), X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.28/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.28/1.66 ), X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 1.28/1.66 ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.28/1.66 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 1.28/1.66 c_Nat_OSuc( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X )
% 1.28/1.66 }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ),
% 1.28/1.66 c_Nat_OSuc( X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = c_Nat_OSuc( X
% 1.28/1.66 ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.28/1.66 { ! Y = c_Nat_OSuc( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 1.28/1.66 , c_Nat_OSuc( X ) ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), Y ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( X ), X ) }
% 1.28/1.66 .
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol4( X, Y ) ) }.
% 1.28/1.66 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ) }.
% 1.28/1.66 { ! X = c_Nat_OSuc( X ) }.
% 1.28/1.66 { ! c_Nat_OSuc( X ) = X }.
% 1.28/1.66 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 1.28/1.66 { ! Y = X, c_Nat_OSuc( Y ) = c_Nat_OSuc( X ) }.
% 1.28/1.66 { ! c_Nat_OSuc( Y ) = c_Nat_OSuc( X ), Y = X }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, c_Int_OPls ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 1.28/1.66 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.66 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.28/1.66 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.66 { ! c_Nat_OSuc( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.66 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.28/1.66 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) = c_Nat_OSuc( X ) }.
% 1.28/1.66 { ! hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) =
% 1.28/1.66 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = c_Nat_OSuc(
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.66 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.66 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP(
% 1.28/1.66 hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc
% 1.28/1.66 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.66 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), c_Nat_OSuc(
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X ) = c_Nat_OSuc(
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.66 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.28/1.66 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) =
% 1.28/1.66 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.28/1.66 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) =
% 1.28/1.66 c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.66 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.28/1.66 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z
% 1.28/1.66 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.66 c_Nat_OSuc( Z ) ), X ), Y = X }.
% 1.28/1.66 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.66 c_Nat_OSuc( Z ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.66 tc_Nat_Onat ), c_Nat_OSuc( Z ) ), X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 1.28/1.66 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 1.28/1.66 ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 1.28/1.66 c_Int_OBit1( X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 1.28/1.66 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 1.28/1.66 ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 1.28/1.66 c_Int_OBit1( X ) ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OPls )
% 1.28/1.66 }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 1.28/1.66 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 1.28/1.66 ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 1.28/1.66 c_Int_OBit0( X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 1.28/1.66 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 1.28/1.66 ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 1.28/1.66 c_Int_OBit0( X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol5( X, Y ) ) }.
% 1.28/1.66 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) }.
% 1.28/1.66 { c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.28/1.66 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 1.28/1.66 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.28/1.66 { c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ),
% 1.28/1.66 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ),
% 1.28/1.66 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) ) }.
% 1.28/1.66 { c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ), !
% 1.28/1.66 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ), !
% 1.28/1.66 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) ) }.
% 1.28/1.66 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ),
% 1.28/1.66 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ), !
% 1.28/1.66 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) ) }.
% 1.28/1.66 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ), !
% 1.28/1.66 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ),
% 1.28/1.66 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) ) }.
% 1.28/1.66 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ), alpha3( X, Y ),
% 1.28/1.66 alpha36( X, Y ) }.
% 1.28/1.66 { ! alpha3( X, Y ), c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 1.28/1.66 { ! alpha36( X, Y ), c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 1.28/1.66 { ! alpha36( X, Y ), ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ) }
% 1.28/1.66 .
% 1.28/1.66 { ! alpha36( X, Y ), ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ) }
% 1.28/1.66 .
% 1.28/1.66 { c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ),
% 1.28/1.66 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ), alpha36( X, Y ) }.
% 1.28/1.66 { ! alpha3( X, Y ), c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ) }.
% 1.28/1.66 { ! alpha3( X, Y ), c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ) }.
% 1.28/1.66 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ), !
% 1.28/1.66 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ), alpha3( X, Y ) }.
% 1.28/1.66 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ),
% 1.28/1.66 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ),
% 1.28/1.66 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ) }.
% 1.28/1.66 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ),
% 1.28/1.66 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.28/1.66 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ),
% 1.28/1.66 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.28/1.66 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ),
% 1.28/1.66 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 1.28/1.66 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ),
% 1.28/1.66 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.28/1.66 { c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ),
% 1.28/1.66 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ), !
% 1.28/1.66 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 1.28/1.66 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 1.28/1.66 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ),
% 1.28/1.66 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ) }.
% 1.28/1.66 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ),
% 1.28/1.66 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint,
% 1.28/1.66 c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) ) }.
% 1.28/1.66 { c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ), !
% 1.28/1.66 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 1.28/1.66 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.66 c_Nat_OSuc( Y ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.66 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.28/1.66 , Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X )
% 1.28/1.66 , Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.28/1.66 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) }.
% 1.28/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) = hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.28/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 1.28/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( Y ) ) }.
% 1.28/1.66 { ! c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ), alpha4( X, Y ), alpha37
% 1.28/1.66 ( X, Y ) }.
% 1.28/1.66 { ! alpha4( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.28/1.66 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 1.28/1.66 { ! alpha37( X, Y ), c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.28/1.66 ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) }.
% 1.28/1.66 { ! alpha37( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.66 { ! alpha37( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.28/1.66 tc_Nat_Onat ) ) }.
% 1.28/1.66 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha37( X, Y ) }.
% 1.28/1.66 { ! alpha4( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.28/1.66 tc_Nat_Onat ) ) }.
% 1.28/1.66 { ! alpha4( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.66 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha4( X, Y ) }.
% 1.28/1.66 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = c_Nat_OSuc(
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha5( X, Y ), alpha38( X
% 1.28/1.66 , Y ) }.
% 1.28/1.66 { ! alpha5( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.28/1.66 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.66 { ! alpha38( X, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.28/1.66 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.66 { ! alpha38( X, Y ), Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.66 { ! alpha38( X, Y ), X = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.28/1.66 tc_Nat_Onat ) ) }.
% 1.28/1.66 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X = c_Nat_OSuc(
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), alpha38( X, Y ) }.
% 1.28/1.66 { ! alpha5( X, Y ), Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.28/1.66 tc_Nat_Onat ) ) }.
% 1.28/1.66 { ! alpha5( X, Y ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.66 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha5( X, Y ) }.
% 1.28/1.66 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.28/1.66 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y = c_Nat_OSuc
% 1.28/1.66 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.66 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.28/1.66 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X = c_Nat_OSuc
% 1.28/1.66 ( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.66 { ! Y = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), ! X =
% 1.28/1.66 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = c_Nat_OSuc(
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.66 { c_Groups_Oone__class_Oone( tc_Nat_Onat ) = c_Nat_OSuc(
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), c_Nat_OSuc
% 1.28/1.66 ( X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Y )
% 1.28/1.66 ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OBit1
% 1.28/1.66 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X )
% 1.28/1.66 }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OBit1(
% 1.28/1.66 X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 1.28/1.66 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 1.28/1.66 ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 1.28/1.66 c_Int_OBit1( X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 1.28/1.66 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 1.28/1.66 ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( Y ),
% 1.28/1.66 c_Int_OBit1( X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OBit0
% 1.28/1.66 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X )
% 1.28/1.66 }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OBit0(
% 1.28/1.66 X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( X ),
% 1.28/1.66 c_Int_OPls ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.28/1.66 c_Int_OPls ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( X ),
% 1.28/1.66 c_Int_OPls ) }.
% 1.28/1.66 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.28/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X ) }.
% 1.28/1.66 { c_Nat_OSuc( X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.28/1.66 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.28/1.66 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ),
% 1.28/1.66 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ) }.
% 1.28/1.66 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ), ! X =
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.66 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, Y ), X =
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.66 c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( tc_Int_Oint ), Y ), X ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semidom( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ) ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.66 ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( T ) ) = hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( T ) ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.28/1.66 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.66 X ), Y ), Z = Y }.
% 1.28/1.66 { ! class_Rings_Oidom( X ), ! hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.28/1.66 , Z ), c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.28/1.66 ) ) ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc(
% 1.28/1.66 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), Z = Y, Z =
% 1.28/1.66 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.28/1.66 { ! class_Rings_Oidom( X ), ! Z = Y, hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( c_Nat_OSuc(
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.28/1.66 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ouminus__class_Ouminus( X, Y ),
% 1.28/1.66 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc(
% 1.28/1.66 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) = hAPP( hAPP
% 1.28/1.66 ( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( c_Nat_OSuc(
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.28/1.66 { ! c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) =
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ),
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) =
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) }.
% 1.28/1.66 { ! c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OPls ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.66 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.66 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.28/1.66 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.28/1.66 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.28/1.66 hAPP( Y, U ) ) }.
% 1.28/1.66 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.66 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.28/1.66 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.66 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 1.28/1.66 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.66 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.28/1.66 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.66 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 1.28/1.66 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.66 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.28/1.66 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 1.28/1.66 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.28/1.66 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 1.28/1.66 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.28/1.66 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.28/1.66 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.66 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 1.28/1.66 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.66 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.28/1.66 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.28/1.66 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.28/1.66 hAPP( Y, U ) ) }.
% 1.28/1.66 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.66 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.28/1.66 ( X, Z, Y ) }.
% 1.28/1.66 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.28/1.66 ( X, Y, Z ) }.
% 1.28/1.66 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.66 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 1.28/1.66 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.66 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.28/1.66 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.28/1.66 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.28/1.66 hAPP( Y, U ) ) }.
% 1.28/1.66 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 1.28/1.66 ( Z, skol6( X, Y, Z ) ), hAPP( Y, skol6( X, Y, Z ) ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semidom( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.66 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone
% 1.28/1.66 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ), Y ) }.
% 1.28/1.66 { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OPls )
% 1.28/1.66 ) = c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.66 { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1( c_Int_OBit1(
% 1.28/1.66 c_Int_OPls ) ) ) = c_Nat_OSuc( c_Nat_OSuc( c_Nat_OSuc(
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ) }.
% 1.28/1.66 { c_Nat_OSuc( c_Nat_OSuc( c_Nat_OSuc( X ) ) ) = c_Groups_Oplus__class_Oplus
% 1.28/1.66 ( tc_Nat_Onat, c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit1
% 1.28/1.66 ( c_Int_OBit1( c_Int_OPls ) ) ), X ) }.
% 1.28/1.66 { c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) =
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.66 c_Int_OPls ) ) ) }.
% 1.28/1.66 { c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.66 c_Int_OPls ) ) ) = c_Nat_OSuc( c_Nat_OSuc( c_Groups_Ozero__class_Ozero(
% 1.28/1.66 tc_Nat_Onat ) ) ) }.
% 1.28/1.66 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X,
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.66 c_Int_OPls ) ) ) ) = c_Nat_OSuc( c_Nat_OSuc( X ) ) }.
% 1.28/1.66 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.66 c_Int_OPls ) ) ), X ) = c_Nat_OSuc( c_Nat_OSuc( X ) ) }.
% 1.28/1.66 { ! c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X ), X = hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.66 c_Int_OPls ) ) ) ), skol7( X ) ) }.
% 1.28/1.66 { ! X = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.66 c_Int_OPls ) ) ) ), Y ), c_Parity_Oeven__odd__class_Oeven( tc_Int_Oint, X
% 1.28/1.66 ) }.
% 1.28/1.66 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.66 c_Int_OPls ) ) ) ), Y ) ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.66 X ), Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Z ), Y ) ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.66 c_Int_OPls ) ) ) ) ) }.
% 1.28/1.66 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Z ), c_Nat_OSuc( hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.66 c_Int_OPls ) ) ) ), Y ) ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.66 X ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Z ), Y ) ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.28/1.66 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.66 c_Int_OPls ) ) ) ), Z ) ) ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.66 c_Int_OPls ) ) ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( X ) ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit1( X ) ) ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit1( c_Int_OBit1(
% 1.28/1.66 c_Int_OPls ) ) ) ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OPls ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 1.28/1.66 tc_Int_Oint ) ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.28/1.66 tc_Int_Oint ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.28/1.66 tc_Int_Oint, X, Y ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.66 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.28/1.66 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( hAPP(
% 1.28/1.66 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.66 c_Int_OPls ) ) ) ), Z ) ) ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.66 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 1.28/1.66 ( X ), c_Int_Onumber__class_Onumber__of( X, c_Int_OMin ) ), c_Nat_OSuc(
% 1.28/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.66 c_Int_OPls ) ) ) ), Y ) ) ) = c_Int_Onumber__class_Onumber__of( X,
% 1.28/1.66 c_Int_OMin ) }.
% 1.28/1.66 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Power_Opower__class_Opower
% 1.28/1.66 ( X ), c_Int_Onumber__class_Onumber__of( X, c_Int_OMin ) ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.66 c_Int_OPls ) ) ) ), Y ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.66 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 1.28/1.66 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.28/1.66 X ) ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( X ) ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.66 tc_Nat_Onat ), c_Nat_OSuc( X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.66 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.66 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.28/1.66 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.28/1.66 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.28/1.66 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.66 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.66 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.66 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.66 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.66 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.66 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.66 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.66 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 1.28/1.66 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 1.28/1.66 .
% 1.28/1.66 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 1.28/1.66 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 1.28/1.66 }.
% 1.28/1.66 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.28/1.66 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 1.28/1.66 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 1.28/1.66 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.28/1.66 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.66 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.28/1.66 , ! Z = Y }.
% 1.28/1.66 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.66 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.66 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.66 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.66 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.66 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.28/1.66 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.66 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.66 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.66 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.28/1.66 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.28/1.66 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.66 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.28/1.66 ( X, Z, Y ) }.
% 1.28/1.66 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.28/1.66 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.28/1.66 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.66 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.66 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.28/1.66 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 1.28/1.66 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.28/1.66 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.66 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.28/1.66 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.66 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.28/1.66 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.66 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.66 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.66 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.66 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.66 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.66 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.28/1.66 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.66 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.66 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.66 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.28/1.66 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.66 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.66 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.66 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.66 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.66 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.28/1.66 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.28/1.66 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.28/1.66 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.66 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.28/1.66 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.28/1.66 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ),
% 1.28/1.66 c_Int_OMin ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.28/1.66 c_Int_OMin ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OMin ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ), c_Int_OMin
% 1.28/1.66 ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OMin, c_Int_OBit0
% 1.28/1.66 ( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OMin, c_Int_OBit0(
% 1.28/1.66 X ) ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OMin, c_Int_OMin )
% 1.28/1.66 }.
% 1.28/1.66 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.28/1.66 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.66 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.28/1.66 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.66 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.66 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.66 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), Y = X,
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), Y = X }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 1.28/1.66 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y ),
% 1.28/1.66 c_NthRoot_Osqrt( X ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 Y, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y ),
% 1.28/1.66 c_NthRoot_Osqrt( X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( Y ),
% 1.28/1.66 c_NthRoot_Osqrt( X ) ) }.
% 1.28/1.66 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 1.28/1.66 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 1.28/1.66 tc_Int_Oint, Y, c_Int_OPls ) }.
% 1.28/1.66 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 1.28/1.66 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.66 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.28/1.66 ( tc_Int_Oint, c_Int_OPls, Y ) }.
% 1.28/1.66 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, Y ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.66 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.66 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.66 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.66 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 1.28/1.66 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.66 ( tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.66 tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.28/1.66 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 1.28/1.66 ), c_Int_Onumber__class_Onumber__of( X, Y ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y ) }.
% 1.28/1.66 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 1.28/1.66 ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, c_Int_OBit1( X
% 1.28/1.66 ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, c_Int_OBit1( X )
% 1.28/1.66 ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ),
% 1.28/1.66 c_Int_OMin ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OMin )
% 1.28/1.66 }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OMin ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ), c_Int_OMin
% 1.28/1.66 ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, c_Int_OPls ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OMin ) }
% 1.28/1.66 .
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, c_Int_OBit0( X
% 1.28/1.66 ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, c_Int_OBit0( X )
% 1.28/1.66 ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OMin, c_Int_OMin ) }
% 1.28/1.66 .
% 1.28/1.66 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.28/1.66 X, Y, Z ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, Y ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.28/1.66 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 1.28/1.66 .
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.28/1.66 ( tc_Nat_Onat, Y, X ), Y ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.28/1.66 ( tc_Nat_Onat, Y, X ), X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.28/1.66 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 1.28/1.66 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.66 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 1.28/1.66 .
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.66 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 1.28/1.66 .
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.28/1.66 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 1.28/1.66 .
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.28/1.66 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 1.28/1.66 , X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ),
% 1.28/1.66 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 1.28/1.66 .
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit0
% 1.28/1.66 ( X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ),
% 1.28/1.66 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 1.28/1.66 .
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit0
% 1.28/1.66 ( X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OPls ) }
% 1.28/1.66 .
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ),
% 1.28/1.66 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 1.28/1.66 .
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit1
% 1.28/1.66 ( X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ),
% 1.28/1.66 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 1.28/1.66 .
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit1
% 1.28/1.66 ( X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.66 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.66 tc_Nat_Onat ), X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.66 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 1.28/1.66 .
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.66 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.66 tc_Nat_Onat ), X ) }.
% 1.28/1.66 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 1.28/1.66 , c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.66 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, Y, Z ), c_Orderings_Oord__class_Oless(
% 1.28/1.66 X, c_Groups_Ouminus__class_Ouminus( X, Z ),
% 1.28/1.66 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.28/1.66 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Z )
% 1.28/1.66 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 1.28/1.66 ( X, Y ), Z ) }.
% 1.28/1.66 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.28/1.66 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus
% 1.28/1.66 ( X, Z ), Y ) }.
% 1.28/1.66 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.66 Y ) ), c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.66 c_Groups_Ouminus__class_Ouminus( X, Z ) ) }.
% 1.28/1.66 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.66 Z ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.66 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.28/1.66 { ! c_Int_OBit0( X ) = c_Int_OMin }.
% 1.28/1.66 { ! c_Int_OMin = c_Int_OBit0( X ) }.
% 1.28/1.66 { ! c_Int_OPls = c_Int_OMin }.
% 1.28/1.66 { ! c_Int_OMin = c_Int_OPls }.
% 1.28/1.66 { ! c_Int_OBit1( X ) = c_Int_OMin, X = c_Int_OMin }.
% 1.28/1.66 { ! X = c_Int_OMin, c_Int_OBit1( X ) = c_Int_OMin }.
% 1.28/1.66 { ! c_Int_OMin = c_Int_OBit1( X ), c_Int_OMin = X }.
% 1.28/1.66 { ! c_Int_OMin = X, c_Int_OMin = c_Int_OBit1( X ) }.
% 1.28/1.66 { c_Int_OBit1( c_Int_OMin ) = c_Int_OMin }.
% 1.28/1.66 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.28/1.66 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, T, Y ) }.
% 1.28/1.66 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 1.28/1.66 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.28/1.66 , Y, Z ) ) }.
% 1.28/1.66 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.28/1.66 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, Z, Y ) }.
% 1.28/1.66 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.28/1.66 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.28/1.66 , T, Y ) ) }.
% 1.28/1.66 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.28/1.66 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 1.28/1.66 , Y, T ) ) }.
% 1.28/1.66 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.28/1.66 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.28/1.66 , T, Y ) ) }.
% 1.28/1.66 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.66 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 1.28/1.66 , T ) ) }.
% 1.28/1.66 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 1.28/1.66 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, Z, Y ) }.
% 1.28/1.66 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.28/1.66 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, Z, Y ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ), alpha6( X, Y ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.28/1.66 { ! alpha6( X, Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) }.
% 1.28/1.66 { ! alpha6( X, Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), alpha6( X, Y ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ), alpha6( X
% 1.28/1.66 , Y ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 1.28/1.66 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), Z ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), c_Nat_OSuc( Y ) = X
% 1.28/1.66 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), X = Y }
% 1.28/1.66 .
% 1.28/1.66 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y = X }
% 1.28/1.66 .
% 1.28/1.66 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X,
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc
% 1.28/1.66 ( X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc( Y ), c_Nat_OSuc(
% 1.28/1.66 X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.28/1.66 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) )
% 1.28/1.66 }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.28/1.66 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.66 Y ) }.
% 1.28/1.66 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.28/1.66 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.66 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.66 Y ), ! Z = Y }.
% 1.28/1.66 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.66 Z ), ! Z = Y }.
% 1.28/1.66 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.28/1.66 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 1.28/1.66 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.66 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.66 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.66 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.28/1.66 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.66 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.28/1.66 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 1.28/1.66 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.28/1.66 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.66 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.28/1.66 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.66 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.28/1.66 , ! Z = Y }.
% 1.28/1.66 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.66 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.66 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.66 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.66 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.28/1.66 , ! Z = Y }.
% 1.28/1.66 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.28/1.66 , ! Y = Z }.
% 1.28/1.66 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.66 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.66 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.28/1.66 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.66 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 1.28/1.66 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.28/1.66 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 1.28/1.66 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.28/1.66 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 1.28/1.66 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.28/1.66 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.28/1.66 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.28/1.66 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.66 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.28/1.66 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.28/1.66 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.28/1.66 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.66 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.66 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.28/1.66 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.66 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.28/1.66 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.28/1.66 ( tc_Int_Oint, c_Int_OBit1( c_Int_OPls ), Y ) }.
% 1.28/1.66 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( c_Int_OPls ), Y
% 1.28/1.66 ), c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 1.28/1.66 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 1.28/1.66 ), c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless(
% 1.28/1.66 tc_Int_Oint, Y, c_Int_OBit1( c_Int_OPls ) ) }.
% 1.28/1.66 { ! class_Int_Onumber__ring( X ), ! class_Rings_Olinordered__idom( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OBit1( c_Int_OPls )
% 1.28/1.66 ), c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X
% 1.28/1.66 , Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 1.28/1.66 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.28/1.66 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.28/1.66 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.28/1.66 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 1.28/1.66 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.66 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.66 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.66 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.28/1.66 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.28/1.66 ( X ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.66 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.66 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.28/1.66 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.28/1.66 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 1.28/1.66 .
% 1.28/1.66 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.28/1.66 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.28/1.66 .
% 1.28/1.66 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.66 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.66 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.28/1.66 ( X ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.66 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.66 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.28/1.66 ( X ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.66 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.28/1.66 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.66 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.66 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.28/1.66 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha7( X, Y, Z, T ),
% 1.28/1.66 alpha39( X, Y, Z, T ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha7( X, Y, Z, T ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha39( X, Y, Z, T ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.66 { ! alpha39( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.66 { ! alpha39( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.66 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha39( X, Y, Z, T ) }.
% 1.28/1.66 { ! alpha7( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 1.28/1.66 { ! alpha7( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 1.28/1.66 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha7( X, Y, Z, T ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha8( X, Y, Z, T ),
% 1.28/1.66 alpha40( X, Y, Z, T ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha8( X, Y, Z, T ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha40( X, Y, Z, T ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.66 { ! alpha40( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.66 { ! alpha40( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.66 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha40( X, Y, Z, T ) }.
% 1.28/1.66 { ! alpha8( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.28/1.66 { ! alpha8( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.28/1.66 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha8( X, Y, Z, T ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.66 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.66 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.66 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 1.28/1.66 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.66 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.66 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 1.28/1.66 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.28/1.66 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 1.28/1.66 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.66 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.28/1.66 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.66 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.66 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.28/1.66 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.66 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 1.28/1.66 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.28/1.66 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.66 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.66 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.28/1.66 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.66 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 1.28/1.66 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 1.28/1.66 ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.66 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.28/1.66 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 1.28/1.66 ) ) }.
% 1.28/1.66 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 1.28/1.66 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.28/1.66 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 1.28/1.66 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 1.28/1.66 , Y, T ) ) }.
% 1.28/1.66 { ! class_Int_Onumber( X ), ! class_Orderings_Olinorder( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 1.28/1.66 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 1.28/1.66 ), c_Int_Onumber__class_Onumber__of( X, Z ) ) }.
% 1.28/1.66 { ! class_Int_Onumber( X ), ! class_Orderings_Olinorder( X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 1.28/1.66 ), c_Int_Onumber__class_Onumber__of( X, Z ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of( X
% 1.28/1.66 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 1.28/1.66 .
% 1.28/1.66 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.28/1.66 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.28/1.66 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.28/1.66 , Y ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.66 , Y ) }.
% 1.28/1.66 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.28/1.66 , Y ) }.
% 1.28/1.66 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.28/1.66 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.66 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ouminus__class_Ouminus( X, Y )
% 1.28/1.66 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.66 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.28/1.66 .
% 1.28/1.66 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.66 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.28/1.66 , Y, c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.28/1.66 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.66 c_Groups_Ouminus__class_Ouminus( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.66 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.66 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 1.28/1.66 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.28/1.66 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 1.28/1.66 ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 1.28/1.66 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( X ),
% 1.28/1.66 c_Int_OMin ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.28/1.66 c_Int_OMin ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OMin ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( X ),
% 1.28/1.66 c_Int_OMin ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OMin, c_Int_OBit1
% 1.28/1.66 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OMin, X )
% 1.28/1.66 }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OMin, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OMin, c_Int_OBit1(
% 1.28/1.66 X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, c_Int_OMin
% 1.28/1.66 ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OMin, c_Int_OPls )
% 1.28/1.66 }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( X ),
% 1.28/1.66 c_Int_OMin ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.28/1.66 c_Int_OMin ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, c_Int_OMin ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit0( X ),
% 1.28/1.66 c_Int_OMin ) }.
% 1.28/1.66 { ! c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OPls ) =
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OMin ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ),
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ),
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ),
% 1.28/1.66 c_Int_OPls ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls )
% 1.28/1.66 }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( X ), c_Int_OPls
% 1.28/1.66 ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( c_Nat_OSuc(
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) ), X =
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X = c_Nat_OSuc(
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.66 ( tc_Nat_Onat ), X ), X = c_Nat_OSuc( skol8( X ) ) }.
% 1.28/1.66 { ! X = c_Nat_OSuc( Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), X =
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.66 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc(
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ), Y =
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha9( X, Y ) }.
% 1.28/1.66 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.28/1.66 { ! alpha9( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.28/1.66 c_Nat_OSuc( X ) ) }.
% 1.28/1.66 { ! alpha9( X, Y ), Y = c_Nat_OSuc( skol9( Z, Y ) ) }.
% 1.28/1.66 { ! alpha9( X, Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol9( X, Y
% 1.28/1.66 ), X ) }.
% 1.28/1.66 { ! Y = c_Nat_OSuc( Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 1.28/1.66 ), alpha9( X, Y ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ),
% 1.28/1.66 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 1.28/1.66 .
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit0
% 1.28/1.66 ( X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ),
% 1.28/1.66 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 1.28/1.66 .
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit1( Y ), c_Int_OBit0
% 1.28/1.66 ( X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ),
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ),
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OBit0( X
% 1.28/1.66 ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OBit0( X )
% 1.28/1.66 ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ),
% 1.28/1.66 c_Int_OPls ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls )
% 1.28/1.66 }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( X ), c_Int_OPls
% 1.28/1.66 ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.66 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.66 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.66 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.28/1.66 tc_Nat_Onat, Y, X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.66 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.28/1.66 tc_Nat_Onat, Y, X ) ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc(
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), X = c_Nat_OSuc(
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol10( X, Y ) ) ) }.
% 1.28/1.66 { ! X = c_Nat_OSuc( c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ), X = Y }
% 1.28/1.66 .
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = Y,
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, c_Nat_OSuc( Y ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, c_Nat_OSuc( X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Nat_OSuc( Y ), X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.66 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.66 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.28/1.66 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.66 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.28/1.66 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.66 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.66 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.66 Y ), X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.66 tc_Nat_Onat ), Z ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.66 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.28/1.66 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.66 tc_Nat_Onat ), Y ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.66 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 1.28/1.66 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.66 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.28/1.66 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 1.28/1.66 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.66 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.28/1.66 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 1.28/1.66 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.28/1.66 { c_Int_OMin = c_Groups_Ouminus__class_Ouminus( tc_Int_Oint,
% 1.28/1.66 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.66 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.28/1.66 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 1.28/1.66 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ), X =
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.28/1.66 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 1.28/1.66 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), c_Int_OMin ), X
% 1.28/1.66 ) = c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.28/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.28/1.66 ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z ) ), Y ),
% 1.28/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Nat_OSuc( Z )
% 1.28/1.66 ), X ) ) }.
% 1.28/1.66 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 1.28/1.66 tc_RealDef_Oreal ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.28/1.66 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 1.28/1.66 .
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.28/1.66 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 1.28/1.66 = X }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.28/1.66 tc_Int_Oint ) ) ) }.
% 1.28/1.66 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.28/1.66 tc_Int_Oint ) ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }
% 1.28/1.66 .
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! c_NthRoot_Osqrt(
% 1.28/1.66 X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ),
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ),
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }
% 1.28/1.66 .
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ),
% 1.28/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 1.28/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 1.28/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt( X ),
% 1.28/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.66 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.28/1.66 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.66 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.66 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.66 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.28/1.66 ), X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.66 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.28/1.66 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.66 tc_Nat_Onat ), Y ) }.
% 1.28/1.66 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.66 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.28/1.66 ), X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.66 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.66 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.28/1.66 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 1.28/1.66 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.28/1.66 { ! class_Int_Onumber__ring( X ), ! c_Int_Oiszero( X,
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( X, c_Int_OMin ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.28/1.66 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.28/1.66 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.28/1.66 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.28/1.66 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.28/1.66 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.28/1.66 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.28/1.66 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.28/1.66 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.66 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.28/1.66 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.28/1.66 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.66 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.66 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.66 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.66 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.66 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.66 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.66 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.66 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.28/1.66 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.66 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.66 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.66 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.28/1.66 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.66 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.28/1.66 ) ) }.
% 1.28/1.66 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.66 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.28/1.66 ) ) }.
% 1.28/1.66 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.66 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.28/1.66 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 1.28/1.66 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.66 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.66 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.28/1.66 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 1.28/1.66 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.66 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.66 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.28/1.66 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.28/1.66 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.28/1.66 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.28/1.66 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.66 ( X ), Y ), c_Int_Onumber__class_Onumber__of( X, c_Int_OMin ) ) =
% 1.28/1.66 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.28/1.66 { ! class_Int_Onumber__ring( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.66 ( X ), c_Int_Onumber__class_Onumber__of( X, c_Int_OMin ) ), Y ) =
% 1.28/1.66 c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 1.28/1.66 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.66 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.28/1.66 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.66 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.28/1.66 { ! class_Int_Onumber__ring( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.66 c_Groups_Oone__class_Oone( X ) ) = c_Int_Onumber__class_Onumber__of( X,
% 1.28/1.66 c_Int_OMin ) }.
% 1.28/1.66 { ! class_Int_Onumber__ring( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.28/1.66 c_Int_OMin ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.66 c_Groups_Oone__class_Oone( X ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.28/1.66 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.28/1.66 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.28/1.66 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ) ) }.
% 1.28/1.66 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 1.28/1.66 { c_Groups_Ouminus__class_Ouminus( tc_Int_Oint, c_Int_OMin ) = c_Int_OBit1
% 1.28/1.66 ( c_Int_OPls ) }.
% 1.28/1.66 { hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), c_Nat_OSuc( X ) ) =
% 1.28/1.66 hAPP( hAPP( Z, Y ), hAPP( hAPP( c_Power_Opower_Opower( U, T, Z ), Y ), X
% 1.28/1.66 ) ) }.
% 1.28/1.66 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.28/1.66 c_RealVector_Onorm__class_Onorm( X, Y ) ), ! Y =
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.66 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless(
% 1.28/1.66 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.28/1.66 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.28/1.66 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) =
% 1.28/1.66 c_Groups_Oone__class_Oone( tc_Int_Oint ), alpha10( X, Y ), alpha41( X, Y
% 1.28/1.66 ) }.
% 1.28/1.66 { ! alpha10( X, Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint
% 1.28/1.66 ), Y ), X ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.28/1.66 { ! alpha41( X, Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint
% 1.28/1.66 ), Y ), X ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.28/1.66 { ! alpha41( X, Y ), Y = c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 1.28/1.66 c_Int_OMin ) }.
% 1.28/1.66 { ! alpha41( X, Y ), X = c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 1.28/1.66 c_Int_OMin ) }.
% 1.28/1.66 { ! Y = c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OMin ), ! X =
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OMin ), alpha41( X,
% 1.28/1.66 Y ) }.
% 1.28/1.66 { ! alpha10( X, Y ), Y = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.28/1.66 { ! alpha10( X, Y ), X = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.28/1.66 { ! Y = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! X =
% 1.28/1.66 c_Groups_Oone__class_Oone( tc_Int_Oint ), alpha10( X, Y ) }.
% 1.28/1.66 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 1.28/1.66 c_Groups_Oone__class_Oone( tc_Int_Oint ), X = c_Groups_Oone__class_Oone(
% 1.28/1.66 tc_Int_Oint ), X = c_Int_Onumber__class_Onumber__of( tc_Int_Oint,
% 1.28/1.66 c_Int_OMin ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OBit1( X
% 1.28/1.66 ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OPls, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OPls, c_Int_OBit1( X )
% 1.28/1.66 ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( X ),
% 1.28/1.66 c_Int_OPls ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls )
% 1.28/1.66 }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( X ),
% 1.28/1.66 c_Int_OPls ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ),
% 1.28/1.66 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 1.28/1.66 ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit1
% 1.28/1.66 ( X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ),
% 1.28/1.66 c_Int_OBit1( X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X
% 1.28/1.66 ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Int_OBit0( Y ), c_Int_OBit1
% 1.28/1.66 ( X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 1.28/1.66 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 1.28/1.66 .
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 1.28/1.66 c_Int_OBit0( X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 1.28/1.66 c_Int_OBit0( X ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }
% 1.28/1.66 .
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Int_OBit1( Y ),
% 1.28/1.66 c_Int_OBit0( X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), Y ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Nat_OSuc(
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 1.28/1.66 { ! class_RealVector_Oreal__normed__algebra( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.66 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.66 tc_Int_Oint ), X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.66 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.66 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.66 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.28/1.66 ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.66 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 1.28/1.66 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 1.28/1.66 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.66 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 1.28/1.66 ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.66 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 1.28/1.66 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 1.28/1.66 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.28/1.66 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.28/1.66 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.28/1.66 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.28/1.66 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.66 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.66 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 1.28/1.66 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.66 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.66 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 1.28/1.66 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.66 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 1.28/1.66 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 1.28/1.66 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.28/1.66 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, U
% 1.28/1.66 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, T ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.28/1.66 tc_Int_Oint ) ), X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.28/1.66 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 1.28/1.66 }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.28/1.66 tc_Int_Oint ) ), X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.28/1.66 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 1.28/1.66 }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.28/1.66 tc_Int_Oint ) ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ), X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 1.28/1.66 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 1.28/1.66 c_Groups_Ouminus__class_Ouminus( tc_RealDef_Oreal, Y ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.66 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.28/1.66 , Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 1.28/1.66 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 1.28/1.66 { ! c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) =
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 1.28/1.66 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.66 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Y ), c_Nat_OSuc( Z ) ),
% 1.28/1.66 c_Groups_Oone__class_Oone( X ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.28/1.66 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.66 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ),
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ),
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Int_OPls ),
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.66 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.28/1.66 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ), U ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 1.28/1.66 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 1.28/1.66 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 1.28/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.28/1.66 tc_Nat_Onat ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0
% 1.28/1.66 ( c_Int_OBit1( c_Int_OPls ) ) ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, c_Int_OPls ), hAPP( hAPP
% 1.28/1.66 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Z ) ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ), X ) ) =
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, c_Int_OPls ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Z ) ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ), X ) ) = hAPP( hAPP
% 1.28/1.66 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ) ), X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ), hAPP( hAPP
% 1.28/1.66 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, c_Int_OPls ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, Y ) ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, X ) ) =
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.66 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.66 c_Int_OPls ) ) ) ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.66 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 1.28/1.66 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ), ! Y =
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero( X
% 1.28/1.66 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.66 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.66 c_Int_OPls ) ) ) ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.66 c_Int_OPls ) ) ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.28/1.66 c_Nat_OSuc( c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_NthRoot_Osqrt(
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 1.28/1.66 c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_NthRoot_Osqrt(
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 1.28/1.66 c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.28/1.66 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.66 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.66 c_Int_OPls ) ) ) ) ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.66 Z, Y ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.66 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Z ), c_Int_Onumber__class_Onumber__of
% 1.28/1.66 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Y ), c_Int_Onumber__class_Onumber__of
% 1.28/1.66 ( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ),
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.66 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 1.28/1.66 ( hAPP( c_Power_Opower__class_Opower( X ), Z ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.66 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.66 c_Int_OPls ) ) ) ) ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__idom( X ), Z = c_Groups_Ozero__class_Ozero( X
% 1.28/1.66 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Power_Opower__class_Opower
% 1.28/1.66 ( X ), Z ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 1.28/1.66 c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower
% 1.28/1.66 ( X ), Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 1.28/1.66 c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) }.
% 1.28/1.66 { ! class_Rings_Olinordered__idom( X ), Y = c_Groups_Ozero__class_Ozero( X
% 1.28/1.66 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.66 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Power_Opower__class_Opower
% 1.28/1.66 ( X ), Z ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 1.28/1.66 c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower
% 1.28/1.66 ( X ), Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0(
% 1.28/1.66 c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Int_Oint, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.66 c_Int_OPls ) ) ) ), X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 1.28/1.66 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), c_NthRoot_Osqrt( X ) )
% 1.28/1.66 , c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1
% 1.28/1.66 ( c_Int_OPls ) ) ) ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.66 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.28/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.28/1.66 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.28/1.66 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.28/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 1.28/1.66 ( tc_Int_Oint ), Y ) }.
% 1.28/1.66 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.28/1.66 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.28/1.66 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.66 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.28/1.66 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 1.28/1.66 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.28/1.66 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.28/1.66 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.28/1.66 { alpha101( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.28/1.66 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.28/1.66 { alpha101( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP(
% 1.28/1.66 hAPP( X, Y ), Z ) ) }.
% 1.28/1.66 { ! alpha101( X, Y, Z ), alpha102( X, Y, Z ), Z = Y }.
% 1.28/1.66 { ! alpha101( X, Y, Z ), alpha102( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ),
% 1.28/1.66 Z ) ) }.
% 1.28/1.66 { ! alpha102( X, Y, Z ), alpha101( X, Y, Z ) }.
% 1.28/1.66 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha101( X, Y, Z ) }.
% 1.28/1.66 { ! alpha102( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 1.28/1.66 }.
% 1.28/1.66 { ! alpha102( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 1.28/1.66 X, Y ), Z ) ), alpha102( X, Y, Z ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.28/1.66 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.28/1.66 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.66 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.28/1.66 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.28/1.66 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.66 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 1.28/1.66 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.28/1.66 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.28/1.66 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.28/1.66 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.28/1.66 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.66 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.28/1.66 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 1.28/1.66 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.66 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 1.28/1.66 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y,
% 1.28/1.66 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X,
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 1.28/1.66 c_Int_OBit1( c_Int_OPls ) ) ) ) ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.66 tc_RealDef_Oreal, Z, c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X
% 1.28/1.66 , c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 1.28/1.66 c_Int_OBit1( c_Int_OPls ) ) ) ) ), ! c_Orderings_Oord__class_Oless__eq(
% 1.28/1.66 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ),
% 1.28/1.66 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_NthRoot_Osqrt(
% 1.28/1.66 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.66 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.28/1.66 tc_RealDef_Oreal ), Z ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 1.28/1.66 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ), X ) }.
% 1.28/1.66 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.66 , ! T = c_Rings_Oinverse__class_Odivide( X, Z, Y ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 1.28/1.66 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.66 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 1.28/1.66 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.28/1.66 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.66 , ! c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z, T = hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.28/1.66 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.66 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.28/1.66 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 1.28/1.66 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.66 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.28/1.66 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 1.28/1.66 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.66 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 1.28/1.66 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.28/1.66 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.66 , ! c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 1.28/1.66 c_Groups_Oone__class_Oone( X ), Z = Y }.
% 1.28/1.66 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.66 , ! Z = Y, c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 1.28/1.66 c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.66 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.66 , c_Rings_Oinverse__class_Odivide( X, Y, Y ) = c_Groups_Oone__class_Oone
% 1.28/1.66 ( X ) }.
% 1.28/1.66 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 1.28/1.66 Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.66 { ! class_Rings_Odivision__ring__inverse__zero( X ), Y =
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 1.28/1.66 Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.28/1.66 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.66 , c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.66 , Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 1.28/1.66 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.28/1.66 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.66 , c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X
% 1.28/1.66 , Z ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 1.28/1.66 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.28/1.66 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.28/1.66 hAPP( c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide
% 1.28/1.66 ( X, T, Y ) ), Z ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.28/1.66 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.28/1.66 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), hAPP
% 1.28/1.66 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.66 c_Groups_Oone__class_Oone( X ), Z ) ), Y ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.28/1.66 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ), alpha11( X,
% 1.28/1.66 Y ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.28/1.66 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ), alpha42( X,
% 1.28/1.66 Y ) }.
% 1.28/1.66 { ! alpha11( X, Y ), ! alpha42( X, Y ), c_Orderings_Oord__class_Oless__eq(
% 1.28/1.66 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.28/1.66 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ) }.
% 1.28/1.66 { ! alpha42( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), alpha42( X, Y ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), alpha42( X, Y ) }.
% 1.28/1.66 { ! alpha11( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y
% 1.28/1.66 , c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.28/1.66 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), alpha11( X, Y ) }.
% 1.28/1.66 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), alpha11( X, Y ) }.
% 1.28/1.66 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 1.28/1.66 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 1.28/1.66 X, Z ) ) = Y, alpha43( X, Y, Z, T ) }.
% 1.28/1.66 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 1.28/1.66 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 1.28/1.66 X, Z ) ) = Y, alpha12( X, Y, Z ) }.
% 1.28/1.66 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 1.28/1.66 alpha43( X, Y, Z, T ), ! alpha12( X, Y, Z ),
% 1.28/1.66 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 1.28/1.66 X, Z ) ) = Y }.
% 1.28/1.66 { ! alpha43( X, Y, Z, T ), c_Int_Onumber__class_Onumber__of( X, Z ) =
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ), T = hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 1.28/1.66 ( X, Z ) ) }.
% 1.28/1.66 { ! c_Int_Onumber__class_Onumber__of( X, Z ) = c_Groups_Ozero__class_Ozero
% 1.28/1.66 ( X ), alpha43( X, Y, Z, T ) }.
% 1.28/1.66 { ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( X, Z ) ), alpha43( X, Y, Z, T ) }.
% 1.28/1.66 { ! alpha12( X, Y, Z ), ! c_Int_Onumber__class_Onumber__of( X, Z ) =
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 1.28/1.66 .
% 1.28/1.66 { c_Int_Onumber__class_Onumber__of( X, Z ) = c_Groups_Ozero__class_Ozero( X
% 1.28/1.66 ), alpha12( X, Y, Z ) }.
% 1.28/1.66 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha12( X, Y, Z ) }.
% 1.28/1.66 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 1.28/1.66 c_Rings_Oinverse__class_Odivide( X, T, Z ) =
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( X, Y ), alpha44( X, Y, Z, T ) }.
% 1.28/1.66 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 1.28/1.66 c_Rings_Oinverse__class_Odivide( X, T, Z ) =
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( X, Y ), alpha13( X, Y, Z ) }.
% 1.28/1.66 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 1.28/1.66 alpha44( X, Y, Z, T ), ! alpha13( X, Y, Z ),
% 1.28/1.66 c_Rings_Oinverse__class_Odivide( X, T, Z ) =
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( X, Y ) }.
% 1.28/1.66 { ! alpha44( X, Y, Z, T ), Z = c_Groups_Ozero__class_Ozero( X ), T = hAPP(
% 1.28/1.66 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( X, Y ) ), Z ) }.
% 1.28/1.66 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha44( X, Y, Z, T ) }.
% 1.28/1.66 { ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( X, Y ) ), Z ), alpha44( X, Y, Z, T ) }
% 1.28/1.66 .
% 1.28/1.66 { ! alpha13( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.28/1.66 ) }.
% 1.28/1.66 { Z = c_Groups_Ozero__class_Ozero( X ), alpha13( X, Y, Z ) }.
% 1.28/1.66 { ! c_Int_Onumber__class_Onumber__of( X, Y ) = c_Groups_Ozero__class_Ozero
% 1.28/1.66 ( X ), alpha13( X, Y, Z ) }.
% 1.28/1.66 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( X, T ) =
% 1.28/1.66 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha45( X, Y, Z, T ) }.
% 1.28/1.66 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( X, T ) =
% 1.28/1.66 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha14( X, Y, T ) }.
% 1.28/1.66 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 1.28/1.66 alpha45( X, Y, Z, T ), ! alpha14( X, Y, T ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( X, T ) =
% 1.28/1.66 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.28/1.66 { ! alpha45( X, Y, Z, T ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP
% 1.28/1.66 ( c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X
% 1.28/1.66 , T ) ), Y ) = Z }.
% 1.28/1.66 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha45( X, Y, Z, T ) }.
% 1.28/1.66 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( X, T ) ), Y ) = Z, alpha45( X, Y, Z, T
% 1.28/1.66 ) }.
% 1.28/1.66 { ! alpha14( X, Y, Z ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( X, Z ) = c_Groups_Ozero__class_Ozero( X
% 1.28/1.66 ) }.
% 1.28/1.66 { Y = c_Groups_Ozero__class_Ozero( X ), alpha14( X, Y, Z ) }.
% 1.28/1.66 { ! c_Int_Onumber__class_Onumber__of( X, Z ) = c_Groups_Ozero__class_Ozero
% 1.28/1.66 ( X ), alpha14( X, Y, Z ) }.
% 1.28/1.66 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), ! T
% 1.28/1.66 = c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of
% 1.28/1.66 ( X, Y ) ), alpha46( X, Y, Z, T ) }.
% 1.28/1.66 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), ! T
% 1.28/1.66 = c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of
% 1.28/1.66 ( X, Y ) ), alpha15( X, Y, T ) }.
% 1.28/1.66 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber( X ), !
% 1.28/1.66 alpha46( X, Y, Z, T ), ! alpha15( X, Y, T ), T =
% 1.28/1.66 c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of(
% 1.28/1.66 X, Y ) ) }.
% 1.28/1.66 { ! alpha46( X, Y, Z, T ), c_Int_Onumber__class_Onumber__of( X, Y ) =
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 1.28/1.66 ( X, Y ) ) = Z }.
% 1.28/1.66 { ! c_Int_Onumber__class_Onumber__of( X, Y ) = c_Groups_Ozero__class_Ozero
% 1.28/1.66 ( X ), alpha46( X, Y, Z, T ) }.
% 1.28/1.66 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 1.28/1.66 c_Int_Onumber__class_Onumber__of( X, Y ) ) = Z, alpha46( X, Y, Z, T ) }.
% 1.28/1.66 { ! alpha15( X, Y, Z ), ! c_Int_Onumber__class_Onumber__of( X, Y ) =
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.28/1.66 .
% 1.28/1.66 { c_Int_Onumber__class_Onumber__of( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.28/1.66 ), alpha15( X, Y, Z ) }.
% 1.28/1.66 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha15( X, Y, Z ) }.
% 1.28/1.66 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X, T
% 1.28/1.66 , Z ) ), Y ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.66 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.28/1.66 { c_NthRoot_Osqrt( c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X
% 1.28/1.66 ) ) = c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, c_NthRoot_Osqrt
% 1.28/1.66 ( Y ), c_NthRoot_Osqrt( X ) ) }.
% 1.28/1.66 { ! class_RealVector_Oreal__normed__field( X ), Y =
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 1.28/1.66 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 1.28/1.66 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 1.28/1.66 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.28/1.66 ( X, Y ) ) }.
% 1.28/1.66 { ! class_Fields_Ofield__inverse__zero( X ), !
% 1.28/1.66 class_RealVector_Oreal__normed__field( X ),
% 1.28/1.66 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Odivide( X, Z
% 1.28/1.66 , Y ) ) = c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 1.28/1.66 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.28/1.66 ( X, Y ) ) }.
% 1.28/1.66 { c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ) =
% 1.28/1.66 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, Y ) }.
% 1.28/1.66 { ! class_RealVector_Oreal__normed__field( X ),
% 1.28/1.66 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 1.28/1.66 ), Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.66 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.66 { ! class_Rings_Odivision__ring( X ), c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.66 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 1.28/1.66 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 1.28/1.66 ), Y ) }.
% 1.28/1.66 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, Y
% 1.28/1.66 , c_Groups_Oone__class_Oone( X ) ) = Y }.
% 1.28/1.66 { ! class_RealVector_Oreal__normed__field( X ),
% 1.28/1.66 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T, Z
% 1.28/1.66 ), Y ) = c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide
% 1.28/1.66 ( X, T, Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.66 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.66 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.28/1.66 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 1.28/1.66 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.66 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), T ), c_Rings_Oinverse__class_Odivide
% 1.28/1.66 ( X, Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.28/1.66 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.28/1.66 { ! class_RealVector_Oreal__normed__field( X ),
% 1.28/1.66 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.28/1.66 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.66 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.28/1.66 c_Rings_Oinverse__class_Odivide( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.66 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.66 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.66 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.28/1.66 }.
% 1.28/1.66 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber__ring( X )
% 1.28/1.66 , c_Rings_Oinverse__class_Odivide( X, Y, c_Int_Onumber__class_Onumber__of
% 1.28/1.66 ( X, c_Int_OPls ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.66 { ! class_Fields_Ofield( X ), ! class_Int_Onumber__ring( X ),
% 1.28/1.66 c_Rings_Oinverse__class_Odivide( X, Y, c_Int_Onumber__class_Onumber__of(
% 1.28/1.67 X, c_Int_OBit1( c_Int_OPls ) ) ) = Y }.
% 1.28/1.67 { ! class_Fields_Ofield( X ), ! class_Int_Onumber__ring( X ),
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, Y, c_Int_Onumber__class_Onumber__of(
% 1.28/1.67 X, c_Int_OBit1( c_Int_OPls ) ) ) = Y }.
% 1.28/1.67 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber__ring( X )
% 1.28/1.67 , c_Rings_Oinverse__class_Odivide( X, Y, c_Int_Onumber__class_Onumber__of
% 1.28/1.67 ( X, c_Int_OMin ) ) = c_Groups_Ouminus__class_Ouminus( X, Y ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 1.28/1.67 X, Z ) ), Y ), alpha47( X, Y, Z, T ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 1.28/1.67 X, Z ) ), Y ), alpha65( X, Y, Z, T ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 class_Int_Onumber( X ), ! alpha47( X, Y, Z, T ), ! alpha65( X, Y, Z, T )
% 1.28/1.67 , c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T
% 1.28/1.67 , c_Int_Onumber__class_Onumber__of( X, Z ) ), Y ) }.
% 1.28/1.67 { ! alpha65( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Z
% 1.28/1.67 ) ), alpha77( X, Y, Z, T ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( X, Z ) ), alpha65( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha77( X, Y, Z, T ), alpha65( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha77( X, Y, Z, T ), alpha89( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha77( X, Y, Z, T ), alpha16( X, Y, Z ) }.
% 1.28/1.67 { ! alpha89( X, Y, Z, T ), ! alpha16( X, Y, Z ), alpha77( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha89( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero( X
% 1.28/1.67 ) ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 1.28/1.67 ( X, Z ) ), T ) }.
% 1.28/1.67 { c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 1.28/1.67 ), c_Groups_Ozero__class_Ozero( X ) ), alpha89( X, Y, Z, T ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 1.28/1.67 ( X, Z ) ), T ), alpha89( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha47( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Z
% 1.28/1.67 ) ), c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 1.28/1.67 ( X, Z ) ) ) }.
% 1.28/1.67 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( X, Z ) ), alpha47( X, Y, Z, T ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 1.28/1.67 ( X, Z ) ) ), alpha47( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha16( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero( X
% 1.28/1.67 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.67 , Y ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X,
% 1.28/1.67 Z ), c_Groups_Ozero__class_Ozero( X ) ), alpha16( X, Y, Z ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.28/1.67 , alpha16( X, Y, Z ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, T, Z ),
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha48( X, Y, Z, T ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, T, Z ),
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha66( X, Y, Z, T ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 class_Int_Onumber( X ), ! alpha48( X, Y, Z, T ), ! alpha66( X, Y, Z, T )
% 1.28/1.67 , c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T
% 1.28/1.67 , Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 1.28/1.67 { ! alpha66( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), Z ), alpha78( X, Y, Z, T ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.28/1.67 , alpha66( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha78( X, Y, Z, T ), alpha66( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha78( X, Y, Z, T ), alpha90( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha78( X, Y, Z, T ), alpha17( X, Y, Z ) }.
% 1.28/1.67 { ! alpha90( X, Y, Z, T ), ! alpha17( X, Y, Z ), alpha78( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha90( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( X, Y ) ), Z ), T ) }.
% 1.28/1.67 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.67 alpha90( X, Y, Z, T ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.28/1.67 Y ) ), Z ), T ), alpha90( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha48( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( X, Y ) ), Z ) ) }.
% 1.28/1.67 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.28/1.67 alpha48( X, Y, Z, T ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.28/1.67 Y ) ), Z ) ), alpha48( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Y
% 1.28/1.67 ) ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.67 , alpha17( X, Y, Z ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha17( X, Y, Z ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( X, T ), c_Rings_Oinverse__class_Odivide
% 1.28/1.67 ( X, Z, Y ) ), alpha49( X, Y, Z, T ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( X, T ), c_Rings_Oinverse__class_Odivide
% 1.28/1.67 ( X, Z, Y ) ), alpha67( X, Y, Z, T ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 class_Int_Onumber( X ), ! alpha49( X, Y, Z, T ), ! alpha67( X, Y, Z, T )
% 1.28/1.67 , c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X,
% 1.28/1.67 T ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.67 { ! alpha67( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), Y ), alpha79( X, Y, Z, T ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.28/1.67 , alpha67( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha79( X, Y, Z, T ), alpha67( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha79( X, Y, Z, T ), alpha91( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha79( X, Y, Z, T ), alpha18( X, Y, T ) }.
% 1.28/1.67 { ! alpha91( X, Y, Z, T ), ! alpha18( X, Y, T ), alpha79( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha91( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( X, T ) ), Y ) ) }.
% 1.28/1.67 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.67 alpha91( X, Y, Z, T ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.28/1.67 T ) ), Y ) ), alpha91( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha49( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( X, T ) ), Y ), Z ) }.
% 1.28/1.67 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.67 alpha49( X, Y, Z, T ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.28/1.67 T ) ), Y ), Z ), alpha49( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha18( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero( X
% 1.28/1.67 ) ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.67 , alpha18( X, Y, Z ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X,
% 1.28/1.67 Z ), c_Groups_Ozero__class_Ozero( X ) ), alpha18( X, Y, Z ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X, T,
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of(
% 1.28/1.67 X, Y ) ) ), alpha50( X, Y, Z, T ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless( X, T,
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of(
% 1.28/1.67 X, Y ) ) ), alpha68( X, Y, Z, T ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 class_Int_Onumber( X ), ! alpha50( X, Y, Z, T ), ! alpha68( X, Y, Z, T )
% 1.28/1.67 , c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.67 , Z, c_Int_Onumber__class_Onumber__of( X, Y ) ) ) }.
% 1.28/1.67 { ! alpha68( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Y
% 1.28/1.67 ) ), alpha80( X, Y, Z, T ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha68( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha80( X, Y, Z, T ), alpha68( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha80( X, Y, Z, T ), alpha92( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha80( X, Y, Z, T ), alpha19( X, Y, T ) }.
% 1.28/1.67 { ! alpha92( X, Y, Z, T ), ! alpha19( X, Y, T ), alpha80( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha92( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.28/1.67 ) ), c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 1.28/1.67 ( X, Y ) ) ) }.
% 1.28/1.67 { c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 1.28/1.67 ), c_Groups_Ozero__class_Ozero( X ) ), alpha92( X, Y, Z, T ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 1.28/1.67 ( X, Y ) ) ), alpha92( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha50( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Y
% 1.28/1.67 ) ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 1.28/1.67 ( X, Y ) ), Z ) }.
% 1.28/1.67 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha50( X, Y, Z, T ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 1.28/1.67 ( X, Y ) ), Z ), alpha50( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.28/1.67 ) ), c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.28/1.67 ) ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X,
% 1.28/1.67 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha19( X, Y, Z ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.67 , alpha19( X, Y, Z ) }.
% 1.28/1.67 { ! class_Fields_Ofield__inverse__zero( X ), ! class_Int_Onumber__ring( X )
% 1.28/1.67 , c_Rings_Oinverse__class_Odivide( X, c_Int_Onumber__class_Onumber__of( X
% 1.28/1.67 , c_Int_OMin ), Y ) = c_Groups_Ouminus__class_Ouminus( X,
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), Y ) )
% 1.28/1.67 }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of(
% 1.28/1.67 X, Y ) ) ), alpha51( X, Y, Z, T ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of(
% 1.28/1.67 X, Y ) ) ), alpha69( X, Y, Z, T ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 class_Int_Onumber( X ), ! alpha51( X, Y, Z, T ), ! alpha69( X, Y, Z, T )
% 1.28/1.67 , c_Orderings_Oord__class_Oless__eq( X, T,
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, Z, c_Int_Onumber__class_Onumber__of(
% 1.28/1.67 X, Y ) ) ) }.
% 1.28/1.67 { ! alpha69( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Y
% 1.28/1.67 ) ), alpha81( X, Y, Z, T ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha69( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha81( X, Y, Z, T ), alpha69( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha81( X, Y, Z, T ), alpha93( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha81( X, Y, Z, T ), alpha20( X, Y, T ) }.
% 1.28/1.67 { ! alpha93( X, Y, Z, T ), ! alpha20( X, Y, T ), alpha81( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha93( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.28/1.67 ) ), c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 1.28/1.67 ( X, Y ) ) ) }.
% 1.28/1.67 { c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Y
% 1.28/1.67 ), c_Groups_Ozero__class_Ozero( X ) ), alpha93( X, Y, Z, T ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 1.28/1.67 ( X, Y ) ) ), alpha93( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha51( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Y
% 1.28/1.67 ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 1.28/1.67 ( X, Y ) ), Z ) }.
% 1.28/1.67 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha51( X, Y, Z, T ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), T ), c_Int_Onumber__class_Onumber__of
% 1.28/1.67 ( X, Y ) ), Z ), alpha51( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha20( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.28/1.67 ) ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X,
% 1.28/1.67 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha20( X, Y, Z ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.28/1.67 ) ), alpha20( X, Y, Z ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( X, T ), c_Rings_Oinverse__class_Odivide
% 1.28/1.67 ( X, Z, Y ) ), alpha52( X, Y, Z, T ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( X, T ), c_Rings_Oinverse__class_Odivide
% 1.28/1.67 ( X, Z, Y ) ), alpha70( X, Y, Z, T ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 class_Int_Onumber( X ), ! alpha52( X, Y, Z, T ), ! alpha70( X, Y, Z, T )
% 1.28/1.67 , c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of
% 1.28/1.67 ( X, T ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.67 { ! alpha70( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), Y ), alpha82( X, Y, Z, T ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.28/1.67 , alpha70( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha82( X, Y, Z, T ), alpha70( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha82( X, Y, Z, T ), alpha94( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha82( X, Y, Z, T ), alpha21( X, Y, T ) }.
% 1.28/1.67 { ! alpha94( X, Y, Z, T ), ! alpha21( X, Y, T ), alpha82( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha94( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.67 , Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( X, T ) ), Y ) ) }.
% 1.28/1.67 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.67 alpha94( X, Y, Z, T ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.28/1.67 T ) ), Y ) ), alpha94( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha52( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless__eq
% 1.28/1.67 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( X, T ) ), Y ), Z ) }.
% 1.28/1.67 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.67 alpha52( X, Y, Z, T ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.28/1.67 T ) ), Y ), Z ), alpha52( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha21( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.67 , c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero(
% 1.28/1.67 X ) ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.67 , alpha21( X, Y, Z ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless__eq( X, c_Int_Onumber__class_Onumber__of
% 1.28/1.67 ( X, Z ), c_Groups_Ozero__class_Ozero( X ) ), alpha21( X, Y, Z ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, T, Z ),
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha53( X, Y, Z, T ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, T, Z ),
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha71( X, Y, Z, T ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 class_Int_Onumber( X ), ! alpha53( X, Y, Z, T ), ! alpha71( X, Y, Z, T )
% 1.28/1.67 , c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide(
% 1.28/1.67 X, T, Z ), c_Int_Onumber__class_Onumber__of( X, Y ) ) }.
% 1.28/1.67 { ! alpha71( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), Z ), alpha83( X, Y, Z, T ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.28/1.67 , alpha71( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha83( X, Y, Z, T ), alpha71( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha83( X, Y, Z, T ), alpha95( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha83( X, Y, Z, T ), alpha22( X, Y, Z ) }.
% 1.28/1.67 { ! alpha95( X, Y, Z, T ), ! alpha22( X, Y, Z ), alpha83( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha95( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.67 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( X, Y ) ), Z ), T ) }.
% 1.28/1.67 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.67 alpha95( X, Y, Z, T ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.28/1.67 Y ) ), Z ), T ), alpha95( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha53( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless__eq
% 1.28/1.67 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( X, Y ) ), Z ) ) }.
% 1.28/1.67 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.28/1.67 alpha53( X, Y, Z, T ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.28/1.67 Y ) ), Z ) ), alpha53( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha22( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.67 , c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.28/1.67 Y ) ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.67 , alpha22( X, Y, Z ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.67 , c_Int_Onumber__class_Onumber__of( X, Y ) ), alpha22( X, Y, Z ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 1.28/1.67 X, Z ) ), Y ), alpha54( X, Y, Z, T ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 class_Int_Onumber( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, T, c_Int_Onumber__class_Onumber__of(
% 1.28/1.67 X, Z ) ), Y ), alpha72( X, Y, Z, T ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 class_Int_Onumber( X ), ! alpha54( X, Y, Z, T ), ! alpha72( X, Y, Z, T )
% 1.28/1.67 , c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide(
% 1.28/1.67 X, T, c_Int_Onumber__class_Onumber__of( X, Z ) ), Y ) }.
% 1.28/1.67 { ! alpha72( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Z
% 1.28/1.67 ) ), alpha84( X, Y, Z, T ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( X, Z ) ), alpha72( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha84( X, Y, Z, T ), alpha72( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha84( X, Y, Z, T ), alpha96( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha84( X, Y, Z, T ), alpha23( X, Y, Z ) }.
% 1.28/1.67 { ! alpha96( X, Y, Z, T ), ! alpha23( X, Y, Z ), alpha84( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha96( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero( X
% 1.28/1.67 ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 1.28/1.67 ( X, Z ) ), T ) }.
% 1.28/1.67 { c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X, Z
% 1.28/1.67 ), c_Groups_Ozero__class_Ozero( X ) ), alpha96( X, Y, Z, T ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 1.28/1.67 ( X, Z ) ), T ), alpha96( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha54( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), c_Int_Onumber__class_Onumber__of( X, Z
% 1.28/1.67 ) ), c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 1.28/1.67 ( X, Z ) ) ) }.
% 1.28/1.67 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( X, Z ) ), alpha54( X, Y, Z, T ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), c_Int_Onumber__class_Onumber__of
% 1.28/1.67 ( X, Z ) ) ), alpha54( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha23( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( X, Z ), c_Groups_Ozero__class_Ozero( X
% 1.28/1.67 ) ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.67 X ), Y ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, c_Int_Onumber__class_Onumber__of( X,
% 1.28/1.67 Z ), c_Groups_Ozero__class_Ozero( X ) ), alpha23( X, Y, Z ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.67 , Y ), alpha23( X, Y, Z ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 class_Int_Onumber__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1( c_Int_OPls
% 1.28/1.67 ) ) ) ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero
% 1.28/1.67 ( X ), Y ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 class_Int_Onumber__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1( c_Int_OPls
% 1.28/1.67 ) ) ) ) ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 class_Int_Onumber__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( X, c_Int_OBit0( c_Int_OBit1( c_Int_OPls
% 1.28/1.67 ) ) ) ) ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 1.28/1.67 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y,
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 1.28/1.67 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 1.28/1.67 c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 1.28/1.67 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 1.28/1.67 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, X ),
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 1.28/1.67 c_Int_OBit1( c_Int_OPls ) ) ) ), X ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 class_Int_Onumber__ring( X ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.67 c_Groups_Oone__class_Oone( X ), c_Int_Onumber__class_Onumber__of( X,
% 1.28/1.67 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) }.
% 1.28/1.67 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.28/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 1.28/1.67 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.28/1.67 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.28/1.67 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.28/1.67 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.28/1.67 .
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.28/1.67 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, c_NthRoot_Osqrt(
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 1.28/1.67 c_Int_OBit1( c_Int_OPls ) ) ) ) ), X ) }.
% 1.28/1.67 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 1.28/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 1.28/1.67 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 1.28/1.67 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.67 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.28/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 1.28/1.67 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.28/1.67 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.67 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 1.28/1.67 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.67 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.67 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.67 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.28/1.67 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.67 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.67 tc_Nat_Onat ), X ), Y ) }.
% 1.28/1.67 { c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X,
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 1.28/1.67 c_Int_OBit1( c_Int_OPls ) ) ) ), c_Rings_Oinverse__class_Odivide(
% 1.28/1.67 tc_RealDef_Oreal, X, c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal,
% 1.28/1.67 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) = X }.
% 1.28/1.67 { ! Z = c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 1.28/1.67 c_Int_OBit1( c_Int_OPls ) ) ) ), X ) ), hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 1.28/1.67 c_Int_OBit1( c_Int_OPls ) ) ) ), Z ) = c_Rings_Oinverse__class_Odivide(
% 1.28/1.67 tc_RealDef_Oreal, Y, X ) }.
% 1.28/1.67 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 1.28/1.67 c_Int_OBit1( c_Int_OPls ) ) ) ), Z ) = c_Rings_Oinverse__class_Odivide(
% 1.28/1.67 tc_RealDef_Oreal, Y, X ), Z = c_Rings_Oinverse__class_Odivide(
% 1.28/1.67 tc_RealDef_Oreal, Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.67 tc_RealDef_Oreal ), c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal,
% 1.28/1.67 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), X ) ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.67 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.67 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.67 , T, Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field( X ), !
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.28/1.67 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.67 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.67 , T, Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 1.28/1.67 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X, U
% 1.28/1.67 , T ) ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.67 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.28/1.67 c_Groups_Ouminus__class_Ouminus( X, c_Rings_Oinverse__class_Odivide( X, Z
% 1.28/1.67 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, Z,
% 1.28/1.67 c_Groups_Ouminus__class_Ouminus( X, Y ) ) }.
% 1.28/1.67 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ouminus__class_Ouminus( X, Z
% 1.28/1.67 ), c_Groups_Ouminus__class_Ouminus( X, Y ) ) =
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.67 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 1.28/1.67 ( X, Y, T ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.28/1.67 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 1.28/1.67 ( X, Z, T ), c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.67 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha24( X, Y, Z ), alpha55
% 1.28/1.67 ( X, Y, Z ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha24( X, Y, Z
% 1.28/1.67 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 1.28/1.67 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha55( X, Y, Z
% 1.28/1.67 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 1.28/1.67 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.67 { ! alpha55( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.67 { ! alpha55( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.28/1.67 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.28/1.67 ( X ), Y ), alpha55( X, Y, Z ) }.
% 1.28/1.67 { ! alpha24( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.28/1.67 { ! alpha24( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.67 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ) ), alpha24( X, Y, Z ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha25( X, Y, Z ), alpha56
% 1.28/1.67 ( X, Y, Z ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha25( X, Y, Z
% 1.28/1.67 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.28/1.67 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha56( X, Y, Z
% 1.28/1.67 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.28/1.67 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.67 { ! alpha56( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.67 { ! alpha56( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.28/1.67 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ) ), alpha56( X, Y, Z ) }.
% 1.28/1.67 { ! alpha25( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.28/1.67 { ! alpha25( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.67 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), Y ), alpha25( X, Y, Z ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.67 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, Y, T ),
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.67 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, Z, T ),
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.67 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.28/1.67 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.28/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 1.28/1.67 , Y, Z ) ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.67 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.28/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 1.28/1.67 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.67 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.67 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.28/1.67 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.67 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 1.28/1.67 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 1.28/1.67 , Y, Z ) ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Z,
% 1.28/1.67 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha26( X, Y, Z ), alpha57( X,
% 1.28/1.67 Y, Z ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha26( X, Y, Z
% 1.28/1.67 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.67 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha57( X, Y, Z
% 1.28/1.67 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.67 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.67 { ! alpha57( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.67 { ! alpha57( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.67 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.67 ), alpha57( X, Y, Z ) }.
% 1.28/1.67 { ! alpha26( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.28/1.67 { ! alpha26( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.28/1.67 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.67 ), alpha26( X, Y, Z ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha27( X, Y, Z ), alpha58
% 1.28/1.67 ( X, Y, Z ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha27( X, Y, Z
% 1.28/1.67 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha58( X, Y, Z
% 1.28/1.67 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.67 { ! alpha58( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.67 { ! alpha58( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.67 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.67 ), alpha58( X, Y, Z ) }.
% 1.28/1.67 { ! alpha27( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.28/1.67 { ! alpha27( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.28/1.67 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.67 ), alpha27( X, Y, Z ) }.
% 1.28/1.67 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha59( X, Y, Z, T ) }.
% 1.28/1.67 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha28( X, Y, T ) }.
% 1.28/1.67 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha59( X, Y, Z, T ), !
% 1.28/1.67 alpha28( X, Y, T ), T = c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.28/1.67 { ! alpha59( X, Y, Z, T ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP
% 1.28/1.67 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 1.28/1.67 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha59( X, Y, Z, T ) }.
% 1.28/1.67 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, alpha59(
% 1.28/1.67 X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha28( X, Y, Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.67 { Y = c_Groups_Ozero__class_Ozero( X ), alpha28( X, Y, Z ) }.
% 1.28/1.67 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha28( X, Y, Z ) }.
% 1.28/1.67 { ! class_Fields_Ofield__inverse__zero( X ), !
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha60( X, Y, Z, T ) }.
% 1.28/1.67 { ! class_Fields_Ofield__inverse__zero( X ), !
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha29( X, Y, Z ) }.
% 1.28/1.67 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha60( X, Y, Z, T ), !
% 1.28/1.67 alpha29( X, Y, Z ), c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y }.
% 1.28/1.67 { ! alpha60( X, Y, Z, T ), Z = c_Groups_Ozero__class_Ozero( X ), T = hAPP(
% 1.28/1.67 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 1.28/1.67 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha60( X, Y, Z, T ) }.
% 1.28/1.67 { ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), alpha60(
% 1.28/1.67 X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha29( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ) }.
% 1.28/1.67 { Z = c_Groups_Ozero__class_Ozero( X ), alpha29( X, Y, Z ) }.
% 1.28/1.67 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha29( X, Y, Z ) }.
% 1.28/1.67 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 1.28/1.67 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 1.28/1.67 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Oinverse__class_Odivide( X, U
% 1.28/1.67 , Y ) = c_Rings_Oinverse__class_Odivide( X, T, Z ), hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) }.
% 1.28/1.67 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ),
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, U, Y ) =
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field( X ), !
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.67 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.28/1.67 ) ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.28/1.67 X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field( X ), !
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.67 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.67 , Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 1.28/1.67 X ) ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field( X ), !
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.67 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 1.28/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.28/1.67 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.67 , Y, U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field( X ), !
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.67 ), ! c_Orderings_Oord__class_Oless( X, Y, Z ), !
% 1.28/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.28/1.67 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 1.28/1.67 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Y,
% 1.28/1.67 U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.67 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 1.28/1.67 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.28/1.67 ! c_Orderings_Oord__class_Oless( X, T, U ), c_Orderings_Oord__class_Oless
% 1.28/1.67 ( X, c_Rings_Oinverse__class_Odivide( X, Y, U ),
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field( X ), !
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.67 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.28/1.67 ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 1.28/1.67 X ) ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field( X ), !
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.28/1.67 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.67 , Z ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.28/1.67 ( X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.67 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.28/1.67 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.28/1.67 Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.67 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 1.28/1.67 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.28/1.67 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.28/1.67 Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.67 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.28/1.67 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 1.28/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.67 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.28/1.67 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 1.28/1.67 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.28/1.67 Y ), Z ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.67 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.28/1.67 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 1.28/1.67 c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.67 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.28/1.67 ( X, Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 1.28/1.67 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.67 Z, Y ) ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.67 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.67 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.28/1.67 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.67 Z, Y ) ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.67 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.67 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.28/1.67 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.28/1.67 Y ), Z ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.67 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.67 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 1.28/1.67 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.67 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.67 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.28/1.67 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.28/1.67 Y ), Z ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.67 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.67 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 1.28/1.67 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.67 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.28/1.67 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.28/1.67 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.67 Z, Y ) ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.28/1.67 Z ), Y ), alpha61( X, Y, Z, T ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.28/1.67 Z ), Y ), alpha73( X, Y, Z, T ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha61( X, Y, Z
% 1.28/1.67 , T ), ! alpha73( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 1.28/1.67 { ! alpha73( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), Z ), alpha85( X, Y, Z, T ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.28/1.67 , alpha73( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha85( X, Y, Z, T ), alpha73( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha85( X, Y, Z, T ), alpha97( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha85( X, Y, Z, T ), alpha30( X, Y, Z ) }.
% 1.28/1.67 { ! alpha97( X, Y, Z, T ), ! alpha30( X, Y, Z ), alpha85( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha97( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 1.28/1.67 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.67 alpha97( X, Y, Z, T ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha97( X, Y, Z, T )
% 1.28/1.67 }.
% 1.28/1.67 { ! alpha61( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.67 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.28/1.67 alpha61( X, Y, Z, T ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha61( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha30( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.67 , alpha30( X, Y, Z ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.28/1.67 , alpha30( X, Y, Z ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.67 Z, Y ) ), alpha62( X, Y, Z, T ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.28/1.67 Z, Y ) ), alpha74( X, Y, Z, T ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha62( X, Y, Z
% 1.28/1.67 , T ), ! alpha74( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.67 { ! alpha74( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), Y ), alpha86( X, Y, Z, T ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.28/1.67 , alpha74( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha86( X, Y, Z, T ), alpha74( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha86( X, Y, Z, T ), alpha98( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha86( X, Y, Z, T ), alpha31( X, Y, T ) }.
% 1.28/1.67 { ! alpha98( X, Y, Z, T ), ! alpha31( X, Y, T ), alpha86( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha98( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.67 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.67 alpha98( X, Y, Z, T ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha98( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha62( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.28/1.67 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.67 alpha62( X, Y, Z, T ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha62( X, Y, Z, T )
% 1.28/1.67 }.
% 1.28/1.67 { ! alpha31( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.67 , alpha31( X, Y, Z ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.67 , alpha31( X, Y, Z ) }.
% 1.28/1.67 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 1.28/1.67 ( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.67 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.67 c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide( X, T, Y
% 1.28/1.67 ), Z ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 1.28/1.67 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }
% 1.28/1.67 .
% 1.28/1.67 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) =
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.28/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) }.
% 1.28/1.67 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.28/1.67 c_Groups_Oplus__class_Oplus( X, T, c_Rings_Oinverse__class_Odivide( X, Z
% 1.28/1.67 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 1.28/1.67 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }
% 1.28/1.67 .
% 1.28/1.67 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, T,
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.28/1.67 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Y ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.67 X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 1.28/1.67 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.28/1.67 c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.67 X, Z, Y ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 1.28/1.67 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.28/1.67 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.28/1.67 ( X, Z, Y ) ), alpha63( X, Y, Z, T ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.28/1.67 ( X, Z, Y ) ), alpha75( X, Y, Z, T ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha63( X, Y, Z
% 1.28/1.67 , T ), ! alpha75( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X, T,
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.28/1.67 { ! alpha75( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), Y ), alpha87( X, Y, Z, T ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.28/1.67 , alpha75( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha87( X, Y, Z, T ), alpha75( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha87( X, Y, Z, T ), alpha99( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha87( X, Y, Z, T ), alpha32( X, Y, T ) }.
% 1.28/1.67 { ! alpha99( X, Y, Z, T ), ! alpha32( X, Y, T ), alpha87( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha99( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.67 , Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.67 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.67 alpha99( X, Y, Z, T ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha99( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha63( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless__eq
% 1.28/1.67 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.28/1.67 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.28/1.67 alpha63( X, Y, Z, T ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha63( X, Y, Z, T )
% 1.28/1.67 }.
% 1.28/1.67 { ! alpha32( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.67 , Z, c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.67 , alpha32( X, Y, Z ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.28/1.67 ) ), alpha32( X, Y, Z ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.67 , T, Z ), Y ), alpha64( X, Y, Z, T ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.67 , T, Z ), Y ), alpha76( X, Y, Z, T ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha64( X, Y, Z
% 1.28/1.67 , T ), ! alpha76( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X,
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 1.28/1.67 { ! alpha76( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), Z ), alpha88( X, Y, Z, T ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.28/1.67 , alpha76( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha88( X, Y, Z, T ), alpha76( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha88( X, Y, Z, T ), alpha100( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha88( X, Y, Z, T ), alpha33( X, Y, Z ) }.
% 1.28/1.67 { ! alpha100( X, Y, Z, T ), ! alpha33( X, Y, Z ), alpha88( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha100( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.67 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 1.28/1.67 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 1.28/1.67 alpha100( X, Y, Z, T ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha100( X, Y, Z, T )
% 1.28/1.67 }.
% 1.28/1.67 { ! alpha64( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless__eq
% 1.28/1.67 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.28/1.67 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.28/1.67 alpha64( X, Y, Z, T ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha64( X, Y, Z, T ) }.
% 1.28/1.67 { ! alpha33( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.28/1.67 , c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.28/1.67 , alpha33( X, Y, Z ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.28/1.67 , Y ), alpha33( X, Y, Z ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.67 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.28/1.67 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.67 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.28/1.67 ( X, Z, Y ) ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.67 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.67 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.67 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.67 , T, Y ), Z ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.67 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.67 , T, Y ), Z ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.67 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.28/1.67 ( X, Z, Y ) ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.67 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.28/1.67 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.67 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.28/1.67 ( X, Z, Y ) ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.67 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.67 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 1.28/1.67 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.67 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.28/1.67 , T, Y ), Z ) }.
% 1.28/1.67 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 1.28/1.67 c_Complex_Oii ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 1.28/1.67 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) =
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( tc_Complex_Ocomplex, c_Int_OMin ) }.
% 1.28/1.67 { c_Transcendental_Oarctan( X ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.28/1.67 ( tc_RealDef_Oreal ), c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal
% 1.28/1.67 , c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), c_Transcendental_Oarctan
% 1.28/1.67 ( c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X,
% 1.28/1.67 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_Groups_Oone__class_Oone
% 1.28/1.67 ( tc_RealDef_Oreal ), c_NthRoot_Osqrt( c_Groups_Oplus__class_Oplus(
% 1.28/1.67 tc_RealDef_Oreal, c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), hAPP(
% 1.28/1.67 hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), X ),
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.67 c_Int_OPls ) ) ) ) ) ) ) ) ) ) }.
% 1.28/1.67 { c_Transcendental_Oarctan( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 1.28/1.67 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.28/1.67 { c_Transcendental_Oarctan( c_Groups_Ouminus__class_Ouminus(
% 1.28/1.67 tc_RealDef_Oreal, X ) ) = c_Groups_Ouminus__class_Ouminus(
% 1.28/1.67 tc_RealDef_Oreal, c_Transcendental_Oarctan( X ) ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.67 c_Transcendental_Oarctan( Y ), c_Transcendental_Oarctan( X ) ) }.
% 1.28/1.67 { ! c_Complex_Oii = c_Int_Onumber__class_Onumber__of( tc_Complex_Ocomplex,
% 1.28/1.67 X ) }.
% 1.28/1.67 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.28/1.67 c_Complex_Oii ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.28/1.67 tc_Complex_Ocomplex ), c_Complex_Oii ), X ) ) =
% 1.28/1.67 c_Groups_Ouminus__class_Ouminus( tc_Complex_Ocomplex, X ) }.
% 1.28/1.67 { ! c_Complex_Oii = c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 1.28/1.67 { ! c_Complex_Oii = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 1.28/1.67 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oarctan
% 1.28/1.67 ( Y ), c_Transcendental_Oarctan( X ) ) }.
% 1.28/1.67 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.28/1.67 c_Complex_Oii ), c_Complex_Ocomplex_OComplex( Y, X ) ) =
% 1.28/1.67 c_Complex_Ocomplex_OComplex( c_Groups_Ouminus__class_Ouminus(
% 1.28/1.67 tc_RealDef_Oreal, X ), Y ) }.
% 1.28/1.67 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.28/1.67 c_Complex_Ocomplex_OComplex( Y, X ) ), c_Complex_Oii ) =
% 1.28/1.67 c_Complex_Ocomplex_OComplex( c_Groups_Ouminus__class_Ouminus(
% 1.28/1.67 tc_RealDef_Oreal, X ), Y ) }.
% 1.28/1.67 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.28/1.67 c_Complex_Oii ), c_Complex_Oii ) = c_Int_Onumber__class_Onumber__of(
% 1.28/1.67 tc_Complex_Ocomplex, c_Int_OMin ) }.
% 1.28/1.67 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.28/1.67 c_Complex_Oii ), c_Complex_Oii ) = c_Groups_Ouminus__class_Ouminus(
% 1.28/1.67 tc_Complex_Ocomplex, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) }
% 1.28/1.67 .
% 1.28/1.67 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Complex_Oii, Y =
% 1.28/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.28/1.67 { ! c_Complex_Ocomplex_OComplex( Y, X ) = c_Complex_Oii, X =
% 1.28/1.67 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.28/1.67 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 1.28/1.67 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ),
% 1.28/1.67 c_Complex_Ocomplex_OComplex( Y, X ) = c_Complex_Oii }.
% 1.28/1.67 { c_Complex_Oii = c_Complex_Ocomplex_OComplex( c_Groups_Ozero__class_Ozero
% 1.28/1.67 ( tc_RealDef_Oreal ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.28/1.67 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.67 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, c_NthRoot_Osqrt(
% 1.28/1.67 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.67 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Y ),
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.67 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.28/1.67 tc_RealDef_Oreal ), X ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 1.28/1.67 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) ) ) ),
% 1.28/1.67 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.28/1.67 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ),
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, c_NthRoot_Osqrt(
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 1.28/1.67 c_Int_OBit1( c_Int_OPls ) ) ) ) ) ), ! c_Orderings_Oord__class_Oless(
% 1.28/1.67 tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Z ),
% 1.28/1.67 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, c_NthRoot_Osqrt(
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, c_Int_OBit0(
% 1.28/1.67 c_Int_OBit1( c_Int_OPls ) ) ) ) ) ), c_Orderings_Oord__class_Oless(
% 1.28/1.67 tc_RealDef_Oreal, c_NthRoot_Osqrt( c_Groups_Oplus__class_Oplus(
% 1.28/1.67 tc_RealDef_Oreal, hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.28/1.67 tc_RealDef_Oreal ), Y ), c_Int_Onumber__class_Onumber__of( tc_Nat_Onat,
% 1.28/1.67 c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ), hAPP( hAPP(
% 1.28/1.67 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ),
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.67 c_Int_OPls ) ) ) ) ) ), X ) }.
% 1.28/1.67 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.28/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.28/1.67 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Y ), hAPP( hAPP(
% 1.28/1.67 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ),
% 1.28/1.67 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal, Z ) ) ), Y =
% 1.28/1.67 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.28/1.67 { ! class_Int_Onumber__ring( X ), !
% 1.28/1.67 class_RealVector_Oreal__normed__algebra__1( X ),
% 1.28/1.67 c_RealVector_Onorm__class_Onorm( X, c_Int_Onumber__class_Onumber__of( X,
% 1.28/1.67 Y ) ) = c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal,
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( tc_RealDef_Oreal, Y ) ) }.
% 1.28/1.67 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 1.28/1.67 ) ) }.
% 1.28/1.67 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 1.28/1.67 .
% 1.28/1.67 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 1.28/1.67 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.28/1.67 tc_Int_Oint ) }.
% 1.28/1.67 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.28/1.67 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 1.28/1.67 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 1.28/1.67 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 1.28/1.67 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 1.28/1.67 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 1.28/1.67 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 1.28/1.67 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 1.28/1.67 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.28/1.67 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 1.28/1.67 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 1.28/1.67 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 1.28/1.67 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 1.28/1.67 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 1.28/1.67 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 1.28/1.67 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 1.28/1.67 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 1.28/1.67 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 1.28/1.67 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 1.28/1.67 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 1.28/1.67 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 1.28/1.67 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 1.28/1.67 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 1.28/1.67 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 1.28/1.67 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 1.28/1.67 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 1.28/1.67 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 1.28/1.67 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 1.28/1.67 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 1.28/1.67 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 1.28/1.67 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 1.28/1.67 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 1.28/1.67 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 1.28/1.67 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 1.28/1.67 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 1.28/1.67 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 1.28/1.67 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 1.28/1.67 { class_Rings_Osemiring__1( tc_Int_Oint ) }.
% 1.28/1.67 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 1.28/1.67 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 1.28/1.67 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 1.28/1.67 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 1.28/1.67 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 1.28/1.67 { class_Int_Onumber__ring( tc_Int_Oint ) }.
% 1.28/1.67 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 1.28/1.67 { class_Orderings_Oord( tc_Int_Oint ) }.
% 1.28/1.67 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 1.28/1.67 { class_Power_Opower( tc_Int_Oint ) }.
% 1.28/1.67 { class_Groups_Ozero( tc_Int_Oint ) }.
% 1.28/1.67 { class_Rings_Oring( tc_Int_Oint ) }.
% 1.28/1.67 { class_Rings_Oidom( tc_Int_Oint ) }.
% 1.28/1.67 { class_Int_Onumber( tc_Int_Oint ) }.
% 1.28/1.67 { class_Groups_Oone( tc_Int_Oint ) }.
% 1.28/1.67 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.28/1.67 tc_Nat_Onat ) }.
% 1.28/1.67 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.28/1.67 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 1.28/1.67 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 1.28/1.67 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 1.28/1.67 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.28/1.67 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 1.28/1.67 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.28/1.67 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 1.28/1.67 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 1.28/1.67 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 1.28/1.67 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 1.28/1.67 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 1.28/1.67 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 1.28/1.67 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 1.28/1.67 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 1.28/1.67 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 1.28/1.67 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 1.28/1.67 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 1.28/1.67 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 1.28/1.67 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 1.28/1.67 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 1.28/1.67 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 1.28/1.67 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 1.28/1.67 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 1.28/1.67 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 1.28/1.67 { class_Rings_Osemiring__1( tc_Nat_Onat ) }.
% 1.28/1.67 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 1.28/1.67 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 1.28/1.67 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 1.28/1.67 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 1.28/1.67 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 1.28/1.67 { class_Power_Opower( tc_Nat_Onat ) }.
% 1.28/1.67 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 1.28/1.67 { class_Int_Onumber( tc_Nat_Onat ) }.
% 1.28/1.67 { class_Groups_Oone( tc_Nat_Onat ) }.
% 1.28/1.67 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 1.28/1.67 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 1.28/1.67 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 1.28/1.67 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.28/1.67 tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 1.28/1.67 .
% 1.28/1.67 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Fields_Olinordered__field__inverse__zero( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_RealVector_Oreal__normed__div__algebra( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Rings_Odivision__ring__inverse__zero( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_RealVector_Oreal__normed__algebra__1( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_RealVector_Oreal__normed__vector( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_RealVector_Oreal__normed__field( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Fields_Ofield__inverse__zero( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Fields_Olinordered__field( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Rings_Odivision__ring( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Rings_Osemiring__1( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Int_Oring__char__0( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Int_Onumber__ring( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Fields_Ofield( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Int_Onumber( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 1.28/1.67 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.28/1.67 tc_Complex_Ocomplex ) }.
% 1.28/1.67 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 1.28/1.67 { class_Rings_Odivision__ring__inverse__zero( tc_Complex_Ocomplex ) }.
% 1.28/1.67 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 1.28/1.67 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 1.28/1.67 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.28/1.67 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.28/1.67 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 1.28/1.67 { class_RealVector_Oreal__normed__field( tc_Complex_Ocomplex ) }.
% 1.28/1.67 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.28/1.67 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.28/1.67 { class_Fields_Ofield__inverse__zero( tc_Complex_Ocomplex ) }.
% 1.28/1.67 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 1.28/1.67 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 1.28/1.67 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.28/1.67 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.28/1.67 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 1.28/1.67 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 1.28/1.67 { class_Rings_Odivision__ring( tc_Complex_Ocomplex ) }.
% 1.28/1.67 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 1.28/1.67 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 1.28/1.67 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 1.28/1.67 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 1.28/1.67 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 1.28/1.67 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 1.28/1.67 { class_Rings_Osemiring__1( tc_Complex_Ocomplex ) }.
% 1.28/1.67 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 1.28/1.67 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 1.28/1.67 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 1.28/1.67 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 1.28/1.67 { class_Int_Onumber__ring( tc_Complex_Ocomplex ) }.
% 1.28/1.67 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 1.28/1.67 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 1.28/1.67 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 1.28/1.67 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 1.28/1.67 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 1.28/1.67 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 1.28/1.67 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 1.28/1.67 { class_Int_Onumber( tc_Complex_Ocomplex ) }.
% 1.28/1.67 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 1.28/1.67 { class_Groups_Oordered__cancel__ab__semigroup__add(
% 1.28/1.67 tc_Code__Numeral_Ocode__numeral ) }.
% 1.28/1.67 { class_Groups_Oordered__ab__semigroup__add__imp__le(
% 1.28/1.67 tc_Code__Numeral_Ocode__numeral ) }.
% 1.28/1.67 { class_Rings_Olinordered__comm__semiring__strict(
% 1.28/1.67 tc_Code__Numeral_Ocode__numeral ) }.
% 1.28/1.67 { class_Rings_Olinordered__semiring__strict(
% 1.28/1.67 tc_Code__Numeral_Ocode__numeral ) }.
% 1.28/1.67 { class_Groups_Oordered__ab__semigroup__add(
% 1.28/1.67 tc_Code__Numeral_Ocode__numeral ) }.
% 1.28/1.67 { class_Groups_Oordered__comm__monoid__add( tc_Code__Numeral_Ocode__numeral
% 1.28/1.67 ) }.
% 1.28/1.67 { class_Groups_Ocancel__ab__semigroup__add( tc_Code__Numeral_Ocode__numeral
% 1.28/1.67 ) }.
% 1.28/1.67 { class_Rings_Oordered__cancel__semiring( tc_Code__Numeral_Ocode__numeral )
% 1.28/1.67 }.
% 1.28/1.67 { class_Rings_Oordered__comm__semiring( tc_Code__Numeral_Ocode__numeral ) }
% 1.28/1.67 .
% 1.28/1.67 { class_Groups_Ocancel__semigroup__add( tc_Code__Numeral_Ocode__numeral ) }
% 1.28/1.67 .
% 1.28/1.67 { class_Rings_Olinordered__semiring( tc_Code__Numeral_Ocode__numeral ) }.
% 1.28/1.67 { class_Rings_Olinordered__semidom( tc_Code__Numeral_Ocode__numeral ) }.
% 1.28/1.67 { class_Groups_Oab__semigroup__mult( tc_Code__Numeral_Ocode__numeral ) }.
% 1.28/1.67 { class_Groups_Ocomm__monoid__mult( tc_Code__Numeral_Ocode__numeral ) }.
% 1.28/1.67 { class_Groups_Oab__semigroup__add( tc_Code__Numeral_Ocode__numeral ) }.
% 1.28/1.67 { class_Rings_Oordered__semiring( tc_Code__Numeral_Ocode__numeral ) }.
% 1.28/1.67 { class_Rings_Ono__zero__divisors( tc_Code__Numeral_Ocode__numeral ) }.
% 1.28/1.67 { class_Groups_Ocomm__monoid__add( tc_Code__Numeral_Ocode__numeral ) }.
% 1.28/1.67 { class_Rings_Ocomm__semiring__1( tc_Code__Numeral_Ocode__numeral ) }.
% 1.28/1.67 { class_Rings_Ocomm__semiring( tc_Code__Numeral_Ocode__numeral ) }.
% 1.28/1.67 { class_Rings_Ozero__neq__one( tc_Code__Numeral_Ocode__numeral ) }.
% 1.28/1.67 { class_Orderings_Opreorder( tc_Code__Numeral_Ocode__numeral ) }.
% 1.28/1.67 { class_Orderings_Olinorder( tc_Code__Numeral_Ocode__numeral ) }.
% 1.28/1.67 { class_Groups_Omonoid__mult( tc_Code__Numeral_Ocode__numeral ) }.
% 1.28/1.67 { class_Groups_Omonoid__add( tc_Code__Numeral_Ocode__numeral ) }.
% 1.28/1.67 { class_Rings_Osemiring__1( tc_Code__Numeral_Ocode__numeral ) }.
% 1.28/1.67 { class_Rings_Osemiring__0( tc_Code__Numeral_Ocode__numeral ) }.
% 1.28/1.67 { class_Rings_Omult__zero( tc_Code__Numeral_Ocode__numeral ) }.
% 1.28/1.67 { class_Orderings_Oorder( tc_Code__Numeral_Ocode__numeral ) }.
% 1.28/1.67 { class_Rings_Osemiring( tc_Code__Numeral_Ocode__numeral ) }.
% 1.28/1.67 { class_Orderings_Oord( tc_Code__Numeral_Ocode__numeral ) }.
% 1.28/1.67 { class_Power_Opower( tc_Code__Numeral_Ocode__numeral ) }.
% 1.28/1.67 { class_Groups_Ozero( tc_Code__Numeral_Ocode__numeral ) }.
% 1.28/1.67 { class_Int_Onumber( tc_Code__Numeral_Ocode__numeral ) }.
% 1.28/1.67 { class_Groups_Oone( tc_Code__Numeral_Ocode__numeral ) }.
% 1.28/1.67 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.28/1.67 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), v_x____ ),
% 1.28/1.67 c_Int_Onumber__class_Onumber__of( tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1(
% 1.28/1.67 c_Int_OPls ) ) ) ), hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.28/1.67 tc_RealDef_Oreal ), v_y____ ), c_Int_Onumber__class_Onumber__of(
% 1.28/1.67 tc_Nat_Onat, c_Int_OBit0( c_Int_OBit1( c_Int_OPls ) ) ) ) ) =
% 1.28/1.67 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.28/1.67
% 1.28/1.67 *** allocated 15000 integers for clauses
% 1.28/1.67 *** allocated 22500 integers for clauses
% 1.28/1.67 *** allocated 33750 integers for clauses
% 1.28/1.67 *** allocated 50625 integers for clauses
% 1.28/1.67 *** allocated 75937 integers for clauses
% 1.28/1.67 *** allocated 113905 integers for clauses
% 1.28/1.67 percentage equality = 0.234577, percentage horn = 0.902106
% 1.28/1.67 This is a problem with some equality
% 1.28/1.67
% 1.28/1.67
% 1.28/1.67
% 1.28/1.67 Options Used:
% 1.28/1.67
% 1.28/1.67 useres = 1
% 1.28/1.67 useparamod = 1
% 1.28/1.67 useeqrefl = 1
% 1.28/1.67 useeqfact = 1
% 1.28/1.67 usefactor = 1
% 1.28/1.67 usesimpsplitting = 0
% 1.28/1.67 usesimpdemod = 5
% 1.28/1.67 usesimpres = 3
% 1.28/1.67
% 1.28/1.67 resimpinuse = 1000
% 1.28/1.67 resimpclauses = 20000
% 1.28/1.67 substype = eqrewr
% 1.28/1.67 backwardsubs = 1
% 1.28/1.67 selectoldest = 5
% 1.28/1.67
% 1.28/1.67 litorderings [0] = split
% 1.28/1.67 litorderings [1] = extend the termordering, first sorting on arguments
% 1.28/1.67
% 1.28/1.67 termordering = kbo
% 1.28/1.67
% 1.28/1.67 litapriori = 0
% 1.28/1.67 termapriori = 1
% 1.28/1.67 litaposteriori = 0
% 1.28/1.67 termaposteriori = 0
% 1.28/1.67 demodaposteriori = 0
% 1.28/1.67 ordereqreflfact = 0
% 1.28/1.67
% 1.28/1.67 litselect = negord
% 1.28/1.67
% 1.28/1.67 maxweight = 15
% 1.28/1.67 maxdepth = 30000
% 1.28/1.67 maxlength = 115
% 1.28/1.67 maxnrvars = 195
% 1.28/1.67 excuselevel = 1
% 1.28/1.67 increasemaxweight = 1
% 1.28/1.67
% 1.28/1.67 maxselected = 10000000
% 1.28/1.67 maxnrclauses = 10000000
% 1.28/1.67
% 1.28/1.67 showgenerated = 0
% 1.28/1.67 showkept = 0
% 1.28/1.67 showselected = 0
% 1.28/1.67 showdeleted = 0
% 1.28/1.67 showresimp = 1
% 1.28/1.67 showstatus = 2000
% 1.28/1.67
% 1.28/1.67 prologoutput = 0
% 1.28/1.67 nrgoals = 5000000
% 1.28/1.67 totalproof = 1
% 1.28/1.67
% 1.28/1.67 Symbols occurring in the translation:
% 1.28/1.67
% 1.28/1.67 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.28/1.67 . [1, 2] (w:1, o:187, a:1, s:1, b:0),
% 1.28/1.67 ! [4, 1] (w:0, o:102, a:1, s:1, b:0),
% 1.28/1.67 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.28/1.67 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.28/1.67 hAPP [38, 2] (w:1, o:211, a:1, s:1, b:0),
% 1.28/1.67 tc_Complex_Ocomplex [39, 0] (w:1, o:13, a:1, s:1, b:0),
% 1.28/1.67 v_z [40, 0] (w:1, o:15, a:1, s:1, b:0),
% 1.28/1.67 c_RealVector_Onorm__class_Onorm [41, 2] (w:1, o:212, a:1, s:1, b:0),
% 1.28/1.67
% 1.28/1.67 tc_RealDef_Oreal [42, 0] (w:1, o:16, a:1, s:1, b:0),
% 1.28/1.67 c_Groups_Oone__class_Oone [43, 1] (w:1, o:108, a:1, s:1, b:0),
% 1.28/1.67 v_x____ [44, 0] (w:1, o:17, a:1, s:1, b:0),
% 1.28/1.67 v_y____ [45, 0] (w:1, o:14, a:1, s:1, b:0),
% 1.28/1.67 c_Complex_Ocomplex_OComplex [46, 2] (w:1, o:213, a:1, s:1, b:0),
% 1.28/1.67 class_Rings_Osemiring__1 [48, 1] (w:1, o:114, a:1, s:1, b:0),
% 1.28/1.67 c_Power_Opower__class_Opower [49, 1] (w:1, o:115, a:1, s:1, b:0),
% 1.28/1.67 tc_Nat_Onat [50, 0] (w:1, o:19, a:1, s:1, b:0),
% 1.28/1.67 c_Int_OPls [51, 0] (w:1, o:20, a:1, s:1, b:0),
% 1.28/1.67 c_Int_OBit1 [52, 1] (w:1, o:117, a:1, s:1, b:0),
% 1.28/1.67 c_Int_OBit0 [53, 1] (w:1, o:116, a:1, s:1, b:0),
% 1.28/1.67 c_Int_Onumber__class_Onumber__of [54, 2] (w:1, o:214, a:1, s:1, b:0)
% 1.28/1.67 ,
% 1.28/1.67 class_Int_Onumber__ring [55, 1] (w:1, o:118, a:1, s:1, b:0),
% 1.28/1.67 c_Groups_Oplus__class_Oplus [56, 3] (w:1, o:238, a:1, s:1, b:0),
% 1.28/1.67 tc_Int_Oint [58, 0] (w:1, o:33, a:1, s:1, b:0),
% 1.28/1.67 class_Int_Oring__char__0 [73, 1] (w:1, o:119, a:1, s:1, b:0),
% 1.28/1.67 class_Int_Onumber [75, 1] (w:1, o:120, a:1, s:1, b:0),
% 1.28/1.67 c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt [77, 1] (w:1, o:107
% 1.28/1.67 , a:1, s:1, b:0),
% 1.28/1.67 class_RealVector_Oreal__normed__div__algebra [79, 1] (w:1, o:121, a:1
% 1.28/1.67 , s:1, b:0),
% 1.28/1.67 class_RealVector_Oreal__normed__algebra__1 [80, 1] (w:1, o:122, a:1
% 1.28/1.67 , s:1, b:0),
% 1.28/1.67 c_Groups_Otimes__class_Otimes [84, 1] (w:1, o:123, a:1, s:1, b:0),
% 1.28/1.67 tc_Code__Numeral_Ocode__numeral [85, 0] (w:1, o:68, a:1, s:1, b:0),
% 1.28/1.67 class_Groups_Omonoid__mult [86, 1] (w:1, o:129, a:1, s:1, b:0),
% 1.28/1.67 class_Rings_Olinordered__idom [87, 1] (w:1, o:130, a:1, s:1, b:0),
% 1.28/1.67 c_Groups_Ozero__class_Ozero [88, 1] (w:1, o:131, a:1, s:1, b:0),
% 1.28/1.67 class_Rings_Oring__1__no__zero__divisors [91, 1] (w:1, o:109, a:1, s:
% 1.28/1.67 1, b:0),
% 1.28/1.67 c_Groups_Ouminus__class_Ouminus [92, 2] (w:1, o:215, a:1, s:1, b:0),
% 1.28/1.67
% 1.28/1.67 c_NthRoot_Osqrt [93, 1] (w:1, o:132, a:1, s:1, b:0),
% 1.28/1.67 class_RealVector_Oreal__normed__vector [94, 1] (w:1, o:133, a:1, s:1
% 1.28/1.67 , b:0),
% 1.28/1.67 class_Power_Opower [96, 1] (w:1, o:138, a:1, s:1, b:0),
% 1.28/1.67 class_Rings_Omult__zero [97, 1] (w:1, o:147, a:1, s:1, b:0),
% 1.28/1.67 class_Rings_Ono__zero__divisors [98, 1] (w:1, o:148, a:1, s:1, b:0),
% 1.28/1.67
% 1.28/1.67 class_Rings_Ozero__neq__one [99, 1] (w:1, o:149, a:1, s:1, b:0),
% 1.28/1.67 class_RealVector_Oreal__normed__algebra [101, 1] (w:1, o:150, a:1, s:
% 1.28/1.67 1, b:0),
% 1.28/1.67 class_Rings_Olinordered__ring__strict [103, 1] (w:1, o:139, a:1, s:1
% 1.28/1.67 , b:0),
% 1.28/1.67 class_Groups_Ocomm__monoid__mult [107, 1] (w:1, o:151, a:1, s:1, b:0)
% 1.28/1.67 ,
% 1.28/1.67 class_Rings_Oring__1 [109, 1] (w:1, o:110, a:1, s:1, b:0),
% 1.28/1.67 class_Rings_Osemiring__0 [110, 1] (w:1, o:113, a:1, s:1, b:0),
% 1.28/1.67 class_Groups_Olinordered__ab__group__add [111, 1] (w:1, o:128, a:1
% 1.28/1.67 , s:1, b:0),
% 1.28/1.67 class_Rings_Osemiring [112, 1] (w:1, o:152, a:1, s:1, b:0),
% 1.28/1.67 class_Rings_Ocomm__semiring__1 [117, 1] (w:1, o:154, a:1, s:1, b:0),
% 1.28/1.67
% 1.28/1.67 class_Rings_Ocomm__ring__1 [120, 1] (w:1, o:153, a:1, s:1, b:0),
% 1.28/1.67 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 1.28/1.67 126, 1] (w:1, o:164, a:1, s:1, b:0),
% 1.28/1.67 class_Groups_Ogroup__add [130, 1] (w:1, o:165, a:1, s:1, b:0),
% 1.28/1.67 c_Complex_Ocomplex_Ocomplex__size [133, 1] (w:1, o:166, a:1, s:1, b:0
% 1.28/1.67 ),
% 1.28/1.67 class_Groups_Oab__group__add [134, 1] (w:1, o:167, a:1, s:1, b:0),
% 1.28/1.67 class_Groups_Ozero [135, 1] (w:1, o:168, a:1, s:1, b:0),
% 1.28/1.67 class_Groups_Oab__semigroup__mult [136, 1] (w:1, o:169, a:1, s:1, b:0
% 1.28/1.67 ),
% 1.28/1.67 class_Groups_Oab__semigroup__add [137, 1] (w:1, o:170, a:1, s:1, b:0)
% 1.28/1.67 ,
% 1.28/1.67 class_Groups_Ocancel__semigroup__add [138, 1] (w:1, o:171, a:1, s:1
% 1.28/1.67 , b:0),
% 1.28/1.67 class_Groups_Ocancel__ab__semigroup__add [139, 1] (w:1, o:172, a:1
% 1.28/1.67 , s:1, b:0),
% 1.28/1.67 class_Groups_Oone [140, 1] (w:1, o:173, a:1, s:1, b:0),
% 1.28/1.67 class_Rings_Oring__no__zero__divisors [142, 1] (w:1, o:111, a:1, s:1
% 1.28/1.67 , b:0),
% 1.28/1.67 class_Groups_Omonoid__add [143, 1] (w:1, o:174, a:1, s:1, b:0),
% 1.28/1.67 class_Groups_Ocomm__monoid__add [144, 1] (w:1, o:175, a:1, s:1, b:0)
% 1.28/1.67 ,
% 1.28/1.67 class_Rings_Ocomm__semiring [145, 1] (w:1, o:155, a:1, s:1, b:0),
% 1.28/1.67 class_Rings_Oidom [147, 1] (w:1, o:156, a:1, s:1, b:0),
% 1.28/1.67 class_Rings_Oring [148, 1] (w:1, o:112, a:1, s:1, b:0),
% 1.28/1.67 c_Int_Oiszero [149, 2] (w:1, o:216, a:1, s:1, b:0),
% 1.28/1.67 c_Orderings_Oord__class_Oless__eq [150, 3] (w:1, o:239, a:1, s:1, b:0
% 1.28/1.67 ),
% 1.28/1.67 c_Nat_Osize__class_Osize [151, 2] (w:1, o:217, a:1, s:1, b:0),
% 1.28/1.67 class_Rings_Olinordered__semidom [155, 1] (w:1, o:141, a:1, s:1, b:0)
% 1.28/1.67 ,
% 1.28/1.67 class_Groups_Oordered__ab__semigroup__add__imp__le [156, 1] (w:1, o:
% 1.28/1.67 176, a:1, s:1, b:0),
% 1.28/1.67 class_Groups_Oordered__ab__semigroup__add [157, 1] (w:1, o:177, a:1
% 1.28/1.67 , s:1, b:0),
% 1.28/1.67 class_Groups_Oordered__ab__group__add [158, 1] (w:1, o:178, a:1, s:1
% 1.28/1.67 , b:0),
% 1.28/1.67 class_Rings_Olinordered__ring [159, 1] (w:1, o:140, a:1, s:1, b:0),
% 1.28/1.67 class_Rings_Oordered__cancel__semiring [160, 1] (w:1, o:157, a:1, s:1
% 1.28/1.67 , b:0),
% 1.28/1.67 class_Rings_Oordered__ring [161, 1] (w:1, o:158, a:1, s:1, b:0),
% 1.28/1.67 class_Rings_Oordered__semiring [162, 1] (w:1, o:159, a:1, s:1, b:0),
% 1.28/1.67
% 1.28/1.67 class_Rings_Oordered__comm__semiring [163, 1] (w:1, o:160, a:1, s:1
% 1.28/1.67 , b:0),
% 1.28/1.67 class_Groups_Oordered__comm__monoid__add [164, 1] (w:1, o:179, a:1
% 1.28/1.67 , s:1, b:0),
% 1.28/1.67 class_Rings_Olinordered__semiring__1 [166, 1] (w:1, o:142, a:1, s:1
% 1.28/1.67 , b:0),
% 1.28/1.67 class_Orderings_Opreorder [167, 1] (w:1, o:136, a:1, s:1, b:0),
% 1.28/1.67 c_Complex_Ocomplex_Ocomplex__rec [169, 3] (w:1, o:240, a:1, s:1, b:0)
% 1.28/1.67 ,
% 1.28/1.67 c_Complex_Ocomplex_Ocomplex__case [170, 3] (w:1, o:241, a:1, s:1, b:0
% 1.28/1.67 ),
% 1.28/1.67 c_Nat_OSuc [171, 1] (w:1, o:180, a:1, s:1, b:0),
% 1.28/1.67 c_Parity_Oeven__odd__class_Oeven [172, 2] (w:1, o:218, a:1, s:1, b:0)
% 1.28/1.67 ,
% 1.28/1.67 class_Orderings_Olinorder [183, 1] (w:1, o:137, a:1, s:1, b:0),
% 1.28/1.67 class_Orderings_Oord [184, 1] (w:1, o:134, a:1, s:1, b:0),
% 1.28/1.67 tc_fun [185, 2] (w:1, o:224, a:1, s:1, b:0),
% 1.28/1.67 class_Orderings_Oorder [186, 1] (w:1, o:135, a:1, s:1, b:0),
% 1.28/1.67 c_Orderings_Oord__class_Oless [187, 3] (w:1, o:242, a:1, s:1, b:0),
% 1.28/1.67 c_Int_OMin [188, 0] (w:1, o:96, a:1, s:1, b:0),
% 1.28/1.67 c_Power_Opower_Opower [189, 3] (w:1, o:243, a:1, s:1, b:0),
% 1.28/1.67 class_Groups_Oordered__cancel__ab__semigroup__add [190, 1] (w:1, o:
% 1.28/1.67 181, a:1, s:1, b:0),
% 1.28/1.67 class_Rings_Olinordered__comm__semiring__strict [191, 1] (w:1, o:143
% 1.28/1.67 , a:1, s:1, b:0),
% 1.28/1.67 class_Rings_Olinordered__semiring__strict [192, 1] (w:1, o:144, a:1
% 1.28/1.67 , s:1, b:0),
% 1.28/1.67 class_Rings_Olinordered__semiring [197, 1] (w:1, o:145, a:1, s:1, b:0
% 1.28/1.67 ),
% 1.28/1.67 class_Rings_Olinordered__semiring__1__strict [202, 1] (w:1, o:146, a:
% 1.28/1.67 1, s:1, b:0),
% 1.28/1.67 hBOOL [207, 1] (w:1, o:182, a:1, s:1, b:0),
% 1.28/1.67 c_Rings_Oinverse__class_Odivide [208, 3] (w:1, o:244, a:1, s:1, b:0)
% 1.28/1.67 ,
% 1.28/1.67 class_Rings_Odivision__ring [209, 1] (w:1, o:161, a:1, s:1, b:0),
% 1.28/1.67 class_Rings_Odivision__ring__inverse__zero [210, 1] (w:1, o:162, a:1
% 1.28/1.67 , s:1, b:0),
% 1.28/1.67 class_Fields_Ofield [211, 1] (w:1, o:124, a:1, s:1, b:0),
% 1.28/1.67 class_Fields_Ofield__inverse__zero [212, 1] (w:1, o:125, a:1, s:1, b:
% 1.28/1.67 0),
% 1.28/1.67 class_RealVector_Oreal__normed__field [213, 1] (w:1, o:163, a:1, s:1
% 1.28/1.67 , b:0),
% 1.28/1.67 class_Fields_Olinordered__field__inverse__zero [214, 1] (w:1, o:126
% 1.28/1.67 , a:1, s:1, b:0),
% 1.28/1.67 class_Fields_Olinordered__field [216, 1] (w:1, o:127, a:1, s:1, b:0)
% 1.28/1.67 ,
% 1.28/1.67 c_Complex_Oii [217, 0] (w:1, o:99, a:1, s:1, b:0),
% 1.28/1.67 c_Transcendental_Oarctan [218, 1] (w:1, o:183, a:1, s:1, b:0),
% 1.28/1.67 c_Groups_Oabs__class_Oabs [219, 2] (w:1, o:225, a:1, s:1, b:0),
% 1.28/1.67 tc_HOL_Obool [222, 0] (w:1, o:32, a:1, s:1, b:0),
% 1.28/1.67 alpha1 [223, 3] (w:1, o:245, a:1, s:1, b:1),
% 1.28/1.67 alpha2 [224, 3] (w:1, o:256, a:1, s:1, b:1),
% 1.28/1.67 alpha3 [225, 2] (w:1, o:226, a:1, s:1, b:1),
% 1.28/1.67 alpha4 [226, 2] (w:1, o:230, a:1, s:1, b:1),
% 1.28/1.67 alpha5 [227, 2] (w:1, o:233, a:1, s:1, b:1),
% 1.28/1.67 alpha6 [228, 2] (w:1, o:234, a:1, s:1, b:1),
% 1.28/1.67 alpha7 [229, 4] (w:1, o:288, a:1, s:1, b:1),
% 1.28/1.67 alpha8 [230, 4] (w:1, o:299, a:1, s:1, b:1),
% 1.28/1.67 alpha9 [231, 2] (w:1, o:235, a:1, s:1, b:1),
% 1.28/1.67 alpha10 [232, 2] (w:1, o:236, a:1, s:1, b:1),
% 1.28/1.67 alpha11 [233, 2] (w:1, o:237, a:1, s:1, b:1),
% 1.28/1.67 alpha12 [234, 3] (w:1, o:246, a:1, s:1, b:1),
% 1.28/1.67 alpha13 [235, 3] (w:1, o:247, a:1, s:1, b:1),
% 1.28/1.67 alpha14 [236, 3] (w:1, o:248, a:1, s:1, b:1),
% 1.28/1.67 alpha15 [237, 3] (w:1, o:249, a:1, s:1, b:1),
% 1.28/1.67 alpha16 [238, 3] (w:1, o:250, a:1, s:1, b:1),
% 1.28/1.67 alpha17 [239, 3] (w:1, o:251, a:1, s:1, b:1),
% 1.28/1.67 alpha18 [240, 3] (w:1, o:252, a:1, s:1, b:1),
% 1.28/1.67 alpha19 [241, 3] (w:1, o:253, a:1, s:1, b:1),
% 1.28/1.67 alpha20 [242, 3] (w:1, o:257, a:1, s:1, b:1),
% 1.28/1.67 alpha21 [243, 3] (w:1, o:258, a:1, s:1, b:1),
% 1.28/1.67 alpha22 [244, 3] (w:1, o:259, a:1, s:1, b:1),
% 1.28/1.67 alpha23 [245, 3] (w:1, o:260, a:1, s:1, b:1),
% 1.28/1.67 alpha24 [246, 3] (w:1, o:261, a:1, s:1, b:1),
% 1.28/1.67 alpha25 [247, 3] (w:1, o:262, a:1, s:1, b:1),
% 1.28/1.67 alpha26 [248, 3] (w:1, o:263, a:1, s:1, b:1),
% 1.28/1.67 alpha27 [249, 3] (w:1, o:264, a:1, s:1, b:1),
% 1.28/1.67 alpha28 [250, 3] (w:1, o:265, a:1, s:1, b:1),
% 1.28/1.67 alpha29 [251, 3] (w:1, o:266, a:1, s:1, b:1),
% 1.28/1.67 alpha30 [252, 3] (w:1, o:267, a:1, s:1, b:1),
% 1.28/1.67 alpha31 [253, 3] (w:1, o:268, a:1, s:1, b:1),
% 1.28/1.67 alpha32 [254, 3] (w:1, o:269, a:1, s:1, b:1),
% 1.28/1.67 alpha33 [255, 3] (w:1, o:270, a:1, s:1, b:1),
% 1.28/1.67 alpha34 [256, 3] (w:1, o:271, a:1, s:1, b:1),
% 1.28/1.67 alpha35 [257, 3] (w:1, o:272, a:1, s:1, b:1),
% 20.44/20.79 alpha36 [258, 2] (w:1, o:227, a:1, s:1, b:1),
% 20.44/20.79 alpha37 [259, 2] (w:1, o:228, a:1, s:1, b:1),
% 20.44/20.79 alpha38 [260, 2] (w:1, o:229, a:1, s:1, b:1),
% 20.44/20.79 alpha39 [261, 4] (w:1, o:300, a:1, s:1, b:1),
% 20.44/20.79 alpha40 [262, 4] (w:1, o:301, a:1, s:1, b:1),
% 20.44/20.79 alpha41 [263, 2] (w:1, o:231, a:1, s:1, b:1),
% 20.44/20.79 alpha42 [264, 2] (w:1, o:232, a:1, s:1, b:1),
% 20.44/20.79 alpha43 [265, 4] (w:1, o:302, a:1, s:1, b:1),
% 20.44/20.79 alpha44 [266, 4] (w:1, o:303, a:1, s:1, b:1),
% 20.44/20.79 alpha45 [267, 4] (w:1, o:304, a:1, s:1, b:1),
% 20.44/20.79 alpha46 [268, 4] (w:1, o:305, a:1, s:1, b:1),
% 20.44/20.79 alpha47 [269, 4] (w:1, o:306, a:1, s:1, b:1),
% 20.44/20.79 alpha48 [270, 4] (w:1, o:307, a:1, s:1, b:1),
% 20.44/20.79 alpha49 [271, 4] (w:1, o:308, a:1, s:1, b:1),
% 20.44/20.79 alpha50 [272, 4] (w:1, o:309, a:1, s:1, b:1),
% 20.44/20.79 alpha51 [273, 4] (w:1, o:310, a:1, s:1, b:1),
% 20.44/20.79 alpha52 [274, 4] (w:1, o:311, a:1, s:1, b:1),
% 20.44/20.79 alpha53 [275, 4] (w:1, o:312, a:1, s:1, b:1),
% 20.44/20.79 alpha54 [276, 4] (w:1, o:313, a:1, s:1, b:1),
% 20.44/20.79 alpha55 [277, 3] (w:1, o:273, a:1, s:1, b:1),
% 20.44/20.79 alpha56 [278, 3] (w:1, o:274, a:1, s:1, b:1),
% 20.44/20.79 alpha57 [279, 3] (w:1, o:275, a:1, s:1, b:1),
% 20.44/20.79 alpha58 [280, 3] (w:1, o:276, a:1, s:1, b:1),
% 20.44/20.79 alpha59 [281, 4] (w:1, o:314, a:1, s:1, b:1),
% 20.44/20.79 alpha60 [282, 4] (w:1, o:278, a:1, s:1, b:1),
% 20.44/20.79 alpha61 [283, 4] (w:1, o:279, a:1, s:1, b:1),
% 20.44/20.79 alpha62 [284, 4] (w:1, o:280, a:1, s:1, b:1),
% 20.44/20.79 alpha63 [285, 4] (w:1, o:281, a:1, s:1, b:1),
% 20.44/20.79 alpha64 [286, 4] (w:1, o:282, a:1, s:1, b:1),
% 20.44/20.79 alpha65 [287, 4] (w:1, o:283, a:1, s:1, b:1),
% 20.44/20.79 alpha66 [288, 4] (w:1, o:284, a:1, s:1, b:1),
% 20.44/20.79 alpha67 [289, 4] (w:1, o:285, a:1, s:1, b:1),
% 20.44/20.79 alpha68 [290, 4] (w:1, o:286, a:1, s:1, b:1),
% 20.44/20.79 alpha69 [291, 4] (w:1, o:287, a:1, s:1, b:1),
% 20.44/20.79 alpha70 [292, 4] (w:1, o:289, a:1, s:1, b:1),
% 20.44/20.79 alpha71 [293, 4] (w:1, o:290, a:1, s:1, b:1),
% 20.44/20.79 alpha72 [294, 4] (w:1, o:291, a:1, s:1, b:1),
% 20.44/20.79 alpha73 [295, 4] (w:1, o:292, a:1, s:1, b:1),
% 20.44/20.79 alpha74 [296, 4] (w:1, o:293, a:1, s:1, b:1),
% 20.44/20.79 alpha75 [297, 4] (w:1, o:294, a:1, s:1, b:1),
% 20.44/20.79 alpha76 [298, 4] (w:1, o:295, a:1, s:1, b:1),
% 20.44/20.79 alpha77 [299, 4] (w:1, o:296, a:1, s:1, b:1),
% 20.44/20.79 alpha78 [300, 4] (w:1, o:297, a:1, s:1, b:1),
% 20.44/20.79 alpha79 [301, 4] (w:1, o:298, a:1, s:1, b:1),
% 20.44/20.79 alpha80 [302, 4] (w:1, o:315, a:1, s:1, b:1),
% 20.44/20.79 alpha81 [303, 4] (w:1, o:316, a:1, s:1, b:1),
% 20.44/20.79 alpha82 [304, 4] (w:1, o:317, a:1, s:1, b:1),
% 20.44/20.79 alpha83 [305, 4] (w:1, o:318, a:1, s:1, b:1),
% 20.44/20.79 alpha84 [306, 4] (w:1, o:319, a:1, s:1, b:1),
% 20.44/20.79 alpha85 [307, 4] (w:1, o:320, a:1, s:1, b:1),
% 20.44/20.79 alpha86 [308, 4] (w:1, o:321, a:1, s:1, b:1),
% 20.44/20.79 alpha87 [309, 4] (w:1, o:322, a:1, s:1, b:1),
% 20.44/20.79 alpha88 [310, 4] (w:1, o:323, a:1, s:1, b:1),
% 20.44/20.79 alpha89 [311, 4] (w:1, o:324, a:1, s:1, b:1),
% 20.44/20.79 alpha90 [312, 4] (w:1, o:325, a:1, s:1, b:1),
% 20.44/20.79 alpha91 [313, 4] (w:1, o:326, a:1, s:1, b:1),
% 20.44/20.79 alpha92 [314, 4] (w:1, o:327, a:1, s:1, b:1),
% 20.44/20.79 alpha93 [315, 4] (w:1, o:328, a:1, s:1, b:1),
% 20.44/20.79 alpha94 [316, 4] (w:1, o:329, a:1, s:1, b:1),
% 20.44/20.79 alpha95 [317, 4] (w:1, o:330, a:1, s:1, b:1),
% 20.44/20.79 alpha96 [318, 4] (w:1, o:331, a:1, s:1, b:1),
% 20.44/20.79 alpha97 [319, 4] (w:1, o:332, a:1, s:1, b:1),
% 20.44/20.79 alpha98 [320, 4] (w:1, o:333, a:1, s:1, b:1),
% 20.44/20.79 alpha99 [321, 4] (w:1, o:334, a:1, s:1, b:1),
% 20.44/20.79 alpha100 [322, 4] (w:1, o:335, a:1, s:1, b:1),
% 20.44/20.79 alpha101 [323, 3] (w:1, o:254, a:1, s:1, b:1),
% 20.44/20.79 alpha102 [324, 3] (w:1, o:255, a:1, s:1, b:1),
% 20.44/20.79 skol1 [325, 2] (w:1, o:219, a:1, s:1, b:1),
% 20.44/20.79 skol2 [326, 0] (w:1, o:12, a:1, s:1, b:1),
% 20.44/20.79 skol3 [327, 1] (w:1, o:184, a:1, s:1, b:1),
% 20.44/20.79 skol4 [328, 2] (w:1, o:220, a:1, s:1, b:1),
% 20.44/20.79 skol5 [329, 2] (w:1, o:221, a:1, s:1, b:1),
% 20.44/20.79 skol6 [330, 3] (w:1, o:277, a:1, s:1, b:1),
% 20.44/20.79 skol7 [331, 1] (w:1, o:185, a:1, s:1, b:1),
% 20.44/20.79 skol8 [332, 1] (w:1, o:186, a:1, s:1, b:1),
% 20.44/20.79 skol9 [333, 2] (w:1, o:222, a:1, s:1, b:1),
% 20.44/20.79 skol10 [334, 2] (w:1, o:223, a:1, s:1, b:1),
% 130.62/131.03 skol11 [335, 0] (w:1, o:11, a:1, s:1, b:1).
% 130.62/131.03
% 130.62/131.03
% 130.62/131.03 Starting Search:
% 130.62/131.03
% 130.62/131.03 *** allocated 170857 integers for clauses
% 130.62/131.03 Resimplifying inuse:
% 130.62/131.03 Done
% 130.62/131.03
% 130.62/131.03
% 130.62/131.03 Intermediate Status:
% 130.62/131.03 Generated: 2814
% 130.62/131.03 Kept: 2015
% 130.62/131.03 Inuse: 6
% 130.62/131.03 Deleted: 0
% 130.62/131.03 Deletedinuse: 0
% 130.62/131.03
% 130.62/131.03 *** allocated 256285 integers for clauses
% 130.62/131.03 Resimplifying inuse:
% 130.62/131.03 Done
% 130.62/131.03
% 130.62/131.03 *** allocated 170857 integers for termspace/termends
% 130.62/131.03
% 130.62/131.03 Intermediate Status:
% 130.62/131.03 Generated: 7909
% 130.62/131.03 Kept: 4031
% 130.62/131.03 Inuse: 225
% 130.62/131.03 Deleted: 16
% 130.62/131.03 Deletedinuse: 5
% 130.62/131.03
% 130.62/131.03 *** allocated 384427 integers for clauses
% 130.62/131.03 Resimplifying inuse:
% 130.62/131.03 Done
% 130.62/131.03
% 130.62/131.03 Resimplifying inuse:
% 130.62/131.03 Done
% 130.62/131.03
% 130.62/131.03 *** allocated 256285 integers for termspace/termends
% 130.62/131.03
% 130.62/131.03 Intermediate Status:
% 130.62/131.03 Generated: 13375
% 130.62/131.03 Kept: 6415
% 130.62/131.03 Inuse: 329
% 130.62/131.03 Deleted: 28
% 130.62/131.03 Deletedinuse: 6
% 130.62/131.03
% 130.62/131.03 Resimplifying inuse:
% 130.62/131.03 Done
% 130.62/131.03
% 130.62/131.03 *** allocated 576640 integers for clauses
% 130.62/131.03 Resimplifying inuse:
% 130.62/131.03 Done
% 130.62/131.03
% 130.62/131.03
% 130.62/131.03 Intermediate Status:
% 130.62/131.03 Generated: 18441
% 130.62/131.03 Kept: 8418
% 130.62/131.03 Inuse: 378
% 130.62/131.03 Deleted: 28
% 130.62/131.03 Deletedinuse: 6
% 130.62/131.03
% 130.62/131.03 Resimplifying inuse:
% 130.62/131.03 Done
% 130.62/131.03
% 130.62/131.03 *** allocated 384427 integers for termspace/termends
% 130.62/131.03 Resimplifying inuse:
% 130.62/131.03 Done
% 130.62/131.03
% 130.62/131.03 *** allocated 864960 integers for clauses
% 130.62/131.03
% 130.62/131.03 Intermediate Status:
% 130.62/131.03 Generated: 23574
% 130.62/131.03 Kept: 10418
% 130.62/131.03 Inuse: 431
% 130.62/131.03 Deleted: 30
% 130.62/131.03 Deletedinuse: 6
% 130.62/131.03
% 130.62/131.03 Resimplifying inuse:
% 130.62/131.03 Done
% 130.62/131.03
% 130.62/131.03 Resimplifying inuse:
% 130.62/131.03 Done
% 130.62/131.03
% 130.62/131.03
% 130.62/131.03 Intermediate Status:
% 130.62/131.03 Generated: 29000
% 130.62/131.03 Kept: 13004
% 130.62/131.03 Inuse: 462
% 130.62/131.03 Deleted: 30
% 130.62/131.03 Deletedinuse: 6
% 130.62/131.03
% 130.62/131.03 Resimplifying inuse:
% 130.62/131.03 Done
% 130.62/131.03
% 130.62/131.03 *** allocated 576640 integers for termspace/termends
% 130.62/131.03
% 130.62/131.03 Intermediate Status:
% 130.62/131.03 Generated: 34778
% 130.62/131.03 Kept: 15554
% 130.62/131.03 Inuse: 507
% 130.62/131.03 Deleted: 30
% 130.62/131.03 Deletedinuse: 6
% 130.62/131.03
% 130.62/131.03 Resimplifying inuse:
% 130.62/131.03 Done
% 130.62/131.03
% 130.62/131.03 *** allocated 1297440 integers for clauses
% 130.62/131.03 Resimplifying inuse:
% 130.62/131.03 Done
% 130.62/131.03
% 130.62/131.03
% 130.62/131.03 Intermediate Status:
% 130.62/131.03 Generated: 38471
% 130.62/131.03 Kept: 17560
% 130.62/131.03 Inuse: 529
% 130.62/131.03 Deleted: 32
% 130.62/131.03 Deletedinuse: 8
% 130.62/131.03
% 130.62/131.03 Resimplifying inuse:
% 130.62/131.03 Done
% 130.62/131.03
% 130.62/131.03 Resimplifying inuse:
% 130.62/131.03 Done
% 130.62/131.03
% 130.62/131.03
% 130.62/131.03 Intermediate Status:
% 130.62/131.03 Generated: 46697
% 130.62/131.03 Kept: 19822
% 130.62/131.03 Inuse: 594
% 130.62/131.03 Deleted: 35
% 130.62/131.03 Deletedinuse: 8
% 130.62/131.03
% 130.62/131.03 Resimplifying inuse:
% 130.62/131.03 Done
% 130.62/131.03
% 130.62/131.03 Resimplifying clauses:
% 130.62/131.03 Done
% 130.62/131.03
% 130.62/131.03 Resimplifying inuse:
% 130.62/131.03 Done
% 130.62/131.03
% 130.62/131.03
% 130.62/131.03 Intermediate Status:
% 130.62/131.03 Generated: 53400
% 130.62/131.03 Kept: 21825
% 130.62/131.03 Inuse: 610
% 130.62/131.03 Deleted: 859
% 130.62/131.03 Deletedinuse: 8
% 130.62/131.03
% 130.62/131.03 Resimplifying inuse:
% 130.62/131.03 Done
% 130.62/131.03
% 130.62/131.03 Resimplifying inuse:
% 130.62/131.03 Done
% 130.62/131.03
% 130.62/131.03
% 130.62/131.03 Intermediate Status:
% 130.62/131.03 Generated: 58482
% 130.62/131.03 Kept: 23838
% 130.62/131.03 Inuse: 637
% 130.62/131.03 Deleted: 859
% 130.62/131.03 Deletedinuse: 8
% 130.62/131.03
% 130.62/131.03 Resimplifying inuse:
% 130.62/131.03 Done
% 130.62/131.03
% 130.62/131.03 *** allocated 864960 integers for termspace/termends
% 130.62/131.03 Resimplifying inuse:
% 130.62/131.03 Done
% 130.62/131.03
% 130.62/131.03
% 130.62/131.03 Intermediate Status:
% 130.62/131.03 Generated: 71007
% 130.62/131.03 Kept: 25850
% 130.62/131.03 Inuse: 657
% 130.62/131.03 Deleted: 859
% 130.62/131.03 Deletedinuse: 8
% 130.62/131.03
% 130.62/131.03 *** allocated 1946160 integers for clauses
% 130.62/131.03
% 130.62/131.03 Intermediate Status:
% 130.62/131.03 Generated: 86696
% 130.62/131.03 Kept: 28168
% 130.62/131.03 Inuse: 664
% 130.62/131.03 Deleted: 859
% 130.62/131.03 Deletedinuse: 8
% 130.62/131.03
% 130.62/131.03 Resimplifying inuse:
% 130.62/131.03 Done
% 130.62/131.03
% 130.62/131.03 Resimplifying inuse:
% 130.62/131.03 Done
% 130.62/131.03
% 130.62/131.03
% 130.62/131.03 Intermediate Status:
% 130.62/131.03 Generated: 96187
% 130.62/131.03 Kept: 30178
% 130.62/131.03 Inuse: 700
% 130.62/131.03 Deleted: 859
% 130.62/131.03 Deletedinuse: 8
% 130.62/131.03
% 130.62/131.03 Resimplifying inuse:
% 130.62/131.03 Done
% 130.62/131.03
% 130.62/131.03 Resimplifying inuse:
% 130.62/131.03 Done
% 130.62/131.03
% 130.62/131.03
% 130.62/131.03 Intermediate Status:
% 130.62/131.03 Generated: 104569
% 130.62/131.03 Kept: 32421
% 130.62/131.03 Inuse: 744
% 130.62/131.03 Deleted: 859
% 130.62/131.03 Deletedinuse: 8
% 130.62/131.03
% 130.62/131.03 Resimplifying inuse:
% 130.62/131.03 Done
% 130.62/131.03
% 130.62/131.03 Resimplifying inuse:
% 130.62/131.03 Done
% 130.62/131.03
% 130.62/131.03 *** allocated 1297440 integers for termspace/termends
% 130.62/131.03
% 130.62/131.03 Intermediate Status:
% 130.62/131.03 Generated: 113170
% 130.62/131.03 Kept: 35926
% 130.62/131.03 Inuse: 759
% 130.62/131.03 Deleted: 860
% 130.62/131.03 Deletedinuse: 9
% 130.62/131.03
% 130.62/131.03 Resimplifying inuse:
% 130.62/131.03 Done
% 130.62/131.03
% 130.62/131.03 Resimplifying inuse:
% 130.62/131.03 Done
% 130.62/131.03
% 130.62/131.03
% 130.62/131.03 Intermediate Status:
% 130.62/131.03 Generated: 117818
% 130.62/131.03 Kept: 37931
% 130.62/131.03 Inuse: 787
% 130.62/131.03 Deleted: 860
% 130.62/131.03 Deletedinuse: 9
% 130.62/131.03
% 130.62/131.03 Resimplifying inuse:
% 130.62/131.03 Done
% 130.62/131.03
% 130.62/131.03 *** allocated 2919240 integers for clauses
% 130.62/131.03
% 130.62/131.03 Intermediate Status:
% 130.62/131.03 Generated: 126357
% 130.62/131.03 Kept: 40849
% 130.62/131.03 Inuse: 803
% 130.62/131.03 Deleted: 861
% 130.62/131.03 Deletedinuse: 9
% 130.62/131.03
% 130.62/131.03 Resimplifying inuse:
% 130.62/131.03 Done
% 130.62/131.03
% 130.62/131.03 Resimplifying clauses:
% 130.62/131.03 Done
% 130.62/131.03
% 130.62/131.03
% 130.62/131.03 Intermediate Status:
% 130.62/131.03 Generated: 130996
% 130.62/131.03 Kept: 42930
% 130.62/131.03 Inuse: 823
% 130.62/131.03 Deleted: 1066
% 130.62/131.03 Deletedinuse: 9
% 130.62/131.03
% 130.62/131.03 Resimplifying inuse:
% 130.62/131.03 Done
% 130.62/131.03
% 130.62/131.03
% 130.62/131.03 Intermediate Status:
% 130.62/131.03 Generated: 158781
% 130.62/131.03 Kept: 46085
% 130.62/131.03 Inuse: 843
% 130.62/131.03 Deleted: 1066
% 130.62/131.03 Deletedinuse: 9
% 130.62/131.03
% 130.62/131.03 Resimplifying inuse:
% 130.62/131.03 Done
% 130.62/131.03
% 130.62/131.03 Resimplifying inuse:
% 130.62/131.03 Done
% 130.62/131.03
% 130.62/131.03
% 130.62/131.03 Intermediate Status:
% 130.62/131.03 Generated: 168181
% 130.62/131.03 Kept: 48378
% 130.62/131.03 Inuse: 878
% 130.62/131.03 Deleted: 1066
% 248.34/248.75 Deletedinuse: 9
% 248.34/248.75
% 248.34/248.75 Resimplifying inuse:
% 248.34/248.75 Done
% 248.34/248.75
% 248.34/248.75
% 248.34/248.75 Intermediate Status:
% 248.34/248.75 Generated: 173359
% 248.34/248.75 Kept: 50588
% 248.34/248.75 Inuse: 898
% 248.34/248.75 Deleted: 1066
% 248.34/248.75 Deletedinuse: 9
% 248.34/248.75
% 248.34/248.75 Resimplifying inuse:
% 248.34/248.75 Done
% 248.34/248.75
% 248.34/248.75 *** allocated 1946160 integers for termspace/termends
% 248.34/248.75
% 248.34/248.75 Intermediate Status:
% 248.34/248.75 Generated: 198275
% 248.34/248.75 Kept: 53112
% 248.34/248.75 Inuse: 913
% 248.34/248.75 Deleted: 1066
% 248.34/248.75 Deletedinuse: 9
% 248.34/248.75
% 248.34/248.75 Resimplifying inuse:
% 248.34/248.75 Done
% 248.34/248.75
% 248.34/248.75 Resimplifying inuse:
% 248.34/248.75 Done
% 248.34/248.75
% 248.34/248.75
% 248.34/248.75 Intermediate Status:
% 248.34/248.75 Generated: 205261
% 248.34/248.75 Kept: 55404
% 248.34/248.75 Inuse: 933
% 248.34/248.75 Deleted: 1067
% 248.34/248.75 Deletedinuse: 10
% 248.34/248.75
% 248.34/248.75 Resimplifying inuse:
% 248.34/248.75 Done
% 248.34/248.75
% 248.34/248.75 Resimplifying inuse:
% 248.34/248.75 Done
% 248.34/248.75
% 248.34/248.75
% 248.34/248.75 Intermediate Status:
% 248.34/248.75 Generated: 221910
% 248.34/248.75 Kept: 58981
% 248.34/248.75 Inuse: 948
% 248.34/248.75 Deleted: 1067
% 248.34/248.75 Deletedinuse: 10
% 248.34/248.75
% 248.34/248.75 Resimplifying inuse:
% 248.34/248.75 Done
% 248.34/248.75
% 248.34/248.75 *** allocated 4378860 integers for clauses
% 248.34/248.75 Resimplifying inuse:
% 248.34/248.75 Done
% 248.34/248.75
% 248.34/248.75 Resimplifying clauses:
% 248.34/248.75 Done
% 248.34/248.75
% 248.34/248.75
% 248.34/248.75 Intermediate Status:
% 248.34/248.75 Generated: 232336
% 248.34/248.75 Kept: 61181
% 248.34/248.75 Inuse: 958
% 248.34/248.75 Deleted: 1412
% 248.34/248.75 Deletedinuse: 10
% 248.34/248.75
% 248.34/248.75 Resimplifying inuse:
% 248.34/248.75 Done
% 248.34/248.75
% 248.34/248.75
% 248.34/248.75 Intermediate Status:
% 248.34/248.75 Generated: 244568
% 248.34/248.75 Kept: 64092
% 248.34/248.75 Inuse: 1003
% 248.34/248.75 Deleted: 1412
% 248.34/248.75 Deletedinuse: 10
% 248.34/248.75
% 248.34/248.75 Resimplifying inuse:
% 248.34/248.75 Done
% 248.34/248.75
% 248.34/248.75 Resimplifying inuse:
% 248.34/248.75 Done
% 248.34/248.75
% 248.34/248.75
% 248.34/248.75 Intermediate Status:
% 248.34/248.75 Generated: 258020
% 248.34/248.75 Kept: 66584
% 248.34/248.75 Inuse: 1023
% 248.34/248.75 Deleted: 1412
% 248.34/248.75 Deletedinuse: 10
% 248.34/248.75
% 248.34/248.75 Resimplifying inuse:
% 248.34/248.75 Done
% 248.34/248.75
% 248.34/248.75 Resimplifying inuse:
% 248.34/248.75 Done
% 248.34/248.75
% 248.34/248.75
% 248.34/248.75 Intermediate Status:
% 248.34/248.75 Generated: 270228
% 248.34/248.75 Kept: 69923
% 248.34/248.75 Inuse: 1038
% 248.34/248.75 Deleted: 1412
% 248.34/248.75 Deletedinuse: 10
% 248.34/248.75
% 248.34/248.75 Resimplifying inuse:
% 248.34/248.75 Done
% 248.34/248.75
% 248.34/248.75 Resimplifying inuse:
% 248.34/248.75 Done
% 248.34/248.75
% 248.34/248.75
% 248.34/248.75 Intermediate Status:
% 248.34/248.75 Generated: 279919
% 248.34/248.75 Kept: 72056
% 248.34/248.75 Inuse: 1063
% 248.34/248.75 Deleted: 1412
% 248.34/248.75 Deletedinuse: 10
% 248.34/248.75
% 248.34/248.75 Resimplifying inuse:
% 248.34/248.75 Done
% 248.34/248.75
% 248.34/248.75
% 248.34/248.75 Intermediate Status:
% 248.34/248.75 Generated: 289455
% 248.34/248.75 Kept: 74166
% 248.34/248.75 Inuse: 1078
% 248.34/248.75 Deleted: 1412
% 248.34/248.75 Deletedinuse: 10
% 248.34/248.75
% 248.34/248.75 *** allocated 2919240 integers for termspace/termends
% 248.34/248.75
% 248.34/248.75 Intermediate Status:
% 248.34/248.75 Generated: 307111
% 248.34/248.75 Kept: 76660
% 248.34/248.75 Inuse: 1088
% 248.34/248.75 Deleted: 1412
% 248.34/248.75 Deletedinuse: 10
% 248.34/248.75
% 248.34/248.75 Resimplifying inuse:
% 248.34/248.75 Done
% 248.34/248.75
% 248.34/248.75
% 248.34/248.75 Intermediate Status:
% 248.34/248.75 Generated: 323118
% 248.34/248.75 Kept: 78769
% 248.34/248.75 Inuse: 1093
% 248.34/248.75 Deleted: 1412
% 248.34/248.75 Deletedinuse: 10
% 248.34/248.75
% 248.34/248.75 Resimplifying inuse:
% 248.34/248.75 Done
% 248.34/248.75
% 248.34/248.75 Resimplifying inuse:
% 248.34/248.75 Done
% 248.34/248.75
% 248.34/248.75
% 248.34/248.75 Intermediate Status:
% 248.34/248.75 Generated: 332411
% 248.34/248.75 Kept: 80927
% 248.34/248.75 Inuse: 1148
% 248.34/248.75 Deleted: 1412
% 248.34/248.75 Deletedinuse: 10
% 248.34/248.75
% 248.34/248.75 Resimplifying inuse:
% 248.34/248.75 Done
% 248.34/248.75
% 248.34/248.75 Resimplifying inuse:
% 248.34/248.75 Done
% 248.34/248.75
% 248.34/248.75 Resimplifying clauses:
% 248.34/248.75 Done
% 248.34/248.75
% 248.34/248.75
% 248.34/248.75 Intermediate Status:
% 248.34/248.75 Generated: 340229
% 248.34/248.75 Kept: 84564
% 248.34/248.75 Inuse: 1163
% 248.34/248.75 Deleted: 1503
% 248.34/248.75 Deletedinuse: 10
% 248.34/248.75
% 248.34/248.75 Resimplifying inuse:
% 248.34/248.75 Done
% 248.34/248.75
% 248.34/248.75 Resimplifying inuse:
% 248.34/248.75 Done
% 248.34/248.75
% 248.34/248.75
% 248.34/248.75 Intermediate Status:
% 248.34/248.75 Generated: 366970
% 248.34/248.75 Kept: 89017
% 248.34/248.75 Inuse: 1198
% 248.34/248.75 Deleted: 1503
% 248.34/248.75 Deletedinuse: 10
% 248.34/248.75
% 248.34/248.75 Resimplifying inuse:
% 248.34/248.75 Done
% 248.34/248.75
% 248.34/248.75 Resimplifying inuse:
% 248.34/248.75 Done
% 248.34/248.75
% 248.34/248.75
% 248.34/248.75 Intermediate Status:
% 248.34/248.75 Generated: 375804
% 248.34/248.75 Kept: 91057
% 248.34/248.75 Inuse: 1233
% 248.34/248.75 Deleted: 1503
% 248.34/248.75 Deletedinuse: 10
% 248.34/248.75
% 248.34/248.75 Resimplifying inuse:
% 248.34/248.75 Done
% 248.34/248.75
% 248.34/248.75
% 248.34/248.75 Intermediate Status:
% 248.34/248.75 Generated: 382457
% 248.34/248.75 Kept: 93534
% 248.34/248.75 Inuse: 1253
% 248.34/248.75 Deleted: 1503
% 248.34/248.75 Deletedinuse: 10
% 248.34/248.75
% 248.34/248.75 Resimplifying inuse:
% 248.34/248.75 Done
% 248.34/248.75
% 248.34/248.75 *** allocated 6568290 integers for clauses
% 248.34/248.75 Resimplifying inuse:
% 248.34/248.75 Done
% 248.34/248.75
% 248.34/248.75
% 248.34/248.75 Intermediate Status:
% 248.34/248.75 Generated: 390977
% 248.34/248.75 Kept: 95535
% 248.34/248.75 Inuse: 1260
% 248.34/248.75 Deleted: 1503
% 248.34/248.75 Deletedinuse: 10
% 248.34/248.75
% 248.34/248.75 Resimplifying inuse:
% 248.34/248.75 Done
% 248.34/248.75
% 248.34/248.75
% 248.34/248.75 Intermediate Status:
% 248.34/248.75 Generated: 396239
% 248.34/248.75 Kept: 97755
% 248.34/248.75 Inuse: 1268
% 248.34/248.75 Deleted: 1504
% 248.34/248.75 Deletedinuse: 11
% 248.34/248.75
% 248.34/248.75
% 248.34/248.75 Intermediate Status:
% 248.34/248.75 Generated: 415156
% 248.34/248.75 Kept: 100379
% 248.34/248.75 Inuse: 1270
% 248.34/248.75 Deleted: 1512
% 248.34/248.75 Deletedinuse: 11
% 248.34/248.75
% 248.34/248.75 Resimplifying inuse:
% 248.34/248.75 Done
% 248.34/248.75
% 248.34/248.75
% 248.34/248.75 Intermediate Status:
% 248.34/248.75 Generated: 444848
% 248.34/248.75 Kept: 103472
% 248.34/248.75 Inuse: 1273
% 248.34/248.75 Deleted: 1524
% 248.34/248.75 Deletedinuse: 11
% 248.34/248.75
% 248.34/248.75 Resimplifying inuse:
% 248.34/248.75 Done
% 248.34/248.75
% 248.34/248.75 Resimplifying clauses:
% 248.34/248.75 Done
% 248.34/248.75
% 248.34/248.75
% 248.34/248.75 Intermediate Status:
% 248.34/248.75 Generated: 475230
% 248.34/248.75 Kept: 106505
% 248.34/248.75 Inuse: 1283
% 248.34/248.75 Deleted: 1908
% 248.34/248.75 Deletedinuse: 11
% 248.34/248.75
% 248.34/248.75 Resimplifying inuse:
% 248.34/248.75 Done
% 248.34/248.75
% 248.34/248.75 *** allocated 4378860 integers for termspace/termends
% 248.34/248.75 Resimplifying inuse:
% 248.34/248.75 Done
% 248.34/248.75
% 248.34/248.75
% 248.34/248.75 Intermediate Status:
% 248.34/248.75 Generated: 488544
% 248.34/248.75 Kept: 110386
% 248.34/248.75 Inuse: 1308
% 248.34/248.75 Deleted: 1908
% 248.34/248.75 Deletedinuse: 11
% 248.34/248.75
% 248.34/248.75 Resimplifying inuse:
% 248.34/248.75 Done
% 248.34/248.75
% 248.34/248.75
% 248.34/248.75 Intermediate Status:
% 248.34/248.75 Generated: 493515
% 248.34/248.75 Kept: 112404
% 248.34/248.75 Inuse: Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------