TSTP Solution File: SWW253+1 by Bliksem---1.12
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%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW253+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n026.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 23:21:35 EDT 2022
% Result : Timeout 300.01s 300.39s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWW253+1 : TPTP v8.1.0. Released v5.2.0.
% 0.12/0.13 % Command : bliksem %s
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % DateTime : Sun Jun 5 09:35:44 EDT 2022
% 0.12/0.35 % CPUTime :
% 1.34/1.72 *** allocated 10000 integers for termspace/termends
% 1.34/1.72 *** allocated 10000 integers for clauses
% 1.34/1.72 *** allocated 10000 integers for justifications
% 1.34/1.72 *** allocated 15000 integers for termspace/termends
% 1.34/1.72 *** allocated 22500 integers for termspace/termends
% 1.34/1.72 *** allocated 33750 integers for termspace/termends
% 1.34/1.72 Bliksem 1.12
% 1.34/1.72
% 1.34/1.72
% 1.34/1.72 Automatic Strategy Selection
% 1.34/1.72
% 1.34/1.72 *** allocated 50625 integers for termspace/termends
% 1.34/1.72 *** allocated 75937 integers for termspace/termends
% 1.34/1.72 *** allocated 113905 integers for termspace/termends
% 1.34/1.72
% 1.34/1.72 Clauses:
% 1.34/1.72
% 1.34/1.72 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 1.34/1.72 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.34/1.72 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 1.34/1.72 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 1.34/1.72 tc_Complex_Ocomplex, v_p ) ) }.
% 1.34/1.72 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), v_w____ ) =
% 1.34/1.72 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 1.34/1.72 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.34/1.72 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.34/1.72 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.34/1.72 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.34/1.72 v_q____ ) ), v_w____ ) ), hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.34/1.72 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) }.
% 1.34/1.72 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 1.34/1.72 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 1.34/1.72 tc_Complex_Ocomplex, v_q____ ) ) }.
% 1.34/1.72 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 1.34/1.72 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 1.34/1.72 tc_Complex_Ocomplex, v_q____ ) ) }.
% 1.34/1.72 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 1.34/1.72 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 1.34/1.72 tc_Complex_Ocomplex, c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 1.34/1.72 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ) ) }.
% 1.34/1.72 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 1.34/1.72 v_q____ ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 1.34/1.72 tc_Complex_Ocomplex, c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 1.34/1.72 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ) }.
% 1.34/1.72 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.34/1.72 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.34/1.72 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.34/1.72 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.34/1.72 v_q____ ) ), skol2 ) = hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.34/1.72 c_Polynomial_Osmult( tc_Complex_Ocomplex,
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, hAPP(
% 1.34/1.72 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), v_q____ ) ),
% 1.34/1.72 skol47 ) }.
% 1.34/1.72 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.34/1.72 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.34/1.72 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.34/1.72 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.34/1.72 v_q____ ) ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 1.34/1.72 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 1.34/1.72 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), X ) = hAPP(
% 1.34/1.72 hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 1.34/1.72 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.34/1.72 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.34/1.72 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.34/1.72 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.34/1.72 v_q____ ) ), X ) ), hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.34/1.72 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) }.
% 1.34/1.72 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) = hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 1.34/1.72 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.34/1.72 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.34/1.72 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.34/1.72 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.34/1.72 v_q____ ) ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ), hAPP
% 1.34/1.72 ( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) }.
% 1.34/1.72 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.72 , c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 1.34/1.72 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), Y ) }
% 1.34/1.72 .
% 1.34/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.34/1.72 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.34/1.72 ( X, Y, c_Groups_Oone__class_Oone( X ) ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.34/1.72 ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ),
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.72 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.34/1.72 ( X, Y, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless(
% 1.34/1.72 X, c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 1.34/1.72 ) ) }.
% 1.34/1.72 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 1.34/1.72 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oone__class_Oone( X ) ) =
% 1.34/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.34/1.72 { ! class_Fields_Ofield( X ), c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 1.34/1.72 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), Y ) }
% 1.34/1.72 .
% 1.34/1.72 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.34/1.72 Y ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X )
% 1.34/1.72 , Y ) }.
% 1.34/1.72 { ! class_RealVector_Oreal__normed__div__algebra( X ), Y =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( X, Y ) ) =
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal,
% 1.34/1.72 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.34/1.72 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(
% 1.34/1.72 tc_Complex_Ocomplex, tc_Complex_Ocomplex, c_Polynomial_Opoly(
% 1.34/1.72 tc_Complex_Ocomplex, v_pa____ ) ) }.
% 1.34/1.72 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 1.34/1.72 v_q____ ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 1.34/1.72 tc_Complex_Ocomplex, v_pa____ ) }.
% 1.34/1.72 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 1.34/1.72 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.34/1.72 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 1.34/1.72 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.34/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 1.34/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.34/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 1.34/1.72 { ! class_Groups_Ozero( X ), !
% 1.34/1.72 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.72 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.34/1.72 tc_Polynomial_Opoly( X ) ),
% 1.34/1.72 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.34/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 1.34/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.34/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 1.34/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.34/1.72 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.72 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.72 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.34/1.72 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.72 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.72 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.72 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.72 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.72 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.34/1.72 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.72 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.34/1.72 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.34/1.72 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.72 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.72 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.72 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.34/1.72 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.72 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.34/1.72 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.34/1.72 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.72 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.72 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.34/1.72 = Y }.
% 1.34/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.34/1.72 = Y }.
% 1.34/1.72 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X, U
% 1.34/1.72 , T ) ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 1.34/1.72 c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.34/1.72 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), T ), c_Rings_Oinverse__class_Odivide
% 1.34/1.72 ( X, Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.34/1.72 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.34/1.72 Z ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.34/1.72 { ! class_RealVector_Oreal__normed__algebra( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.72 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.72 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 1.34/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.72 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ) ) }.
% 1.34/1.72 { ! c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ), hAPP(
% 1.34/1.72 X, T ) = hAPP( X, U ) }.
% 1.34/1.72 { ! hAPP( X, skol3( X ) ) = hAPP( X, skol48( X ) ),
% 1.34/1.72 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( Z, Y, X ) }.
% 1.34/1.72 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.34/1.72 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.34/1.72 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 1.34/1.72 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.34/1.72 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.34/1.72 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.34/1.72 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.34/1.72 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.34/1.72 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.34/1.72 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.34/1.72 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.34/1.72 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.34/1.72 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.34/1.72 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.34/1.72 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.34/1.72 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.34/1.72 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.34/1.72 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.34/1.72 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 1.34/1.72 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.34/1.72 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.34/1.72 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.72 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.72 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.34/1.72 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.34/1.72 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.34/1.72 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.34/1.72 ( X ) ) }.
% 1.34/1.72 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.34/1.72 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.34/1.72 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.34/1.72 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 1.34/1.72 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.34/1.72 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.34/1.72 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.34/1.72 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 1.34/1.72 .
% 1.34/1.72 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.34/1.72 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.34/1.72 .
% 1.34/1.72 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.34/1.72 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.72 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.34/1.72 ( X ) ) }.
% 1.34/1.72 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.34/1.72 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.72 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.34/1.72 ( X ) ) }.
% 1.34/1.72 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.34/1.72 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.34/1.72 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.72 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.34/1.72 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.34/1.72 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.34/1.72 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.34/1.72 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 1.34/1.72 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.34/1.72 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.34/1.72 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha1( X, Y, Z, T ),
% 1.34/1.72 alpha25( X, Y, Z, T ) }.
% 1.34/1.72 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha1( X, Y, Z, T ),
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.34/1.72 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha25( X, Y, Z, T ),
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.34/1.72 { ! alpha25( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.72 { ! alpha25( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.34/1.72 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.72 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha25( X, Y, Z, T ) }.
% 1.34/1.72 { ! alpha1( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 1.34/1.72 { ! alpha1( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.34/1.72 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 1.34/1.72 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha1( X, Y, Z, T ) }.
% 1.34/1.72 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha2( X, Y, Z, T ),
% 1.34/1.72 alpha26( X, Y, Z, T ) }.
% 1.34/1.72 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha2( X, Y, Z, T ),
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.34/1.72 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha26( X, Y, Z, T ),
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.34/1.72 { ! alpha26( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.72 { ! alpha26( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 1.34/1.72 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.72 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha26( X, Y, Z, T ) }.
% 1.34/1.72 { ! alpha2( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.34/1.72 { ! alpha2( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.34/1.72 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.34/1.72 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha2( X, Y, Z, T ) }.
% 1.34/1.72 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.34/1.72 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.72 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.34/1.72 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.34/1.72 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 1.34/1.72 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.34/1.72 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.72 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 1.34/1.72 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.34/1.72 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.72 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.34/1.72 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 1.34/1.72 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Oinverse__class_Odivide( X, U
% 1.34/1.72 , Y ) = c_Rings_Oinverse__class_Odivide( X, T, Z ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Y ) }.
% 1.34/1.72 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Y ),
% 1.34/1.72 c_Rings_Oinverse__class_Odivide( X, U, Y ) =
% 1.34/1.72 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 1.34/1.72 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.34/1.72 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 1.34/1.72 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 1.34/1.72 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.34/1.72 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.34/1.72 c_Rings_Oinverse__class_Odivide( X, T, Z ) }.
% 1.34/1.72 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.72 , ! c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z, T = hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.34/1.72 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.72 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.34/1.72 c_Rings_Oinverse__class_Odivide( X, T, Y ) = Z }.
% 1.34/1.72 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.72 , ! T = c_Rings_Oinverse__class_Odivide( X, Z, Y ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 1.34/1.72 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.72 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 1.34/1.72 c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.34/1.72 { ! class_Fields_Ofield__inverse__zero( X ), !
% 1.34/1.72 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha27( X, Y, Z, T ) }.
% 1.34/1.72 { ! class_Fields_Ofield__inverse__zero( X ), !
% 1.34/1.72 c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y, alpha3( X, Y, Z ) }.
% 1.34/1.72 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha27( X, Y, Z, T ), !
% 1.34/1.72 alpha3( X, Y, Z ), c_Rings_Oinverse__class_Odivide( X, T, Z ) = Y }.
% 1.34/1.72 { ! alpha27( X, Y, Z, T ), Z = c_Groups_Ozero__class_Ozero( X ), T = hAPP(
% 1.34/1.72 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 1.34/1.72 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha27( X, Y, Z, T ) }.
% 1.34/1.72 { ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), alpha27(
% 1.34/1.72 X, Y, Z, T ) }.
% 1.34/1.72 { ! alpha3( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.72 { Z = c_Groups_Ozero__class_Ozero( X ), alpha3( X, Y, Z ) }.
% 1.34/1.72 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha3( X, Y, Z ) }.
% 1.34/1.72 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 1.34/1.72 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha28( X, Y, Z, T ) }.
% 1.34/1.72 { ! class_Fields_Ofield__inverse__zero( X ), ! T =
% 1.34/1.72 c_Rings_Oinverse__class_Odivide( X, Z, Y ), alpha4( X, Y, T ) }.
% 1.34/1.72 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha28( X, Y, Z, T ), !
% 1.34/1.72 alpha4( X, Y, T ), T = c_Rings_Oinverse__class_Odivide( X, Z, Y ) }.
% 1.34/1.72 { ! alpha28( X, Y, Z, T ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP
% 1.34/1.72 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 1.34/1.72 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha28( X, Y, Z, T ) }.
% 1.34/1.72 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, alpha28(
% 1.34/1.72 X, Y, Z, T ) }.
% 1.34/1.72 { ! alpha4( X, Y, Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.72 { Y = c_Groups_Ozero__class_Ozero( X ), alpha4( X, Y, Z ) }.
% 1.34/1.72 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha4( X, Y, Z ) }.
% 1.34/1.72 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.72 , Z = c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse
% 1.34/1.72 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP(
% 1.34/1.72 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( X, Z ) ),
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.34/1.72 { ! class_Rings_Odivision__ring( X ), ! hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = c_Groups_Oone__class_Oone
% 1.34/1.72 ( X ), c_Rings_Oinverse__class_Oinverse( X, Z ) = Y }.
% 1.34/1.72 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, Z
% 1.34/1.72 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.34/1.72 { ! class_Fields_Ofield( X ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 1.34/1.72 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.34/1.72 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.72 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 1.34/1.72 tc_RealDef_Oreal ) ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.72 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.34/1.72 Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.72 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 1.34/1.72 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.34/1.72 Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.72 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.34/1.72 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.72 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.34/1.72 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.34/1.72 Y ), Z ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.72 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.34/1.72 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.72 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.34/1.72 ( X, Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.34/1.72 Z, Y ) ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.72 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.34/1.72 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.34/1.72 Z, Y ) ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.72 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.34/1.72 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.34/1.72 Y ), Z ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.72 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.34/1.72 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ),
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.72 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.34/1.72 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.34/1.72 Y ), Z ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.72 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.34/1.72 ( X, T, c_Rings_Oinverse__class_Odivide( X, Z, Y ) ),
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.72 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.34/1.72 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.34/1.72 Z, Y ) ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.34/1.72 Z ), Y ), alpha29( X, Y, Z, T ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.34/1.72 Z ), Y ), alpha47( X, Y, Z, T ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha29( X, Y, Z
% 1.34/1.72 , T ), ! alpha47( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.34/1.72 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 1.34/1.72 { ! alpha47( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), Z ), alpha56( X, Y, Z, T ) }.
% 1.34/1.72 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.34/1.72 , alpha47( X, Y, Z, T ) }.
% 1.34/1.72 { ! alpha56( X, Y, Z, T ), alpha47( X, Y, Z, T ) }.
% 1.34/1.72 { ! alpha56( X, Y, Z, T ), alpha66( X, Y, Z, T ) }.
% 1.34/1.72 { ! alpha56( X, Y, Z, T ), alpha5( X, Y, Z ) }.
% 1.34/1.72 { ! alpha66( X, Y, Z, T ), ! alpha5( X, Y, Z ), alpha56( X, Y, Z, T ) }.
% 1.34/1.72 { ! alpha66( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.34/1.72 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 1.34/1.72 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 1.34/1.72 alpha66( X, Y, Z, T ) }.
% 1.34/1.72 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha66( X, Y, Z, T )
% 1.34/1.72 }.
% 1.34/1.72 { ! alpha29( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 1.34/1.72 T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.34/1.72 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.34/1.72 alpha29( X, Y, Z, T ) }.
% 1.34/1.72 { ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha29( X, Y, Z, T ) }.
% 1.34/1.72 { ! alpha5( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.34/1.72 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.72 , alpha5( X, Y, Z ) }.
% 1.34/1.72 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.34/1.72 , alpha5( X, Y, Z ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.34/1.72 Z, Y ) ), alpha30( X, Y, Z, T ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.34/1.72 Z, Y ) ), alpha48( X, Y, Z, T ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha30( X, Y, Z
% 1.34/1.72 , T ), ! alpha48( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 1.34/1.72 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.34/1.72 { ! alpha48( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), Y ), alpha57( X, Y, Z, T ) }.
% 1.34/1.72 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.34/1.72 , alpha48( X, Y, Z, T ) }.
% 1.34/1.72 { ! alpha57( X, Y, Z, T ), alpha48( X, Y, Z, T ) }.
% 1.34/1.72 { ! alpha57( X, Y, Z, T ), alpha67( X, Y, Z, T ) }.
% 1.34/1.72 { ! alpha57( X, Y, Z, T ), alpha6( X, Y, T ) }.
% 1.34/1.72 { ! alpha67( X, Y, Z, T ), ! alpha6( X, Y, T ), alpha57( X, Y, Z, T ) }.
% 1.34/1.72 { ! alpha67( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.34/1.72 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.34/1.72 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.34/1.72 alpha67( X, Y, Z, T ) }.
% 1.34/1.72 { ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha67( X, Y, Z, T ) }.
% 1.34/1.72 { ! alpha30( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 1.34/1.72 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.34/1.72 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.34/1.72 alpha30( X, Y, Z, T ) }.
% 1.34/1.72 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha30( X, Y, Z, T )
% 1.34/1.72 }.
% 1.34/1.72 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.72 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.72 , alpha6( X, Y, Z ) }.
% 1.34/1.72 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.72 , alpha6( X, Y, Z ) }.
% 1.34/1.72 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.72 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 1.34/1.72 c_Groups_Oone__class_Oone( X ) }.
% 1.34/1.72 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.34/1.72 hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( X, Y ) ), Y ) =
% 1.34/1.72 c_Groups_Oone__class_Oone( X ) }.
% 1.34/1.72 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.72 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ),
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( X, Y ) ) = c_Groups_Oone__class_Oone( X
% 1.34/1.72 ) }.
% 1.34/1.72 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.34/1.72 X, Y, Z ) }.
% 1.34/1.72 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 1.34/1.72 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( X, Y ), Z = Y }.
% 1.34/1.72 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Z = Y,
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( X, Z ) =
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( X, Y ) }.
% 1.34/1.72 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse( X
% 1.34/1.72 , Y ) ) = Y }.
% 1.34/1.72 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.34/1.72 c_Groups_Oone__class_Oone( X ) }.
% 1.34/1.72 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.72 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.34/1.72 c_Rings_Oinverse__class_Odivide( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.72 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.72 { ! class_RealVector_Oreal__normed__field( X ),
% 1.34/1.72 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.34/1.72 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.72 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.72 }.
% 1.34/1.72 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.34/1.72 c_RealVector_Onorm__class_Onorm( X, Y ) = c_Groups_Ozero__class_Ozero(
% 1.34/1.72 tc_RealDef_Oreal ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X, Y )
% 1.34/1.72 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.34/1.72 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.34/1.72 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.34/1.72 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 1.34/1.72 , Z ) = c_Rings_Oinverse__class_Oinverse( X, Y ), Z =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z
% 1.34/1.72 = Y }.
% 1.34/1.72 { ! class_Rings_Odivision__ring( X ), ! c_Rings_Oinverse__class_Oinverse( X
% 1.34/1.72 , Y ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 1.34/1.72 ( X ) }.
% 1.34/1.72 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.72 , c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Oinverse(
% 1.34/1.72 X, Y ) ) = Y }.
% 1.34/1.72 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.72 , ! c_Rings_Oinverse__class_Oinverse( X, Y ) =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.72 { ! class_Rings_Odivision__ring__inverse__zero( X ), !
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.34/1.72 ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.72 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 1.34/1.72 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.72 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.72 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( X, c_Groups_Ozero__class_Ozero( X ) ) =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.72 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X, Y
% 1.34/1.72 , c_Groups_Oone__class_Oone( X ) ) = Y }.
% 1.34/1.72 { ! class_Fields_Ofield__inverse__zero( X ), !
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( X, Y ) = c_Groups_Oone__class_Oone( X )
% 1.34/1.72 , Y = c_Groups_Oone__class_Oone( X ) }.
% 1.34/1.72 { ! class_Fields_Ofield__inverse__zero( X ), ! Y =
% 1.34/1.72 c_Groups_Oone__class_Oone( X ), c_Rings_Oinverse__class_Oinverse( X, Y )
% 1.34/1.72 = c_Groups_Oone__class_Oone( X ) }.
% 1.34/1.72 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.34/1.72 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.34/1.72 { ! class_Fields_Ofield__inverse__zero( X ), !
% 1.34/1.72 class_RealVector_Oreal__normed__field( X ),
% 1.34/1.72 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Odivide( X, Z
% 1.34/1.72 , Y ) ) = c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 1.34/1.72 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.34/1.72 ( X, Y ) ) }.
% 1.34/1.72 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( X, c_Rings_Oinverse__class_Odivide( X,
% 1.34/1.72 Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X, Y, Z ) }.
% 1.34/1.72 { ! class_RealVector_Oreal__normed__div__algebra( X ), !
% 1.34/1.72 class_Rings_Odivision__ring__inverse__zero( X ),
% 1.34/1.72 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Oinverse( X,
% 1.34/1.72 Y ) ) = c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal,
% 1.34/1.72 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.34/1.72 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.34/1.72 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.34/1.72 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.34/1.72 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 1.34/1.72 .
% 1.34/1.72 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.72 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.34/1.72 c_Rings_Oinverse__class_Odivide( X, Y, T ),
% 1.34/1.72 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.72 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless( X,
% 1.34/1.72 c_Rings_Oinverse__class_Odivide( X, Z, T ),
% 1.34/1.72 c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.72 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.34/1.72 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.34/1.72 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 1.34/1.72 , Y, Z ) ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.72 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.34/1.72 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 1.34/1.72 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.72 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.34/1.72 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.34/1.72 ( X, c_Rings_Oinverse__class_Odivide( X, Y, Z ),
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.72 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.34/1.72 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 1.34/1.72 ( X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X
% 1.34/1.72 , Y, Z ) ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Z,
% 1.34/1.72 Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha7( X, Y, Z ), alpha31( X, Y
% 1.34/1.72 , Z ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha7( X, Y, Z
% 1.34/1.72 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 1.34/1.72 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha31( X, Y, Z
% 1.34/1.72 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X
% 1.34/1.72 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.72 { ! alpha31( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.72 { ! alpha31( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.34/1.72 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.72 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.72 ), alpha31( X, Y, Z ) }.
% 1.34/1.72 { ! alpha7( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.34/1.72 { ! alpha7( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.72 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.34/1.72 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.72 ), alpha7( X, Y, Z ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.72 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha8( X, Y, Z ), alpha32
% 1.34/1.72 ( X, Y, Z ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha8( X, Y, Z
% 1.34/1.72 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.72 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha32( X, Y, Z
% 1.34/1.72 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.72 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.34/1.72 { ! alpha32( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.72 { ! alpha32( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.72 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.72 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.72 ), alpha32( X, Y, Z ) }.
% 1.34/1.72 { ! alpha8( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.34/1.72 { ! alpha8( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.34/1.72 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.34/1.72 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.72 ), alpha8( X, Y, Z ) }.
% 1.34/1.72 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.72 , ! c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 1.34/1.72 c_Groups_Oone__class_Oone( X ), Z = Y }.
% 1.34/1.72 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.72 , ! Z = Y, c_Rings_Oinverse__class_Odivide( X, Z, Y ) =
% 1.34/1.72 c_Groups_Oone__class_Oone( X ) }.
% 1.34/1.72 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.72 , c_Rings_Oinverse__class_Odivide( X, Y, Y ) = c_Groups_Oone__class_Oone
% 1.34/1.72 ( X ) }.
% 1.34/1.72 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 1.34/1.72 Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.72 { ! class_Rings_Odivision__ring__inverse__zero( X ), Y =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Odivide( X, Y,
% 1.34/1.72 Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.72 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.72 X, c_Rings_Oinverse__class_Oinverse( X, Z ),
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.72 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 1.34/1.72 ( X ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.34/1.72 .
% 1.34/1.72 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.72 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.72 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.72 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 1.34/1.72 X, c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero
% 1.34/1.72 ( X ) ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.72 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 1.34/1.72 , Y ) ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.34/1.72 .
% 1.34/1.72 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.72 X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.34/1.72 X, c_Groups_Ozero__class_Ozero( X ), c_Rings_Oinverse__class_Oinverse( X
% 1.34/1.72 , Y ) ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 1.34/1.72 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.34/1.72 , Y, c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 1.34/1.72 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.34/1.72 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.34/1.72 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.34/1.72 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.34/1.72 c_RealVector_Onorm__class_Onorm( X, Y ) ), ! Y =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.72 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless(
% 1.34/1.72 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.34/1.72 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.34/1.72 { ! class_RealVector_Oreal__normed__field( X ), Y =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), c_RealVector_Onorm__class_Onorm( X,
% 1.34/1.72 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 1.34/1.72 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 1.34/1.72 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.34/1.72 ( X, Y ) ) }.
% 1.34/1.72 { c_Rings_Oinverse__class_Odivide( tc_Complex_Ocomplex, Y, X ) = hAPP( hAPP
% 1.34/1.72 ( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), Y ),
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex, X ) ) }.
% 1.34/1.72 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.34/1.72 c_Polynomial_Osmult( X, T, Z ) ), Y ) = hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( c_Polynomial_Opoly( X, Z )
% 1.34/1.72 , Y ) ) }.
% 1.34/1.72 { ! class_Rings_Ocomm__semiring__1( X ), c_Polynomial_Osmult( X,
% 1.34/1.72 c_Groups_Oone__class_Oone( X ), Y ) = Y }.
% 1.34/1.72 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.34/1.72 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.34/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 1.34/1.72 c_Groups_Oone__class_Oone( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.34/1.72 c_Groups_Oone__class_Oone( X ) }.
% 1.34/1.72 { ! class_Rings_Oidom( X ), ! c_Polynomial_Osmult( X, Z, Y ) =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.34/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.72 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.72 c_Polynomial_Osmult( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.34/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.72 { ! class_Rings_Oidom( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.34/1.72 tc_Polynomial_Opoly( X ) ), c_Polynomial_Osmult( X, Z, Y ) =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.72 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.34/1.72 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.72 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.34/1.72 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Z
% 1.34/1.72 ) ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.34/1.72 c_Polynomial_Opoly( X, T ), Y ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y )
% 1.34/1.72 ) }.
% 1.34/1.72 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.72 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.34/1.72 = Y }.
% 1.34/1.72 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.34/1.72 = Y }.
% 1.34/1.72 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.34/1.72 = Y }.
% 1.34/1.72 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_c____ ) =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.34/1.72 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y ) =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.72 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Y ),
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.72 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ),
% 1.34/1.72 c_Polynomial_Osmult( X, Z, Y ) ) = c_Polynomial_Osmult( X, Z, hAPP( hAPP
% 1.34/1.72 ( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ) ) }
% 1.34/1.72 .
% 1.34/1.72 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.34/1.72 c_Polynomial_Osmult( X, T, Z ) ), Y ) = c_Polynomial_Osmult( X, T, hAPP(
% 1.34/1.72 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y )
% 1.34/1.72 ) }.
% 1.34/1.72 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.72 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 1.34/1.72 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.34/1.72 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 1.34/1.72 c_Groups_Oone__class_Oone( X ) }.
% 1.34/1.72 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 1.34/1.72 c_Groups_Oone__class_Oone( X ) = Y }.
% 1.34/1.72 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 1.34/1.72 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ), Z = Y }.
% 1.34/1.72 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Z = Y,
% 1.34/1.72 c_Polynomial_Opoly( X, Z ) = c_Polynomial_Opoly( X, Y ) }.
% 1.34/1.72 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), !
% 1.34/1.72 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ), Y =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.72 { ! class_Int_Oring__char__0( X ), ! class_Rings_Oidom( X ), ! Y =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ),
% 1.34/1.72 c_Polynomial_Opoly( X, Y ) = c_Polynomial_Opoly( X,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) }.
% 1.34/1.72 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, Y,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) ) =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.72 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.34/1.72 = Y }.
% 1.34/1.72 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_c____ ) =
% 1.34/1.72 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) }.
% 1.34/1.72 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.72 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex, X
% 1.34/1.72 ), c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 1.34/1.72 tc_Complex_Ocomplex, v_pa____ ) ),
% 1.34/1.72 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant( tc_Complex_Ocomplex
% 1.34/1.72 , tc_Complex_Ocomplex, c_Polynomial_Opoly( tc_Complex_Ocomplex, X ) ),
% 1.34/1.72 hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), skol4( X ) ) =
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.34/1.72 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.72 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.34/1.72 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.34/1.72 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.34/1.72 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), X ) ) ) }.
% 1.34/1.72 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X ) ), X ) =
% 1.34/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.34/1.72 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) ),
% 1.34/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X ) ), T ), hAPP(
% 1.34/1.72 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Y ) ), Z ) ) }.
% 1.34/1.72 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) ),
% 1.34/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), T ),
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X ) ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ),
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Y ) ) ) }.
% 1.34/1.72 { c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) = hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X ) ) }.
% 1.34/1.72 { c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) = hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 1.34/1.72 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, X ) ) }.
% 1.34/1.72 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.72 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.34/1.72 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_c____ ) ),
% 1.34/1.72 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.34/1.72 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), X ) ) ) }.
% 1.34/1.72 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), X ) = hAPP(
% 1.34/1.72 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ),
% 1.34/1.72 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_c____, X ) ) }.
% 1.34/1.72 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 1.34/1.72 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 1.34/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), Y = X,
% 1.34/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 1.34/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.34/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), Y = X }.
% 1.34/1.72 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 1.34/1.72 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 1.34/1.72 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, X ) }.
% 1.34/1.72 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ) }.
% 1.34/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Z ),
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, Z ) }.
% 1.34/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ), Y = X }.
% 1.34/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.34/1.72 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ), alpha9( X, Y
% 1.34/1.72 ) }.
% 1.34/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.34/1.72 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ), alpha33( X,
% 1.34/1.72 Y ) }.
% 1.34/1.72 { ! alpha9( X, Y ), ! alpha33( X, Y ), c_Orderings_Oord__class_Oless__eq(
% 1.34/1.72 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.34/1.72 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, Y, X ) ) }.
% 1.34/1.72 { ! alpha33( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.34/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), alpha33( X, Y ) }.
% 1.34/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), alpha33( X, Y ) }.
% 1.34/1.72 { ! alpha9( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y
% 1.34/1.72 , c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }.
% 1.34/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), alpha9( X, Y ) }.
% 1.34/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), alpha9( X, Y ) }.
% 1.34/1.72 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 1.34/1.72 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 1.34/1.72 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.72 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha10( X, Y
% 1.34/1.72 , Z ), alpha34( X, Y, Z ) }.
% 1.34/1.72 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha10( X, Y, Z ),
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.72 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.34/1.72 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha34( X, Y, Z ),
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.72 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.34/1.72 { ! alpha34( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.72 { ! alpha34( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.72 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.34/1.72 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) ), alpha34( X, Y, Z ) }.
% 1.34/1.72 { ! alpha10( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.34/1.72 { ! alpha10( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.34/1.72 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.72 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), Y ), alpha10( X, Y, Z ) }.
% 1.34/1.72 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.34/1.72 ( X ) ), alpha11( X, Y, Z ), alpha35( X, Y, Z ) }.
% 1.34/1.72 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha11( X, Y, Z ),
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.34/1.72 ( X ) ) }.
% 1.34/1.72 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha35( X, Y, Z ),
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.34/1.72 ( X ) ) }.
% 1.34/1.72 { ! alpha35( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.72 { ! alpha35( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.34/1.72 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.34/1.72 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.34/1.72 ( X ), Y ), alpha35( X, Y, Z ) }.
% 1.34/1.72 { ! alpha11( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.34/1.72 { ! alpha11( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.72 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.72 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) ), alpha11( X, Y, Z ) }.
% 1.34/1.72 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.72 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.34/1.72 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.34/1.72 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.72 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.34/1.72 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.72 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.72 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.34/1.72 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.72 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.72 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.34/1.72 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.34/1.72 ( X ) ) }.
% 1.34/1.72 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.34/1.72 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.72 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.34/1.72 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.34/1.72 { ! class_Rings_Oordered__semiring( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.34/1.72 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.34/1.72 { ! class_Rings_Oordered__semiring( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.34/1.72 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.34/1.72 { ! class_Rings_Oordered__comm__semiring( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.34/1.72 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.34/1.72 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.34/1.72 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.34/1.72 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.34/1.72 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.34/1.72 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.34/1.72 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.34/1.72 { ! class_Rings_Oordered__semiring( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.34/1.72 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.34/1.72 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.34/1.72 { ! class_Rings_Oordered__semiring( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.72 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.34/1.72 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.34/1.72 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.34/1.72 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.72 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.34/1.72 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.34/1.72 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.34/1.72 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.72 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.34/1.72 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.34/1.72 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.34/1.72 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.34/1.72 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.72 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.72 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.34/1.72 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.34/1.72 ( X ) ) }.
% 1.34/1.72 { ! class_Rings_Olinordered__semidom( X ),
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.72 c_Groups_Oone__class_Oone( X ) ) }.
% 1.34/1.72 { ! class_Rings_Olinordered__semidom( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.72 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 1.34/1.72 ( X, Y, T ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.34/1.72 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 1.34/1.72 ( X, Z, T ), c_Rings_Oinverse__class_Odivide( X, Y, T ) ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.34/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.34/1.72 , Z, Y ), c_Groups_Ozero__class_Ozero( X ) ), alpha12( X, Y, Z ), alpha36
% 1.34/1.72 ( X, Y, Z ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha12( X, Y, Z
% 1.34/1.72 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 1.34/1.72 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha36( X, Y, Z
% 1.34/1.72 ), c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide
% 1.34/1.72 ( X, Z, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.72 { ! alpha36( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.72 { ! alpha36( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.34/1.72 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.34/1.72 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.34/1.72 ( X ), Y ), alpha36( X, Y, Z ) }.
% 1.34/1.72 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.72 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.34/1.73 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ), alpha12( X, Y, Z ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.73 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ), alpha13( X, Y, Z ), alpha37
% 1.34/1.73 ( X, Y, Z ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha13( X, Y, Z
% 1.34/1.73 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.34/1.73 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha37( X, Y, Z
% 1.34/1.73 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.34/1.73 ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.34/1.73 { ! alpha37( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.73 { ! alpha37( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.34/1.73 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ), alpha37( X, Y, Z ) }.
% 1.34/1.73 { ! alpha13( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.34/1.73 { ! alpha13( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), Y ), alpha13( X, Y, Z ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.34/1.73 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 ), c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.73 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Ozero__class_Ozero( X
% 1.34/1.73 ) ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.73 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.73 ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.73 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.34/1.73 ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( X, Y ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.34/1.73 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.34/1.73 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.34/1.73 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.34/1.73 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.34/1.73 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.34/1.73 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.34/1.73 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.34/1.73 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.34/1.73 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.34/1.73 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.34/1.73 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.34/1.73 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.34/1.73 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.34/1.73 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 1.34/1.73 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.34/1.73 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 1.34/1.73 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.34/1.73 ) ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 , Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.73 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 1.34/1.73 X ) ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.34/1.73 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.34/1.73 , Y, U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless( X, Y, Z ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.34/1.73 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Odivide( X, Y,
% 1.34/1.73 U ), c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.73 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.34/1.73 ! c_Orderings_Oord__class_Oless( X, T, U ), c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, c_Rings_Oinverse__class_Odivide( X, Y, U ),
% 1.34/1.73 c_Rings_Oinverse__class_Odivide( X, Z, T ) ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.34/1.73 ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.73 c_Rings_Oinverse__class_Odivide( X, Y, Z ), c_Groups_Ozero__class_Ozero(
% 1.34/1.73 X ) ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 , Z ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( X ), c_Rings_Oinverse__class_Odivide( X, Y, Z ) ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.34/1.73 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.34/1.73 , Z ), c_Rings_Oinverse__class_Oinverse( X, Y ) ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.34/1.73 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.34/1.73 , Y ), c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse( X
% 1.34/1.73 , Y ), c_Groups_Oone__class_Oone( X ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 1.34/1.73 , Y ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 ), c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.73 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Groups_Oone__class_Oone( X )
% 1.34/1.73 ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 1.34/1.73 , c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Oinverse
% 1.34/1.73 ( X, Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( X, Y ), c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_RealDef_Oreal ) ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 1.34/1.73 tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( X, Y ),
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( X, Z ) ),
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( X, Y ) ) ) }.
% 1.34/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 1.34/1.73 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ), X ) =
% 1.34/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP
% 1.34/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.34/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) =
% 1.34/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y )
% 1.34/1.73 }.
% 1.34/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.34/1.73 , T, Z ), c_Rings_Oinverse__class_Odivide( X, T, Y ) ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.34/1.73 , T, Y ), c_Rings_Oinverse__class_Odivide( X, T, Z ) ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.73 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.34/1.73 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.73 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.34/1.73 , T, Y ), Z ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.73 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.34/1.73 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.73 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.34/1.73 ( X, Z, Y ) ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.73 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.34/1.73 ( X, Z, Y ) ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.73 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.34/1.73 , T, Y ), Z ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.73 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.34/1.73 , T, Y ), Z ), c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.73 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.34/1.73 , T, Y ), Z ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.73 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.34/1.73 ( X, Z, Y ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.73 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.34/1.73 ( X, Z, Y ) ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.34/1.73 , T, Z ), Y ), alpha38( X, Y, Z, T ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Rings_Oinverse__class_Odivide( X
% 1.34/1.73 , T, Z ), Y ), alpha49( X, Y, Z, T ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha38( X, Y, Z
% 1.34/1.73 , T ), ! alpha49( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.73 c_Rings_Oinverse__class_Odivide( X, T, Z ), Y ) }.
% 1.34/1.73 { ! alpha49( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), Z ), alpha58( X, Y, Z, T ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.34/1.73 , alpha49( X, Y, Z, T ) }.
% 1.34/1.73 { ! alpha58( X, Y, Z, T ), alpha49( X, Y, Z, T ) }.
% 1.34/1.73 { ! alpha58( X, Y, Z, T ), alpha68( X, Y, Z, T ) }.
% 1.34/1.73 { ! alpha58( X, Y, Z, T ), alpha14( X, Y, Z ) }.
% 1.34/1.73 { ! alpha68( X, Y, Z, T ), ! alpha14( X, Y, Z ), alpha58( X, Y, Z, T ) }.
% 1.34/1.73 { ! alpha68( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.34/1.73 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 1.34/1.73 alpha68( X, Y, Z, T ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha68( X, Y, Z, T )
% 1.34/1.73 }.
% 1.34/1.73 { ! alpha38( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless__eq
% 1.34/1.73 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.34/1.73 alpha38( X, Y, Z, T ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha38( X, Y, Z, T ) }.
% 1.34/1.73 { ! alpha14( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.34/1.73 , c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.73 , alpha14( X, Y, Z ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 , Y ), alpha14( X, Y, Z ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.34/1.73 ( X, Z, Y ) ), alpha39( X, Y, Z, T ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, T, c_Rings_Oinverse__class_Odivide
% 1.34/1.73 ( X, Z, Y ) ), alpha50( X, Y, Z, T ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha39( X, Y, Z
% 1.34/1.73 , T ), ! alpha50( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X, T,
% 1.34/1.73 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.34/1.73 { ! alpha50( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), Y ), alpha59( X, Y, Z, T ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.34/1.73 , alpha50( X, Y, Z, T ) }.
% 1.34/1.73 { ! alpha59( X, Y, Z, T ), alpha50( X, Y, Z, T ) }.
% 1.34/1.73 { ! alpha59( X, Y, Z, T ), alpha69( X, Y, Z, T ) }.
% 1.34/1.73 { ! alpha59( X, Y, Z, T ), alpha15( X, Y, T ) }.
% 1.34/1.73 { ! alpha69( X, Y, Z, T ), ! alpha15( X, Y, T ), alpha59( X, Y, Z, T ) }.
% 1.34/1.73 { ! alpha69( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.34/1.73 , Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.34/1.73 alpha69( X, Y, Z, T ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha69( X, Y, Z, T ) }.
% 1.34/1.73 { ! alpha39( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless__eq
% 1.34/1.73 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.34/1.73 alpha39( X, Y, Z, T ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha39( X, Y, Z, T )
% 1.34/1.73 }.
% 1.34/1.73 { ! alpha15( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.34/1.73 , Z, c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.73 , alpha15( X, Y, Z ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.34/1.73 ) ), alpha15( X, Y, Z ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.73 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 1.34/1.73 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.34/1.73 c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 1.34/1.73 ), c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq(
% 1.34/1.73 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 1.34/1.73 X, c_Groups_Oone__class_Oone( X ), Y ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 ), c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X
% 1.34/1.73 , Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, c_Rings_Oinverse__class_Oinverse( X, Y
% 1.34/1.73 ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.34/1.73 c_Rings_Oinverse__class_Oinverse( X, Y ) ), c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.34/1.73 c_Rings_Oinverse__class_Oinverse( X, Y ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 1.34/1.73 }.
% 1.34/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.34/1.73 ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X )
% 1.34/1.73 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 1.34/1.73 , c_Rings_Oinverse__class_Oinverse( X, Y ) ) }.
% 1.34/1.73 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP
% 1.34/1.73 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 1.34/1.73 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 1.34/1.73 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP(
% 1.34/1.73 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) }.
% 1.34/1.73 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP
% 1.34/1.73 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 1.34/1.73 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 1.34/1.73 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP(
% 1.34/1.73 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) }.
% 1.34/1.73 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.34/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) = X }.
% 1.34/1.73 { c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 1.34/1.73 { ! hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), v_c____ ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), hAPP(
% 1.34/1.73 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ), skol5 ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__div__algebra( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z,
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( X, Y ) ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Oinverse( X,
% 1.34/1.73 Y ) ), c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal, Z ) ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( X, Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( X, T ) ) ), Z =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ), X =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.34/1.73 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 1.34/1.73 { ! class_Rings_Oidom( X ), ! hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ), ! c_Polynomial_Oorder( X, Y, Z ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ), hAPP( c_Polynomial_Opoly( X, Z ), Y ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Rings_Oidom( X ), c_Polynomial_Oorder( X, Y, Z ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( c_Polynomial_Opoly( X,
% 1.34/1.73 Z ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 1.34/1.73 , Y ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__field( X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol6( Z, T ) ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__field( X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Odivide( X, Z
% 1.34/1.73 , Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol6( X, Y ) ) ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.34/1.73 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.34/1.73 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 1.34/1.73 , Y ) = c_Groups_Oplus__class_Oplus( X, Y, Z ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 1.34/1.73 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 1.34/1.73 ( X, Z, c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, T
% 1.34/1.73 , c_Groups_Oplus__class_Oplus( X, Z, Y ) ) = c_Groups_Oplus__class_Oplus
% 1.34/1.73 ( X, c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.34/1.73 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.34/1.73 ( X, c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.34/1.73 , Y ) ) = c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X
% 1.34/1.73 , U, Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.34/1.73 { ! class_Groups_Oab__semigroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.34/1.73 ( X, T, c_Groups_Oplus__class_Oplus( X, Z, Y ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( c_Polynomial_Opoly( X,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 1.34/1.73 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.34/1.73 ( tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Y ),
% 1.34/1.73 c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.34/1.73 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 T, Y ), Z = Y }.
% 1.34/1.73 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 T, Y ) }.
% 1.34/1.73 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 Y, Z ), T = Y }.
% 1.34/1.73 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 Y, Z ) }.
% 1.34/1.73 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 T, Y ), Z = Y }.
% 1.34/1.73 { ! class_Groups_Ocancel__ab__semigroup__add( X ), !
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, T, Z ) = c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 T, Y ), Z = Y }.
% 1.34/1.73 { ! class_Groups_Ocancel__semigroup__add( X ), !
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, Z, T ) = c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 Y, T ), Z = Y }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 1.34/1.73 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.34/1.73 ( X, Y ) ) ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( X, Z ), Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( X, U ), T ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( X, c_Groups_Oplus__class_Oplus( X, Z, U
% 1.34/1.73 ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Y, T ) ) }.
% 1.34/1.73 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.34/1.73 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.34/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) = c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.34/1.73 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, Y, Y ) }.
% 1.34/1.73 { ! class_Groups_Omonoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.34/1.73 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.34/1.73 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), Y ) = Y }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.34/1.73 , c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.34/1.73 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.34/1.73 ( X ), ! Z = c_Groups_Oplus__class_Oplus( X, Z, Y ), Y =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.34/1.73 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.34/1.73 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.34/1.73 Z ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.34/1.73 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.34/1.73 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.34/1.73 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.34/1.73 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.34/1.73 U ), c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.34/1.73 T ), c_Groups_Oplus__class_Oplus( X, Y, T ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.34/1.73 Z ), c_Groups_Oplus__class_Oplus( X, T, Y ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.34/1.73 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ), c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, T, Y ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 1.34/1.73 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.34/1.73 , Y, Z ) ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.34/1.73 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, Z, Y ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.34/1.73 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.34/1.73 , T, Y ) ) }.
% 1.34/1.73 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.34/1.73 X, c_Groups_Oplus__class_Oplus( X, Z, T ), c_Groups_Oplus__class_Oplus( X
% 1.34/1.73 , Y, T ) ) }.
% 1.34/1.73 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.34/1.73 X, c_Groups_Oplus__class_Oplus( X, T, Z ), c_Groups_Oplus__class_Oplus( X
% 1.34/1.73 , T, Y ) ) }.
% 1.34/1.73 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, U, T ), c_Orderings_Oord__class_Oless( X,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X, Y
% 1.34/1.73 , T ) ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, T )
% 1.34/1.73 , c_Groups_Oplus__class_Oplus( X, Y, T ) ), c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, Z, Y ) }.
% 1.34/1.73 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, T, Z )
% 1.34/1.73 , c_Groups_Oplus__class_Oplus( X, T, Y ) ), c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, Z, Y ) }.
% 1.34/1.73 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.34/1.73 ( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.73 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.34/1.73 ), U = Z, T = Y }.
% 1.34/1.73 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.34/1.73 ( X ), ! U = Z, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.73 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.34/1.73 ) }.
% 1.34/1.73 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.34/1.73 ( X ), ! T = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.73 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T )
% 1.34/1.73 ) }.
% 1.34/1.73 { ! class_Rings_Osemiring( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP
% 1.34/1.73 ( c_Groups_Otimes__class_Otimes( X ), U ), T ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.73 ( X ), Z ), T ), Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, U, Z
% 1.34/1.73 ) ), T ), Y ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Y
% 1.34/1.73 ) ), Z ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.34/1.73 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.34/1.73 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.34/1.73 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, T, Z
% 1.34/1.73 ) ), Y ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.34/1.73 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.34/1.73 ( X ), U = T, Z = Y, ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.73 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.34/1.73 ) }.
% 1.34/1.73 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.34/1.73 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.73 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.34/1.73 ), ! U = T }.
% 1.34/1.73 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.34/1.73 ( X ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.73 ( X ), U ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z )
% 1.34/1.73 ), ! Z = Y }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 Z, Y ) ) = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.34/1.73 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Groups_Oplus__class_Oplus
% 1.34/1.73 ( X, c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 1.34/1.73 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__field( X ),
% 1.34/1.73 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T, Z
% 1.34/1.73 ), Y ) = c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide
% 1.34/1.73 ( X, T, Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 1.34/1.73 ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 1.34/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 1.34/1.73 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.34/1.73 ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 1.34/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 1.34/1.73 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.34/1.73 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.34/1.73 , c_Groups_Oplus__class_Oplus( X, Y, Z ), c_Groups_Ozero__class_Ozero( X
% 1.34/1.73 ) ) }.
% 1.34/1.73 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 Z, Y ) ) }.
% 1.34/1.73 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 Y, Z ) ) }.
% 1.34/1.73 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 1.34/1.73 .
% 1.34/1.73 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 X ), Z ), ! c_Groups_Oplus__class_Oplus( X, Y, Z ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.34/1.73 .
% 1.34/1.73 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 1.34/1.73 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Z )
% 1.34/1.73 ) }.
% 1.34/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X, Y,
% 1.34/1.73 Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 ) }.
% 1.34/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X
% 1.34/1.73 , Y, Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, Y, Y ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.73 ) }.
% 1.34/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.73 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.34/1.73 ), c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 1.34/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, Y, Y ) ), c_Orderings_Oord__class_Oless(
% 1.34/1.73 X, c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.34/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, Y, Y ) ) }.
% 1.34/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.34/1.73 , c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y
% 1.34/1.73 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.34/1.73 , c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.73 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.34/1.73 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.34/1.73 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.34/1.73 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.34/1.73 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.34/1.73 , c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.34/1.73 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 1.34/1.73 X, T, c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.34/1.73 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 1.34/1.73 X, c_Groups_Oplus__class_Oplus( X, Z, U ), c_Groups_Oplus__class_Oplus( X
% 1.34/1.73 , Y, T ) ) }.
% 1.34/1.73 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Z, U )
% 1.34/1.73 , c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.34/1.73 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.34/1.73 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, !
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, W, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, U, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.34/1.73 , Y, c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) )
% 1.34/1.73 ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = hAPP(
% 1.34/1.73 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X
% 1.34/1.73 , Z, c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Z
% 1.34/1.73 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP
% 1.34/1.73 ( c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y,
% 1.34/1.73 c_Groups_Oone__class_Oone( X ) ) ), Z ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), c_Groups_Oplus__class_Oplus( X, Y
% 1.34/1.73 , Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.34/1.73 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.34/1.73 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.34/1.73 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.34/1.73 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 , c_Groups_Oplus__class_Oplus( X, Y, Z ) ) }.
% 1.34/1.73 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.34/1.73 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.34/1.73 ) ) }.
% 1.34/1.73 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.34/1.73 ) ) }.
% 1.34/1.73 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.34/1.73 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.34/1.73 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 1.34/1.73 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.73 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.34/1.73 ) ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, Y
% 1.34/1.73 , Z ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.34/1.73 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 c_Groups_Oone__class_Oone( X ), c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.34/1.73 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, T,
% 1.34/1.73 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) =
% 1.34/1.73 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z,
% 1.34/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Y ) }.
% 1.34/1.73 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, T, c_Rings_Oinverse__class_Odivide( X, Z
% 1.34/1.73 , Y ) ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 1.34/1.73 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }
% 1.34/1.73 .
% 1.34/1.73 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 c_Rings_Oinverse__class_Odivide( X, T, Y ), Z ) =
% 1.34/1.73 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, T,
% 1.34/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) }.
% 1.34/1.73 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, c_Rings_Oinverse__class_Odivide( X, T, Y
% 1.34/1.73 ), Z ) = c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus
% 1.34/1.73 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }
% 1.34/1.73 .
% 1.34/1.73 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 1.34/1.73 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 1.34/1.73 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, hAPP
% 1.34/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.73 X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z,
% 1.34/1.73 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 1.34/1.73 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.34/1.73 c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.73 X, Z, Y ), c_Orderings_Oord__class_Oless( X,
% 1.34/1.73 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oplus__class_Oplus( X, Z, Y
% 1.34/1.73 ), c_Groups_Oplus__class_Oplus( X, c_Groups_Oone__class_Oone( X ),
% 1.34/1.73 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.34/1.73 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.34/1.73 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.34/1.73 Y ) ), c_Groups_Oplus__class_Oplus( X, Y, Z ) ) ),
% 1.34/1.73 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.34/1.73 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.34/1.73 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oplus__class_Oplus( X, Y, Z
% 1.34/1.73 ) ), c_Rings_Oinverse__class_Oinverse( X, Y ) ) ),
% 1.34/1.73 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.34/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.34/1.73 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.34/1.73 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.34/1.73 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.34/1.73 hAPP( Y, U ) ) }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.34/1.73 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.34/1.73 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 1.34/1.73 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.34/1.73 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.34/1.73 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.34/1.73 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.34/1.73 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 1.34/1.73 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 1.34/1.73 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.34/1.73 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.34/1.73 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.34/1.73 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.34/1.73 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.34/1.73 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.34/1.73 hAPP( Y, U ) ) }.
% 1.34/1.73 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.34/1.73 ( X, Z, Y ) }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.34/1.73 ( X, Y, Z ) }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.34/1.73 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 1.34/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.34/1.73 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.34/1.73 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.34/1.73 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.34/1.73 hAPP( Y, U ) ) }.
% 1.34/1.73 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 1.34/1.73 ( Z, skol7( X, Y, Z ) ), hAPP( Y, skol7( X, Y, Z ) ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 1.34/1.73 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.34/1.73 Y ) }.
% 1.34/1.73 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.34/1.73 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.34/1.73 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.34/1.73 Y ), ! Z = Y }.
% 1.34/1.73 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.34/1.73 Z ), ! Z = Y }.
% 1.34/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.34/1.73 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 1.34/1.73 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.34/1.73 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.34/1.73 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.34/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.34/1.73 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.34/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.34/1.73 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 1.34/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.34/1.73 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.34/1.73 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.34/1.73 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.34/1.73 , ! Z = Y }.
% 1.34/1.73 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.34/1.73 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.34/1.73 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.34/1.73 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.34/1.73 , ! Z = Y }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.34/1.73 , ! Y = Z }.
% 1.34/1.73 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.34/1.73 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.34/1.73 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.34/1.73 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 1.34/1.73 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 1.34/1.73 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.34/1.73 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 1.34/1.73 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.34/1.73 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.34/1.73 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.34/1.73 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.34/1.73 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.34/1.73 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.34/1.73 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.34/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.34/1.73 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.34/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.34/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 1.34/1.73 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.34/1.73 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.34/1.73 .
% 1.34/1.73 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.34/1.73 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.34/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 1.34/1.73 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.34/1.73 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 1.34/1.73 .
% 1.34/1.73 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.34/1.73 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 1.34/1.73 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.34/1.73 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.34/1.73 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.34/1.73 { alpha80( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.34/1.73 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.34/1.73 { alpha80( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 1.34/1.73 ( X, Y ), Z ) ) }.
% 1.34/1.73 { ! alpha80( X, Y, Z ), alpha84( X, Y, Z ), Z = Y }.
% 1.34/1.73 { ! alpha80( X, Y, Z ), alpha84( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 1.34/1.73 ) ) }.
% 1.34/1.73 { ! alpha84( X, Y, Z ), alpha80( X, Y, Z ) }.
% 1.34/1.73 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha80( X, Y, Z ) }.
% 1.34/1.73 { ! alpha84( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 1.34/1.73 }.
% 1.34/1.73 { ! alpha84( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 1.34/1.73 X, Y ), Z ) ), alpha84( X, Y, Z ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semiring__1( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 X ), W ), ! c_Groups_Oplus__class_Oplus( X, U, W ) =
% 1.34/1.73 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.73 ( X ), U ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), T )
% 1.34/1.73 ), Y ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), U ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 1.34/1.73 ), ! c_Groups_Oplus__class_Oplus( X, U, W ) = c_Groups_Oone__class_Oone
% 1.34/1.73 ( X ), c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.34/1.73 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.34/1.73 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.34/1.73 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.34/1.73 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.34/1.73 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.34/1.73 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.34/1.73 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.34/1.73 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.34/1.73 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.34/1.73 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.34/1.73 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.34/1.73 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.34/1.73 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.34/1.73 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.34/1.73 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.34/1.73 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.34/1.73 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.34/1.73 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.34/1.73 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.34/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 1.34/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.34/1.73 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.34/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.34/1.73 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.34/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.34/1.73 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.34/1.73 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.34/1.73 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.34/1.73 ( X, Z, Y ) }.
% 1.34/1.73 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.34/1.73 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.34/1.73 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.34/1.73 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.34/1.73 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.34/1.73 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.34/1.73 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.34/1.73 , ! Z = Y }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.34/1.73 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.34/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.34/1.73 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.34/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.34/1.73 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.34/1.73 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.34/1.73 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.34/1.73 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.34/1.73 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.34/1.73 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.34/1.73 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.34/1.73 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Nat_Onat ), X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 1.34/1.73 .
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.34/1.73 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.34/1.73 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.34/1.73 Y ), X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Nat_Onat ), Z ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.34/1.73 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Nat_Onat ), Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 1.34/1.73 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.34/1.73 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 1.34/1.73 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.34/1.73 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 1.34/1.73 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.34/1.73 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Nat_Onat ), X ) }.
% 1.34/1.73 { c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ) =
% 1.34/1.73 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, Y ) }.
% 1.34/1.73 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 1.34/1.73 skol8 ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 1.34/1.73 tc_Complex_Ocomplex, v_pa____ ) }.
% 1.34/1.73 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, skol8 ), X ) = hAPP(
% 1.34/1.73 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_c____, X ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.34/1.73 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.73 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.34/1.73 ) ), ! Z = c_Groups_Ozero__class_Ozero( X ), ! Y =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.34/1.73 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.34/1.73 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 1.34/1.73 X, c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 1.34/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 }.
% 1.34/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 }.
% 1.34/1.73 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oplus__class_Oplus( X,
% 1.34/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.73 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.34/1.73 ) = c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X
% 1.34/1.73 ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.73 ( X ), Z ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y )
% 1.34/1.73 ) = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X
% 1.34/1.73 ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol9( X, Y ) ) }.
% 1.34/1.73 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, skol10( X, Y ) ) }.
% 1.34/1.73 { ! X = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.34/1.73 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, T ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ), X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ), X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.34/1.73 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 1.34/1.73 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 1.34/1.73 .
% 1.34/1.73 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 1.34/1.73 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 1.34/1.73 }.
% 1.34/1.73 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.34/1.73 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 1.34/1.73 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 1.34/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.34/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 1.34/1.73 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.34/1.73 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 1.34/1.73 tc_Nat_Onat ) }.
% 1.34/1.73 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 1.34/1.73 tc_Nat_Onat ) }.
% 1.34/1.73 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.34/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.34/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 1.34/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.34/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.34/1.73 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.34/1.73 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.34/1.73 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 1.34/1.73 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.34/1.73 , Y ), X ) }.
% 1.34/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 1.34/1.73 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Nat_Onat ), X ) = X }.
% 1.34/1.73 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Nat_Onat ) ) = X }.
% 1.34/1.73 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Nat_Onat, Y, X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) = Y, X =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.34/1.73 ( tc_Nat_Onat, Y, X ), Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.34/1.73 ( tc_Nat_Onat, Y, X ), X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.34/1.73 ( tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) )
% 1.34/1.73 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Nat_Onat, Z, Y ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }
% 1.34/1.73 .
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Nat_Onat, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 1.34/1.73 .
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Nat_Onat, Y, T ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }
% 1.34/1.73 .
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, X ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oplus__class_Oplus
% 1.34/1.73 ( tc_Nat_Onat, Y, Z ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y
% 1.34/1.73 , X ) }.
% 1.34/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, Y ) ), X ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.34/1.73 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Polynomial_Opoly( X ), Y, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ) ) = Y }.
% 1.34/1.73 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Polynomial_Opoly( X ), c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ), Y ) = Y }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ),
% 1.34/1.73 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Polynomial_Opoly( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), T ), Y ), hAPP
% 1.34/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ), Z ), Y
% 1.34/1.73 ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Nat_Onat, Y, X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Nat_Onat, Y, X ) ) }.
% 1.34/1.73 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.34/1.73 { ! c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.34/1.73 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 1.34/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 1.34/1.73 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.34/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 1.34/1.73 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 1.34/1.73 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.34/1.73 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.34/1.73 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.73 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.34/1.73 tc_Nat_Onat ), X ), Y ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.34/1.73 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 1.34/1.73 ) ), c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X
% 1.34/1.73 ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.34/1.73 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.34/1.73 , c_Groups_Oplus__class_Oplus( X, Y, Y ), c_Groups_Ozero__class_Ozero( X
% 1.34/1.73 ) ) }.
% 1.34/1.73 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ), Z = X }.
% 1.34/1.73 { ! Z = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 1.34/1.73 { ! c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ), Y = X }.
% 1.34/1.73 { ! Y = X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, Y ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) }.
% 1.34/1.73 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) }.
% 1.34/1.73 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, c_Groups_Oplus__class_Oplus
% 1.34/1.73 ( tc_Nat_Onat, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.34/1.73 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) }.
% 1.34/1.73 { c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), X ) ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_Groups_Oplus__class_Oplus
% 1.34/1.73 ( tc_Nat_Onat, T, Y ) ), Z ), X ) }.
% 1.34/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, Y, Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 , Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), c_Groups_Oplus__class_Oplus( X, Y, Y )
% 1.34/1.73 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.34/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.34/1.73 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.34/1.73 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.34/1.73 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.34/1.73 .
% 1.34/1.73 { c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( tc_Complex_Ocomplex,
% 1.34/1.73 skol11 ) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(
% 1.34/1.73 tc_Complex_Ocomplex, v_pa____ ) }.
% 1.34/1.73 { hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex, skol11 ), X ) = hAPP(
% 1.34/1.73 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_pa____ ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, v_c____, X ) ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol12( Z, T ) ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol12( X, Y ) ) ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol13( Z, T ) ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol13( X, Y ) ) ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol14( Y ) ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol14( X ) ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Z, X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Z ) ) }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! c_SEQ_Odecseq( X, Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z ) ) }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 1.34/1.73 tc_Nat_Onat, skol15( X, Y ), skol49( X, Y ) ), c_SEQ_Odecseq( X, Y ) }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.73 hAPP( Y, skol49( X, Y ) ), hAPP( Y, skol15( X, Y ) ) ), c_SEQ_Odecseq( X
% 1.34/1.73 , Y ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol16( Z, T ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Z ), Y ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.34/1.73 c_Polynomial_Opoly( tc_Complex_Ocomplex, X ), Z ) ), skol16( X, Y ) ) }.
% 1.34/1.73 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.34/1.73 hAPP( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol17( Z, Y
% 1.34/1.73 ), Y ) }.
% 1.34/1.73 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.34/1.73 hAPP( X, Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.34/1.73 skol17( X, Y ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 1.34/1.73 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.34/1.73 hAPP( X, Y ) ), hBOOL( hAPP( X, c_Groups_Oplus__class_Oplus( tc_Nat_Onat
% 1.34/1.73 , skol17( X, Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__field( X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol18( Z, T ) ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__field( X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( X, c_Rings_Oinverse__class_Odivide( X, Z
% 1.34/1.73 , Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol18( X, Y ) ) ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol19( Y ) ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( X, Y ) ),
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( X, Z ) ) ), skol19( X ) ) ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol20( Z, T ) ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol20( X, Y ) ) ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol21( Z, T ) ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( X, Z ) ), skol21( X, Y ) ) ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.73 skol22( X, T, U ) ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, skol22( X, T, U ),
% 1.34/1.73 c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.34/1.73 , Y ) }.
% 1.34/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), skol22( X, Y, Z ) ), Z ), Y ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol23( Z, T ) ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), skol23( X, Y ) ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol50( X, Y, Z ) ) ), Z ),
% 1.34/1.73 c_SEQ_OBseq( X, Y ) }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! c_SEQ_Oincseq( X, Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, Z ), hAPP( Y, T ) ) }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 1.34/1.73 tc_Nat_Onat, skol24( X, Y ), skol51( X, Y ) ), c_SEQ_Oincseq( X, Y ) }.
% 1.34/1.73 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.73 hAPP( Y, skol24( X, Y ) ), hAPP( Y, skol51( X, Y ) ) ), c_SEQ_Oincseq( X
% 1.34/1.73 , Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.34/1.73 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 1.34/1.73 , c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatceiling( X ),
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.34/1.73 { c_Complex_Oexpi( c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) =
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 1.34/1.73 { c_RComplete_Onatceiling( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 1.34/1.73 ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatceiling( X )
% 1.34/1.73 ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 1.34/1.73 Y ), c_RComplete_Onatceiling( X ) ) }.
% 1.34/1.73 { c_RComplete_Onatceiling( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 1.34/1.73 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.34/1.73 c_RComplete_Onatceiling( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.34/1.73 }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling
% 1.34/1.73 ( X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 1.34/1.73 X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.34/1.73 { c_Complex_Oexpi( c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X )
% 1.34/1.73 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.34/1.73 c_Complex_Oexpi( Y ) ), c_Complex_Oexpi( X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.34/1.73 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( X ),
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.34/1.73 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.34/1.73 tc_RealDef_Oreal, X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.34/1.73 c_RealDef_Oreal( tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone(
% 1.34/1.73 tc_RealDef_Oreal ) ) ), c_RComplete_Onatceiling( X ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, c_Groups_Oone__class_Oone(
% 1.34/1.73 tc_Nat_Onat ) ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol25( Z, T ) ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, Z ) ), skol25( X, Y ) ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( X, hAPP( Z, skol26( X, Y, Z ) ) ), Y ),
% 1.34/1.73 c_SEQ_OBseq( X, Z ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.34/1.73 tc_Nat_Onat, X ) ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.34/1.73 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), c_Groups_Oone__class_Oone(
% 1.34/1.73 tc_RealDef_Oreal ) ) ) }.
% 1.34/1.73 { c_RComplete_Onatfloor( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 1.34/1.73 { c_RComplete_Onatceiling( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.34/1.73 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.34/1.73 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 1.34/1.73 , c_RComplete_Onatfloor( X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_RComplete_Onatfloor
% 1.34/1.73 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_RealDef_Oreal( tc_Nat_Onat, Y ), X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.34/1.73 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 1.34/1.73 , c_RComplete_Onatfloor( X ) ) }.
% 1.34/1.73 { ! c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat, X ),
% 1.34/1.73 Y = X }.
% 1.34/1.73 { ! Y = X, c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat
% 1.34/1.73 , X ) }.
% 1.34/1.73 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.34/1.73 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.34/1.73 { ! c_RealDef_Oreal( tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_RealDef_Oreal ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RealDef_Oreal(
% 1.34/1.73 tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.34/1.73 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.34/1.73 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.34/1.73 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.34/1.73 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.34/1.73 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 1.34/1.73 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.73 c_RComplete_Onatfloor( X ), Y ) }.
% 1.34/1.73 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.34/1.73 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.34/1.73 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal
% 1.34/1.73 ( tc_Nat_Onat, X ) ) }.
% 1.34/1.73 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y
% 1.34/1.73 , X ) ) = c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal
% 1.34/1.73 ( tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.34/1.73 c_RComplete_Onatfloor( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 1.34/1.73 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Nat_Onat, c_RComplete_Onatfloor( X ), Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_RComplete_Onatfloor( Y ),
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, c_RealDef_Oreal(
% 1.34/1.73 tc_Nat_Onat, X ) ) }.
% 1.34/1.73 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oone__class_Oone( tc_Nat_Onat ) )
% 1.34/1.73 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.34/1.73 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal
% 1.34/1.73 , X, c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.34/1.73 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 1.34/1.73 c_RComplete_Onatfloor( X ) = Y }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 1.34/1.73 tc_Nat_Onat, c_RComplete_Onatceiling( X ) ) ) }.
% 1.34/1.73 { c_RComplete_Onatfloor( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 1.34/1.73 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) )
% 1.34/1.73 }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatfloor( Y
% 1.34/1.73 ), c_RComplete_Onatfloor( X ) ) }.
% 1.34/1.73 { c_RComplete_Onatfloor( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.34/1.73 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.34/1.73 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_RealDef_Oreal
% 1.34/1.73 ( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.73 c_RComplete_Onatceiling( Y ), X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_RComplete_Onatfloor
% 1.34/1.73 ( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.34/1.73 tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.34/1.73 tc_Nat_Onat, X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.34/1.73 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.34/1.73 c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.34/1.73 tc_Nat_Onat, Y ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.34/1.73 c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless(
% 1.34/1.73 tc_Nat_Onat, Y, X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.34/1.73 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.34/1.73 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 1.34/1.73 tc_RealDef_Oreal ) ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.34/1.73 tc_Nat_Onat, Y ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.34/1.73 c_RealDef_Oreal( tc_Nat_Onat, X ), c_Groups_Oone__class_Oone(
% 1.34/1.73 tc_RealDef_Oreal ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 1.34/1.73 , X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 1.34/1.73 X ), Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.34/1.73 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 1.34/1.73 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.73 c_RComplete_Onatceiling( X ), Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Groups_Oone__class_Oone
% 1.34/1.73 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.34/1.73 c_RComplete_Onatceiling( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X
% 1.34/1.73 , c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Nat_Onat, c_RComplete_Onatceiling( X ), Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_RComplete_Onatfloor( X )
% 1.34/1.73 ), c_RComplete_Onatfloor( Y ) ), c_RComplete_Onatfloor( hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Nat_Onat ), Y ), c_RComplete_Onatfloor(
% 1.34/1.73 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 1.34/1.73 tc_Nat_Onat, Y ) ) ) = c_Divides_Odiv__class_Odiv( tc_Nat_Onat,
% 1.34/1.73 c_RComplete_Onatfloor( X ), Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.34/1.73 tc_Nat_Onat, Y ) ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 1.34/1.73 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, X,
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), Y ) ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, skol27( U, W, V0, T )
% 1.34/1.73 ), c_SEQ_OBseq( X, Y ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( X, hAPP( Y, skol27( X, Y, Z, T ) ) ), Z
% 1.34/1.73 ), c_SEQ_OBseq( X, Y ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP
% 1.34/1.73 ( hAPP( c_Power_Opower__class_Opower( tc_Polynomial_Opoly( X ) ), T ), Z
% 1.34/1.73 ) ), Y ) = hAPP( hAPP( c_Power_Opower__class_Opower( X ), hAPP(
% 1.34/1.73 c_Polynomial_Opoly( X, T ), Y ) ), Z ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__div__algebra( X ),
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.34/1.73 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( X, hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.34/1.73 c_RealVector_Onorm__class_Onorm( X, Z ) ), Y ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.34/1.73 tc_Nat_Onat ) ) = Y }.
% 1.34/1.73 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.34/1.73 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.34/1.73 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 1.34/1.73 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Nat_Onat, Z, Y ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 1.34/1.73 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) =
% 1.34/1.73 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.34/1.73 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 1.34/1.73 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.34/1.73 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.73 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.34/1.73 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 1.34/1.73 alpha16( X, Z ) }.
% 1.34/1.73 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 1.34/1.73 alpha40( X, Y, Z ) }.
% 1.34/1.73 { ! alpha16( X, Z ), ! alpha40( X, Y, Z ), hBOOL( hAPP( Z,
% 1.34/1.73 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ) }.
% 1.34/1.73 { ! alpha40( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.34/1.73 alpha51( X, Y, Z ) }.
% 1.34/1.73 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha40( X, Y, Z ) }.
% 1.34/1.73 { ! alpha51( X, Y, Z ), alpha40( X, Y, Z ) }.
% 1.34/1.73 { ! alpha51( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 1.34/1.73 ), alpha60( X, Y, Z, T ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol28( X, T, U ), X ),
% 1.34/1.73 alpha51( X, Y, Z ) }.
% 1.34/1.73 { ! alpha60( X, Y, Z, skol28( X, Y, Z ) ), alpha51( X, Y, Z ) }.
% 1.34/1.73 { ! alpha60( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.34/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 1.34/1.73 hBOOL( hAPP( Z, U ) ) }.
% 1.34/1.73 { ! hBOOL( hAPP( Z, skol29( U, W, Z, V0 ) ) ), alpha60( X, Y, Z, T ) }.
% 1.34/1.73 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol29( X, Y, Z, T ) )
% 1.34/1.73 , T ), alpha60( X, Y, Z, T ) }.
% 1.34/1.73 { ! alpha16( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.34/1.73 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.34/1.73 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha16( X, Y ) }.
% 1.34/1.73 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha16
% 1.34/1.73 ( X, Y ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.34/1.73 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 1.34/1.73 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.34/1.73 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, Y, X ) ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 1.34/1.73 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.34/1.73 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.34/1.73 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.34/1.73 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.34/1.73 ), X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.34/1.73 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 1.34/1.73 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.34/1.73 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.34/1.73 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) = c_RealDef_Oreal( tc_Nat_Onat,
% 1.34/1.73 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.34/1.73 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.34/1.73 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.34/1.73 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) }.
% 1.34/1.73 { ! X = c_RealDef_Oreal( tc_Nat_Onat, c_RComplete_Onatfloor( X ) ),
% 1.34/1.73 c_RComplete_Onatfloor( hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.34/1.73 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP( c_Power_Opower__class_Opower
% 1.34/1.73 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ), Y ) }.
% 1.34/1.73 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( X ) }.
% 1.34/1.73 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.34/1.73 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.34/1.73 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.34/1.73 = c_Groups_Oone__class_Oone( X ) }.
% 1.34/1.73 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 }.
% 1.34/1.73 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X, T
% 1.34/1.73 , Z ) ), Y ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.34/1.73 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 1.34/1.73 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 1.34/1.73 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 1.34/1.73 { ! class_Rings_Odivision__ring__inverse__zero( X ),
% 1.34/1.73 c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Z
% 1.34/1.73 ) ), Y ) }.
% 1.34/1.73 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.34/1.73 tc_Nat_Onat ) ) = Y }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.73 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ), Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.73 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, Z ),
% 1.34/1.73 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, Z ) ) }.
% 1.34/1.73 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 1.34/1.73 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 1.34/1.73 tc_Nat_Onat, Z, Y ), X ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semidom( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.73 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.34/1.73 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semidom( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.34/1.73 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semidom( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 1.34/1.73 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.34/1.73 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.34/1.73 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.34/1.73 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.34/1.73 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.34/1.73 .
% 1.34/1.73 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.34/1.73 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.34/1.73 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Nat_Onat ) }.
% 1.34/1.73 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.34/1.73 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.34/1.73 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 1.34/1.73 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 1.34/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 1.34/1.73 { ! class_Divides_Osemiring__div( X ), ! T = c_Groups_Ozero__class_Ozero( X
% 1.34/1.73 ), c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Divides_Osemiring__div( X ), T = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.34/1.73 c_Divides_Odiv__class_Odiv( X, Z, Y ) }.
% 1.34/1.73 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = Z }.
% 1.34/1.73 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) = Z }.
% 1.34/1.73 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.34/1.73 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 1.34/1.73 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 1.34/1.73 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 1.34/1.73 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.34/1.73 hAPP( c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide
% 1.34/1.73 ( X, T, Y ) ), Z ) = c_Rings_Oinverse__class_Odivide( X, hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.34/1.73 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 , c_Divides_Odiv__class_Odiv( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 1.34/1.73 }.
% 1.34/1.73 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.34/1.73 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.34/1.73 c_Groups_Oone__class_Oone( X ) }.
% 1.34/1.73 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), T ), c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Nat_Onat, Z, Y ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.34/1.73 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.34/1.73 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 , c_Rings_Oinverse__class_Oinverse( X, hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Oinverse( X, Y
% 1.34/1.73 ) ), Z ) }.
% 1.34/1.73 { ! class_Fields_Ofield__inverse__zero( X ),
% 1.34/1.73 c_Rings_Oinverse__class_Odivide( X, c_Groups_Oone__class_Oone( X ), hAPP
% 1.34/1.73 ( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.34/1.73 c_Groups_Oone__class_Oone( X ), Z ) ), Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.34/1.73 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 1.34/1.73 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.34/1.73 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.34/1.73 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.34/1.73 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.34/1.73 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.34/1.73 ) = c_Groups_Oone__class_Oone( X ) }.
% 1.34/1.73 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.34/1.73 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.73 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 1.34/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 1.34/1.73 ) }.
% 1.34/1.73 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, T, hAPP
% 1.34/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( X, Z, c_Divides_Odiv__class_Odiv( X, T, Y )
% 1.34/1.73 ) }.
% 1.34/1.73 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Y, Z ),
% 1.34/1.73 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 1.34/1.73 ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.34/1.73 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.73 , c_Divides_Odiv__class_Odiv( X, c_Groups_Oplus__class_Oplus( X, Z, Y ),
% 1.34/1.73 Y ) = c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Z, Y
% 1.34/1.73 ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.34/1.73 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.34/1.73 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.34/1.73 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.34/1.73 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.34/1.73 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 1.34/1.73 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semidom( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 1.34/1.73 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 1.34/1.73 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.73 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ),
% 1.34/1.73 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 1.34/1.73 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) = Y }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 1.34/1.73 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.34/1.73 tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 1.34/1.73 tc_Nat_Onat, Y, X ), Y ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.34/1.73 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 1.34/1.73 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.34/1.73 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 1.34/1.73 { ! class_Rings_Olinordered__semidom( X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.34/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 1.34/1.73 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.34/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.34/1.73 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 1.34/1.73 { X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), Y =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 1.34/1.73 ( tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex
% 1.34/1.73 , c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex,
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), X ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol30( X, Y ) ), Y
% 1.34/1.73 ) ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.34/1.73 { ! class_Power_Opower( X ), c_Power_Opower__class_Opower( X ) =
% 1.34/1.73 c_Power_Opower_Opower( X, c_Groups_Oone__class_Oone( X ),
% 1.34/1.73 c_Groups_Otimes__class_Otimes( X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.34/1.73 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Nat_Onat ), Y ) }.
% 1.34/1.73 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.34/1.73 ), X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.34/1.73 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 1.34/1.73 alpha17( X, Z ) }.
% 1.34/1.73 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 1.34/1.73 alpha41( X, Y, Z ) }.
% 1.34/1.73 { ! alpha17( X, Z ), ! alpha41( X, Y, Z ), hBOOL( hAPP( Z,
% 1.34/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ) }.
% 1.34/1.73 { ! alpha41( X, Y, Z ), alpha52( X, Y, Z ) }.
% 1.34/1.73 { ! alpha41( X, Y, Z ), alpha61( X, Y, Z ) }.
% 1.34/1.73 { ! alpha52( X, Y, Z ), ! alpha61( X, Y, Z ), alpha41( X, Y, Z ) }.
% 1.34/1.73 { ! alpha61( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha70( X, Y, Z ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha61( X, Y, Z ) }.
% 1.34/1.73 { ! alpha70( X, Y, Z ), alpha61( X, Y, Z ) }.
% 1.34/1.73 { ! alpha70( X, Y, Z ), ! alpha74( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 1.34/1.73 { ! hBOOL( hAPP( Z, skol31( T, U, Z ) ) ), alpha70( X, Y, Z ) }.
% 1.34/1.73 { alpha74( X, Y, skol31( X, Y, Z ) ), alpha70( X, Y, Z ) }.
% 1.34/1.73 { ! alpha74( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.34/1.73 skol32( X, T, U ) ) }.
% 1.34/1.73 { ! alpha74( X, Y, Z ), alpha78( X, Y, Z, skol32( X, Y, Z ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha78( X, Y, Z
% 1.34/1.73 , T ), alpha74( X, Y, Z ) }.
% 1.34/1.73 { ! alpha78( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.34/1.73 { ! alpha78( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.34/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 1.34/1.73 .
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha78( X,
% 1.34/1.73 Y, Z, T ) }.
% 1.34/1.73 { ! alpha52( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha62( X, Y, Z ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Int_Oint ), X ), alpha52( X, Y, Z ) }.
% 1.34/1.73 { ! alpha62( X, Y, Z ), alpha52( X, Y, Z ) }.
% 1.34/1.73 { ! alpha62( X, Y, Z ), ! alpha71( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 1.34/1.73 { ! hBOOL( hAPP( Z, skol33( T, U, Z ) ) ), alpha62( X, Y, Z ) }.
% 1.34/1.73 { alpha71( X, Y, skol33( X, Y, Z ) ), alpha62( X, Y, Z ) }.
% 1.34/1.73 { ! alpha71( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), skol34( T, U, W ) ) }.
% 1.34/1.73 { ! alpha71( X, Y, Z ), alpha75( X, Y, Z, skol34( X, Y, Z ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha75( X, Y, Z, T )
% 1.34/1.73 , alpha71( X, Y, Z ) }.
% 1.34/1.73 { ! alpha75( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 1.34/1.73 ) }.
% 1.34/1.73 { ! alpha75( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.34/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 1.34/1.73 .
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha75( X,
% 1.34/1.73 Y, Z, T ) }.
% 1.34/1.73 { ! alpha17( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.34/1.73 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.34/1.73 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha17( X, Y ) }.
% 1.34/1.73 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha17
% 1.34/1.73 ( X, Y ) }.
% 1.34/1.73 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), alpha81( X,
% 1.34/1.73 Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), Z =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.34/1.73 tc_Int_Oint, T, Z ) = Y }.
% 1.34/1.73 { ! T = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), alpha81( X,
% 1.34/1.73 Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.34/1.73 tc_Int_Oint, T, Z ) = Y }.
% 1.34/1.73 { ! alpha81( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.34/1.73 { ! alpha81( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha81( X, Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y )
% 1.34/1.73 , alpha81( X, Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, hAPP(
% 1.34/1.73 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 1.34/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.34/1.73 tc_Int_Oint, Z, Y ), X ) }.
% 1.34/1.73 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.34/1.73 ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.34/1.73 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 1.34/1.73 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ), T ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.34/1.73 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.34/1.73 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ), Z ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ), X ) ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.34/1.73 ( tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.34/1.73 Z ), Y ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.34/1.73 ), Y ), X ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.34/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, c_Groups_Oone__class_Oone
% 1.34/1.73 ( tc_Int_Oint ), Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Int_Oint ), X ), ! X = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.34/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.34/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ) ), X ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.34/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.34/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 1.34/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 1.34/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 1.34/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 1.34/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 1.34/1.73 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.34/1.73 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 1.34/1.73 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.34/1.73 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.34/1.73 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 1.34/1.73 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.34/1.73 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 1.34/1.73 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ) =
% 1.34/1.73 c_Polynomial_Osmult( X, T, c_Divides_Odiv__class_Odiv(
% 1.34/1.73 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 1.34/1.73 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Odiv(
% 1.34/1.73 tc_Polynomial_Opoly( X ), T, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.34/1.73 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) = c_Divides_Odiv__class_Odiv(
% 1.34/1.73 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 1.34/1.73 ( X ), T, Z ), Y ) }.
% 1.34/1.73 { hAPP( hAPP( c_Power_Opower_Opower( T, Z, Y ), X ),
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = Z }.
% 1.34/1.73 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.73 c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly( X ), T,
% 1.34/1.73 c_Polynomial_Osmult( X, Y, Z ) ) = c_Polynomial_Osmult( X,
% 1.34/1.73 c_Rings_Oinverse__class_Oinverse( X, Y ), c_Divides_Odiv__class_Odiv(
% 1.34/1.73 tc_Polynomial_Opoly( X ), T, Z ) ) }.
% 1.34/1.73 { ! class_Rings_Ocomm__ring__1( X ), hAPP( c_Polynomial_Opoly( X, hAPP(
% 1.34/1.73 hAPP( c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.34/1.73 c_Polynomial_Omonom( X, c_Groups_Oone__class_Oone( X ), T ) ), Z ) ), Y )
% 1.34/1.73 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( X ), Y ), T ) ), hAPP( c_Polynomial_Opoly(
% 1.34/1.73 X, Z ), Y ) ) }.
% 1.34/1.73 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ),
% 1.34/1.73 c_Complex_Orcis( Z, Y ) ), X ) = c_Complex_Orcis( hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.34/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.34/1.73 tc_Nat_Onat, X ) ), Y ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol35( Z, T ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol35( X, Y ) ), X ) =
% 1.34/1.73 Y }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), ! hAPP( hAPP(
% 1.34/1.73 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), Z ), X ) = Y, Z =
% 1.34/1.73 skol35( X, Y ) }.
% 1.34/1.73 { ! c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha18( X, Y ) }.
% 1.34/1.73 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.34/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.34/1.73 { ! alpha18( X, Y ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.34/1.73 { ! alpha18( X, Y ), alpha42( X, Y ), alpha53( X, Y ) }.
% 1.34/1.73 { ! alpha42( X, Y ), alpha18( X, Y ) }.
% 1.34/1.73 { ! alpha53( X, Y ), alpha18( X, Y ) }.
% 1.34/1.73 { ! alpha53( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.34/1.73 { ! alpha53( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ), alpha53( X, Y ) }.
% 1.34/1.73 { ! alpha42( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.34/1.73 { ! alpha42( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), alpha42( X, Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.34/1.73 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.34/1.73 tc_Int_Oint, Y, X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.34/1.73 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 1.34/1.73 , Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 1.34/1.73 , Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.34/1.73 tc_Int_Oint, Y, X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Int_Oint ), Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.34/1.73 tc_Int_Oint, X, Y ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.34/1.73 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 1.34/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 1.34/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.34/1.73 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y
% 1.34/1.73 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.34/1.73 tc_Int_Oint, Y, X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.34/1.73 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 1.34/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.34/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ),
% 1.34/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 1.34/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.34/1.73 tc_Int_Oint, X, Y ), X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.34/1.73 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.34/1.73 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Int_Oint ), Y ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.34/1.73 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.34/1.73 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.34/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, X ) =
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.34/1.73 tc_Int_Oint, X, Y ) ) }.
% 1.34/1.73 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, T, Z ) =
% 1.34/1.73 c_Polynomial_Omonom( X, Y, Z ), T = Y }.
% 1.34/1.73 { ! class_Groups_Ozero( X ), ! T = Y, c_Polynomial_Omonom( X, T, Z ) =
% 1.34/1.73 c_Polynomial_Omonom( X, Y, Z ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.34/1.73 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 1.34/1.73 ( tc_Int_Oint ) }.
% 1.34/1.73 { ! c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Int_Oint, c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ) =
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.34/1.73 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Int_Oint ), X ) = X }.
% 1.34/1.73 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero
% 1.34/1.73 ( tc_Int_Oint ) ) = X }.
% 1.34/1.73 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) =
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ) }.
% 1.34/1.73 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, c_Groups_Oplus__class_Oplus
% 1.34/1.73 ( tc_Int_Oint, Y, X ) ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 1.34/1.73 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Int_Oint, Y, Z ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 1.34/1.73 .
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Int_Oint, Y, T ), c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Z ) ) }
% 1.34/1.73 .
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, Y ),
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 1.34/1.73 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.34/1.73 tc_Int_Oint ) ), X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.73 tc_Int_Oint ), c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus
% 1.34/1.73 ( tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.34/1.73 tc_Int_Oint, c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.34/1.73 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ), X ),
% 1.34/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.34/1.73 tc_Int_Oint ) ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X )
% 1.34/1.73 }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, c_Groups_Oone__class_Oone(
% 1.34/1.73 tc_Int_Oint ) ), X ) }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.34/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.34/1.73 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y
% 1.34/1.73 = X }.
% 1.34/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.34/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.34/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.34/1.74 tc_Int_Oint ) ) ) }.
% 1.34/1.74 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.34/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.34/1.74 tc_Int_Oint ) ) ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.34/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.34/1.74 tc_Int_Oint ) ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X )
% 1.34/1.74 }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.34/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.34/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, c_Groups_Oone__class_Oone(
% 1.34/1.74 tc_Int_Oint ) ) ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.74 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 1.34/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.74 tc_Int_Oint ), X ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.34/1.74 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.74 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 1.34/1.74 { ! class_Groups_Ozero( X ), c_Polynomial_Omonom( X,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.34/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Groups_Ozero( X ), ! c_Polynomial_Omonom( X, Z, Y ) =
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ), Z =
% 1.34/1.74 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.74 { ! class_Groups_Ozero( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.74 c_Polynomial_Omonom( X, Z, Y ) = c_Groups_Ozero__class_Ozero(
% 1.34/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__semiring__0( X ), c_Polynomial_Osmult( X, T,
% 1.34/1.74 c_Polynomial_Omonom( X, Z, Y ) ) = c_Polynomial_Omonom( X, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) }.
% 1.34/1.74 { ! class_Groups_Ocomm__monoid__add( X ), c_Groups_Oplus__class_Oplus(
% 1.34/1.74 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 1.34/1.74 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 1.34/1.74 c_Groups_Oplus__class_Oplus( X, T, Y ), Z ) }.
% 1.34/1.74 { c_Complex_Orcis( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) =
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( c_Polynomial_Opoly( X,
% 1.34/1.74 c_Polynomial_Omonom( X, T, Z ) ), Y ) = hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.34/1.74 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__semiring__0( X ), hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Polynomial_Opoly( X ) ),
% 1.34/1.74 c_Polynomial_Omonom( X, U, T ) ), c_Polynomial_Omonom( X, Z, Y ) ) =
% 1.34/1.74 c_Polynomial_Omonom( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U
% 1.34/1.74 ), Z ), c_Groups_Oplus__class_Oplus( tc_Nat_Onat, T, Y ) ) }.
% 1.34/1.74 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ),
% 1.34/1.74 c_Complex_Orcis( T, Z ) ), c_Complex_Orcis( Y, X ) ) = c_Complex_Orcis(
% 1.34/1.74 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), T ), Y ),
% 1.34/1.74 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, Z, X ) ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.34/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.34/1.74 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.34/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.34/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.34/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.34/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.34/1.74 tc_Int_Oint, X, Y ) ) }.
% 1.34/1.74 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 1.34/1.74 tc_Int_Oint ) ) }.
% 1.34/1.74 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.34/1.74 tc_Int_Oint ) ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.74 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.34/1.74 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol36( Z, T ) ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.74 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 1.34/1.74 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), skol36( X, Y ) ), X ) =
% 1.34/1.74 Y }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.34/1.74 c_Transcendental_Oln( hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.34/1.74 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.34/1.74 tc_Nat_Onat, Y ) ), c_Transcendental_Oln( X ) ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.34/1.74 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.34/1.74 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 1.34/1.74 ), c_Transcendental_Oln( Y ) ), c_Orderings_Oord__class_Oless(
% 1.34/1.74 tc_RealDef_Oreal, X, Y ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.34/1.74 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.34/1.74 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Y ),
% 1.34/1.74 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 1.34/1.74 ), c_Transcendental_Oln( Y ) ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.34/1.74 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.34/1.74 c_Transcendental_Oln( X ) = c_Transcendental_Oln( Y ), X = Y }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.34/1.74 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), ! X = Y,
% 1.34/1.74 c_Transcendental_Oln( X ) = c_Transcendental_Oln( Y ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.34/1.74 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 1.34/1.74 ), X ) }.
% 1.34/1.74 { c_Transcendental_Oln( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.34/1.74 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.34/1.74 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 1.34/1.74 ( X ), c_Transcendental_Oln( Y ) ), c_Orderings_Oord__class_Oless__eq(
% 1.34/1.74 tc_RealDef_Oreal, X, Y ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.34/1.74 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.34/1.74 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ),
% 1.34/1.74 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 1.34/1.74 ( X ), c_Transcendental_Oln( Y ) ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 1.34/1.74 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 1.34/1.74 ) ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 1.34/1.74 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 1.34/1.74 ) ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.34/1.74 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 1.34/1.74 ) ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.34/1.74 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 1.34/1.74 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 1.34/1.74 ) ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.34/1.74 c_Transcendental_Oln( X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 1.34/1.74 ), X = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), ! X =
% 1.34/1.74 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), c_Transcendental_Oln( X )
% 1.34/1.74 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.34/1.74 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 1.34/1.74 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.34/1.74 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 1.34/1.74 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.34/1.74 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 1.34/1.74 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.34/1.74 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 1.34/1.74 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.34/1.74 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 1.34/1.74 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.34/1.74 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_Transcendental_Oln( X
% 1.34/1.74 ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 1.34/1.74 ) ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.34/1.74 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.34/1.74 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 1.34/1.74 ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.34/1.74 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 1.34/1.74 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 1.34/1.74 ) ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Transcendental_Oln( X
% 1.34/1.74 ) ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.34/1.74 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.34/1.74 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.34/1.74 c_Transcendental_Oln( hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.34/1.74 tc_RealDef_Oreal ), X ), Y ) ) = c_Groups_Oplus__class_Oplus(
% 1.34/1.74 tc_RealDef_Oreal, c_Transcendental_Oln( X ), c_Transcendental_Oln( Y ) )
% 1.34/1.74 }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.34/1.74 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_Transcendental_Oln
% 1.34/1.74 ( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) ), X ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.74 ( tc_Nat_Onat ), X ), c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 1.34/1.74 c_RealDef_Oreal( tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) =
% 1.34/1.74 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.34/1.74 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 1.34/1.74 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.34/1.74 tc_Nat_Onat, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ),
% 1.34/1.74 c_RealDef_Oreal( tc_Nat_Onat, X ) ) ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.34/1.74 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv
% 1.34/1.74 ( tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X )
% 1.34/1.74 ) ), ! alpha19( X, Y, T, U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.34/1.74 ( tc_Int_Oint ), X ), alpha19( X, Y, skol37( X, Y, Z ), skol52( X, Y, Z )
% 1.34/1.74 ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X )
% 1.34/1.74 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.34/1.74 ( tc_Int_Oint ), X ), ! hBOOL( hAPP( hAPP( Z, skol37( X, Y, Z ) ), skol52
% 1.34/1.74 ( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z, c_Divides_Odiv__class_Odiv(
% 1.34/1.74 tc_Int_Oint, Y, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) )
% 1.34/1.74 ) }.
% 1.34/1.74 { ! alpha19( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ) }.
% 1.34/1.74 { ! alpha19( X, Y, Z, T ), alpha43( X, Y, Z, T ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha43( X, Y, Z, T )
% 1.34/1.74 , alpha19( X, Y, Z, T ) }.
% 1.34/1.74 { ! alpha43( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 1.34/1.74 ) }.
% 1.34/1.74 { ! alpha43( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.34/1.74 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 1.34/1.74 .
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y =
% 1.34/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha43( X,
% 1.34/1.74 Y, Z, T ) }.
% 1.34/1.74 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.34/1.74 tc_Int_Oint, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.34/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.34/1.74 tc_Int_Oint, Z, X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.34/1.74 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.34/1.74 tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, X ),
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 1.34/1.74 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 1.34/1.74 tc_Int_Oint ) ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.34/1.74 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, c_Groups_Ozero__class_Ozero(
% 1.34/1.74 tc_Int_Oint ) ) = X }.
% 1.34/1.74 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Omod(
% 1.34/1.74 tc_Int_Oint, Y, X ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.34/1.74 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y = hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol38( X, Y ) ) }.
% 1.34/1.74 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z )
% 1.34/1.74 , c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) =
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.34/1.74 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Z ) =
% 1.34/1.74 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.34/1.74 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) =
% 1.34/1.74 c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 1.34/1.74 c_Groups_Oone__class_Oone( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.34/1.74 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Z ) =
% 1.34/1.74 c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.34/1.74 c_Groups_Oplus__class_Oplus( X, T, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) =
% 1.34/1.74 c_Divides_Odiv__class_Omod( X, T, Y ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 1.34/1.74 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Groups_Ozero__class_Ozero
% 1.34/1.74 ( X ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.74 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 1.34/1.74 { ! c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol39( X, Y ) ) }.
% 1.34/1.74 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z )
% 1.34/1.74 , c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.34/1.74 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.34/1.74 tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z
% 1.34/1.74 ), Y ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 1.34/1.74 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 1.34/1.74 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 1.34/1.74 c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, T, W ), Z
% 1.34/1.74 ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X, Y, U
% 1.34/1.74 ), Z ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.34/1.74 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Z ), Y
% 1.34/1.74 ), Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 1.34/1.74 T, Y ), Z ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.34/1.74 c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z, Y )
% 1.34/1.74 ), Y ) = c_Divides_Odiv__class_Omod( X, c_Groups_Oplus__class_Oplus( X,
% 1.34/1.74 T, Z ), Y ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.34/1.74 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 1.34/1.74 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 1.34/1.74 ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.34/1.74 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 1.34/1.74 ( X, c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Omod( X, T, Y
% 1.34/1.74 ), Z ), Y ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.34/1.74 c_Groups_Oplus__class_Oplus( X, T, Z ), Y ) = c_Divides_Odiv__class_Omod
% 1.34/1.74 ( X, c_Groups_Oplus__class_Oplus( X, T, c_Divides_Odiv__class_Omod( X, Z
% 1.34/1.74 , Y ) ), Y ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.34/1.74 c_Groups_Oplus__class_Oplus( X, Z, Y ), Z ) = c_Divides_Odiv__class_Omod
% 1.34/1.74 ( X, Y, Z ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.34/1.74 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod
% 1.34/1.74 ( X, Z, Y ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.34/1.74 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.34/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 1.34/1.74 ( tc_Int_Oint, Y, X ) ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 1.34/1.74 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.74 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.34/1.74 { c_Divides_Odiv__class_Omod( tc_Int_Oint, X, X ) =
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.74 }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, Y, Y
% 1.34/1.74 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.74 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), Y ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.34/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.34/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.34/1.74 tc_Int_Oint, X, Y ) ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.34/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ), X ) }.
% 1.34/1.74 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.34/1.74 tc_Nat_Onat, Z, Y ), X ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.34/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 1.34/1.74 tc_Nat_Onat, Z, X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 1.34/1.74 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.34/1.74 tc_Nat_Onat, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, X ),
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.34/1.74 c_Divides_Odiv__class_Omod( X, Z, Y ), Y ) = c_Divides_Odiv__class_Omod(
% 1.34/1.74 X, Z, Y ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.34/1.74 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 1.34/1.74 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.74 ( X ), T ), c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.34/1.74 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 1.34/1.74 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.74 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ), Z ), Y ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.34/1.74 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ) =
% 1.34/1.74 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.74 ( X ), c_Divides_Odiv__class_Omod( X, T, Y ) ),
% 1.34/1.74 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.34/1.74 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), T ), c_Divides_Odiv__class_Omod( X, Z
% 1.34/1.74 , Y ) ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.34/1.74 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X, T, Y )
% 1.34/1.74 ), Z ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Omod( X, hAPP
% 1.34/1.74 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Omod( X
% 1.34/1.74 , T, Z ) ), Y ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, T,
% 1.34/1.74 Z ) = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod
% 1.34/1.74 ( X, W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 1.34/1.74 c_Divides_Odiv__class_Omod( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.74 ( X ), T ), W ), Z ) = c_Divides_Odiv__class_Omod( X, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), U ), Z ) }.
% 1.34/1.74 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) }.
% 1.34/1.74 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) }.
% 1.34/1.74 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.34/1.74 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) =
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.34/1.74 { c_Divides_Odiv__class_Omod( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.74 c_Power_Opower__class_Opower( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.34/1.74 tc_Int_Oint, Z, Y ) ), X ), Y ) = c_Divides_Odiv__class_Omod( tc_Int_Oint
% 1.34/1.74 , hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ), Y )
% 1.34/1.74 }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 1.34/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.74 ( X ), c_Divides_Odiv__class_Odiv( X, T, Z ) ), Z ),
% 1.34/1.74 c_Divides_Odiv__class_Omod( X, T, Z ) ), Y ) =
% 1.34/1.74 c_Groups_Oplus__class_Oplus( X, T, Y ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 1.34/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.74 ( X ), T ), c_Divides_Odiv__class_Odiv( X, Z, T ) ),
% 1.34/1.74 c_Divides_Odiv__class_Omod( X, Z, T ) ), Y ) =
% 1.34/1.74 c_Groups_Oplus__class_Oplus( X, Z, Y ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 1.34/1.74 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X
% 1.34/1.74 , Z, Y ) ), Y ), c_Divides_Odiv__class_Omod( X, Z, Y ) ) = Z }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X, hAPP
% 1.34/1.74 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.34/1.74 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), c_Divides_Odiv__class_Omod( X, Y
% 1.34/1.74 , Z ) ) = Y }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), c_Groups_Oplus__class_Oplus( X,
% 1.34/1.74 c_Divides_Odiv__class_Omod( X, Z, Y ), hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Z, Y )
% 1.34/1.74 ), Y ) ) = Z }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.74 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ), X ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.34/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) = X }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.34/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ),
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.34/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, c_Divides_Odiv__class_Omod
% 1.34/1.74 ( tc_Int_Oint, Y, X ) ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.34/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ),
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.34/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) = X }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.34/1.74 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.34/1.74 tc_Int_Oint, Y, X ) ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.34/1.74 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ), X ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.34/1.74 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.34/1.74 tc_Int_Oint, Y, X ) ) }.
% 1.34/1.74 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), X ) =
% 1.34/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.34/1.74 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ),
% 1.34/1.74 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ), X ) ) }.
% 1.34/1.74 { c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 1.34/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 1.34/1.74 tc_Nat_Onat, Z, Y ), X ) ), c_Divides_Odiv__class_Omod( tc_Nat_Onat, Z, Y
% 1.34/1.74 ) ) }.
% 1.34/1.74 { Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 1.34/1.74 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) }.
% 1.34/1.74 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), X ) =
% 1.34/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.34/1.74 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.34/1.74 c_Divides_Odiv__class_Odiv( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) ) }.
% 1.34/1.74 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.34/1.74 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.34/1.74 ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ),
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, Z ) ), X ) =
% 1.34/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Y, X ) }.
% 1.34/1.74 { c_Groups_Oplus__class_Oplus( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.34/1.74 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.34/1.74 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, Y ) ), Y ),
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ) ), X ) =
% 1.34/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, Z, X ) }.
% 1.34/1.74 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 1.34/1.74 alpha20( X, Y, Z ) }.
% 1.34/1.74 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ),
% 1.34/1.74 alpha44( X, Y, Z ) }.
% 1.34/1.74 { ! alpha20( X, Y, Z ), ! alpha44( X, Y, Z ), hBOOL( hAPP( Z,
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) ) ) }.
% 1.34/1.74 { ! alpha44( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.34/1.74 alpha54( X, Y, Z ) }.
% 1.34/1.74 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha44( X, Y, Z ) }.
% 1.34/1.74 { ! alpha54( X, Y, Z ), alpha44( X, Y, Z ) }.
% 1.34/1.74 { ! alpha54( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 1.34/1.74 ), alpha63( X, Y, Z, T ) }.
% 1.34/1.74 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol40( X, T, U ), X ),
% 1.34/1.74 alpha54( X, Y, Z ) }.
% 1.34/1.74 { ! alpha63( X, Y, Z, skol40( X, Y, Z ) ), alpha54( X, Y, Z ) }.
% 1.34/1.74 { ! alpha63( X, Y, Z, T ), ! Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.34/1.74 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ), T ),
% 1.34/1.74 hBOOL( hAPP( Z, T ) ) }.
% 1.34/1.74 { Y = c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol41( X, Y, T ) ), T
% 1.34/1.74 ), alpha63( X, Y, Z, T ) }.
% 1.34/1.74 { ! hBOOL( hAPP( Z, T ) ), alpha63( X, Y, Z, T ) }.
% 1.34/1.74 { ! alpha20( X, Y, Z ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.34/1.74 hBOOL( hAPP( Z, Y ) ) }.
% 1.34/1.74 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha20( X, Y, Z ) }.
% 1.34/1.74 { ! hBOOL( hAPP( Z, Y ) ), alpha20( X, Y, Z ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.74 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 1.34/1.74 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.34/1.74 c_Groups_Oplus__class_Oplus( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ),
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Nat_Onat, T, X ) ), Z ), hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.34/1.74 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y ),
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), c_Divides_Odiv__class_Omod
% 1.34/1.74 ( tc_Int_Oint, X, Y ) = c_Groups_Oplus__class_Oplus( tc_Int_Oint, X, Y )
% 1.34/1.74 }.
% 1.34/1.74 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ),
% 1.34/1.74 alpha21( X, Y, Z ) }.
% 1.34/1.74 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ),
% 1.34/1.74 alpha45( X, Y, Z ) }.
% 1.34/1.74 { ! alpha21( X, Y, Z ), ! alpha45( X, Y, Z ), hBOOL( hAPP( Z,
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 1.34/1.74 { ! alpha45( X, Y, Z ), alpha55( X, Y, Z ) }.
% 1.34/1.74 { ! alpha45( X, Y, Z ), alpha64( X, Y, Z ) }.
% 1.34/1.74 { ! alpha55( X, Y, Z ), ! alpha64( X, Y, Z ), alpha45( X, Y, Z ) }.
% 1.34/1.74 { ! alpha64( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha72( X, Y, Z ) }.
% 1.34/1.74 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha64( X, Y, Z ) }.
% 1.34/1.74 { ! alpha72( X, Y, Z ), alpha64( X, Y, Z ) }.
% 1.34/1.74 { ! alpha72( X, Y, Z ), ! alpha76( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 1.34/1.74 { ! hBOOL( hAPP( Z, skol42( T, U, Z ) ) ), alpha72( X, Y, Z ) }.
% 1.34/1.74 { alpha76( X, Y, skol42( X, Y, Z ) ), alpha72( X, Y, Z ) }.
% 1.34/1.74 { ! alpha76( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z )
% 1.34/1.74 }.
% 1.34/1.74 { ! alpha76( X, Y, Z ), alpha79( X, Y, Z ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), ! alpha79( X, Y, Z
% 1.34/1.74 ), alpha76( X, Y, Z ) }.
% 1.34/1.74 { ! alpha79( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.34/1.74 { ! alpha79( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP
% 1.34/1.74 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol43( X, Y,
% 1.34/1.74 Z ) ), Z ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 1.34/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), T ), Z ), alpha79( X,
% 1.34/1.74 Y, Z ) }.
% 1.34/1.74 { ! alpha55( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha65( X, Y, Z ) }.
% 1.34/1.74 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.34/1.74 tc_Int_Oint ), X ), alpha55( X, Y, Z ) }.
% 1.34/1.74 { ! alpha65( X, Y, Z ), alpha55( X, Y, Z ) }.
% 1.34/1.74 { ! alpha65( X, Y, Z ), ! alpha73( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 1.34/1.74 { ! hBOOL( hAPP( Z, skol44( T, U, Z ) ) ), alpha65( X, Y, Z ) }.
% 1.34/1.74 { alpha73( X, Y, skol44( X, Y, Z ) ), alpha65( X, Y, Z ) }.
% 1.34/1.74 { ! alpha73( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ) }.
% 1.34/1.74 { ! alpha73( X, Y, Z ), alpha77( X, Y, Z ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), ! alpha77( X, Y, Z ),
% 1.34/1.74 alpha73( X, Y, Z ) }.
% 1.34/1.74 { ! alpha77( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X )
% 1.34/1.74 }.
% 1.34/1.74 { ! alpha77( X, Y, Z ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP
% 1.34/1.74 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), skol45( X, Y,
% 1.34/1.74 Z ) ), Z ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ), ! Y =
% 1.34/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), T ), Z ), alpha77( X,
% 1.34/1.74 Y, Z ) }.
% 1.34/1.74 { ! alpha21( X, Y, Z ), ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.34/1.74 hBOOL( hAPP( Z, Y ) ) }.
% 1.34/1.74 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha21( X, Y, Z ) }.
% 1.34/1.74 { ! hBOOL( hAPP( Z, Y ) ), alpha21( X, Y, Z ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.34/1.74 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 1.34/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, Z ),
% 1.34/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oplus__class_Oplus(
% 1.34/1.74 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.34/1.74 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ) ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.34/1.74 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 1.34/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, Z ),
% 1.34/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Oplus__class_Oplus(
% 1.34/1.74 tc_Int_Oint, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z
% 1.34/1.74 ), c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ), hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.34/1.74 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y
% 1.34/1.74 ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.34/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ),
% 1.34/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ) ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.34/1.74 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, Y
% 1.34/1.74 ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.34/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Int_Oint, T, X ) ), Y ),
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.34/1.74 { ! Z = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), T ), X ), alpha82( X,
% 1.34/1.74 Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), Y =
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.34/1.74 tc_Int_Oint, Z, Y ) = X }.
% 1.34/1.74 { ! Z = c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), T ), X ), alpha82( X,
% 1.34/1.74 Y ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.34/1.74 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Y =
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Omod(
% 1.34/1.74 tc_Int_Oint, Z, Y ) = X }.
% 1.34/1.74 { ! alpha82( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.34/1.74 { ! alpha82( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.34/1.74 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.34/1.74 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha82( X, Y ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.34/1.74 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y )
% 1.34/1.74 , alpha82( X, Y ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.34/1.74 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, hAPP(
% 1.34/1.74 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 1.34/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ),
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.34/1.74 tc_Int_Oint, Z, Y ), X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y
% 1.34/1.74 ) ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 1.34/1.74 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ), ! alpha22( X, Y, T,
% 1.34/1.74 U ), hBOOL( hAPP( hAPP( Z, T ), U ) ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha22( X, Y, skol46( X, Y
% 1.34/1.74 , Z ), skol53( X, Y, Z ) ), hBOOL( hAPP( hAPP( Z,
% 1.34/1.74 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! hBOOL( hAPP( hAPP( Z,
% 1.34/1.74 skol46( X, Y, Z ) ), skol53( X, Y, Z ) ) ), hBOOL( hAPP( hAPP( Z,
% 1.34/1.74 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ),
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ) ) }.
% 1.34/1.74 { ! alpha22( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T
% 1.34/1.74 ) }.
% 1.34/1.74 { ! alpha22( X, Y, Z, T ), alpha46( X, Y, Z, T ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha46( X, Y, Z
% 1.34/1.74 , T ), alpha22( X, Y, Z, T ) }.
% 1.34/1.74 { ! alpha46( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.34/1.74 T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.34/1.74 { ! alpha46( X, Y, Z, T ), Y = c_Groups_Oplus__class_Oplus( tc_Int_Oint,
% 1.34/1.74 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ) }
% 1.34/1.74 .
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y =
% 1.34/1.74 c_Groups_Oplus__class_Oplus( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ), T ), alpha46( X,
% 1.34/1.74 Y, Z, T ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.74 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.34/1.74 c_RealDef_Oreal( tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y
% 1.34/1.74 , X ) ) = c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 1.34/1.74 c_RealDef_Oreal( tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }
% 1.34/1.74 .
% 1.34/1.74 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.34/1.74 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.34/1.74 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_RealDef_Oreal(
% 1.34/1.74 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 1.34/1.74 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.34/1.74 { c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, X ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.74 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X ), T,
% 1.34/1.74 c_Polynomial_Osmult( X, Y, Z ) ) = c_Divides_Odiv__class_Omod(
% 1.34/1.74 tc_Polynomial_Opoly( X ), T, Z ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.34/1.74 ), c_Divides_Odiv__class_Omod( X, Y, Z ) = c_Groups_Ozero__class_Ozero(
% 1.34/1.74 X ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), ! c_Divides_Odiv__class_Omod( X, Y,
% 1.34/1.74 Z ) = c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.34/1.74 ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.34/1.74 ), c_Divides_Odiv__class_Omod( X, Y, Z ) = c_Groups_Ozero__class_Ozero(
% 1.34/1.74 X ) }.
% 1.34/1.74 { ! class_Divides_Oring__div( X ), ! c_Divides_Odiv__class_Omod( X, T, Z )
% 1.34/1.74 = c_Divides_Odiv__class_Omod( X, Y, Z ), ! c_Divides_Odiv__class_Omod( X
% 1.34/1.74 , W, Z ) = c_Divides_Odiv__class_Omod( X, U, Z ),
% 1.34/1.74 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T, W ),
% 1.34/1.74 Z ) = c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, Y
% 1.34/1.74 , U ), Z ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, T,
% 1.34/1.74 c_Divides_Odiv__class_Omod( X, Z, Y ) ), ! c_Rings_Odvd__class_Odvd( X, T
% 1.34/1.74 , Y ), c_Rings_Odvd__class_Odvd( X, T, Z ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.34/1.74 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z
% 1.34/1.74 , c_Divides_Odiv__class_Omod( X, Y, T ) ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.34/1.74 ), c_Divides_Odiv__class_Omod( X, c_Divides_Odiv__class_Omod( X, T, Y )
% 1.34/1.74 , Z ) = c_Divides_Odiv__class_Omod( X, T, Z ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.34/1.74 ), ! c_Rings_Odvd__class_Odvd( X, Z, c_Divides_Odiv__class_Omod( X, T, Y
% 1.34/1.74 ) ), c_Rings_Odvd__class_Odvd( X, Z, T ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.34/1.74 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z
% 1.34/1.74 , c_Divides_Odiv__class_Omod( X, T, Y ) ) }.
% 1.34/1.74 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.34/1.74 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.34/1.74 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 1.34/1.74 c_Divides_Odiv__class_Omod( X, T, Y ), c_Divides_Odiv__class_Omod( X, Z,
% 1.34/1.74 Y ) ), Y ) }.
% 1.34/1.74 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.34/1.74 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.34/1.74 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X,
% 1.34/1.74 c_Divides_Odiv__class_Omod( X, T, Y ), Z ), Y ) }.
% 1.34/1.74 { ! class_Divides_Oring__div( X ), c_Divides_Odiv__class_Omod( X,
% 1.34/1.74 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.34/1.74 c_Divides_Odiv__class_Omod( X, c_Groups_Ominus__class_Ominus( X, T,
% 1.34/1.74 c_Divides_Odiv__class_Omod( X, Z, Y ) ), Y ) }.
% 1.34/1.74 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 1.34/1.74 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ) =
% 1.34/1.74 c_Polynomial_Osmult( X, T, c_Divides_Odiv__class_Omod(
% 1.34/1.74 tc_Polynomial_Opoly( X ), Z, Y ) ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.34/1.74 Y ), c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 1.34/1.74 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.34/1.74 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.34/1.74 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.34/1.74 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.34/1.74 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, T,
% 1.34/1.74 Z ) ), Y ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.34/1.74 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.34/1.74 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.34/1.74 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), T ), c_Groups_Ominus__class_Ominus( X
% 1.34/1.74 , Z, Y ) ) = c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.34/1.74 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), Y ),
% 1.34/1.74 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.34/1.74 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), Y ),
% 1.34/1.74 c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 1.34/1.74 { ! class_Rings_Odvd( X ), ! Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.74 ( X ), Y ), T ), c_Rings_Odvd__class_Odvd( X, Y, Z ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.34/1.74 Y ), ! c_Rings_Odvd__class_Odvd( X, U, T ), c_Rings_Odvd__class_Odvd( X,
% 1.34/1.74 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.34/1.74 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.34/1.74 Y ), c_Rings_Odvd__class_Odvd( X, Z, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.34/1.74 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.34/1.74 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.34/1.74 { ! class_RealVector_Oreal__normed__field( X ),
% 1.34/1.74 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X, T,
% 1.34/1.74 Z ), Y ) = c_Groups_Ominus__class_Ominus( X,
% 1.34/1.74 c_Rings_Oinverse__class_Odivide( X, T, Y ),
% 1.34/1.74 c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.34/1.74 { ! class_Rings_Odivision__ring( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.34/1.74 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.34/1.74 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.34/1.74 Y ), c_Rings_Oinverse__class_Odivide( X, Z, Y ) ) }.
% 1.34/1.74 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.34/1.74 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 1.34/1.74 Y ) ) = c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 1.34/1.74 ( X, Y, Z ) ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X, Y, Y
% 1.34/1.74 ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.34/1.74 Y ), ! c_Rings_Odvd__class_Odvd( X, Y, T ), c_Rings_Odvd__class_Odvd( X,
% 1.34/1.74 Z, T ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__ring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y )
% 1.34/1.74 , ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X, Z,
% 1.34/1.74 c_Groups_Ominus__class_Ominus( X, Y, T ) ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__ring( X ), hAPP( c_Polynomial_Opoly( X,
% 1.34/1.74 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), T, Z ) ), Y ) =
% 1.34/1.74 c_Groups_Ominus__class_Ominus( X, hAPP( c_Polynomial_Opoly( X, T ), Y ),
% 1.34/1.74 hAPP( c_Polynomial_Opoly( X, Z ), Y ) ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X,
% 1.34/1.74 c_Groups_Ominus__class_Ominus( X, T, Z ), Y ) =
% 1.34/1.74 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 1.34/1.74 c_Polynomial_Osmult( X, T, Y ), c_Polynomial_Osmult( X, Z, Y ) ) }.
% 1.34/1.74 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.34/1.74 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! U = T, Z = Y }.
% 1.34/1.74 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.34/1.74 U, T ) = c_Groups_Ominus__class_Ominus( X, Z, Y ), ! Z = Y, U = T }.
% 1.34/1.74 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.34/1.74 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.34/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), alpha23( X, Y ), Y = X }
% 1.34/1.74 .
% 1.34/1.74 { ! alpha23( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.34/1.74 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.34/1.74 { ! alpha23( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.34/1.74 { ! alpha23( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.34/1.74 ( tc_Nat_Onat, X, Y ), alpha23( X, Y ) }.
% 1.34/1.74 { ! alpha24( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.34/1.74 { ! alpha24( X, Y ), ! Y = X }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, alpha24( X, Y ) }
% 1.34/1.74 .
% 1.34/1.74 { ! alpha24( X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.34/1.74 { ! alpha24( X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.34/1.74 ( tc_Nat_Onat, X, Y ), alpha24( X, Y ) }.
% 1.34/1.74 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ),
% 1.34/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.34/1.74 { Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.34/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.34/1.74 { ! Y = X, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.34/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), X = Y }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Y,
% 1.34/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.34/1.74 ( tc_Nat_Onat, Y, X ), Y = X }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.34/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X,
% 1.34/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), Y = X, !
% 1.34/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ) }.
% 1.34/1.74 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.34/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), ! X = Z,
% 1.34/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.34/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.34/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ), Y = X }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.34/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 1.34/1.74 tc_Nat_Onat, Y, Z ) }.
% 1.34/1.74 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.34/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 1.34/1.74 tc_Nat_Onat, Y, Z ) }.
% 1.34/1.74 { ! Y = X, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.34/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 1.34/1.74 ( tc_Nat_Onat, Z, Y ) }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.34/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 1.34/1.74 tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.34/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), c_Rings_Odvd__class_Odvd(
% 1.34/1.74 tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.34/1.74 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.34/1.74 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.34/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.34/1.74 ( tc_Nat_Onat, X, Y ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.34/1.74 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.34/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.34/1.74 ( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.34/1.74 ( tc_Nat_Onat, X, Y ), ! X = Y }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.34/1.74 ( tc_Nat_Onat, X, Y ), ! X = Z, c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y
% 1.34/1.74 , Z ) }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.34/1.74 ( tc_Nat_Onat, X, Y ), ! X = Z, ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat,
% 1.34/1.74 Z, Y ) }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.34/1.74 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.34/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ) }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.34/1.74 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ), !
% 1.34/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.34/1.74 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.34/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.34/1.74 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.34/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), c_Rings_Odvd__class_Odvd(
% 1.34/1.74 tc_Nat_Onat, Y, Z ) }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.34/1.74 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Z ),
% 1.34/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, X ), ! c_Rings_Odvd__class_Odvd
% 1.34/1.74 ( tc_Nat_Onat, Z, Y ) }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.34/1.74 ( tc_Nat_Onat, X, Y ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, Y ),
% 1.34/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), Z =
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd(
% 1.34/1.74 tc_Nat_Onat, Y, X ) }.
% 1.34/1.74 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.34/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.34/1.74 ( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.34/1.74 Z ), Y ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.34/1.74 X ) ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.74 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y
% 1.34/1.74 ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.34/1.74 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Y, X ),
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.34/1.74 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus(
% 1.34/1.74 tc_Nat_Onat, X, Y ) ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), c_Rings_Odvd__class_Odvd
% 1.34/1.74 ( tc_Nat_Onat, Y, c_Groups_Oplus__class_Oplus( tc_Nat_Onat, X, Y ) ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.34/1.74 Y ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Rings_Odvd__class_Odvd( X,
% 1.34/1.74 Z, c_Groups_Oplus__class_Oplus( X, Y, T ) ) }.
% 1.34/1.74 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.34/1.74 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.34/1.74 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, U, T ),
% 1.34/1.74 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.34/1.74 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.34/1.74 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.34/1.74 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 1.34/1.74 c_Orderings_Oord__class_Oless( X, U, T ) }.
% 1.34/1.74 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X,
% 1.34/1.74 c_Groups_Oplus__class_Oplus( X, Z, Y ), Y ) = Z }.
% 1.34/1.74 { ! class_Groups_Ogroup__add( X ), c_Groups_Oplus__class_Oplus( X,
% 1.34/1.74 c_Groups_Ominus__class_Ominus( X, Z, Y ), Y ) = Z }.
% 1.34/1.74 { ! class_Groups_Oab__group__add( X ), c_Groups_Ominus__class_Ominus(
% 1.34/1.74 tc_Polynomial_Opoly( X ), c_Polynomial_Omonom( X, T, Z ),
% 1.34/1.74 c_Polynomial_Omonom( X, Y, Z ) ) = c_Polynomial_Omonom( X,
% 1.34/1.74 c_Groups_Ominus__class_Ominus( X, T, Y ), Z ) }.
% 1.34/1.74 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.34/1.74 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.34/1.74 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.34/1.74 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.34/1.74 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.34/1.74 c_Groups_Ominus__class_Ominus( X, U, T ) = c_Groups_Ominus__class_Ominus
% 1.34/1.74 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.34/1.74 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 1.34/1.74 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.34/1.74 { ! class_Groups_Ogroup__add( X ), c_Groups_Ominus__class_Ominus( X, Y, Y )
% 1.34/1.74 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.74 { ! class_Groups_Oab__group__add( X ), ! Z = Y,
% 1.34/1.74 c_Groups_Ominus__class_Ominus( X, Z, Y ) = c_Groups_Ozero__class_Ozero( X
% 1.34/1.74 ) }.
% 1.34/1.74 { ! class_Groups_Oab__group__add( X ), ! c_Groups_Ominus__class_Ominus( X,
% 1.34/1.74 Z, Y ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.34/1.74 { ! class_Groups_Ogroup__add( X ), ! c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.34/1.74 ) = c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.34/1.74 { ! class_Groups_Ogroup__add( X ), ! Z = Y, c_Groups_Ominus__class_Ominus(
% 1.34/1.74 X, Z, Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__semiring__1( X ), c_Rings_Odvd__class_Odvd( X,
% 1.34/1.74 c_Groups_Oone__class_Oone( X ), Y ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( X ), Y ), Y = c_Groups_Ozero__class_Ozero( X
% 1.34/1.74 ) }.
% 1.34/1.74 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.34/1.74 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.34/1.74 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.34/1.74 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 1.34/1.74 c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ) }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, X, c_Groups_Oone__class_Oone(
% 1.34/1.74 tc_Nat_Onat ) ), X = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.34/1.74 { ! X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Rings_Odvd__class_Odvd
% 1.34/1.74 ( tc_Nat_Onat, X, c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.34/1.74 { ! class_Rings_Oring( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.34/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.74 ( X ), U ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.34/1.74 Z ) ), Y ) ) }.
% 1.34/1.74 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.34/1.74 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), U ), T ), hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.34/1.74 c_Groups_Oplus__class_Oplus( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.34/1.74 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.34/1.74 X, U, Z ) ), c_Groups_Ominus__class_Ominus( X, T, Y ) ), hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, U,
% 1.34/1.74 Z ) ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.34/1.74 c_Groups_Ominus__class_Ominus( X, T, Y ) ) ) }.
% 1.34/1.74 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.34/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.74 ( X ), Z ), U ), Y ), T = c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.34/1.74 W ) ), U ), Y ) }.
% 1.34/1.74 { ! class_Rings_Oring( X ), ! T = c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.34/1.74 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.34/1.74 X, Z, W ) ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.34/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.74 ( X ), Z ), U ), Y ) }.
% 1.34/1.74 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.34/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.74 ( X ), Z ), U ), Y ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.34/1.74 Z ) ), U ), T ) = Y }.
% 1.34/1.74 { ! class_Rings_Oring( X ), ! c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.34/1.74 Z ) ), U ), T ) = Y, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ) =
% 1.34/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.74 ( X ), Z ), U ), Y ) }.
% 1.34/1.74 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.34/1.74 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.34/1.74 X, c_Groups_Ominus__class_Ominus( X, Z, Y ), c_Groups_Ozero__class_Ozero
% 1.34/1.74 ( X ) ) }.
% 1.34/1.74 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.34/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Ominus__class_Ominus( X, Z, Y
% 1.34/1.74 ), c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.34/1.74 , Z, Y ) }.
% 1.34/1.74 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.34/1.74 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.34/1.74 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.34/1.74 , Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.34/1.74 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.34/1.74 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ominus__class_Ominus( X, Z
% 1.34/1.74 , Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.34/1.74 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.34/1.74 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ),
% 1.34/1.74 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), T ) = c_Divides_Odiv__class_Odiv
% 1.34/1.74 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.34/1.74 ( c_Power_Opower__class_Opower( X ), Z ), T ) ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X,
% 1.34/1.74 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), Y ), !
% 1.34/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, Z ),
% 1.34/1.74 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.34/1.74 ), T ), U ), Y ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.34/1.74 Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, T ),
% 1.34/1.74 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.34/1.74 ), Z ), U ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ) ) }
% 1.34/1.74 .
% 1.34/1.74 { ! class_Rings_Ocomm__semiring__1( X ), !
% 1.34/1.74 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 1.34/1.74 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Power_Opower__class_Opower( X
% 1.34/1.74 ), T ), Z ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ) ) }
% 1.34/1.74 .
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.34/1.74 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), c_Divides_Odiv__class_Odiv( X
% 1.34/1.74 , c_Groups_Oplus__class_Oplus( X, Y, T ), Z ) =
% 1.34/1.74 c_Groups_Oplus__class_Oplus( X, c_Divides_Odiv__class_Odiv( X, Y, Z ),
% 1.34/1.74 c_Divides_Odiv__class_Odiv( X, T, Z ) ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.34/1.74 ), ! c_Rings_Odvd__class_Odvd( X, U, T ), hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), c_Divides_Odiv__class_Odiv( X, Y, Z )
% 1.34/1.74 ), c_Divides_Odiv__class_Odiv( X, T, U ) ) = c_Divides_Odiv__class_Odiv
% 1.34/1.74 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.34/1.74 ( c_Groups_Otimes__class_Otimes( X ), Z ), U ) ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.34/1.74 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.34/1.74 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), T ) = c_Divides_Odiv__class_Odiv
% 1.34/1.74 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.34/1.74 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.34/1.74 c_Divides_Odiv__class_Odiv( X, Y, Z ) ), Z ) = Y }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.34/1.74 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ),
% 1.34/1.74 c_Divides_Odiv__class_Odiv( X, Y, Z ) ) = c_Divides_Odiv__class_Odiv( X,
% 1.34/1.74 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.34/1.74 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ),
% 1.34/1.74 c_Divides_Odiv__class_Odiv( X, Y, Z ) ) = Y }.
% 1.34/1.74 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), T =
% 1.34/1.74 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, Z, Y ) }.
% 1.34/1.74 { ! class_Rings_Oidom( X ), ! T = c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.74 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.34/1.74 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 1.34/1.74 }.
% 1.34/1.74 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y ),
% 1.34/1.74 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.34/1.74 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) )
% 1.34/1.74 }.
% 1.34/1.74 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Z =
% 1.34/1.74 c_Groups_Ozero__class_Ozero( X ), c_Rings_Odvd__class_Odvd( X, T, Y ) }.
% 1.34/1.74 { ! class_Rings_Oidom( X ), ! Z = c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.74 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.34/1.74 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 1.34/1.74 }.
% 1.34/1.74 { ! class_Rings_Oidom( X ), ! c_Rings_Odvd__class_Odvd( X, T, Y ),
% 1.34/1.74 c_Rings_Odvd__class_Odvd( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X
% 1.34/1.74 ), T ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) )
% 1.34/1.74 }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.34/1.74 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), ! c_Rings_Odvd__class_Odvd( X
% 1.34/1.74 , c_Divides_Odiv__class_Odiv( X, Y, Z ), c_Divides_Odiv__class_Odiv( X, T
% 1.34/1.74 , Z ) ), c_Rings_Odvd__class_Odvd( X, Y, T ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), ! c_Rings_Odvd__class_Odvd( X, Z, Y
% 1.34/1.74 ), ! c_Rings_Odvd__class_Odvd( X, Z, T ), ! c_Rings_Odvd__class_Odvd( X
% 1.34/1.74 , Y, T ), c_Rings_Odvd__class_Odvd( X, c_Divides_Odiv__class_Odiv( X, Y,
% 1.34/1.74 Z ), c_Divides_Odiv__class_Odiv( X, T, Z ) ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.74 , ! c_Rings_Odvd__class_Odvd( X, Y, Z ), ! c_Divides_Odiv__class_Odiv( X
% 1.34/1.74 , Z, Y ) = T, Z = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y
% 1.34/1.74 ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.74 , ! c_Rings_Odvd__class_Odvd( X, Y, Z ), ! Z = hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Y ), c_Divides_Odiv__class_Odiv
% 1.34/1.74 ( X, Z, Y ) = T }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.74 , Z = c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Odvd__class_Odvd( X, Y
% 1.34/1.74 , T ), ! c_Rings_Odvd__class_Odvd( X, Z, U ), !
% 1.34/1.74 c_Divides_Odiv__class_Odiv( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U
% 1.34/1.74 , Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP(
% 1.34/1.74 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), U ) }.
% 1.34/1.74 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.74 , Z = c_Groups_Ozero__class_Ozero( X ), ! c_Rings_Odvd__class_Odvd( X, Y
% 1.34/1.74 , T ), ! c_Rings_Odvd__class_Odvd( X, Z, U ), ! hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Z ) = hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), U ), c_Divides_Odiv__class_Odiv
% 1.34/1.74 ( X, T, Y ) = c_Divides_Odiv__class_Odiv( X, U, Z ) }.
% 1.34/1.74 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.34/1.74 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.34/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.74 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.74 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ) }.
% 1.34/1.74 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.34/1.74 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, W,
% 1.34/1.74 Z ) ), U ), T ), Y ), c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.74 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.34/1.74 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.34/1.74 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.34/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.74 ( X ), Z ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X, T,
% 1.34/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.74 ( X ), c_Groups_Ominus__class_Ominus( X, Z, W ) ), U ), Y ) ) }.
% 1.34/1.74 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.34/1.74 , T, c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.34/1.74 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless__eq( X,
% 1.34/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.74 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.34/1.74 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.34/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.74 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.34/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.34/1.74 hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus(
% 1.34/1.74 X, W, Z ) ), U ), T ), Y ) }.
% 1.34/1.74 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.34/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.74 ( X ), c_Groups_Ominus__class_Ominus( X, W, Z ) ), U ), T ), Y ),
% 1.34/1.74 c_Orderings_Oord__class_Oless( X, c_Groups_Oplus__class_Oplus( X, hAPP(
% 1.34/1.74 hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ), T ),
% 1.34/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.74 ( X ), Z ), U ), Y ) ) }.
% 1.34/1.74 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.34/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.74 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ),
% 1.34/1.74 c_Orderings_Oord__class_Oless( X, T, c_Groups_Oplus__class_Oplus( X, hAPP
% 1.34/1.74 ( hAPP( c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus
% 1.34/1.74 ( X, Z, W ) ), U ), Y ) ) }.
% 1.34/1.74 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 1.34/1.74 , c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ominus__class_Ominus( X, Z,
% 1.34/1.74 W ) ), U ), Y ) ), c_Orderings_Oord__class_Oless( X,
% 1.34/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.74 ( X ), W ), U ), T ), c_Groups_Oplus__class_Oplus( X, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), Z ), U ), Y ) ) }.
% 1.34/1.74 { ! class_Rings_Oring__1( X ), c_Groups_Ominus__class_Ominus( X, hAPP( hAPP
% 1.34/1.74 ( c_Groups_Otimes__class_Otimes( X ), Y ), Y ), c_Groups_Oone__class_Oone
% 1.34/1.74 ( X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ),
% 1.34/1.74 c_Groups_Oplus__class_Oplus( X, Y, c_Groups_Oone__class_Oone( X ) ) ),
% 1.34/1.74 c_Groups_Ominus__class_Ominus( X, Y, c_Groups_Oone__class_Oone( X ) ) ) }
% 1.34/1.74 .
% 1.34/1.74 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.74 c_Groups_Ominus__class_Ominus( X, T, c_Rings_Oinverse__class_Odivide( X,
% 1.34/1.74 Z, Y ) ) = c_Rings_Oinverse__class_Odivide( X,
% 1.34/1.74 c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), T ), Z ), Y ) }.
% 1.34/1.74 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ),
% 1.34/1.74 c_Groups_Ominus__class_Ominus( X, c_Rings_Oinverse__class_Odivide( X, T,
% 1.34/1.74 Y ), Z ) = c_Rings_Oinverse__class_Odivide( X,
% 1.34/1.74 c_Groups_Ominus__class_Ominus( X, T, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y ) }.
% 1.34/1.74 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.34/1.74 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X,
% 1.34/1.74 c_Rings_Oinverse__class_Odivide( X, U, Y ),
% 1.34/1.74 c_Rings_Oinverse__class_Odivide( X, T, Z ) ) =
% 1.34/1.74 c_Rings_Oinverse__class_Odivide( X, c_Groups_Ominus__class_Ominus( X,
% 1.34/1.74 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ), hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.34/1.74 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.34/1.74 , Z = c_Groups_Ozero__class_Ozero( X ), c_Groups_Ominus__class_Ominus( X
% 1.34/1.74 , c_Rings_Oinverse__class_Oinverse( X, Y ),
% 1.34/1.74 c_Rings_Oinverse__class_Oinverse( X, Z ) ) = hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Oinverse( X,
% 1.34/1.74 Y ) ), c_Groups_Ominus__class_Ominus( X, Z, Y ) ) ),
% 1.34/1.74 c_Rings_Oinverse__class_Oinverse( X, Z ) ) }.
% 1.34/1.74 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.34/1.74 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.34/1.74 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.34/1.74 ( X, Y ) ), c_RealVector_Onorm__class_Onorm( X,
% 1.34/1.74 c_Groups_Oplus__class_Oplus( X, Z, Y ) ) ) }.
% 1.34/1.74 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.34/1.74 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.74 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, Z,
% 1.34/1.74 Y ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.34/1.74 c_RealVector_Onorm__class_Onorm( X, Z ), c_RealVector_Onorm__class_Onorm
% 1.34/1.74 ( X, Y ) ) ) }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.34/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.74 tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.34/1.74 ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.74 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 1.34/1.74 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.34/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.74 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Z, Y ),
% 1.34/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 1.34/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.34/1.74 tc_Nat_Onat ), Z ), c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ) }.
% 1.34/1.74 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.34/1.74 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.34/1.74 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex, Y, X ) ),
% 1.34/1.74 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, Y ) ),
% 1.34/1.74 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, X ) ) }.
% 1.34/1.74 { ! class_Fields_Ofield( X ), c_Divides_Odiv__class_Omod(
% 1.34/1.74 tc_Polynomial_Opoly( X ), T, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.34/1.74 tc_Polynomial_Opoly( X ) ), Z ), Y ) ) = c_Groups_Oplus__class_Oplus(
% 1.34/1.74 tc_Polynomial_Opoly( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.34/1.74 tc_Polynomial_Opoly( X ) ), Z ), c_Divides_Odiv__class_Omod(
% 1.34/1.74 tc_Polynomial_Opoly( X ), c_Divides_Odiv__class_Odiv( tc_Polynomial_Opoly
% 1.34/1.74 ( X ), T, Z ), Y ) ), c_Divides_Odiv__class_Omod( tc_Polynomial_Opoly( X
% 1.34/1.74 ), T, Z ) ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Orderings_Oord__class_Oless(
% 1.34/1.74 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 1.34/1.74 c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP( c_Power_Opower__class_Opower
% 1.34/1.74 ( X ), Y ), Z ) ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__semiring__1( X ), ! Y = c_Groups_Oone__class_Oone( X
% 1.34/1.74 ), c_Rings_Odvd__class_Odvd( X, Y, hAPP( hAPP(
% 1.34/1.74 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.34/1.74 { c_Rings_Oinverse__class_Odivide( tc_Complex_Ocomplex, c_Complex_Orcis( T
% 1.34/1.74 , Z ), c_Complex_Orcis( Y, X ) ) = c_Complex_Orcis(
% 1.34/1.74 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, T, Y ),
% 1.34/1.74 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, Z, X ) ) }.
% 1.34/1.74 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.34/1.74 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.74 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X,
% 1.34/1.74 c_Groups_Oplus__class_Oplus( X, U, T ), c_Groups_Oplus__class_Oplus( X, Z
% 1.34/1.74 , Y ) ) ), c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal,
% 1.34/1.74 c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus( X, U,
% 1.34/1.74 Z ) ), c_RealVector_Onorm__class_Onorm( X, c_Groups_Ominus__class_Ominus
% 1.34/1.74 ( X, T, Y ) ) ) ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.74 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 1.34/1.74 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ), Y =
% 1.34/1.74 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.74 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 1.34/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.74 ( tc_Nat_Onat ), X ), ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP
% 1.34/1.74 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ), Y =
% 1.34/1.74 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.34/1.74 ( tc_Nat_Onat ), X ), ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ),
% 1.34/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.34/1.74 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.34/1.74 c_Transcendental_Oln( c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal,
% 1.34/1.74 X, Y ) ) = c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.34/1.74 c_Transcendental_Oln( X ), c_Transcendental_Oln( Y ) ) }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.74 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.34/1.74 c_Power_Opower__class_Opower( tc_Nat_Onat ), Z ), X ) ), !
% 1.34/1.74 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.34/1.74 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.34/1.74 ) }.
% 1.34/1.74 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal, X,
% 1.34/1.74 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), c_RealDef_Oreal(
% 1.34/1.74 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ) ) }.
% 1.34/1.74 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.34/1.74 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal,
% 1.34/1.74 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.34/1.74 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_RealDef_Oreal(
% 1.34/1.74 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ) ) }.
% 1.34/1.74 { ! class_RealVector_Oreal__field( X ), c_Rings_Oinverse__class_Odivide( X
% 1.34/1.74 , c_Groups_Ominus__class_Ominus( X, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), W ), U ), hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) =
% 1.34/1.74 c_Groups_Oplus__class_Oplus( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.34/1.74 ( X ), W ), c_Rings_Oinverse__class_Odivide( X,
% 1.34/1.74 c_Groups_Ominus__class_Ominus( X, U, Z ), Y ) ), hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( X ), c_Rings_Oinverse__class_Odivide( X,
% 1.34/1.74 c_Groups_Ominus__class_Ominus( X, W, T ), Y ) ), Z ) ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.34/1.74 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.34/1.74 c_Groups_Oplus__class_Oplus( X, U, T ) ), c_Rings_Odvd__class_Odvd( X, Z
% 1.34/1.74 , c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U,
% 1.34/1.74 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__ring( X ), ! class_Rings_Odvd( X ), !
% 1.34/1.74 c_Rings_Odvd__class_Odvd( X, Z, Y ), ! c_Rings_Odvd__class_Odvd( X, Z,
% 1.34/1.74 c_Groups_Oplus__class_Oplus( X, c_Groups_Ominus__class_Ominus( X, U, hAPP
% 1.34/1.74 ( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), Y ) ), T ) ),
% 1.34/1.74 c_Rings_Odvd__class_Odvd( X, Z, c_Groups_Oplus__class_Oplus( X, U, T ) )
% 1.34/1.74 }.
% 1.34/1.74 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.34/1.74 tc_Nat_Onat, Y, X ), X ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) = Y }.
% 1.34/1.74 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Nat_Onat, Y, X ) =
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.34/1.74 tc_Nat_Onat, Y, X ), X ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Nat_Onat, X, Y ) =
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Nat_Onat, c_Groups_Ominus__class_Ominus(
% 1.34/1.74 tc_Nat_Onat, X, Y ), Y ) }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, c_Divides_Odiv__class_Omod(
% 1.34/1.74 tc_Int_Oint, Y, X ) ), ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, X ),
% 1.34/1.74 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Z, Y ) }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, X ), !
% 1.34/1.74 c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, Z ), c_Rings_Odvd__class_Odvd(
% 1.34/1.74 tc_Int_Oint, Y, c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Z ) ) }.
% 1.34/1.74 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 1.34/1.74 tc_Int_Oint, c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ), X ), Y ) =
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 1.34/1.74 tc_Int_Oint, Z, X ), Y ) }.
% 1.34/1.74 { c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 1.34/1.74 tc_Int_Oint, Z, c_Divides_Odiv__class_Omod( tc_Int_Oint, Y, X ) ), X ) =
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Int_Oint, c_Groups_Ominus__class_Ominus(
% 1.34/1.74 tc_Int_Oint, Z, Y ), X ) }.
% 1.34/1.74 { ! c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y ) =
% 1.34/1.74 c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ), c_Rings_Odvd__class_Odvd
% 1.34/1.74 ( tc_Int_Oint, Y, c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, X ) ) }
% 1.34/1.74 .
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Int_Oint, Y, c_Groups_Ominus__class_Ominus
% 1.34/1.74 ( tc_Int_Oint, Z, X ) ), c_Divides_Odiv__class_Omod( tc_Int_Oint, Z, Y )
% 1.34/1.74 = c_Divides_Odiv__class_Omod( tc_Int_Oint, X, Y ) }.
% 1.34/1.74 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ),
% 1.34/1.74 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Y, X ) ) =
% 1.34/1.74 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.34/1.74 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.34/1.74 c_Groups_Ominus__class_Ominus( tc_Int_Oint, Z, Y ) ), X ) =
% 1.34/1.74 c_Groups_Ominus__class_Ominus( tc_Int_Oint, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ), hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.34/1.74 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ),
% 1.34/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Y, X ) ) =
% 1.34/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.34/1.74 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.34/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, Z, Y ) ), X ) =
% 1.34/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.34/1.74 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 1.34/1.74 tc_Polynomial_Opoly( X ), c_Polynomial_Osmult( X, T, Z ), Y ),
% 1.34/1.74 c_Rings_Odvd__class_Odvd( tc_Polynomial_Opoly( X ), Z, Y ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__semiring__1( X ), ! c_Rings_Odvd__class_Odvd(
% 1.34/1.74 tc_Polynomial_Opoly( X ), Z, Y ), c_Rings_Odvd__class_Odvd(
% 1.34/1.74 tc_Polynomial_Opoly( X ), Z, c_Polynomial_Osmult( X, T, Y ) ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__ring( X ), c_Polynomial_Osmult( X, T,
% 1.34/1.74 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ), Z, Y ) ) =
% 1.34/1.74 c_Groups_Ominus__class_Ominus( tc_Polynomial_Opoly( X ),
% 1.34/1.74 c_Polynomial_Osmult( X, T, Z ), c_Polynomial_Osmult( X, T, Y ) ) }.
% 1.34/1.74 { ! c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, X ), !
% 1.34/1.74 c_Rings_Odvd__class_Odvd( tc_Nat_Onat, Y, Z ), c_Rings_Odvd__class_Odvd(
% 1.34/1.74 tc_Nat_Onat, Y, c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Z ) ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.34/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.34/1.74 tc_Nat_Onat, X, Z ), Y ) = c_Groups_Oplus__class_Oplus( tc_Nat_Onat,
% 1.34/1.74 c_Groups_Ominus__class_Ominus( tc_Nat_Onat, X, Y ), Z ) }.
% 1.34/1.74 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.34/1.74 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { class_Groups_Ocancel__comm__monoid__add( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 1.34/1.74 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 1.34/1.74 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 1.34/1.74 ) ) }.
% 1.34/1.74 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 1.34/1.74 .
% 1.34/1.74 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 1.34/1.74 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.34/1.74 tc_Int_Oint ) }.
% 1.34/1.74 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.34/1.74 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 1.34/1.74 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 1.34/1.74 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 1.34/1.74 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 1.34/1.74 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 1.34/1.74 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 1.34/1.74 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 1.34/1.74 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.34/1.74 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 1.34/1.74 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 1.34/1.74 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 1.34/1.74 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 1.34/1.74 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 1.34/1.74 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 1.34/1.74 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 1.34/1.74 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 1.34/1.74 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 1.34/1.74 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 1.34/1.74 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 1.34/1.74 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 1.34/1.74 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 1.34/1.74 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 1.34/1.74 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 1.34/1.74 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 1.34/1.74 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 1.34/1.74 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 1.34/1.74 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 1.34/1.74 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 1.34/1.74 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 1.34/1.74 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 1.34/1.74 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 1.34/1.74 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 1.34/1.74 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 1.34/1.74 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 1.34/1.74 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 1.34/1.74 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 1.34/1.74 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 1.34/1.74 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 1.34/1.74 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 1.34/1.74 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 1.34/1.74 { class_Divides_Oring__div( tc_Int_Oint ) }.
% 1.34/1.74 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 1.34/1.74 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 1.34/1.74 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 1.34/1.74 { class_Int_Oring__char__0( tc_Int_Oint ) }.
% 1.34/1.74 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 1.34/1.74 { class_Orderings_Oord( tc_Int_Oint ) }.
% 1.34/1.74 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 1.34/1.74 { class_Power_Opower( tc_Int_Oint ) }.
% 1.34/1.74 { class_Groups_Ozero( tc_Int_Oint ) }.
% 1.34/1.74 { class_Rings_Oring( tc_Int_Oint ) }.
% 1.34/1.74 { class_Rings_Oidom( tc_Int_Oint ) }.
% 1.34/1.74 { class_Groups_Oone( tc_Int_Oint ) }.
% 1.34/1.74 { class_Rings_Odvd( tc_Int_Oint ) }.
% 1.34/1.74 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.34/1.74 tc_Nat_Onat ) }.
% 1.34/1.74 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.34/1.74 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 1.34/1.74 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 1.34/1.74 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 1.34/1.74 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.34/1.74 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 1.34/1.74 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.34/1.74 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 1.34/1.74 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 1.34/1.74 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 1.34/1.74 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 1.34/1.74 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 1.34/1.74 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 1.34/1.74 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 1.34/1.74 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 1.34/1.74 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 1.34/1.74 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 1.34/1.74 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 1.34/1.74 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 1.34/1.74 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 1.34/1.74 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 1.34/1.74 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 1.34/1.74 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 1.34/1.74 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 1.34/1.74 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 1.34/1.74 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 1.34/1.74 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 1.34/1.74 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 1.34/1.74 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 1.34/1.74 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 1.34/1.74 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 1.34/1.74 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 1.34/1.74 { class_Power_Opower( tc_Nat_Onat ) }.
% 1.34/1.74 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 1.34/1.74 { class_Groups_Oone( tc_Nat_Onat ) }.
% 1.34/1.74 { class_Rings_Odvd( tc_Nat_Onat ) }.
% 1.34/1.74 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 1.34/1.74 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 1.34/1.74 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 1.34/1.74 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.34/1.74 tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 1.34/1.74 .
% 1.34/1.74 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Fields_Olinordered__field__inverse__zero( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_RealVector_Oreal__normed__div__algebra( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Rings_Odivision__ring__inverse__zero( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_RealVector_Oreal__normed__algebra__1( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_RealVector_Oreal__normed__vector( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_RealVector_Oreal__normed__field( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Fields_Ofield__inverse__zero( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Fields_Olinordered__field( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Rings_Ocomm__semiring__0( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_RealVector_Oreal__field( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Rings_Odivision__ring( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Rings_Ocomm__ring( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Int_Oring__char__0( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Fields_Ofield( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Rings_Odvd( tc_RealDef_Oreal ) }.
% 1.34/1.74 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.34/1.74 tc_Complex_Ocomplex ) }.
% 1.34/1.74 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { class_Rings_Odivision__ring__inverse__zero( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { class_RealVector_Oreal__normed__field( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { class_Fields_Ofield__inverse__zero( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { class_RealVector_Oreal__field( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { class_Rings_Odivision__ring( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { class_Int_Oring__char__0( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { class_Rings_Odvd( tc_Complex_Ocomplex ) }.
% 1.34/1.74 { ! class_Rings_Oidom( X ),
% 1.34/1.74 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.34/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Rings_Olinordered__idom( X ),
% 1.34/1.74 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 1.34/1.74 ) ) }.
% 1.34/1.74 { ! class_Rings_Olinordered__idom( X ),
% 1.34/1.74 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 1.34/1.74 X ) ) }.
% 1.34/1.74 { ! class_Rings_Olinordered__idom( X ),
% 1.34/1.74 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 1.34/1.74 ) }.
% 1.34/1.74 { ! class_Rings_Olinordered__idom( X ),
% 1.34/1.74 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 1.34/1.74 }.
% 1.34/1.74 { ! class_Rings_Olinordered__idom( X ),
% 1.34/1.74 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Rings_Olinordered__idom( X ),
% 1.34/1.74 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Rings_Olinordered__idom( X ),
% 1.34/1.74 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Rings_Olinordered__idom( X ),
% 1.34/1.74 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.34/1.74 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 1.34/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Rings_Olinordered__idom( X ),
% 1.34/1.74 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Rings_Olinordered__idom( X ),
% 1.34/1.74 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 1.34/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Rings_Olinordered__idom( X ),
% 1.34/1.74 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Rings_Olinordered__idom( X ),
% 1.34/1.74 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Rings_Olinordered__idom( X ),
% 1.34/1.74 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.34/1.74 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 1.34/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 1.34/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 1.34/1.74 ( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 1.34/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 1.34/1.74 ( tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 1.34/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 1.34/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 1.34/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 1.34/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 1.34/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 1.34/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 1.34/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 1.34/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 1.34/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 1.34/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 1.34/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 1.34/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 1.34/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 1.34/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 1.34/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 1.34/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 1.34/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 1.34/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 1.34/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Fields_Ofield( X ), class_Divides_Oring__div( tc_Polynomial_Opoly
% 1.34/1.74 ( X ) ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 1.34/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 1.34/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 1.34/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Rings_Olinordered__idom( X ), class_Int_Oring__char__0(
% 1.34/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 1.34/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 1.34/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 1.34/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 1.34/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 1.34/1.74 }.
% 1.34/1.74 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 1.34/1.74 ) ) }.
% 1.34/1.74 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 1.34/1.74 .
% 1.34/1.74 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 1.34/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Odvd(
% 1.34/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.34/1.74 { alpha83, c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.34/1.74 c_Rings_Oinverse__class_Odivide( tc_Complex_Ocomplex, hAPP(
% 1.34/1.74 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), v_w____ ), hAPP(
% 1.34/1.74 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) ),
% 1.34/1.74 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.34/1.74 { alpha83, ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.34/1.74 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.34/1.74 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.34/1.74 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.34/1.74 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.34/1.74 v_q____ ) ), v_w____ ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 1.34/1.74 }.
% 1.34/1.74 { ! alpha83, c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.34/1.74 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.34/1.74 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.34/1.74 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.34/1.74 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.34/1.74 v_q____ ) ), v_w____ ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 1.34/1.74 }.
% 1.34/1.74 { ! alpha83, ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.34/1.74 c_Rings_Oinverse__class_Odivide( tc_Complex_Ocomplex, hAPP(
% 1.34/1.74 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), v_w____ ), hAPP(
% 1.34/1.74 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) ),
% 1.34/1.74 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.34/1.74 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex, hAPP(
% 1.34/1.74 c_Polynomial_Opoly( tc_Complex_Ocomplex, c_Polynomial_Osmult(
% 1.34/1.74 tc_Complex_Ocomplex, c_Rings_Oinverse__class_Oinverse(
% 1.34/1.74 tc_Complex_Ocomplex, hAPP( c_Polynomial_Opoly( tc_Complex_Ocomplex,
% 1.34/1.74 v_q____ ), c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ),
% 1.34/1.74 v_q____ ) ), v_w____ ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 1.34/1.74 , c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.34/1.74 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex,
% 1.34/1.74 c_Rings_Oinverse__class_Odivide( tc_Complex_Ocomplex, hAPP(
% 1.34/1.74 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ), v_w____ ), hAPP(
% 1.34/1.74 c_Polynomial_Opoly( tc_Complex_Ocomplex, v_q____ ),
% 1.34/1.74 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) ) ) ),
% 1.34/1.74 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), alpha83 }.
% 1.34/1.74
% 1.34/1.74 *** allocated 15000 integers for clauses
% 1.34/1.74 *** allocated 22500 integers for clauses
% 1.34/1.74 *** allocated 33750 integers for clauses
% 1.34/1.74 *** allocated 50625 integers for clauses
% 1.34/1.74 *** allocated 75937 integers for clauses
% 1.34/1.74 *** allocated 113905 integers for clauses
% 1.34/1.74 percentage equality = 0.219111, percentage horn = 0.891018
% 1.34/1.74 This is a problem with some equality
% 1.34/1.74
% 1.34/1.74
% 1.34/1.74
% 1.34/1.74 Options Used:
% 1.34/1.74
% 1.34/1.74 useres = 1
% 1.34/1.74 useparamod = 1
% 1.34/1.74 useeqrefl = 1
% 1.34/1.74 useeqfact = 1
% 1.34/1.74 usefactor = 1
% 1.34/1.74 usesimpsplitting = 0
% 1.34/1.74 usesimpdemod = 5
% 1.34/1.74 usesimpres = 3
% 1.34/1.74
% 1.34/1.74 resimpinuse = 1000
% 1.34/1.74 resimpclauses = 20000
% 1.34/1.74 substype = eqrewr
% 1.34/1.74 backwardsubs = 1
% 1.34/1.74 selectoldest = 5
% 1.34/1.74
% 1.34/1.74 litorderings [0] = split
% 1.34/1.74 litorderings [1] = extend the termordering, first sorting on arguments
% 1.34/1.74
% 1.34/1.74 termordering = kbo
% 1.34/1.74
% 1.34/1.74 litapriori = 0
% 1.34/1.74 termapriori = 1
% 1.34/1.74 litaposteriori = 0
% 1.34/1.74 termaposteriori = 0
% 1.34/1.74 demodaposteriori = 0
% 1.34/1.74 ordereqreflfact = 0
% 1.34/1.74
% 1.34/1.74 litselect = negord
% 1.34/1.74
% 1.34/1.74 maxweight = 15
% 1.34/1.74 maxdepth = 30000
% 1.34/1.74 maxlength = 115
% 1.34/1.74 maxnrvars = 195
% 1.34/1.74 excuselevel = 1
% 1.34/1.74 increasemaxweight = 1
% 1.34/1.74
% 1.34/1.74 maxselected = 10000000
% 1.34/1.74 maxnrclauses = 10000000
% 1.34/1.74
% 1.34/1.74 showgenerated = 0
% 1.34/1.74 showkept = 0
% 1.34/1.74 showselected = 0
% 1.34/1.74 showdeleted = 0
% 1.34/1.74 showresimp = 1
% 1.34/1.74 showstatus = 2000
% 1.34/1.74
% 1.34/1.74 prologoutput = 0
% 1.34/1.74 nrgoals = 5000000
% 1.34/1.74 totalproof = 1
% 1.34/1.74
% 1.34/1.74 Symbols occurring in the translation:
% 1.34/1.74
% 1.34/1.74 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.34/1.74 . [1, 2] (w:1, o:204, a:1, s:1, b:0),
% 1.34/1.74 ! [4, 1] (w:0, o:115, a:1, s:1, b:0),
% 1.34/1.74 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.34/1.74 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.34/1.74 hAPP [38, 2] (w:1, o:228, a:1, s:1, b:0),
% 1.34/1.74 tc_Complex_Ocomplex [39, 0] (w:1, o:19, a:1, s:1, b:0),
% 1.34/1.74 v_q____ [40, 0] (w:1, o:22, a:1, s:1, b:0),
% 1.34/1.74 c_Polynomial_Opoly [41, 2] (w:1, o:229, a:1, s:1, b:0),
% 1.34/1.74 c_Groups_Ozero__class_Ozero [42, 1] (w:1, o:120, a:1, s:1, b:0),
% 1.34/1.74 v_p [43, 0] (w:1, o:20, a:1, s:1, b:0),
% 1.34/1.74 c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant [44, 3] (w:1, o:
% 1.34/1.74 272, a:1, s:1, b:0),
% 1.34/1.74 v_w____ [45, 0] (w:1, o:23, a:1, s:1, b:0),
% 1.34/1.74 c_Groups_Otimes__class_Otimes [46, 1] (w:1, o:121, a:1, s:1, b:0),
% 1.34/1.74 c_Rings_Oinverse__class_Oinverse [47, 2] (w:1, o:230, a:1, s:1, b:0)
% 1.34/1.74 ,
% 1.34/1.74 c_Polynomial_Osmult [48, 3] (w:1, o:275, a:1, s:1, b:0),
% 1.34/1.74 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [49, 2] (w:1, o:231
% 1.34/1.74 , a:1, s:1, b:0),
% 1.34/1.74 c_Groups_Oone__class_Oone [51, 1] (w:1, o:122, a:1, s:1, b:0),
% 1.34/1.74 class_Rings_Odivision__ring [55, 1] (w:1, o:128, a:1, s:1, b:0),
% 1.34/1.74 c_Rings_Oinverse__class_Odivide [56, 3] (w:1, o:276, a:1, s:1, b:0),
% 1.34/1.74
% 1.34/1.74 class_Fields_Olinordered__field__inverse__zero [58, 1] (w:1, o:129
% 1.34/1.74 , a:1, s:1, b:0),
% 1.34/1.74 c_Orderings_Oord__class_Oless [59, 3] (w:1, o:273, a:1, s:1, b:0),
% 1.34/1.74 class_Fields_Olinordered__field [60, 1] (w:1, o:130, a:1, s:1, b:0),
% 1.34/1.74
% 1.34/1.74 class_RealVector_Oreal__normed__algebra__1 [61, 1] (w:1, o:131, a:1
% 1.34/1.74 , s:1, b:0),
% 1.34/1.74 c_RealVector_Onorm__class_Onorm [62, 2] (w:1, o:232, a:1, s:1, b:0),
% 1.34/1.74
% 1.34/1.74 tc_RealDef_Oreal [63, 0] (w:1, o:33, a:1, s:1, b:0),
% 1.34/1.74 class_Fields_Ofield [64, 1] (w:1, o:132, a:1, s:1, b:0),
% 1.34/1.74 class_RealVector_Oreal__normed__div__algebra [65, 1] (w:1, o:133, a:1
% 1.34/1.74 , s:1, b:0),
% 1.34/1.74 v_pa____ [66, 0] (w:1, o:21, a:1, s:1, b:0),
% 1.34/1.74 class_Rings_Ocomm__semiring__1 [70, 1] (w:1, o:126, a:1, s:1, b:0),
% 1.34/1.74 class_Groups_Ozero [75, 1] (w:1, o:135, a:1, s:1, b:0),
% 1.34/1.74 tc_Nat_Onat [76, 0] (w:1, o:53, a:1, s:1, b:0),
% 1.34/1.74 tc_Polynomial_Opoly [77, 1] (w:1, o:141, a:1, s:1, b:0),
% 1.34/1.74 class_Rings_Ono__zero__divisors [79, 1] (w:1, o:152, a:1, s:1, b:0),
% 1.34/1.74
% 1.34/1.74 class_Rings_Oring__no__zero__divisors [82, 1] (w:1, o:153, a:1, s:1
% 1.34/1.74 , b:0),
% 1.34/1.74 class_RealVector_Oreal__normed__algebra [83, 1] (w:1, o:154, a:1, s:1
% 1.34/1.74 , b:0),
% 1.34/1.74 class_Rings_Omult__zero [84, 1] (w:1, o:151, a:1, s:1, b:0),
% 1.34/1.74 class_Fields_Ofield__inverse__zero [87, 1] (w:1, o:134, a:1, s:1, b:0
% 1.34/1.74 ),
% 1.34/1.74 class_Rings_Olinordered__ring__strict [92, 1] (w:1, o:142, a:1, s:1
% 1.34/1.74 , b:0),
% 1.34/1.74 class_Rings_Olinordered__comm__semiring__strict [93, 1] (w:1, o:143
% 1.34/1.74 , a:1, s:1, b:0),
% 1.34/1.74 class_Rings_Olinordered__semiring__strict [94, 1] (w:1, o:145, a:1
% 1.34/1.74 , s:1, b:0),
% 1.34/1.74 class_Rings_Olinordered__ring [96, 1] (w:1, o:144, a:1, s:1, b:0),
% 1.34/1.74 class_Rings_Olinordered__semidom [99, 1] (w:1, o:146, a:1, s:1, b:0)
% 1.34/1.74 ,
% 1.34/1.74 class_RealVector_Oreal__normed__vector [103, 1] (w:1, o:155, a:1, s:1
% 1.34/1.74 , b:0),
% 1.34/1.74 class_Rings_Olinordered__idom [104, 1] (w:1, o:147, a:1, s:1, b:0),
% 1.34/1.74 class_Rings_Odivision__ring__inverse__zero [105, 1] (w:1, o:156, a:1
% 1.34/1.74 , s:1, b:0),
% 1.34/1.74 class_Rings_Ozero__neq__one [106, 1] (w:1, o:157, a:1, s:1, b:0),
% 1.34/1.74 class_RealVector_Oreal__normed__field [107, 1] (w:1, o:158, a:1, s:1
% 1.34/1.74 , b:0),
% 1.34/1.74 class_Rings_Ocomm__semiring__0 [109, 1] (w:1, o:125, a:1, s:1, b:0),
% 1.34/1.74
% 1.34/1.74 class_Rings_Oidom [110, 1] (w:1, o:159, a:1, s:1, b:0),
% 1.34/1.74 class_Groups_Ocomm__monoid__mult [112, 1] (w:1, o:160, a:1, s:1, b:0)
% 1.34/1.74 ,
% 1.34/1.74 class_Groups_Omonoid__mult [113, 1] (w:1, o:162, a:1, s:1, b:0),
% 1.34/1.74 v_c____ [114, 0] (w:1, o:77, a:1, s:1, b:0),
% 1.34/1.74 class_Groups_Oab__semigroup__mult [115, 1] (w:1, o:163, a:1, s:1, b:0
% 1.34/1.74 ),
% 1.34/1.74 class_Groups_Oone [116, 1] (w:1, o:164, a:1, s:1, b:0),
% 1.34/1.74 class_Int_Oring__char__0 [118, 1] (w:1, o:165, a:1, s:1, b:0),
% 1.34/1.74 c_Orderings_Oord__class_Oless__eq [120, 3] (w:1, o:274, a:1, s:1, b:0
% 1.34/1.74 ),
% 1.34/1.74 c_Groups_Oplus__class_Oplus [125, 3] (w:1, o:277, a:1, s:1, b:0),
% 1.34/1.74 class_Rings_Oordered__cancel__semiring [129, 1] (w:1, o:166, a:1, s:1
% 1.34/1.74 , b:0),
% 1.34/1.74 class_Rings_Oordered__ring [130, 1] (w:1, o:167, a:1, s:1, b:0),
% 1.34/1.74 class_Rings_Oordered__semiring [131, 1] (w:1, o:168, a:1, s:1, b:0),
% 1.34/1.74
% 1.34/1.74 class_Rings_Oordered__comm__semiring [132, 1] (w:1, o:169, a:1, s:1
% 1.34/1.74 , b:0),
% 1.34/1.74 class_Rings_Olinordered__semiring [134, 1] (w:1, o:148, a:1, s:1, b:0
% 1.34/1.74 ),
% 1.34/1.74 c_Polynomial_Oorder [138, 3] (w:1, o:278, a:1, s:1, b:0),
% 1.34/1.74 class_Orderings_Opreorder [139, 1] (w:1, o:172, a:1, s:1, b:0),
% 1.34/1.74 class_Groups_Oab__semigroup__add [143, 1] (w:1, o:173, a:1, s:1, b:0)
% 1.34/1.74 ,
% 1.34/1.74 class_Groups_Ocancel__semigroup__add [144, 1] (w:1, o:174, a:1, s:1
% 1.34/1.74 , b:0),
% 1.34/1.74 class_Groups_Ocancel__ab__semigroup__add [145, 1] (w:1, o:175, a:1
% 1.34/1.74 , s:1, b:0),
% 1.34/1.74 class_Groups_Omonoid__add [146, 1] (w:1, o:176, a:1, s:1, b:0),
% 1.34/1.74 class_Groups_Ocomm__monoid__add [147, 1] (w:1, o:177, a:1, s:1, b:0)
% 1.34/1.74 ,
% 1.34/1.74 class_Groups_Olinordered__ab__group__add [148, 1] (w:1, o:161, a:1
% 1.34/1.74 , s:1, b:0),
% 1.34/1.74 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 1.34/1.74 149, 1] (w:1, o:185, a:1, s:1, b:0),
% 1.34/1.74 class_Groups_Oordered__ab__semigroup__add__imp__le [150, 1] (w:1, o:
% 1.34/1.74 186, a:1, s:1, b:0),
% 1.34/1.74 class_Groups_Oordered__ab__semigroup__add [151, 1] (w:1, o:187, a:1
% 1.34/1.74 , s:1, b:0),
% 1.34/1.74 class_Groups_Oordered__cancel__ab__semigroup__add [152, 1] (w:1, o:
% 1.34/1.74 188, a:1, s:1, b:0),
% 1.34/1.74 class_Rings_Osemiring [154, 1] (w:1, o:181, a:1, s:1, b:0),
% 1.34/1.74 class_Rings_Ocomm__semiring [157, 1] (w:1, o:127, a:1, s:1, b:0),
% 1.34/1.74 class_Groups_Oordered__comm__monoid__add [162, 1] (w:1, o:189, a:1
% 1.34/1.74 , s:1, b:0),
% 1.34/1.74 class_Orderings_Olinorder [163, 1] (w:1, o:190, a:1, s:1, b:0),
% 1.34/1.74 class_Orderings_Oord [164, 1] (w:1, o:170, a:1, s:1, b:0),
% 1.34/1.74 tc_fun [165, 2] (w:1, o:255, a:1, s:1, b:0),
% 1.34/1.74 class_Orderings_Oorder [166, 1] (w:1, o:171, a:1, s:1, b:0),
% 1.34/1.74 hBOOL [169, 1] (w:1, o:191, a:1, s:1, b:0),
% 1.34/1.74 class_Rings_Olinordered__semiring__1 [171, 1] (w:1, o:149, a:1, s:1
% 1.34/1.74 , b:0),
% 1.34/1.74 class_Rings_Olinordered__semiring__1__strict [172, 1] (w:1, o:150, a:
% 1.34/1.74 1, s:1, b:0),
% 1.34/1.74 c_SEQ_Odecseq [181, 2] (w:1, o:257, a:1, s:1, b:0),
% 1.34/1.74 c_SEQ_OBseq [184, 2] (w:1, o:258, a:1, s:1, b:0),
% 1.34/1.74 c_SEQ_Oincseq [185, 2] (w:1, o:259, a:1, s:1, b:0),
% 1.34/1.74 c_RComplete_Onatceiling [186, 1] (w:1, o:192, a:1, s:1, b:0),
% 1.34/1.74 c_Complex_Oexpi [187, 1] (w:1, o:193, a:1, s:1, b:0),
% 1.34/1.74 c_RComplete_Onatfloor [188, 1] (w:1, o:194, a:1, s:1, b:0),
% 1.34/1.74 c_RealDef_Oreal [189, 2] (w:1, o:256, a:1, s:1, b:0),
% 1.34/1.74 c_Divides_Odiv__class_Odiv [191, 3] (w:1, o:279, a:1, s:1, b:0),
% 1.34/1.74 c_Power_Opower__class_Opower [192, 1] (w:1, o:195, a:1, s:1, b:0),
% 1.34/1.74 tc_Int_Oint [195, 0] (w:1, o:107, a:1, s:1, b:0),
% 1.34/1.74 class_Rings_Oring__1__no__zero__divisors [196, 1] (w:1, o:178, a:1
% 1.34/1.74 , s:1, b:0),
% 1.34/1.74 class_Divides_Osemiring__div [197, 1] (w:1, o:197, a:1, s:1, b:0),
% 1.34/1.74 class_Power_Opower [198, 1] (w:1, o:198, a:1, s:1, b:0),
% 1.34/1.74 class_Rings_Osemiring__0 [199, 1] (w:1, o:182, a:1, s:1, b:0),
% 1.34/1.74 c_Power_Opower_Opower [201, 3] (w:1, o:280, a:1, s:1, b:0),
% 1.34/1.74 class_Rings_Ocomm__ring__1 [209, 1] (w:1, o:123, a:1, s:1, b:0),
% 1.34/1.74 c_Polynomial_Omonom [210, 3] (w:1, o:281, a:1, s:1, b:0),
% 1.34/1.74 c_Complex_Orcis [211, 2] (w:1, o:260, a:1, s:1, b:0),
% 1.34/1.74 c_Transcendental_Oln [218, 1] (w:1, o:199, a:1, s:1, b:0),
% 1.34/1.74 c_Divides_Odiv__class_Omod [219, 3] (w:1, o:282, a:1, s:1, b:0),
% 1.34/1.74 c_Rings_Odvd__class_Odvd [221, 3] (w:1, o:283, a:1, s:1, b:0),
% 1.34/1.74 c_Groups_Ominus__class_Ominus [222, 3] (w:1, o:284, a:1, s:1, b:0),
% 1.34/1.74 class_Divides_Oring__div [223, 1] (w:1, o:196, a:1, s:1, b:0),
% 1.34/1.74 class_Rings_Odvd [224, 1] (w:1, o:183, a:1, s:1, b:0),
% 1.34/1.74 class_Rings_Ocomm__ring [225, 1] (w:1, o:124, a:1, s:1, b:0),
% 1.47/1.89 class_Groups_Oab__group__add [226, 1] (w:1, o:200, a:1, s:1, b:0),
% 1.47/1.89 class_Groups_Oordered__ab__group__add [227, 1] (w:1, o:201, a:1, s:1
% 1.47/1.89 , b:0),
% 1.47/1.89 class_Groups_Ogroup__add [228, 1] (w:1, o:202, a:1, s:1, b:0),
% 1.47/1.89 class_Rings_Oring [229, 1] (w:1, o:179, a:1, s:1, b:0),
% 1.47/1.89 class_Rings_Oring__1 [231, 1] (w:1, o:180, a:1, s:1, b:0),
% 1.47/1.89 class_RealVector_Oreal__field [233, 1] (w:1, o:184, a:1, s:1, b:0),
% 1.47/1.89 class_Groups_Ocancel__comm__monoid__add [238, 1] (w:1, o:203, a:1, s:
% 1.47/1.89 1, b:0),
% 1.47/1.89 tc_HOL_Obool [240, 0] (w:1, o:106, a:1, s:1, b:0),
% 1.47/1.89 alpha1 [241, 4] (w:1, o:346, a:1, s:1, b:1),
% 1.47/1.89 alpha2 [242, 4] (w:1, o:348, a:1, s:1, b:1),
% 1.47/1.89 alpha3 [243, 3] (w:1, o:287, a:1, s:1, b:1),
% 1.47/1.89 alpha4 [244, 3] (w:1, o:294, a:1, s:1, b:1),
% 1.47/1.89 alpha5 [245, 3] (w:1, o:299, a:1, s:1, b:1),
% 1.47/1.89 alpha6 [246, 3] (w:1, o:304, a:1, s:1, b:1),
% 1.47/1.89 alpha7 [247, 3] (w:1, o:309, a:1, s:1, b:1),
% 1.47/1.89 alpha8 [248, 3] (w:1, o:318, a:1, s:1, b:1),
% 1.47/1.89 alpha9 [249, 2] (w:1, o:263, a:1, s:1, b:1),
% 1.47/1.89 alpha10 [250, 3] (w:1, o:319, a:1, s:1, b:1),
% 1.47/1.89 alpha11 [251, 3] (w:1, o:320, a:1, s:1, b:1),
% 1.47/1.89 alpha12 [252, 3] (w:1, o:321, a:1, s:1, b:1),
% 1.47/1.89 alpha13 [253, 3] (w:1, o:322, a:1, s:1, b:1),
% 1.47/1.89 alpha14 [254, 3] (w:1, o:323, a:1, s:1, b:1),
% 1.47/1.89 alpha15 [255, 3] (w:1, o:324, a:1, s:1, b:1),
% 1.47/1.89 alpha16 [256, 2] (w:1, o:264, a:1, s:1, b:1),
% 1.47/1.89 alpha17 [257, 2] (w:1, o:265, a:1, s:1, b:1),
% 1.47/1.89 alpha18 [258, 2] (w:1, o:266, a:1, s:1, b:1),
% 1.47/1.89 alpha19 [259, 4] (w:1, o:347, a:1, s:1, b:1),
% 1.47/1.89 alpha20 [260, 3] (w:1, o:285, a:1, s:1, b:1),
% 1.47/1.89 alpha21 [261, 3] (w:1, o:286, a:1, s:1, b:1),
% 1.47/1.89 alpha22 [262, 4] (w:1, o:349, a:1, s:1, b:1),
% 1.47/1.89 alpha23 [263, 2] (w:1, o:267, a:1, s:1, b:1),
% 1.47/1.89 alpha24 [264, 2] (w:1, o:268, a:1, s:1, b:1),
% 1.47/1.89 alpha25 [265, 4] (w:1, o:350, a:1, s:1, b:1),
% 1.47/1.89 alpha26 [266, 4] (w:1, o:351, a:1, s:1, b:1),
% 1.47/1.89 alpha27 [267, 4] (w:1, o:352, a:1, s:1, b:1),
% 1.47/1.89 alpha28 [268, 4] (w:1, o:353, a:1, s:1, b:1),
% 1.47/1.89 alpha29 [269, 4] (w:1, o:354, a:1, s:1, b:1),
% 1.47/1.89 alpha30 [270, 4] (w:1, o:355, a:1, s:1, b:1),
% 1.47/1.89 alpha31 [271, 3] (w:1, o:288, a:1, s:1, b:1),
% 1.47/1.89 alpha32 [272, 3] (w:1, o:289, a:1, s:1, b:1),
% 1.47/1.89 alpha33 [273, 2] (w:1, o:269, a:1, s:1, b:1),
% 1.47/1.89 alpha34 [274, 3] (w:1, o:290, a:1, s:1, b:1),
% 1.47/1.89 alpha35 [275, 3] (w:1, o:291, a:1, s:1, b:1),
% 1.47/1.89 alpha36 [276, 3] (w:1, o:292, a:1, s:1, b:1),
% 1.47/1.89 alpha37 [277, 3] (w:1, o:293, a:1, s:1, b:1),
% 1.47/1.89 alpha38 [278, 4] (w:1, o:356, a:1, s:1, b:1),
% 1.47/1.89 alpha39 [279, 4] (w:1, o:357, a:1, s:1, b:1),
% 1.47/1.89 alpha40 [280, 3] (w:1, o:295, a:1, s:1, b:1),
% 1.47/1.89 alpha41 [281, 3] (w:1, o:296, a:1, s:1, b:1),
% 1.47/1.89 alpha42 [282, 2] (w:1, o:270, a:1, s:1, b:1),
% 1.47/1.89 alpha43 [283, 4] (w:1, o:358, a:1, s:1, b:1),
% 1.47/1.89 alpha44 [284, 3] (w:1, o:297, a:1, s:1, b:1),
% 1.47/1.89 alpha45 [285, 3] (w:1, o:298, a:1, s:1, b:1),
% 1.47/1.89 alpha46 [286, 4] (w:1, o:359, a:1, s:1, b:1),
% 1.47/1.89 alpha47 [287, 4] (w:1, o:360, a:1, s:1, b:1),
% 1.47/1.89 alpha48 [288, 4] (w:1, o:361, a:1, s:1, b:1),
% 1.47/1.89 alpha49 [289, 4] (w:1, o:362, a:1, s:1, b:1),
% 1.47/1.89 alpha50 [290, 4] (w:1, o:363, a:1, s:1, b:1),
% 1.47/1.89 alpha51 [291, 3] (w:1, o:300, a:1, s:1, b:1),
% 1.47/1.89 alpha52 [292, 3] (w:1, o:301, a:1, s:1, b:1),
% 1.47/1.89 alpha53 [293, 2] (w:1, o:271, a:1, s:1, b:1),
% 1.47/1.89 alpha54 [294, 3] (w:1, o:302, a:1, s:1, b:1),
% 1.47/1.89 alpha55 [295, 3] (w:1, o:303, a:1, s:1, b:1),
% 1.47/1.89 alpha56 [296, 4] (w:1, o:364, a:1, s:1, b:1),
% 1.47/1.89 alpha57 [297, 4] (w:1, o:365, a:1, s:1, b:1),
% 1.47/1.89 alpha58 [298, 4] (w:1, o:366, a:1, s:1, b:1),
% 1.47/1.89 alpha59 [299, 4] (w:1, o:367, a:1, s:1, b:1),
% 1.47/1.89 alpha60 [300, 4] (w:1, o:368, a:1, s:1, b:1),
% 1.47/1.89 alpha61 [301, 3] (w:1, o:305, a:1, s:1, b:1),
% 1.47/1.89 alpha62 [302, 3] (w:1, o:306, a:1, s:1, b:1),
% 1.47/1.89 alpha63 [303, 4] (w:1, o:369, a:1, s:1, b:1),
% 1.47/1.89 alpha64 [304, 3] (w:1, o:307, a:1, s:1, b:1),
% 1.47/1.89 alpha65 [305, 3] (w:1, o:308, a:1, s:1, b:1),
% 1.47/1.89 alpha66 [306, 4] (w:1, o:370, a:1, s:1, b:1),
% 16.55/16.93 alpha67 [307, 4] (w:1, o:371, a:1, s:1, b:1),
% 16.55/16.93 alpha68 [308, 4] (w:1, o:372, a:1, s:1, b:1),
% 16.55/16.93 alpha69 [309, 4] (w:1, o:373, a:1, s:1, b:1),
% 16.55/16.93 alpha70 [310, 3] (w:1, o:310, a:1, s:1, b:1),
% 16.55/16.93 alpha71 [311, 3] (w:1, o:311, a:1, s:1, b:1),
% 16.55/16.93 alpha72 [312, 3] (w:1, o:312, a:1, s:1, b:1),
% 16.55/16.93 alpha73 [313, 3] (w:1, o:313, a:1, s:1, b:1),
% 16.55/16.93 alpha74 [314, 3] (w:1, o:314, a:1, s:1, b:1),
% 16.55/16.93 alpha75 [315, 4] (w:1, o:374, a:1, s:1, b:1),
% 16.55/16.93 alpha76 [316, 3] (w:1, o:315, a:1, s:1, b:1),
% 16.55/16.93 alpha77 [317, 3] (w:1, o:316, a:1, s:1, b:1),
% 16.55/16.93 alpha78 [318, 4] (w:1, o:375, a:1, s:1, b:1),
% 16.55/16.93 alpha79 [319, 3] (w:1, o:317, a:1, s:1, b:1),
% 16.55/16.93 alpha80 [320, 3] (w:1, o:325, a:1, s:1, b:1),
% 16.55/16.93 alpha81 [321, 2] (w:1, o:261, a:1, s:1, b:1),
% 16.55/16.93 alpha82 [322, 2] (w:1, o:262, a:1, s:1, b:1),
% 16.55/16.93 alpha83 [323, 0] (w:1, o:114, a:1, s:1, b:1),
% 16.55/16.93 alpha84 [324, 3] (w:1, o:326, a:1, s:1, b:1),
% 16.55/16.93 skol1 [325, 2] (w:1, o:233, a:1, s:1, b:1),
% 16.55/16.93 skol2 [326, 0] (w:1, o:15, a:1, s:1, b:1),
% 16.55/16.93 skol3 [327, 1] (w:1, o:136, a:1, s:1, b:1),
% 16.55/16.93 skol4 [328, 1] (w:1, o:137, a:1, s:1, b:1),
% 16.55/16.93 skol5 [329, 0] (w:1, o:17, a:1, s:1, b:1),
% 16.55/16.93 skol6 [330, 2] (w:1, o:235, a:1, s:1, b:1),
% 16.55/16.93 skol7 [331, 3] (w:1, o:327, a:1, s:1, b:1),
% 16.55/16.93 skol8 [332, 0] (w:1, o:18, a:1, s:1, b:1),
% 16.55/16.93 skol9 [333, 2] (w:1, o:236, a:1, s:1, b:1),
% 16.55/16.93 skol10 [334, 2] (w:1, o:237, a:1, s:1, b:1),
% 16.55/16.93 skol11 [335, 0] (w:1, o:14, a:1, s:1, b:1),
% 16.55/16.93 skol12 [336, 2] (w:1, o:238, a:1, s:1, b:1),
% 16.55/16.93 skol13 [337, 2] (w:1, o:239, a:1, s:1, b:1),
% 16.55/16.93 skol14 [338, 1] (w:1, o:138, a:1, s:1, b:1),
% 16.55/16.93 skol15 [339, 2] (w:1, o:240, a:1, s:1, b:1),
% 16.55/16.93 skol16 [340, 2] (w:1, o:241, a:1, s:1, b:1),
% 16.55/16.93 skol17 [341, 2] (w:1, o:242, a:1, s:1, b:1),
% 16.55/16.93 skol18 [342, 2] (w:1, o:243, a:1, s:1, b:1),
% 16.55/16.93 skol19 [343, 1] (w:1, o:139, a:1, s:1, b:1),
% 16.55/16.93 skol20 [344, 2] (w:1, o:244, a:1, s:1, b:1),
% 16.55/16.93 skol21 [345, 2] (w:1, o:245, a:1, s:1, b:1),
% 16.55/16.93 skol22 [346, 3] (w:1, o:328, a:1, s:1, b:1),
% 16.55/16.93 skol23 [347, 2] (w:1, o:246, a:1, s:1, b:1),
% 16.55/16.93 skol24 [348, 2] (w:1, o:247, a:1, s:1, b:1),
% 16.55/16.93 skol25 [349, 2] (w:1, o:248, a:1, s:1, b:1),
% 16.55/16.93 skol26 [350, 3] (w:1, o:329, a:1, s:1, b:1),
% 16.55/16.93 skol27 [351, 4] (w:1, o:376, a:1, s:1, b:1),
% 16.55/16.93 skol28 [352, 3] (w:1, o:330, a:1, s:1, b:1),
% 16.55/16.93 skol29 [353, 4] (w:1, o:377, a:1, s:1, b:1),
% 16.55/16.93 skol30 [354, 2] (w:1, o:249, a:1, s:1, b:1),
% 16.55/16.93 skol31 [355, 3] (w:1, o:331, a:1, s:1, b:1),
% 16.55/16.93 skol32 [356, 3] (w:1, o:332, a:1, s:1, b:1),
% 16.55/16.93 skol33 [357, 3] (w:1, o:333, a:1, s:1, b:1),
% 16.55/16.93 skol34 [358, 3] (w:1, o:334, a:1, s:1, b:1),
% 16.55/16.93 skol35 [359, 2] (w:1, o:250, a:1, s:1, b:1),
% 16.55/16.93 skol36 [360, 2] (w:1, o:251, a:1, s:1, b:1),
% 16.55/16.93 skol37 [361, 3] (w:1, o:335, a:1, s:1, b:1),
% 16.55/16.93 skol38 [362, 2] (w:1, o:252, a:1, s:1, b:1),
% 16.55/16.93 skol39 [363, 2] (w:1, o:253, a:1, s:1, b:1),
% 16.55/16.93 skol40 [364, 3] (w:1, o:336, a:1, s:1, b:1),
% 16.55/16.93 skol41 [365, 3] (w:1, o:337, a:1, s:1, b:1),
% 16.55/16.93 skol42 [366, 3] (w:1, o:338, a:1, s:1, b:1),
% 16.55/16.93 skol43 [367, 3] (w:1, o:339, a:1, s:1, b:1),
% 16.55/16.93 skol44 [368, 3] (w:1, o:340, a:1, s:1, b:1),
% 16.55/16.93 skol45 [369, 3] (w:1, o:341, a:1, s:1, b:1),
% 16.55/16.93 skol46 [370, 3] (w:1, o:342, a:1, s:1, b:1),
% 16.55/16.93 skol47 [371, 0] (w:1, o:16, a:1, s:1, b:1),
% 16.55/16.93 skol48 [372, 1] (w:1, o:140, a:1, s:1, b:1),
% 16.55/16.93 skol49 [373, 2] (w:1, o:254, a:1, s:1, b:1),
% 16.55/16.93 skol50 [374, 3] (w:1, o:343, a:1, s:1, b:1),
% 16.55/16.93 skol51 [375, 2] (w:1, o:234, a:1, s:1, b:1),
% 16.55/16.93 skol52 [376, 3] (w:1, o:344, a:1, s:1, b:1),
% 16.55/16.93 skol53 [377, 3] (w:1, o:345, a:1, s:1, b:1).
% 16.55/16.93
% 16.55/16.93
% 16.55/16.93 Starting Search:
% 16.55/16.93
% 16.55/16.93 *** allocated 170857 integers for clauses
% 16.55/16.93
% 16.55/16.93 Intermediate Status:
% 16.55/16.93 Generated: 2838
% 16.55/16.93 Kept: 2020
% 16.55/16.93 Inuse: 0
% 16.55/16.93 Deleted: 0
% 16.55/16.93 Deletedinuse: 0
% 16.55/16.93
% 16.55/16.93 Resimplifying inuse:
% 16.55/16.93 Done
% 16.55/16.93
% 16.55/16.93 *** allocated 256285 integers for clauses
% 16.55/16.93 *** allocated 170857 integers for termspace/termends
% 16.55/16.93 Resimplifying inuse:
% 16.55/16.93 Done
% 16.55/16.93
% 16.55/16.93
% 16.55/16.93 Intermediate Status:
% 16.55/16.93 Generated: 9416
% 16.55/16.93 Kept: 4023
% 60.56/60.94 Inuse: 180
% 60.56/60.94 Deleted: 10
% 60.56/60.94 Deletedinuse: 0
% 60.56/60.94
% 60.56/60.94 Resimplifying inuse:
% 60.56/60.94 Done
% 60.56/60.94
% 60.56/60.94 *** allocated 384427 integers for clauses
% 60.56/60.94 *** allocated 256285 integers for termspace/termends
% 60.56/60.94 Resimplifying inuse:
% 60.56/60.94 Done
% 60.56/60.94
% 60.56/60.94
% 60.56/60.94 Intermediate Status:
% 60.56/60.94 Generated: 14489
% 60.56/60.94 Kept: 6033
% 60.56/60.94 Inuse: 290
% 60.56/60.94 Deleted: 10
% 60.56/60.94 Deletedinuse: 0
% 60.56/60.94
% 60.56/60.94 Resimplifying inuse:
% 60.56/60.94 Done
% 60.56/60.94
% 60.56/60.94 *** allocated 576640 integers for clauses
% 60.56/60.94 Resimplifying inuse:
% 60.56/60.94 Done
% 60.56/60.94
% 60.56/60.94 *** allocated 384427 integers for termspace/termends
% 60.56/60.94
% 60.56/60.94 Intermediate Status:
% 60.56/60.94 Generated: 23689
% 60.56/60.94 Kept: 9247
% 60.56/60.94 Inuse: 406
% 60.56/60.94 Deleted: 10
% 60.56/60.94 Deletedinuse: 0
% 60.56/60.94
% 60.56/60.94 Resimplifying inuse:
% 60.56/60.94 Done
% 60.56/60.94
% 60.56/60.94 Resimplifying inuse:
% 60.56/60.94 Done
% 60.56/60.94
% 60.56/60.94 *** allocated 576640 integers for termspace/termends
% 60.56/60.94 *** allocated 864960 integers for clauses
% 60.56/60.94
% 60.56/60.94 Intermediate Status:
% 60.56/60.94 Generated: 49365
% 60.56/60.94 Kept: 11845
% 60.56/60.94 Inuse: 431
% 60.56/60.94 Deleted: 10
% 60.56/60.94 Deletedinuse: 0
% 60.56/60.94
% 60.56/60.94 Resimplifying inuse:
% 60.56/60.94 Done
% 60.56/60.94
% 60.56/60.94 Resimplifying inuse:
% 60.56/60.94 Done
% 60.56/60.94
% 60.56/60.94
% 60.56/60.94 Intermediate Status:
% 60.56/60.94 Generated: 58132
% 60.56/60.94 Kept: 13874
% 60.56/60.94 Inuse: 456
% 60.56/60.94 Deleted: 10
% 60.56/60.94 Deletedinuse: 0
% 60.56/60.94
% 60.56/60.94 Resimplifying inuse:
% 60.56/60.94 Done
% 60.56/60.94
% 60.56/60.94
% 60.56/60.94 Intermediate Status:
% 60.56/60.94 Generated: 63826
% 60.56/60.94 Kept: 16393
% 60.56/60.94 Inuse: 471
% 60.56/60.94 Deleted: 10
% 60.56/60.94 Deletedinuse: 0
% 60.56/60.94
% 60.56/60.94 Resimplifying inuse:
% 60.56/60.94 Done
% 60.56/60.94
% 60.56/60.94 *** allocated 1297440 integers for clauses
% 60.56/60.94
% 60.56/60.94 Intermediate Status:
% 60.56/60.94 Generated: 73842
% 60.56/60.94 Kept: 18653
% 60.56/60.94 Inuse: 496
% 60.56/60.94 Deleted: 10
% 60.56/60.94 Deletedinuse: 0
% 60.56/60.94
% 60.56/60.94 Resimplifying inuse:
% 60.56/60.94 Done
% 60.56/60.94
% 60.56/60.94 *** allocated 864960 integers for termspace/termends
% 60.56/60.94
% 60.56/60.94 Intermediate Status:
% 60.56/60.94 Generated: 78534
% 60.56/60.94 Kept: 20698
% 60.56/60.94 Inuse: 511
% 60.56/60.94 Deleted: 10
% 60.56/60.94 Deletedinuse: 0
% 60.56/60.94
% 60.56/60.94 Resimplifying inuse:
% 60.56/60.94 Done
% 60.56/60.94
% 60.56/60.94 Resimplifying clauses:
% 60.56/60.94 Done
% 60.56/60.94
% 60.56/60.94 Resimplifying inuse:
% 60.56/60.94 Done
% 60.56/60.94
% 60.56/60.94
% 60.56/60.94 Intermediate Status:
% 60.56/60.94 Generated: 83728
% 60.56/60.94 Kept: 22706
% 60.56/60.94 Inuse: 526
% 60.56/60.94 Deleted: 156
% 60.56/60.94 Deletedinuse: 0
% 60.56/60.94
% 60.56/60.94 Resimplifying inuse:
% 60.56/60.94 Done
% 60.56/60.94
% 60.56/60.94 Resimplifying inuse:
% 60.56/60.94 Done
% 60.56/60.94
% 60.56/60.94
% 60.56/60.94 Intermediate Status:
% 60.56/60.94 Generated: 90214
% 60.56/60.94 Kept: 24732
% 60.56/60.94 Inuse: 561
% 60.56/60.94 Deleted: 156
% 60.56/60.94 Deletedinuse: 0
% 60.56/60.94
% 60.56/60.94 Resimplifying inuse:
% 60.56/60.94 Done
% 60.56/60.94
% 60.56/60.94 Resimplifying inuse:
% 60.56/60.94 Done
% 60.56/60.94
% 60.56/60.94
% 60.56/60.94 Intermediate Status:
% 60.56/60.94 Generated: 95182
% 60.56/60.94 Kept: 26757
% 60.56/60.94 Inuse: 591
% 60.56/60.94 Deleted: 156
% 60.56/60.94 Deletedinuse: 0
% 60.56/60.94
% 60.56/60.94 Resimplifying inuse:
% 60.56/60.94 Done
% 60.56/60.94
% 60.56/60.94 Resimplifying inuse:
% 60.56/60.94 Done
% 60.56/60.94
% 60.56/60.94
% 60.56/60.94 Intermediate Status:
% 60.56/60.94 Generated: 100558
% 60.56/60.94 Kept: 28889
% 60.56/60.94 Inuse: 656
% 60.56/60.94 Deleted: 156
% 60.56/60.94 Deletedinuse: 0
% 60.56/60.94
% 60.56/60.94 *** allocated 1946160 integers for clauses
% 60.56/60.94 Resimplifying inuse:
% 60.56/60.94 Done
% 60.56/60.94
% 60.56/60.94 Resimplifying inuse:
% 60.56/60.94 Done
% 60.56/60.94
% 60.56/60.94
% 60.56/60.94 Intermediate Status:
% 60.56/60.94 Generated: 105708
% 60.56/60.94 Kept: 30920
% 60.56/60.94 Inuse: 718
% 60.56/60.94 Deleted: 156
% 60.56/60.94 Deletedinuse: 0
% 60.56/60.94
% 60.56/60.94 Resimplifying inuse:
% 60.56/60.94 Done
% 60.56/60.94
% 60.56/60.94 *** allocated 1297440 integers for termspace/termends
% 60.56/60.94 Resimplifying inuse:
% 60.56/60.94 Done
% 60.56/60.94
% 60.56/60.94
% 60.56/60.94 Intermediate Status:
% 60.56/60.94 Generated: 110419
% 60.56/60.94 Kept: 32937
% 60.56/60.94 Inuse: 766
% 60.56/60.94 Deleted: 156
% 60.56/60.94 Deletedinuse: 0
% 60.56/60.94
% 60.56/60.94 Resimplifying inuse:
% 60.56/60.94 Done
% 60.56/60.94
% 60.56/60.94
% 60.56/60.94 Intermediate Status:
% 60.56/60.94 Generated: 119344
% 60.56/60.94 Kept: 35206
% 60.56/60.94 Inuse: 781
% 60.56/60.94 Deleted: 156
% 60.56/60.94 Deletedinuse: 0
% 60.56/60.94
% 60.56/60.94 Resimplifying inuse:
% 60.56/60.94 Done
% 60.56/60.94
% 60.56/60.94 Resimplifying inuse:
% 60.56/60.94 Done
% 60.56/60.94
% 60.56/60.94
% 60.56/60.94 Intermediate Status:
% 60.56/60.94 Generated: 128095
% 60.56/60.94 Kept: 37803
% 60.56/60.94 Inuse: 791
% 60.56/60.94 Deleted: 156
% 60.56/60.94 Deletedinuse: 0
% 60.56/60.94
% 60.56/60.94 Resimplifying inuse:
% 60.56/60.94 Done
% 60.56/60.94
% 60.56/60.94 Resimplifying inuse:
% 60.56/60.94 Done
% 60.56/60.94
% 60.56/60.94
% 60.56/60.94 Intermediate Status:
% 60.56/60.94 Generated: 135847
% 60.56/60.94 Kept: 39824
% 60.56/60.94 Inuse: 803
% 60.56/60.94 Deleted: 156
% 60.56/60.94 Deletedinuse: 0
% 60.56/60.94
% 60.56/60.94 Resimplifying inuse:
% 60.56/60.94 Done
% 60.56/60.94
% 60.56/60.94 Resimplifying clauses:
% 60.56/60.94 Done
% 60.56/60.94
% 60.56/60.94
% 60.56/60.94 Intermediate Status:
% 60.56/60.94 Generated: 142734
% 60.56/60.94 Kept: 42595
% 60.56/60.94 Inuse: 831
% 60.56/60.94 Deleted: 254
% 60.56/60.94 Deletedinuse: 0
% 60.56/60.94
% 60.56/60.94 Resimplifying inuse:
% 60.56/60.94 Done
% 60.56/60.94
% 60.56/60.94 *** allocated 2919240 integers for clauses
% 60.56/60.94
% 60.56/60.94 Intermediate Status:
% 60.56/60.94 Generated: 174539
% 60.56/60.94 Kept: 44748
% 60.56/60.94 Inuse: 846
% 60.56/60.94 Deleted: 254
% 60.56/60.94 Deletedinuse: 0
% 60.56/60.94
% 60.56/60.94 Resimplifying inuse:
% 60.56/60.94 Done
% 60.56/60.94
% 60.56/60.94
% 60.56/60.94 Intermediate Status:
% 60.56/60.94 Generated: 178698
% 60.56/60.94 Kept: 46836
% 60.56/60.94 Inuse: 851
% 60.56/60.94 Deleted: 254
% 60.56/60.94 Deletedinuse: 0
% 60.56/60.94
% 60.56/60.94 Resimplifying inuse:
% 60.56/60.94 Done
% 60.56/60.94
% 60.56/60.94 Resimplifying inuse:
% 60.56/60.94 Done
% 60.56/60.94
% 60.56/60.94
% 60.56/60.94 Intermediate Status:
% 60.56/60.94 Generated: 187654
% 60.56/60.94 Kept: 50736
% 60.56/60.94 Inuse: 861
% 60.56/60.94 Deleted: 254
% 60.56/60.94 Deletedinuse: 0
% 60.56/60.94
% 60.56/60.94 Resimplifying inuse:
% 60.56/60.94 Done
% 60.56/60.94
% 60.56/60.94 *** allocated 1946160 integers for termspace/termends
% 60.56/60.94 Resimplifying inuse:
% 60.56/60.94 Done
% 60.56/60.94
% 60.56/60.94
% 60.56/60.94 Intermediate Status:
% 60.56/60.94 Generated: 195745
% 60.56/60.94 Kept: 53957
% 60.56/60.94 Inuse: 886
% 60.56/60.94 Deleted: 254
% 60.56/60.94 Deletedinuse: 0
% 60.56/60.94
% 60.56/60.94 Resimplifying inuse:
% 60.56/60.94 Done
% 60.56/60.94
% 60.56/60.94 Resimplifying inuse:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09
% 155.73/156.09 Intermediate Status:
% 155.73/156.09 Generated: 203075
% 155.73/156.09 Kept: 55976
% 155.73/156.09 Inuse: 917
% 155.73/156.09 Deleted: 254
% 155.73/156.09 Deletedinuse: 0
% 155.73/156.09
% 155.73/156.09 Resimplifying inuse:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09 Resimplifying inuse:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09
% 155.73/156.09 Intermediate Status:
% 155.73/156.09 Generated: 209969
% 155.73/156.09 Kept: 58049
% 155.73/156.09 Inuse: 941
% 155.73/156.09 Deleted: 254
% 155.73/156.09 Deletedinuse: 0
% 155.73/156.09
% 155.73/156.09 Resimplifying inuse:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09 Resimplifying inuse:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09
% 155.73/156.09 Intermediate Status:
% 155.73/156.09 Generated: 216567
% 155.73/156.09 Kept: 60057
% 155.73/156.09 Inuse: 968
% 155.73/156.09 Deleted: 254
% 155.73/156.09 Deletedinuse: 0
% 155.73/156.09
% 155.73/156.09 Resimplifying inuse:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09 Resimplifying clauses:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09 Resimplifying inuse:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09
% 155.73/156.09 Intermediate Status:
% 155.73/156.09 Generated: 221997
% 155.73/156.09 Kept: 62059
% 155.73/156.09 Inuse: 1006
% 155.73/156.09 Deleted: 571
% 155.73/156.09 Deletedinuse: 1
% 155.73/156.09
% 155.73/156.09 Resimplifying inuse:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09 Resimplifying inuse:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09
% 155.73/156.09 Intermediate Status:
% 155.73/156.09 Generated: 240143
% 155.73/156.09 Kept: 65885
% 155.73/156.09 Inuse: 1045
% 155.73/156.09 Deleted: 571
% 155.73/156.09 Deletedinuse: 1
% 155.73/156.09
% 155.73/156.09 Resimplifying inuse:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09 Resimplifying inuse:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09 *** allocated 4378860 integers for clauses
% 155.73/156.09
% 155.73/156.09 Intermediate Status:
% 155.73/156.09 Generated: 251583
% 155.73/156.09 Kept: 69059
% 155.73/156.09 Inuse: 1060
% 155.73/156.09 Deleted: 571
% 155.73/156.09 Deletedinuse: 1
% 155.73/156.09
% 155.73/156.09 Resimplifying inuse:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09 Resimplifying inuse:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09
% 155.73/156.09 Intermediate Status:
% 155.73/156.09 Generated: 258471
% 155.73/156.09 Kept: 71066
% 155.73/156.09 Inuse: 1080
% 155.73/156.09 Deleted: 571
% 155.73/156.09 Deletedinuse: 1
% 155.73/156.09
% 155.73/156.09 Resimplifying inuse:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09
% 155.73/156.09 Intermediate Status:
% 155.73/156.09 Generated: 265621
% 155.73/156.09 Kept: 73206
% 155.73/156.09 Inuse: 1105
% 155.73/156.09 Deleted: 571
% 155.73/156.09 Deletedinuse: 1
% 155.73/156.09
% 155.73/156.09 Resimplifying inuse:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09
% 155.73/156.09 Intermediate Status:
% 155.73/156.09 Generated: 272803
% 155.73/156.09 Kept: 76644
% 155.73/156.09 Inuse: 1125
% 155.73/156.09 Deleted: 571
% 155.73/156.09 Deletedinuse: 1
% 155.73/156.09
% 155.73/156.09 Resimplifying inuse:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09 *** allocated 2919240 integers for termspace/termends
% 155.73/156.09 Resimplifying inuse:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09
% 155.73/156.09 Intermediate Status:
% 155.73/156.09 Generated: 281588
% 155.73/156.09 Kept: 78668
% 155.73/156.09 Inuse: 1150
% 155.73/156.09 Deleted: 571
% 155.73/156.09 Deletedinuse: 1
% 155.73/156.09
% 155.73/156.09 Resimplifying inuse:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09
% 155.73/156.09 Intermediate Status:
% 155.73/156.09 Generated: 298564
% 155.73/156.09 Kept: 81384
% 155.73/156.09 Inuse: 1160
% 155.73/156.09 Deleted: 571
% 155.73/156.09 Deletedinuse: 1
% 155.73/156.09
% 155.73/156.09 Resimplifying inuse:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09 Resimplifying clauses:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09 Resimplifying inuse:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09
% 155.73/156.09 Intermediate Status:
% 155.73/156.09 Generated: 306477
% 155.73/156.09 Kept: 83441
% 155.73/156.09 Inuse: 1195
% 155.73/156.09 Deleted: 661
% 155.73/156.09 Deletedinuse: 1
% 155.73/156.09
% 155.73/156.09 Resimplifying inuse:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09 Resimplifying inuse:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09
% 155.73/156.09 Intermediate Status:
% 155.73/156.09 Generated: 314830
% 155.73/156.09 Kept: 85473
% 155.73/156.09 Inuse: 1224
% 155.73/156.09 Deleted: 661
% 155.73/156.09 Deletedinuse: 1
% 155.73/156.09
% 155.73/156.09
% 155.73/156.09 Intermediate Status:
% 155.73/156.09 Generated: 319653
% 155.73/156.09 Kept: 88180
% 155.73/156.09 Inuse: 1225
% 155.73/156.09 Deleted: 661
% 155.73/156.09 Deletedinuse: 1
% 155.73/156.09
% 155.73/156.09 Resimplifying inuse:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09
% 155.73/156.09 Intermediate Status:
% 155.73/156.09 Generated: 326673
% 155.73/156.09 Kept: 91662
% 155.73/156.09 Inuse: 1235
% 155.73/156.09 Deleted: 661
% 155.73/156.09 Deletedinuse: 1
% 155.73/156.09
% 155.73/156.09 Resimplifying inuse:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09 Resimplifying inuse:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09
% 155.73/156.09 Intermediate Status:
% 155.73/156.09 Generated: 336145
% 155.73/156.09 Kept: 93684
% 155.73/156.09 Inuse: 1243
% 155.73/156.09 Deleted: 661
% 155.73/156.09 Deletedinuse: 1
% 155.73/156.09
% 155.73/156.09 Resimplifying inuse:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09
% 155.73/156.09 Intermediate Status:
% 155.73/156.09 Generated: 347296
% 155.73/156.09 Kept: 96155
% 155.73/156.09 Inuse: 1265
% 155.73/156.09 Deleted: 661
% 155.73/156.09 Deletedinuse: 1
% 155.73/156.09
% 155.73/156.09 Resimplifying inuse:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09 Resimplifying inuse:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09
% 155.73/156.09 Intermediate Status:
% 155.73/156.09 Generated: 355317
% 155.73/156.09 Kept: 98170
% 155.73/156.09 Inuse: 1287
% 155.73/156.09 Deleted: 661
% 155.73/156.09 Deletedinuse: 1
% 155.73/156.09
% 155.73/156.09 Resimplifying inuse:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09 *** allocated 6568290 integers for clauses
% 155.73/156.09
% 155.73/156.09 Intermediate Status:
% 155.73/156.09 Generated: 363616
% 155.73/156.09 Kept: 103121
% 155.73/156.09 Inuse: 1290
% 155.73/156.09 Deleted: 663
% 155.73/156.09 Deletedinuse: 3
% 155.73/156.09
% 155.73/156.09 Resimplifying inuse:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09 Resimplifying clauses:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09
% 155.73/156.09 Intermediate Status:
% 155.73/156.09 Generated: 373632
% 155.73/156.09 Kept: 105741
% 155.73/156.09 Inuse: 1291
% 155.73/156.09 Deleted: 2876
% 155.73/156.09 Deletedinuse: 3
% 155.73/156.09
% 155.73/156.09 Resimplifying inuse:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09
% 155.73/156.09 Intermediate Status:
% 155.73/156.09 Generated: 385500
% 155.73/156.09 Kept: 108736
% 155.73/156.09 Inuse: 1310
% 155.73/156.09 Deleted: 2879
% 155.73/156.09 Deletedinuse: 6
% 155.73/156.09
% 155.73/156.09 Resimplifying inuse:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09 Resimplifying inuse:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09
% 155.73/156.09 Intermediate Status:
% 155.73/156.09 Generated: 393305
% 155.73/156.09 Kept: 110862
% 155.73/156.09 Inuse: 1355
% 155.73/156.09 Deleted: 2879
% 155.73/156.09 Deletedinuse: 6
% 155.73/156.09
% 155.73/156.09 Resimplifying inuse:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09 Resimplifying inuse:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09
% 155.73/156.09 Intermediate Status:
% 155.73/156.09 Generated: 399073
% 155.73/156.09 Kept: 112872
% 155.73/156.09 Inuse: 1390
% 155.73/156.09 Deleted: 2879
% 155.73/156.09 Deletedinuse: 6
% 155.73/156.09
% 155.73/156.09 Resimplifying inuse:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09 Resimplifying inuse:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09
% 155.73/156.09 Intermediate Status:
% 155.73/156.09 Generated: 405277
% 155.73/156.09 Kept: 114957
% 155.73/156.09 Inuse: 1430
% 155.73/156.09 Deleted: 2879
% 155.73/156.09 Deletedinuse: 6
% 155.73/156.09
% 155.73/156.09 Resimplifying inuse:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09 Resimplifying inuse:
% 155.73/156.09 Done
% 155.73/156.09
% 155.73/156.09
% 155.73/156.09 IntCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------