TSTP Solution File: SWW212+1 by Bliksem---1.12
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Bliksem---1.12
% Problem : SWW212+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : bliksem %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Wed Jul 20 23:21:16 EDT 2022
% Result : Timeout 300.04s 300.55s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWW212+1 : TPTP v8.1.0. Released v5.2.0.
% 0.06/0.12 % Command : bliksem %s
% 0.14/0.34 % Computer : n025.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % DateTime : Mon Jun 6 07:04:33 EDT 2022
% 0.14/0.34 % CPUTime :
% 1.30/1.71 *** allocated 10000 integers for termspace/termends
% 1.30/1.71 *** allocated 10000 integers for clauses
% 1.30/1.71 *** allocated 10000 integers for justifications
% 1.30/1.71 *** allocated 15000 integers for termspace/termends
% 1.30/1.71 *** allocated 22500 integers for termspace/termends
% 1.30/1.71 *** allocated 33750 integers for termspace/termends
% 1.30/1.71 Bliksem 1.12
% 1.30/1.71
% 1.30/1.71
% 1.30/1.71 Automatic Strategy Selection
% 1.30/1.71
% 1.30/1.71 *** allocated 50625 integers for termspace/termends
% 1.30/1.71 *** allocated 75937 integers for termspace/termends
% 1.30/1.71 *** allocated 113905 integers for termspace/termends
% 1.30/1.71 *** allocated 170857 integers for termspace/termends
% 1.30/1.71
% 1.30/1.71 Clauses:
% 1.30/1.71
% 1.30/1.71 { ! hAPP( Y, skol1( X, Y ) ) = hAPP( X, skol1( X, Y ) ), Y = X }.
% 1.30/1.71 { c_SEQ_Osubseq( v_ga____ ) }.
% 1.30/1.71 { c_SEQ_Osubseq( v_f____ ) }.
% 1.30/1.71 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.30/1.71 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.30/1.71 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP(
% 1.30/1.71 c_RealVector_Onorm__class_Onorm( X ), Y ) ), ! Y =
% 1.30/1.71 c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.71 { ! class_RealVector_Oreal__normed__vector( X ), Y =
% 1.30/1.71 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless(
% 1.30/1.71 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP(
% 1.30/1.71 c_RealVector_Onorm__class_Onorm( X ), Y ) ) }.
% 1.30/1.71 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.30/1.71 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP(
% 1.30/1.71 c_RealVector_Onorm__class_Onorm( X ), Y ), c_Groups_Ozero__class_Ozero(
% 1.30/1.71 tc_RealDef_Oreal ) ) }.
% 1.30/1.71 { ! class_RealVector_Oreal__normed__vector( X ), hAPP(
% 1.30/1.71 c_RealVector_Onorm__class_Onorm( X ), c_Groups_Ozero__class_Ozero( X ) )
% 1.30/1.71 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.30/1.71 { ! class_RealVector_Oreal__normed__vector( X ), ! hAPP(
% 1.30/1.71 c_RealVector_Onorm__class_Onorm( X ), Y ) = c_Groups_Ozero__class_Ozero(
% 1.30/1.71 tc_RealDef_Oreal ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.71 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 1.30/1.71 c_Groups_Ozero__class_Ozero( X ), hAPP( c_RealVector_Onorm__class_Onorm(
% 1.30/1.71 X ), Y ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.30/1.71 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.30/1.71 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.30/1.71 X, hAPP( hAPP( c_Groups_Ominus__class_Ominus( X ), Z ), Y ),
% 1.30/1.71 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.71 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.30/1.71 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.30/1.71 ( X ) ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.30/1.71 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.30/1.71 ( X ) ) }.
% 1.30/1.71 { ! class_Groups_Oordered__ab__group__add( X ), !
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.30/1.71 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.30/1.71 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.30/1.71 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex ), hAPP( v_s, X ) )
% 1.30/1.71 , v_r ) }.
% 1.30/1.71 { ! class_Orderings_Opreorder( X ), c_Orderings_Oord__class_Oless__eq( X, Y
% 1.30/1.71 , Y ) }.
% 1.30/1.71 { ! c_SEQ_Osubseq( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y,
% 1.30/1.71 hAPP( X, Y ) ) }.
% 1.30/1.71 { ! class_RealVector_Oreal__normed__vector( X ), hAPP(
% 1.30/1.71 c_RealVector_Onorm__class_Onorm( X ), hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ) = hAPP(
% 1.30/1.71 c_RealVector_Onorm__class_Onorm( X ), hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( X ), Y ), Z ) ) }.
% 1.30/1.71 { ! class_Groups_Oordered__ab__group__add( X ), ! hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( X ), U ), T ) = hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), Y ), !
% 1.30/1.71 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 1.30/1.71 X, Z, Y ) }.
% 1.30/1.71 { ! class_Groups_Oordered__ab__group__add( X ), ! hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( X ), U ), T ) = hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), Y ), !
% 1.30/1.71 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.30/1.71 X, U, T ) }.
% 1.30/1.71 { ! class_Groups_Oordered__ab__group__add( X ), ! hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( X ), U ), T ) = hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), Y ), !
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.30/1.71 { ! class_Groups_Oordered__ab__group__add( X ), ! hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( X ), U ), T ) = hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), Y ), !
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( X, U, T ) }.
% 1.30/1.71 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.30/1.71 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), v_r ) }.
% 1.30/1.71 { c_SEQ_Osubseq( c_Fun_Ocomp( tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat,
% 1.30/1.71 v_f____, v_ga____ ) ) }.
% 1.30/1.71 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.30/1.71 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex ), hAPP( v_s,
% 1.30/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), v_r ) }.
% 1.30/1.71 { ! c_SEQ_Osubseq( X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z
% 1.30/1.71 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( X, Y ), hAPP( X, Z
% 1.30/1.71 ) ) }.
% 1.30/1.71 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol2( X ), skol47( X ) ),
% 1.30/1.71 c_SEQ_Osubseq( X ) }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( X, skol2( X ) ), hAPP
% 1.30/1.71 ( X, skol47( X ) ) ), c_SEQ_Osubseq( X ) }.
% 1.30/1.71 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal ), hAPP(
% 1.30/1.71 c_RealVector_Onorm__class_Onorm( X ), Z ) ), hAPP(
% 1.30/1.71 c_RealVector_Onorm__class_Onorm( X ), Y ) ), hAPP(
% 1.30/1.71 c_RealVector_Onorm__class_Onorm( X ), hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ) ) }.
% 1.30/1.71 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.30/1.71 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP(
% 1.30/1.71 c_RealVector_Onorm__class_Onorm( X ), Y ) ) }.
% 1.30/1.71 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.30/1.71 c_RealVector_Onorm__class_Onorm( X ), Y ), c_Groups_Ozero__class_Ozero(
% 1.30/1.71 tc_RealDef_Oreal ) ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.71 { ! class_RealVector_Oreal__normed__vector( X ), ! Y =
% 1.30/1.71 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq(
% 1.30/1.71 tc_RealDef_Oreal, hAPP( c_RealVector_Onorm__class_Onorm( X ), Y ),
% 1.30/1.71 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.30/1.71 { ! class_Groups_Ozero( X ), ! c_Groups_Ozero__class_Ozero( X ) = Y, Y =
% 1.30/1.71 c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.71 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X ),
% 1.30/1.71 c_Groups_Ozero__class_Ozero( X ) = Y }.
% 1.30/1.71 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.30/1.71 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.30/1.71 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.30/1.71 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.30/1.71 hAPP( Y, U ) ) }.
% 1.30/1.71 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.30/1.71 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.30/1.71 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.30/1.71 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 1.30/1.71 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.30/1.71 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.30/1.71 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.30/1.71 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 1.30/1.71 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.30/1.71 , Y ), ! Z = T, c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.30/1.71 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y
% 1.30/1.71 ), ! Y = T, c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.30/1.71 { ! class_Orderings_Oorder( X ), ! Z = Y, !
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 1.30/1.71 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.30/1.71 ( X, Y, T ), c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.30/1.71 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.30/1.71 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Y = Z }.
% 1.30/1.71 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.30/1.71 , Y ), ! Y = Z, c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.30/1.71 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.30/1.71 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.30/1.71 hAPP( Y, U ) ) }.
% 1.30/1.71 { ! class_Orderings_Opreorder( X ), ! Z = Y,
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.30/1.71 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.30/1.71 ( X, Z, Y ) }.
% 1.30/1.71 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.30/1.71 ( X, Y, Z ) }.
% 1.30/1.71 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.30/1.71 , Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), Z = Y }.
% 1.30/1.71 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.30/1.71 , Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.30/1.71 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.30/1.71 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Z, U ),
% 1.30/1.71 hAPP( Y, U ) ) }.
% 1.30/1.71 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( X, hAPP
% 1.30/1.71 ( Z, skol3( X, Y, Z ) ), hAPP( Y, skol3( X, Y, Z ) ) ),
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }.
% 1.30/1.71 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.30/1.71 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.30/1.71 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.30/1.71 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.30/1.71 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.30/1.71 , ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.30/1.71 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.30/1.71 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.30/1.71 Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 1.30/1.71 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.30/1.71 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.30/1.71 , ! Z = T, c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.30/1.71 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y ),
% 1.30/1.71 ! Y = T, c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.30/1.71 { ! class_Orderings_Oorder( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless(
% 1.30/1.71 X, T, Y ), c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.30/1.71 { ! class_Orderings_Oord( X ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X
% 1.30/1.71 , Y, T ), c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.30/1.71 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.30/1.71 , ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.30/1.71 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.30/1.71 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.30/1.71 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.30/1.71 , ! Y = Z }.
% 1.30/1.71 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.30/1.71 , ! Z = Y }.
% 1.30/1.71 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.30/1.71 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.30/1.71 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.30/1.71 Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.30/1.71 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.30/1.71 , ! Z = Y }.
% 1.30/1.71 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.30/1.71 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.30/1.71 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.30/1.71 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Y = Z }.
% 1.30/1.71 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.30/1.71 ), ! Y = Z, ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.30/1.71 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.30/1.71 ), Z = Y, c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.30/1.71 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.30/1.71 ), c_Orderings_Oord__class_Oless( X, Y, Z ), Z = Y }.
% 1.30/1.71 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.30/1.71 Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.30/1.71 { ! class_Orderings_Olinorder( X ), ! Z = Y, !
% 1.30/1.71 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.30/1.71 { ! class_Orderings_Olinorder( X ), Z = Y, c_Orderings_Oord__class_Oless( X
% 1.30/1.71 , Z, Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.30/1.71 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.30/1.71 Y ), ! Z = Y }.
% 1.30/1.71 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.30/1.71 Z ), ! Z = Y }.
% 1.30/1.71 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.30/1.71 Y ) }.
% 1.30/1.71 { ! class_Groups_Oab__group__add( X ), ! hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( X ), U ), T ) = hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), Y ), ! U = T, Z = Y }.
% 1.30/1.71 { ! class_Groups_Oab__group__add( X ), ! hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( X ), U ), T ) = hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), Y ), ! Z = Y, U = T }.
% 1.30/1.71 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.30/1.71 , Y ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.30/1.71 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.30/1.71 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.30/1.71 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, T ),
% 1.30/1.71 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.30/1.71 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.30/1.71 , ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.30/1.71 c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.30/1.71 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.30/1.71 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, T ),
% 1.30/1.71 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.30/1.71 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.30/1.71 , Y ), Y = Z, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.30/1.71 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.30/1.71 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.30/1.71 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.30/1.71 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.30/1.71 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.30/1.71 , Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.30/1.71 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.30/1.71 , Z, Y ), ! Z = Y, ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.30/1.71 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.30/1.71 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.30/1.71 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.30/1.71 , Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.30/1.71 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.30/1.71 ( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.30/1.71 { ! class_Orderings_Oorder( X ), Z = Y, ! c_Orderings_Oord__class_Oless__eq
% 1.30/1.71 ( X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.30/1.71 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.30/1.71 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ), Z = Y }.
% 1.30/1.71 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.30/1.71 ), ! Z = Y, c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.30/1.71 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.30/1.71 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.30/1.71 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.30/1.71 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.30/1.71 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.30/1.71 , Y ), c_Orderings_Oord__class_Oless( X, Z, Y ), Z = Y }.
% 1.30/1.71 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.30/1.71 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.30/1.71 { ! class_Orderings_Oorder( X ), ! Z = Y, c_Orderings_Oord__class_Oless__eq
% 1.30/1.71 ( X, Z, Y ) }.
% 1.30/1.71 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.30/1.71 Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.30/1.71 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.30/1.71 Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.30/1.71 { ! class_Orderings_Opreorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.30/1.71 , Z, Y ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ),
% 1.30/1.71 c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.30/1.71 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.30/1.71 , c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.30/1.71 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless( X, Z, Y )
% 1.30/1.71 , ! Z = Y }.
% 1.30/1.71 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X, Z
% 1.30/1.71 , Y ), Z = Y, c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.30/1.71 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.30/1.71 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.30/1.71 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless__eq( X, Z
% 1.30/1.71 , Y ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.30/1.71 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.30/1.71 Z ), ! c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.30/1.71 { ! class_Orderings_Olinorder( X ), c_Orderings_Oord__class_Oless( X, Z, Y
% 1.30/1.71 ), c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.30/1.71 { ! class_Orderings_Olinorder( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.30/1.71 , Y, Z ), ! c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.30/1.71 { ! class_Groups_Ogroup__add( X ), ! hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) =
% 1.30/1.71 c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.30/1.71 { ! class_Groups_Ogroup__add( X ), ! Z = Y, hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) =
% 1.30/1.71 c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.71 { ! class_Groups_Oab__group__add( X ), ! Z = Y, hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) =
% 1.30/1.71 c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.71 { ! class_Groups_Oab__group__add( X ), ! hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) =
% 1.30/1.71 c_Groups_Ozero__class_Ozero( X ), Z = Y }.
% 1.30/1.71 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( X ), Y ), Y ) =
% 1.30/1.71 c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.71 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.30/1.71 ) = Y }.
% 1.30/1.71 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.30/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.30/1.71 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), Y = X }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 1.30/1.71 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ),
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), ! Y = X }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), Y = X,
% 1.30/1.71 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ) }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal ), Y ), X ),
% 1.30/1.71 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal ), Y ), X ),
% 1.30/1.71 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ) }.
% 1.30/1.71 { ! class_Orderings_Oorder( X ), ! c_SEQ_Odecseq( X, Y ), !
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z ) ) }.
% 1.30/1.71 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 1.30/1.71 tc_Nat_Onat, skol4( X, Y ), skol48( X, Y ) ), c_SEQ_Odecseq( X, Y ) }.
% 1.30/1.71 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.30/1.71 hAPP( Y, skol48( X, Y ) ), hAPP( Y, skol4( X, Y ) ) ), c_SEQ_Odecseq( X,
% 1.30/1.71 Y ) }.
% 1.30/1.71 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.30/1.71 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.30/1.71 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol5( Z, T ) ) }.
% 1.30/1.71 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.30/1.71 c_RealVector_Onorm__class_Onorm( X ), hAPP( Y, Z ) ), skol5( X, Y ) ) }.
% 1.30/1.71 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.30/1.71 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.30/1.71 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ), !
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.30/1.71 c_RealVector_Onorm__class_Onorm( X ), hAPP( Y, skol49( X, Y, Z ) ) ), Z )
% 1.30/1.71 , c_SEQ_OBseq( X, Y ) }.
% 1.30/1.71 { ! class_Orderings_Oorder( X ), ! c_SEQ_Oincseq( X, Y ), !
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, Z ), hAPP( Y, T ) ) }.
% 1.30/1.71 { ! class_Orderings_Oorder( X ), c_Orderings_Oord__class_Oless__eq(
% 1.30/1.71 tc_Nat_Onat, skol6( X, Y ), skol50( X, Y ) ), c_SEQ_Oincseq( X, Y ) }.
% 1.30/1.71 { ! class_Orderings_Oorder( X ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.30/1.71 hAPP( Y, skol6( X, Y ) ), hAPP( Y, skol50( X, Y ) ) ), c_SEQ_Oincseq( X,
% 1.30/1.71 Y ) }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.30/1.71 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol7( X ), Y ),
% 1.30/1.71 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP(
% 1.30/1.71 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex ), hAPP( v_s, hAPP(
% 1.30/1.71 c_Fun_Ocomp( tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____, v_ga____ ),
% 1.30/1.71 Y ) ) ), hAPP( hAPP( c_Complex_Ocomplex_OComplex, v_x____ ), v_y____ ) )
% 1.30/1.71 ), X ) }.
% 1.30/1.71 { ! class_Orderings_Oorder( X ), ! c_SEQ_Omonoseq( X, Y ), alpha1( X, Y ),
% 1.30/1.71 alpha23( X, Y ) }.
% 1.30/1.71 { ! class_Orderings_Oorder( X ), ! alpha1( X, Y ), c_SEQ_Omonoseq( X, Y ) }
% 1.30/1.71 .
% 1.30/1.71 { ! class_Orderings_Oorder( X ), ! alpha23( X, Y ), c_SEQ_Omonoseq( X, Y )
% 1.30/1.71 }.
% 1.30/1.71 { ! alpha23( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T
% 1.30/1.71 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, T ), hAPP( Y, Z ) ) }
% 1.30/1.71 .
% 1.30/1.71 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol8( X, Y ), skol51( X
% 1.30/1.71 , Y ) ), alpha23( X, Y ) }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, skol51( X, Y ) ), hAPP(
% 1.30/1.71 Y, skol8( X, Y ) ) ), alpha23( X, Y ) }.
% 1.30/1.71 { ! alpha1( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T
% 1.30/1.71 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, Z ), hAPP( Y, T ) ) }
% 1.30/1.71 .
% 1.30/1.71 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol9( X, Y ), skol52( X
% 1.30/1.71 , Y ) ), alpha1( X, Y ) }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( Y, skol9( X, Y ) ), hAPP( Y
% 1.30/1.71 , skol52( X, Y ) ) ), alpha1( X, Y ) }.
% 1.30/1.71 { ! hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) =
% 1.30/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) =
% 1.30/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) =
% 1.30/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ),
% 1.30/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Z ) ) }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.30/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.30/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.30/1.71 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.30/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.30/1.71 tc_Nat_Onat ), X ) }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.30/1.71 ( tc_Nat_Onat ), X ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }
% 1.30/1.71 .
% 1.30/1.71 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.30/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ), ! Y = X }.
% 1.30/1.71 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ),
% 1.30/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 1.30/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.30/1.71 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat )
% 1.30/1.71 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ),
% 1.30/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.30/1.71 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ),
% 1.30/1.71 Y ), X ) ) }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X,
% 1.30/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.30/1.71 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ),
% 1.30/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 1.30/1.71 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), X ) =
% 1.30/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.30/1.71 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 1.30/1.71 X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Z, Y ) }
% 1.30/1.71 .
% 1.30/1.71 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless( tc_fun( T,
% 1.30/1.71 X ), Z, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z )
% 1.30/1.71 }.
% 1.30/1.71 { ! class_Orderings_Oord( X ), ! c_Orderings_Oord__class_Oless__eq( tc_fun
% 1.30/1.71 ( T, X ), Z, Y ), c_Orderings_Oord__class_Oless__eq( tc_fun( T, X ), Y, Z
% 1.30/1.71 ), c_Orderings_Oord__class_Oless( tc_fun( T, X ), Z, Y ) }.
% 1.30/1.71 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 1.30/1.71 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), X ) ), Y ) }.
% 1.30/1.71 { ! class_Orderings_Oorder( X ), ! c_SEQ_Odecseq( X, Y ), c_SEQ_Omonoseq( X
% 1.30/1.71 , Y ) }.
% 1.30/1.71 { ! class_Orderings_Oorder( X ), ! c_SEQ_Oincseq( X, Y ), c_SEQ_Omonoseq( X
% 1.30/1.71 , Y ) }.
% 1.30/1.71 { Y = X, c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.30/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Y ) }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.30/1.71 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.30/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 1.30/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ), Y ) }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, X ) }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X =
% 1.30/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! X = Y }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.30/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), Z ), X ) }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.30/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.30/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.30/1.71 { ! hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) =
% 1.30/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) =
% 1.30/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.30/1.71 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.30/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.30/1.71 tc_Nat_Onat ), X ) }.
% 1.30/1.71 { alpha67( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, Z ),
% 1.30/1.71 hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.30/1.71 { alpha67( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ), hBOOL( hAPP( hAPP
% 1.30/1.71 ( X, Y ), Z ) ) }.
% 1.30/1.71 { ! alpha67( X, Y, Z ), alpha71( X, Y, Z ), Z = Y }.
% 1.30/1.71 { ! alpha67( X, Y, Z ), alpha71( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z
% 1.30/1.71 ) ) }.
% 1.30/1.71 { ! alpha71( X, Y, Z ), alpha67( X, Y, Z ) }.
% 1.30/1.71 { ! Z = Y, hBOOL( hAPP( hAPP( X, Y ), Z ) ), alpha67( X, Y, Z ) }.
% 1.30/1.71 { ! alpha71( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y )
% 1.30/1.71 }.
% 1.30/1.71 { ! alpha71( X, Y, Z ), ! hBOOL( hAPP( hAPP( X, Y ), Z ) ) }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ), hBOOL( hAPP( hAPP(
% 1.30/1.71 X, Y ), Z ) ), alpha71( X, Y, Z ) }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ), Y = X }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ), !
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Z ),
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, Z ) }.
% 1.30/1.71 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Y ) }.
% 1.30/1.71 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, X ) }.
% 1.30/1.71 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, X ) }.
% 1.30/1.71 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ) }.
% 1.30/1.71 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ) }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Y ), Y = X }.
% 1.30/1.71 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.30/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 1.30/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X =
% 1.30/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.30/1.71 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X,
% 1.30/1.71 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! Y = X }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 1.30/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.30/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), Y = X }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.30/1.71 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), Y = X,
% 1.30/1.71 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.30/1.71 { ! Y = X, c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.30/1.71 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ), Y ) }.
% 1.30/1.71 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.30/1.71 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), X ), hAPP( hAPP(
% 1.30/1.71 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Z ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ) = Y }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ), X = Z }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), ! X = Z, hAPP(
% 1.30/1.72 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP
% 1.30/1.72 ( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Z ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, Z ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, Z ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat, X, Z ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.30/1.72 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex ), hAPP(
% 1.30/1.72 hAPP( c_Complex_Ocomplex_OComplex, T ), Z ) ), hAPP( hAPP(
% 1.30/1.72 c_Complex_Ocomplex_OComplex, Y ), X ) ) = hAPP( hAPP(
% 1.30/1.72 c_Complex_Ocomplex_OComplex, hAPP( hAPP( c_Groups_Ominus__class_Ominus(
% 1.30/1.72 tc_RealDef_Oreal ), T ), Y ) ), hAPP( hAPP( c_Groups_Ominus__class_Ominus
% 1.30/1.72 ( tc_RealDef_Oreal ), Z ), X ) ) }.
% 1.30/1.72 { ! hAPP( hAPP( c_Complex_Ocomplex_OComplex, Y ), X ) =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), Y =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.30/1.72 { ! hAPP( hAPP( c_Complex_Ocomplex_OComplex, Y ), X ) =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), X =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.30/1.72 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.30/1.72 c_Complex_Ocomplex_OComplex, Y ), X ) = c_Groups_Ozero__class_Ozero(
% 1.30/1.72 tc_Complex_Ocomplex ) }.
% 1.30/1.72 { c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) = hAPP( hAPP(
% 1.30/1.72 c_Complex_Ocomplex_OComplex, c_Groups_Ozero__class_Ozero(
% 1.30/1.72 tc_RealDef_Oreal ) ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }
% 1.30/1.72 .
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol10( Z, T ) ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), hAPP( Y, Z ) ), skol10( X, Y ) ) }
% 1.30/1.72 .
% 1.30/1.72 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), hAPP( Z, skol11( X, Y, Z ) ) ), Y )
% 1.30/1.72 , c_SEQ_OBseq( X, Z ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, skol12( U, W, V0, T )
% 1.30/1.72 ), c_SEQ_OBseq( X, Y ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), hAPP( Y, skol12( X, Y, Z, T ) ) ),
% 1.30/1.72 Z ), c_SEQ_OBseq( X, Y ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol13( X ), Y ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP(
% 1.30/1.72 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal ), hAPP( c_Complex_OIm,
% 1.30/1.72 hAPP( v_s, hAPP( v_f____, hAPP( v_ga____, Y ) ) ) ) ), v_y____ ) ), X ) }
% 1.30/1.72 .
% 1.30/1.72 { ! class_Groups_Ozero( X ), !
% 1.30/1.72 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.72 { ! class_Groups_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.30/1.72 tc_Polynomial_Opoly( X ) ),
% 1.30/1.72 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize( X, Y ) =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.30/1.72 { c_Complex_Ocomplex_Ocomplex__size( hAPP( hAPP(
% 1.30/1.72 c_Complex_Ocomplex_OComplex, Y ), X ) ) = c_Groups_Ozero__class_Ozero(
% 1.30/1.72 tc_Nat_Onat ) }.
% 1.30/1.72 { hAPP( c_Complex_OIm, c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) )
% 1.30/1.72 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.30/1.72 { ! class_Groups_Oordered__ab__group__add__abs( X ), hAPP(
% 1.30/1.72 c_Groups_Oabs__class_Oabs( X ), hAPP( c_Groups_Oabs__class_Oabs( X ), Y )
% 1.30/1.72 ) = hAPP( c_Groups_Oabs__class_Oabs( X ), Y ) }.
% 1.30/1.72 { hAPP( c_RealVector_Onorm__class_Onorm( tc_RealDef_Oreal ), X ) = hAPP(
% 1.30/1.72 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal ), X ) }.
% 1.30/1.72 { hAPP( c_Complex_OIm, hAPP( hAPP( c_Complex_Ocomplex_OComplex, Y ), X ) )
% 1.30/1.72 = X }.
% 1.30/1.72 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.30/1.72 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal ), hAPP( c_Complex_OIm, X ) )
% 1.30/1.72 , hAPP( c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex ), X ) ) }.
% 1.30/1.72 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! hAPP(
% 1.30/1.72 c_Groups_Oabs__class_Oabs( X ), Y ) = c_Groups_Ozero__class_Ozero( X ), Y
% 1.30/1.72 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.72 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), hAPP( c_Groups_Oabs__class_Oabs( X ), Y
% 1.30/1.72 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.72 { ! class_Groups_Oordered__ab__group__add__abs( X ), hAPP(
% 1.30/1.72 c_Groups_Oabs__class_Oabs( X ), c_Groups_Ozero__class_Ozero( X ) ) =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.72 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( c_Groups_Oabs__class_Oabs( X
% 1.30/1.72 ), Z ), Y ), c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.30/1.72 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, Y, hAPP( c_Groups_Oabs__class_Oabs
% 1.30/1.72 ( X ), Y ) ) }.
% 1.30/1.72 { ! class_Groups_Oordered__ab__group__add__abs( X ), hAPP(
% 1.30/1.72 c_Groups_Oabs__class_Oabs( X ), hAPP( hAPP( c_Groups_Ominus__class_Ominus
% 1.30/1.72 ( X ), Z ), Y ) ) = hAPP( c_Groups_Oabs__class_Oabs( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( X ), Y ), Z ) ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__vector( X ), hAPP(
% 1.30/1.72 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal ), hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), Y ) ) = hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), Y ) }.
% 1.30/1.72 { hAPP( c_Complex_OIm, hAPP( hAPP( c_Groups_Ominus__class_Ominus(
% 1.30/1.72 tc_Complex_Ocomplex ), Y ), X ) ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal ), hAPP( c_Complex_OIm, Y
% 1.30/1.72 ) ), hAPP( c_Complex_OIm, X ) ) }.
% 1.30/1.72 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.30/1.72 ), hAPP( c_Groups_Oabs__class_Oabs( X ), Y ) = Y }.
% 1.30/1.72 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( c_Groups_Oabs__class_Oabs( X
% 1.30/1.72 ), Y ), c_Groups_Ozero__class_Ozero( X ) ), Y =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.72 { ! class_Groups_Oordered__ab__group__add__abs( X ), ! Y =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless__eq( X,
% 1.30/1.72 hAPP( c_Groups_Oabs__class_Oabs( X ), Y ), c_Groups_Ozero__class_Ozero( X
% 1.30/1.72 ) ) }.
% 1.30/1.72 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.30/1.72 hAPP( c_Groups_Oabs__class_Oabs( X ), Y ) ) }.
% 1.30/1.72 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.30/1.72 hAPP( c_Groups_Oabs__class_Oabs( X ), Y ) = Y }.
% 1.30/1.72 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.30/1.72 ( c_Groups_Oabs__class_Oabs( X ), Y ) ), ! Y =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.72 { ! class_Groups_Oordered__ab__group__add__abs( X ), Y =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), hAPP( c_Groups_Oabs__class_Oabs( X ), Y
% 1.30/1.72 ) ) }.
% 1.30/1.72 { ! class_Groups_Oordered__ab__group__add__abs( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Oabs__class_Oabs( X ), Y
% 1.30/1.72 ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.72 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( X ), hAPP( c_Groups_Oabs__class_Oabs( X )
% 1.30/1.72 , Z ) ), hAPP( c_Groups_Oabs__class_Oabs( X ), Y ) ), hAPP(
% 1.30/1.72 c_Groups_Oabs__class_Oabs( X ), hAPP( hAPP( c_Groups_Ominus__class_Ominus
% 1.30/1.72 ( X ), Y ), Z ) ) ) }.
% 1.30/1.72 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( X ), hAPP( c_Groups_Oabs__class_Oabs( X )
% 1.30/1.72 , Z ) ), hAPP( c_Groups_Oabs__class_Oabs( X ), Y ) ), hAPP(
% 1.30/1.72 c_Groups_Oabs__class_Oabs( X ), hAPP( hAPP( c_Groups_Ominus__class_Ominus
% 1.30/1.72 ( X ), Z ), Y ) ) ) }.
% 1.30/1.72 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( c_Groups_Oabs__class_Oabs( X
% 1.30/1.72 ), hAPP( hAPP( c_Groups_Ominus__class_Ominus( X ), hAPP(
% 1.30/1.72 c_Groups_Oabs__class_Oabs( X ), Z ) ), hAPP( c_Groups_Oabs__class_Oabs( X
% 1.30/1.72 ), Y ) ) ), hAPP( c_Groups_Oabs__class_Oabs( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ) ) }.
% 1.30/1.72 { ! hAPP( W, hAPP( U, T ) ) = hAPP( Z, hAPP( Y, X ) ), hAPP( c_Fun_Ocomp(
% 1.30/1.72 V4, V3, V2, W, U ), T ) = hAPP( c_Fun_Ocomp( V1, V3, V0, Z, Y ), X ) }.
% 1.30/1.72 { ! hAPP( hAPP( c_Complex_Ocomplex_OComplex, T ), Z ) = hAPP( hAPP(
% 1.30/1.72 c_Complex_Ocomplex_OComplex, Y ), X ), T = Y }.
% 1.30/1.72 { ! hAPP( hAPP( c_Complex_Ocomplex_OComplex, T ), Z ) = hAPP( hAPP(
% 1.30/1.72 c_Complex_Ocomplex_OComplex, Y ), X ), Z = X }.
% 1.30/1.72 { ! T = Y, ! Z = X, hAPP( hAPP( c_Complex_Ocomplex_OComplex, T ), Z ) =
% 1.30/1.72 hAPP( hAPP( c_Complex_Ocomplex_OComplex, Y ), X ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.30/1.72 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal ), hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), Z ) ), hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), Y ) ) ), hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ) ) }.
% 1.30/1.72 { c_Nat_Osize__class_Osize( tc_Complex_Ocomplex, hAPP( hAPP(
% 1.30/1.72 c_Complex_Ocomplex_OComplex, Y ), X ) ) = c_Groups_Ozero__class_Ozero(
% 1.30/1.72 tc_Nat_Onat ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol14( X ), Y ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP(
% 1.30/1.72 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal ), hAPP( c_Complex_ORe,
% 1.30/1.72 hAPP( v_s, hAPP( v_f____, Y ) ) ) ), v_x____ ) ), X ) }.
% 1.30/1.72 { c_Complex_Ocomplex_Ocomplex__rec( T, Z, hAPP( hAPP(
% 1.30/1.72 c_Complex_Ocomplex_OComplex, Y ), X ) ) = hAPP( hAPP( Z, Y ), X ) }.
% 1.30/1.72 { c_Complex_Ocomplex_Ocomplex__case( T, Z, hAPP( hAPP(
% 1.30/1.72 c_Complex_Ocomplex_OComplex, Y ), X ) ) = hAPP( hAPP( Z, Y ), X ) }.
% 1.30/1.72 { c_SEQ_Omonoseq( tc_RealDef_Oreal, c_COMBB( tc_Complex_Ocomplex,
% 1.30/1.72 tc_RealDef_Oreal, tc_Nat_Onat, c_Complex_OIm, c_COMBB( tc_Nat_Onat,
% 1.30/1.72 tc_Complex_Ocomplex, tc_Nat_Onat, v_s, c_COMBB( tc_Nat_Onat, tc_Nat_Onat
% 1.30/1.72 , tc_Nat_Onat, v_f____, v_ga____ ) ) ) ) }.
% 1.30/1.72 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.30/1.72 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal ), hAPP( c_Complex_OIm, hAPP
% 1.30/1.72 ( v_s, X ) ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal
% 1.30/1.72 ), v_r ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol15( T, U, W ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP(
% 1.30/1.72 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal ), X ), T ) ), skol15( X
% 1.30/1.72 , Y, Z ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, T ) }
% 1.30/1.72 .
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, Z ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP(
% 1.30/1.72 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal ), X ), T ) ), skol15( X
% 1.30/1.72 , Y, Z ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, T, Z ) }
% 1.30/1.72 .
% 1.30/1.72 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), hAPP( Y, skol16( X, Y, Z ) ) ), Z )
% 1.30/1.72 , c_SEQ_OBseq( X, Y ) }.
% 1.30/1.72 { c_SEQ_Omonoseq( tc_RealDef_Oreal, c_COMBB( tc_Complex_Ocomplex,
% 1.30/1.72 tc_RealDef_Oreal, tc_Nat_Onat, c_Complex_ORe, c_COMBB( tc_Nat_Onat,
% 1.30/1.72 tc_Complex_Ocomplex, tc_Nat_Onat, v_s, v_f____ ) ) ) }.
% 1.30/1.72 { ! class_Groups_Oab__group__add( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), U ), T ) ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( X ), U ), Z ) ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( X ), T ), Y ) ) }.
% 1.30/1.72 { ! class_Groups_Oone( X ), ! c_Groups_Oone__class_Oone( X ) = Y, Y =
% 1.30/1.72 c_Groups_Oone__class_Oone( X ) }.
% 1.30/1.72 { ! class_Groups_Oone( X ), ! Y = c_Groups_Oone__class_Oone( X ),
% 1.30/1.72 c_Groups_Oone__class_Oone( X ) = Y }.
% 1.30/1.72 { ! class_Groups_Oab__semigroup__add( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.30/1.72 ( X ), T ), Z ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T
% 1.30/1.72 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) }.
% 1.30/1.72 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), T ), Y ), Z = Y }.
% 1.30/1.72 { ! class_Groups_Ocancel__semigroup__add( X ), ! Z = Y, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), T ), Y ) }.
% 1.30/1.72 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), Z ), T = Y }.
% 1.30/1.72 { ! class_Groups_Ocancel__semigroup__add( X ), ! T = Y, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) }.
% 1.30/1.72 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), T ), Y ), Z = Y }.
% 1.30/1.72 { ! class_Groups_Ocancel__ab__semigroup__add( X ), ! hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), T ), Z ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), T ), Y ), Z = Y }.
% 1.30/1.72 { ! class_Groups_Ocancel__semigroup__add( X ), ! hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Z ), T ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), T ), Z = Y }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__algebra__1( X ), hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), c_Groups_Oone__class_Oone( X ) ) =
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), Z ) ), hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), Y ) ) ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), Z ), Y ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), U ), T ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Z ), U ) ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Y ), T ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP(
% 1.30/1.72 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal ), X ) ),
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) }.
% 1.30/1.72 { ! class_Groups_Omonoid__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.30/1.72 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) = Y }.
% 1.30/1.72 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.30/1.72 = Y }.
% 1.30/1.72 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), Y ), Y =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.72 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), c_Groups_Ozero__class_Ozero( X ) = hAPP
% 1.30/1.72 ( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ) }.
% 1.30/1.72 { ! class_Groups_Omonoid__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.30/1.72 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) = Y }.
% 1.30/1.72 { ! class_Groups_Ocomm__monoid__add( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.30/1.72 = Y }.
% 1.30/1.72 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), T ), Z ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.30/1.72 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, T, Y ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), T ), Z ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) }.
% 1.30/1.72 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), T ), Z ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.30/1.72 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), T ), Z ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) }.
% 1.30/1.72 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Z ), T ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) }.
% 1.30/1.72 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, Z, Y ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), T ), Z ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) }.
% 1.30/1.72 { ! class_Groups_Oordered__ab__semigroup__add( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Z ), U ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) }.
% 1.30/1.72 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Z ), T ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.30/1.72 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), T ), Z ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.30/1.72 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.30/1.72 ( X ), T ), Z ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) )
% 1.30/1.72 , c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.30/1.72 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, T, Y ), c_Orderings_Oord__class_Oless(
% 1.30/1.72 X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Z ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) }.
% 1.30/1.72 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.30/1.72 ( X ), T ), Z ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Y ) )
% 1.30/1.72 , c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.30/1.72 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.30/1.72 X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Z ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) }.
% 1.30/1.72 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.30/1.72 X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), T ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) }.
% 1.30/1.72 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.30/1.72 X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Z ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) }.
% 1.30/1.72 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.30/1.72 ( X, U, T ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Z ), U ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) }.
% 1.30/1.72 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.30/1.72 ( X ), Z ), T ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), T ) )
% 1.30/1.72 , c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.30/1.72 { ! class_Groups_Oordered__ab__semigroup__add__imp__le( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.30/1.72 ( X ), T ), Z ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Y ) )
% 1.30/1.72 , c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.30/1.72 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.30/1.72 ( X ), hAPP( hAPP( c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ), Y ) =
% 1.30/1.72 Z }.
% 1.30/1.72 { ! class_Groups_Ogroup__add( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ), Y ) = Z }.
% 1.30/1.72 { ! hAPP( c_Complex_ORe, Y ) = hAPP( c_Complex_ORe, X ), ! hAPP(
% 1.30/1.72 c_Complex_OIm, Y ) = hAPP( c_Complex_OIm, X ), Y = X }.
% 1.30/1.72 { ! Y = X, hAPP( c_Complex_ORe, Y ) = hAPP( c_Complex_ORe, X ) }.
% 1.30/1.72 { ! Y = X, hAPP( c_Complex_OIm, Y ) = hAPP( c_Complex_OIm, X ) }.
% 1.30/1.72 { ! hAPP( c_Complex_ORe, Y ) = hAPP( c_Complex_ORe, X ), ! hAPP(
% 1.30/1.72 c_Complex_OIm, Y ) = hAPP( c_Complex_OIm, X ), Y = X }.
% 1.30/1.72 { hAPP( c_Complex_ORe, hAPP( hAPP( c_Complex_Ocomplex_OComplex, Y ), X ) )
% 1.30/1.72 = Y }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Z ), Y ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Z ), X ) ) }.
% 1.30/1.72 { ! class_Groups_Oordered__ab__group__add__abs( X ), hAPP(
% 1.30/1.72 c_Groups_Oabs__class_Oabs( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.30/1.72 X ), hAPP( c_Groups_Oabs__class_Oabs( X ), Z ) ), hAPP(
% 1.30/1.72 c_Groups_Oabs__class_Oabs( X ), Y ) ) ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), hAPP( c_Groups_Oabs__class_Oabs( X ), Z
% 1.30/1.72 ) ), hAPP( c_Groups_Oabs__class_Oabs( X ), Y ) ) }.
% 1.30/1.72 { ! c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) =
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), U ), T ) ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( X ), U ), Z ) ) ), hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( X ), T ), Y ) ) ) ) }.
% 1.30/1.72 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), hAPP(
% 1.30/1.72 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal ), X ) ) ) }.
% 1.30/1.72 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.30/1.72 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.30/1.72 ) }.
% 1.30/1.72 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.30/1.72 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.30/1.72 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ) }.
% 1.30/1.72 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), Y ), c_Groups_Ozero__class_Ozero(
% 1.30/1.72 X ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.72 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.30/1.72 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), Y ), c_Groups_Ozero__class_Ozero(
% 1.30/1.72 X ) ) }.
% 1.30/1.72 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.30/1.72 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.30/1.72 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.30/1.72 ( X ), Y ), Z ) ) }.
% 1.30/1.72 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.30/1.72 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.30/1.72 X ), Z ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 1.30/1.72 .
% 1.30/1.72 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.30/1.72 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.30/1.72 X ), Z ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.30/1.72 .
% 1.30/1.72 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.30/1.72 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.30/1.72 X ), Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), ! Z =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.30/1.72 ( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.72 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.30/1.72 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) }.
% 1.30/1.72 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.30/1.72 ), ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) }.
% 1.30/1.72 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.30/1.72 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.30/1.72 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ),
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.72 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.30/1.72 ( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.30/1.72 .
% 1.30/1.72 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.30/1.72 ( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ) ) }.
% 1.30/1.72 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.30/1.72 ( X ), Y ), Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.30/1.72 .
% 1.30/1.72 { ! class_Groups_Olinordered__ab__group__add( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.30/1.72 ( X ), Y ), Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.72 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.30/1.72 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.30/1.72 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.30/1.72 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) }.
% 1.30/1.72 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.30/1.72 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.30/1.72 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), Z ), c_Groups_Ozero__class_Ozero(
% 1.30/1.72 X ) ) }.
% 1.30/1.72 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, U, T ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.30/1.72 ( X ), Z ), U ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), T ) )
% 1.30/1.72 }.
% 1.30/1.72 { ! class_Groups_Oordered__cancel__ab__semigroup__add( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, U, T ), c_Orderings_Oord__class_Oless(
% 1.30/1.72 X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), U ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) }.
% 1.30/1.72 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( c_Complex_ORe
% 1.30/1.72 , X ), hAPP( c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex ), X )
% 1.30/1.72 ) }.
% 1.30/1.72 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( c_Groups_Oabs__class_Oabs( X
% 1.30/1.72 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ), hAPP( hAPP
% 1.30/1.72 ( c_Groups_Oplus__class_Oplus( X ), hAPP( c_Groups_Oabs__class_Oabs( X )
% 1.30/1.72 , Z ) ), hAPP( c_Groups_Oabs__class_Oabs( X ), Y ) ) ) }.
% 1.30/1.72 { hAPP( hAPP( c_Complex_Ocomplex_OComplex, hAPP( c_Complex_ORe, X ) ), hAPP
% 1.30/1.72 ( c_Complex_OIm, X ) ) = X }.
% 1.30/1.72 { hAPP( c_Complex_ORe, c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) )
% 1.30/1.72 = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.30/1.72 { hAPP( c_Complex_ORe, hAPP( hAPP( c_Groups_Ominus__class_Ominus(
% 1.30/1.72 tc_Complex_Ocomplex ), Y ), X ) ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal ), hAPP( c_Complex_ORe, Y
% 1.30/1.72 ) ), hAPP( c_Complex_ORe, X ) ) }.
% 1.30/1.72 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.30/1.72 ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.30/1.72 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.30/1.72 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) }.
% 1.30/1.72 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.30/1.72 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.30/1.72 , Z ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.30/1.72 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) }.
% 1.30/1.72 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.30/1.72 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) }.
% 1.30/1.72 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.30/1.72 ), ! c_Orderings_Oord__class_Oless( X, T, Z ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) }.
% 1.30/1.72 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.30/1.72 ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.30/1.72 ) ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), Z ), c_Groups_Ozero__class_Ozero(
% 1.30/1.72 X ) ) }.
% 1.30/1.72 { ! class_Groups_Oordered__comm__monoid__add( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.30/1.72 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.30/1.72 ) ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), Z ), c_Groups_Ozero__class_Ozero(
% 1.30/1.72 X ) ) }.
% 1.30/1.72 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.30/1.72 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal ), hAPP( c_Complex_ORe, X ) )
% 1.30/1.72 , hAPP( c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex ), X ) ) }.
% 1.30/1.72 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( c_Groups_Oabs__class_Oabs( X
% 1.30/1.72 ), hAPP( hAPP( c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ), hAPP(
% 1.30/1.72 hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( c_Groups_Oabs__class_Oabs(
% 1.30/1.72 X ), Z ) ), hAPP( c_Groups_Oabs__class_Oabs( X ), Y ) ) ) }.
% 1.30/1.72 { ! class_Groups_Oordered__ab__group__add__abs( X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( c_Groups_Oabs__class_Oabs( X
% 1.30/1.72 ), hAPP( hAPP( c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), U ), T ) ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), hAPP( c_Groups_Oabs__class_Oabs( X ),
% 1.30/1.72 hAPP( hAPP( c_Groups_Ominus__class_Ominus( X ), U ), Z ) ) ), hAPP(
% 1.30/1.72 c_Groups_Oabs__class_Oabs( X ), hAPP( hAPP( c_Groups_Ominus__class_Ominus
% 1.30/1.72 ( X ), T ), Y ) ) ) ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), Z ) ), hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), Y ) ) ) }.
% 1.30/1.72 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex ), Y ), X ) ), hAPP(
% 1.30/1.72 hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP(
% 1.30/1.72 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal ), hAPP( c_Complex_ORe, Y
% 1.30/1.72 ) ), hAPP( c_Complex_ORe, X ) ) ) ), hAPP( c_Groups_Oabs__class_Oabs(
% 1.30/1.72 tc_RealDef_Oreal ), hAPP( hAPP( c_Groups_Ominus__class_Ominus(
% 1.30/1.72 tc_RealDef_Oreal ), hAPP( c_Complex_OIm, Y ) ), hAPP( c_Complex_OIm, X )
% 1.30/1.72 ) ) ) ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal ), hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), Z ) ), hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), Y ) ), hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) ) }.
% 1.30/1.72 { c_SEQ_Osubseq( skol17 ) }.
% 1.30/1.72 { c_SEQ_Omonoseq( tc_RealDef_Oreal, c_COMBB( tc_Nat_Onat, tc_RealDef_Oreal
% 1.30/1.72 , tc_Nat_Onat, c_Fun_Ocomp( tc_Nat_Onat, tc_RealDef_Oreal, tc_Nat_Onat,
% 1.30/1.72 c_Fun_Ocomp( tc_Complex_Ocomplex, tc_RealDef_Oreal, tc_Nat_Onat,
% 1.30/1.72 c_Complex_OIm, v_s ), v_f____ ), skol17 ) ) }.
% 1.30/1.72 { c_SEQ_Osubseq( skol18 ) }.
% 1.30/1.72 { c_SEQ_Omonoseq( tc_RealDef_Oreal, c_COMBB( tc_Complex_Ocomplex,
% 1.30/1.72 tc_RealDef_Oreal, tc_Nat_Onat, c_Complex_OIm, c_COMBB( tc_Nat_Onat,
% 1.30/1.72 tc_Complex_Ocomplex, tc_Nat_Onat, v_s, c_COMBB( tc_Nat_Onat, tc_Nat_Onat
% 1.30/1.72 , tc_Nat_Onat, v_f____, skol18 ) ) ) ) }.
% 1.30/1.72 { c_SEQ_Osubseq( skol19 ) }.
% 1.30/1.72 { c_SEQ_Omonoseq( tc_RealDef_Oreal, c_COMBB( tc_Nat_Onat, tc_RealDef_Oreal
% 1.30/1.72 , tc_Nat_Onat, c_Fun_Ocomp( tc_Complex_Ocomplex, tc_RealDef_Oreal,
% 1.30/1.72 tc_Nat_Onat, c_Complex_ORe, v_s ), skol19 ) ) }.
% 1.30/1.72 { c_SEQ_Oconvergent( tc_RealDef_Oreal, c_COMBB( tc_Complex_Ocomplex,
% 1.30/1.72 tc_RealDef_Oreal, tc_Nat_Onat, c_Complex_OIm, c_COMBB( tc_Nat_Onat,
% 1.30/1.72 tc_Complex_Ocomplex, tc_Nat_Onat, v_s, c_COMBB( tc_Nat_Onat, tc_Nat_Onat
% 1.30/1.72 , tc_Nat_Onat, v_f____, v_ga____ ) ) ) ) }.
% 1.30/1.72 { c_SEQ_Oconvergent( tc_RealDef_Oreal, c_COMBB( tc_Complex_Ocomplex,
% 1.30/1.72 tc_RealDef_Oreal, tc_Nat_Onat, c_Complex_ORe, c_COMBB( tc_Nat_Onat,
% 1.30/1.72 tc_Complex_Ocomplex, tc_Nat_Onat, v_s, v_f____ ) ) ) }.
% 1.30/1.72 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.30/1.72 , hAPP( c_Groups_Oabs__class_Oabs( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( X ), T ), Z ) ), Y ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( X ), Z ), Y ), T ) }.
% 1.30/1.72 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.30/1.72 , hAPP( c_Groups_Oabs__class_Oabs( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( X ), T ), Z ) ), Y ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) }.
% 1.30/1.72 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.30/1.72 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( X ), Z ), Y ), T ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Oabs__class_Oabs( X ),
% 1.30/1.72 hAPP( hAPP( c_Groups_Ominus__class_Ominus( X ), T ), Z ) ), Y ) }.
% 1.30/1.72 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.30/1.72 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.30/1.72 c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.30/1.72 { c_Limits_Otendsto( tc_Nat_Onat, tc_RealDef_Oreal, c_COMBB(
% 1.30/1.72 tc_Complex_Ocomplex, tc_RealDef_Oreal, tc_Nat_Onat, c_Complex_OIm,
% 1.30/1.72 c_COMBB( tc_Nat_Onat, tc_Complex_Ocomplex, tc_Nat_Onat, v_s, c_COMBB(
% 1.30/1.72 tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____, v_ga____ ) ) ), v_y____,
% 1.30/1.72 c_Limits_Osequentially ) }.
% 1.30/1.72 { c_Limits_Otendsto( tc_Nat_Onat, tc_RealDef_Oreal, c_COMBB(
% 1.30/1.72 tc_Complex_Ocomplex, tc_RealDef_Oreal, tc_Nat_Onat, c_Complex_ORe,
% 1.30/1.72 c_COMBB( tc_Nat_Onat, tc_Complex_Ocomplex, tc_Nat_Onat, v_s, v_f____ ) )
% 1.30/1.72 , v_x____, c_Limits_Osequentially ) }.
% 1.30/1.72 { ! c_Limits_Otendsto( tc_Nat_Onat, tc_RealDef_Oreal, Y, X,
% 1.30/1.72 c_Limits_Osequentially ), c_Limits_Otendsto( tc_Nat_Onat,
% 1.30/1.72 tc_RealDef_Oreal, c_COMBB( tc_RealDef_Oreal, tc_RealDef_Oreal,
% 1.30/1.72 tc_Nat_Onat, c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal ), Y ), hAPP(
% 1.30/1.72 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal ), X ),
% 1.30/1.72 c_Limits_Osequentially ) }.
% 1.30/1.72 { ! class_RealVector_Ometric__space( X ), c_SEQ_Oconvergent( X, c_COMBK( X
% 1.30/1.72 , tc_Nat_Onat, Y ) ) }.
% 1.30/1.72 { ! class_RealVector_Ometric__space( X ), ! c_Limits_Otendsto( tc_Nat_Onat
% 1.30/1.72 , X, c_COMBK( X, tc_Nat_Onat, Z ), Y, c_Limits_Osequentially ), Z = Y }.
% 1.30/1.72 { ! class_RealVector_Ometric__space( X ), ! Z = Y, c_Limits_Otendsto(
% 1.30/1.72 tc_Nat_Onat, X, c_COMBK( X, tc_Nat_Onat, Z ), Y, c_Limits_Osequentially )
% 1.30/1.72 }.
% 1.30/1.72 { ! class_RealVector_Otopological__space( X ), c_Limits_Otendsto(
% 1.30/1.72 tc_Nat_Onat, X, c_COMBK( X, tc_Nat_Onat, Y ), Y, c_Limits_Osequentially )
% 1.30/1.72 }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! c_Limits_Otendsto(
% 1.30/1.72 tc_Nat_Onat, X, Z, Y, c_Limits_Osequentially ), c_Limits_Otendsto(
% 1.30/1.72 tc_Nat_Onat, tc_RealDef_Oreal, c_COMBB( X, tc_RealDef_Oreal, tc_Nat_Onat
% 1.30/1.72 , c_RealVector_Onorm__class_Onorm( X ), Z ), hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), Y ), c_Limits_Osequentially ) }.
% 1.30/1.72 { ! class_RealVector_Otopological__space( X ), ! c_Limits_Otendsto(
% 1.30/1.72 tc_Nat_Onat, X, Z, Y, c_Limits_Osequentially ), c_Limits_Otendsto(
% 1.30/1.72 tc_Nat_Onat, X, c_COMBB( tc_Nat_Onat, X, tc_Nat_Onat, Z, c_COMBC(
% 1.30/1.72 tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.30/1.72 tc_Nat_Onat ), T ) ), Y, c_Limits_Osequentially ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! c_Limits_Otendsto(
% 1.30/1.72 tc_Nat_Onat, X, Z, Y, c_Limits_Osequentially ), c_Limits_Otendsto(
% 1.30/1.72 tc_Nat_Onat, X, c_COMBC( tc_Nat_Onat, X, X, c_COMBB( X, tc_fun( X, X ),
% 1.30/1.72 tc_Nat_Onat, c_Groups_Oplus__class_Oplus( X ), Z ), T ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), T ), c_Limits_Osequentially ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! c_Limits_Otendsto(
% 1.30/1.72 tc_Nat_Onat, X, Z, Y, c_Limits_Osequentially ), ! c_Limits_Otendsto(
% 1.30/1.72 tc_Nat_Onat, X, U, T, c_Limits_Osequentially ), c_Limits_Otendsto(
% 1.30/1.72 tc_Nat_Onat, X, c_COMBS( tc_Nat_Onat, X, X, c_COMBB( X, tc_fun( X, X ),
% 1.30/1.72 tc_Nat_Onat, c_Groups_Oplus__class_Oplus( X ), Z ), U ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), T ), c_Limits_Osequentially ) }.
% 1.30/1.72 { ! class_RealVector_Otopological__space( X ), ! c_Limits_Otendsto(
% 1.30/1.72 tc_Nat_Onat, X, c_COMBB( tc_Nat_Onat, X, tc_Nat_Onat, Z, c_COMBC(
% 1.30/1.72 tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.30/1.72 tc_Nat_Onat ), T ) ), Y, c_Limits_Osequentially ), c_Limits_Otendsto(
% 1.30/1.72 tc_Nat_Onat, X, Z, Y, c_Limits_Osequentially ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! c_Limits_Otendsto(
% 1.30/1.72 tc_Nat_Onat, X, Z, Y, c_Limits_Osequentially ), ! c_Limits_Otendsto(
% 1.30/1.72 tc_Nat_Onat, X, U, T, c_Limits_Osequentially ), c_Limits_Otendsto(
% 1.30/1.72 tc_Nat_Onat, X, c_COMBS( tc_Nat_Onat, X, X, c_COMBB( X, tc_fun( X, X ),
% 1.30/1.72 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( X ), Z ), U ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( X ), Y ), T ), c_Limits_Osequentially ) }
% 1.30/1.72 .
% 1.30/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! c_Limits_Otendsto(
% 1.30/1.72 tc_Nat_Onat, X, Z, Y, c_Limits_Osequentially ), c_Limits_Otendsto(
% 1.30/1.72 tc_Nat_Onat, X, c_COMBC( tc_Nat_Onat, X, X, c_COMBB( X, tc_fun( X, X ),
% 1.30/1.72 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( X ), Z ), T ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( X ), Y ), T ), c_Limits_Osequentially ) }
% 1.30/1.72 .
% 1.30/1.72 { ! c_SEQ_Odecseq( tc_RealDef_Oreal, X ), ! c_Limits_Otendsto( tc_Nat_Onat
% 1.30/1.72 , tc_RealDef_Oreal, X, Y, c_Limits_Osequentially ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, hAPP( X, Z ) ) }
% 1.30/1.72 .
% 1.30/1.72 { ! c_SEQ_Oincseq( tc_RealDef_Oreal, X ), ! c_Limits_Otendsto( tc_Nat_Onat
% 1.30/1.72 , tc_RealDef_Oreal, X, Y, c_Limits_Osequentially ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( X, Z ), Y ) }
% 1.30/1.72 .
% 1.30/1.72 { ! class_RealVector_Ometric__space( X ), ! c_Limits_Otendsto( tc_Nat_Onat
% 1.30/1.72 , X, Z, Y, c_Limits_Osequentially ), ! c_Limits_Otendsto( tc_Nat_Onat, X
% 1.30/1.72 , Z, T, c_Limits_Osequentially ), Y = T }.
% 1.30/1.72 { ! class_RealVector_Ometric__space( X ), ! c_Limits_Otendsto( tc_Nat_Onat
% 1.30/1.72 , X, Y, Z, c_Limits_Osequentially ), c_SEQ_Oconvergent( X, Y ) }.
% 1.30/1.72 { ! class_RealVector_Ometric__space( X ), ! c_SEQ_Oconvergent( X, Y ),
% 1.30/1.72 c_Limits_Otendsto( tc_Nat_Onat, X, Y, skol20( X, Y ),
% 1.30/1.72 c_Limits_Osequentially ) }.
% 1.30/1.72 { ! class_RealVector_Ometric__space( X ), ! c_Limits_Otendsto( tc_Nat_Onat
% 1.30/1.72 , X, Y, Z, c_Limits_Osequentially ), c_SEQ_Oconvergent( X, Y ) }.
% 1.30/1.72 { ! c_Limits_Otendsto( tc_Nat_Onat, tc_RealDef_Oreal, Y, X,
% 1.30/1.72 c_Limits_Osequentially ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 1.30/1.72 , T, skol21( U, W, T ) ), c_Orderings_Oord__class_Oless__eq(
% 1.30/1.72 tc_RealDef_Oreal, Z, X ) }.
% 1.30/1.72 { ! c_Limits_Otendsto( tc_Nat_Onat, tc_RealDef_Oreal, Y, X,
% 1.30/1.72 c_Limits_Osequentially ), ! c_Orderings_Oord__class_Oless__eq(
% 1.30/1.72 tc_RealDef_Oreal, Z, hAPP( Y, skol21( Y, Z, T ) ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, X ) }.
% 1.30/1.72 { ! c_Limits_Otendsto( tc_Nat_Onat, tc_RealDef_Oreal, Y, X,
% 1.30/1.72 c_Limits_Osequentially ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 1.30/1.72 , T, skol22( U, W, T ) ), c_Orderings_Oord__class_Oless__eq(
% 1.30/1.72 tc_RealDef_Oreal, X, Z ) }.
% 1.30/1.72 { ! c_Limits_Otendsto( tc_Nat_Onat, tc_RealDef_Oreal, Y, X,
% 1.30/1.72 c_Limits_Osequentially ), ! c_Orderings_Oord__class_Oless__eq(
% 1.30/1.72 tc_RealDef_Oreal, hAPP( Y, skol22( Y, Z, T ) ), Z ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Z ) }.
% 1.30/1.72 { ! c_Limits_Otendsto( tc_Nat_Onat, tc_RealDef_Oreal, Y, X,
% 1.30/1.72 c_Limits_Osequentially ), ! c_Limits_Otendsto( tc_Nat_Onat,
% 1.30/1.72 tc_RealDef_Oreal, T, Z, c_Limits_Osequentially ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, skol23( W, V0, U ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Z ) }.
% 1.30/1.72 { ! c_Limits_Otendsto( tc_Nat_Onat, tc_RealDef_Oreal, Y, X,
% 1.30/1.72 c_Limits_Osequentially ), ! c_Limits_Otendsto( tc_Nat_Onat,
% 1.30/1.72 tc_RealDef_Oreal, T, Z, c_Limits_Osequentially ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( Y, skol23( Y,
% 1.30/1.72 T, U ) ), hAPP( T, skol23( Y, T, U ) ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, Z ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! c_Limits_Otendsto(
% 1.30/1.72 tc_Nat_Onat, tc_RealDef_Oreal, c_COMBB( X, tc_RealDef_Oreal, tc_Nat_Onat
% 1.30/1.72 , c_RealVector_Onorm__class_Onorm( X ), Y ), c_Groups_Ozero__class_Ozero
% 1.30/1.72 ( tc_RealDef_Oreal ), c_Limits_Osequentially ), c_Limits_Otendsto(
% 1.30/1.72 tc_Nat_Onat, X, Y, c_Groups_Ozero__class_Ozero( X ),
% 1.30/1.72 c_Limits_Osequentially ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! c_Limits_Otendsto(
% 1.30/1.72 tc_Nat_Onat, X, Y, c_Groups_Ozero__class_Ozero( X ),
% 1.30/1.72 c_Limits_Osequentially ), c_Limits_Otendsto( tc_Nat_Onat,
% 1.30/1.72 tc_RealDef_Oreal, c_COMBB( X, tc_RealDef_Oreal, tc_Nat_Onat,
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), Y ), c_Groups_Ozero__class_Ozero(
% 1.30/1.72 tc_RealDef_Oreal ), c_Limits_Osequentially ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! c_Limits_Otendsto(
% 1.30/1.72 tc_Nat_Onat, X, Z, Y, c_Limits_Osequentially ), ! c_Limits_Otendsto(
% 1.30/1.72 tc_Nat_Onat, X, c_COMBS( tc_Nat_Onat, X, X, c_COMBB( X, tc_fun( X, X ),
% 1.30/1.72 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( X ), T ), Z ),
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), c_Limits_Osequentially ),
% 1.30/1.72 c_Limits_Otendsto( tc_Nat_Onat, X, T, Y, c_Limits_Osequentially ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! c_Limits_Otendsto(
% 1.30/1.72 tc_Nat_Onat, X, Z, Y, c_Limits_Osequentially ), ! c_Limits_Otendsto(
% 1.30/1.72 tc_Nat_Onat, X, c_COMBS( tc_Nat_Onat, X, X, c_COMBB( X, tc_fun( X, X ),
% 1.30/1.72 tc_Nat_Onat, c_Groups_Ominus__class_Ominus( X ), Z ), T ),
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), c_Limits_Osequentially ),
% 1.30/1.72 c_Limits_Otendsto( tc_Nat_Onat, X, T, Y, c_Limits_Osequentially ) }.
% 1.30/1.72 { ! c_Limits_Otendsto( tc_Nat_Onat, tc_RealDef_Oreal, c_COMBB(
% 1.30/1.72 tc_RealDef_Oreal, tc_RealDef_Oreal, tc_Nat_Onat,
% 1.30/1.72 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal ), X ),
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Limits_Osequentially )
% 1.30/1.72 , c_Limits_Otendsto( tc_Nat_Onat, tc_RealDef_Oreal, X,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Limits_Osequentially )
% 1.30/1.72 }.
% 1.30/1.72 { ! c_Limits_Otendsto( tc_Nat_Onat, tc_RealDef_Oreal, X,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Limits_Osequentially )
% 1.30/1.72 , c_Limits_Otendsto( tc_Nat_Onat, tc_RealDef_Oreal, c_COMBB(
% 1.30/1.72 tc_RealDef_Oreal, tc_RealDef_Oreal, tc_Nat_Onat,
% 1.30/1.72 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal ), X ),
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_Limits_Osequentially )
% 1.30/1.72 }.
% 1.30/1.72 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = Y, X
% 1.30/1.72 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.30/1.72 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.30/1.72 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.30/1.72 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), ! X =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.30/1.72 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ),
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) = X }.
% 1.30/1.72 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) = X }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ), X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), ! hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), T ), X ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ), X ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ), Y ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ), X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X = hAPP( hAPP
% 1.30/1.72 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), skol24( X, Y ) ) }.
% 1.30/1.72 { ! X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.30/1.72 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) }.
% 1.30/1.72 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) }.
% 1.30/1.72 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), X ) }.
% 1.30/1.72 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) }.
% 1.30/1.72 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 1.30/1.72 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) }.
% 1.30/1.72 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ), Y ) = X }.
% 1.30/1.72 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ), X ) = Y }.
% 1.30/1.72 { ! class_RealVector_Otopological__space( X ), ! c_Limits_Otendsto(
% 1.30/1.72 tc_Nat_Onat, X, Z, Y, c_Limits_Osequentially ), ! c_SEQ_Osubseq( T ),
% 1.30/1.72 c_Limits_Otendsto( tc_Nat_Onat, X, c_Fun_Ocomp( tc_Nat_Onat, X,
% 1.30/1.72 tc_Nat_Onat, Z, T ), Y, c_Limits_Osequentially ) }.
% 1.30/1.72 { ! c_SEQ_Omonoseq( tc_RealDef_Oreal, X ), ! c_Limits_Otendsto( tc_Nat_Onat
% 1.30/1.72 , tc_RealDef_Oreal, X, Y, c_Limits_Osequentially ), alpha68( X, Y ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, hAPP( X, Z ) ) }
% 1.30/1.72 .
% 1.30/1.72 { ! c_SEQ_Omonoseq( tc_RealDef_Oreal, X ), ! c_Limits_Otendsto( tc_Nat_Onat
% 1.30/1.72 , tc_RealDef_Oreal, X, Y, c_Limits_Osequentially ), alpha68( X, Y ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( X, T ), hAPP(
% 1.30/1.72 X, Z ) ) }.
% 1.30/1.72 { ! alpha68( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.30/1.72 hAPP( X, Z ), Y ) }.
% 1.30/1.72 { ! alpha68( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, T
% 1.30/1.72 ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( X, Z ),
% 1.30/1.72 hAPP( X, T ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( X, skol25( X
% 1.30/1.72 , Y ) ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol53( X )
% 1.30/1.72 , skol56( X ) ), alpha68( X, Y ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( X, skol25( X
% 1.30/1.72 , Y ) ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP
% 1.30/1.72 ( X, skol53( X ) ), hAPP( X, skol56( X ) ) ), alpha68( X, Y ) }.
% 1.30/1.72 { ! c_SEQ_OBseq( tc_RealDef_Oreal, X ), ! c_SEQ_Omonoseq( tc_RealDef_Oreal
% 1.30/1.72 , X ), c_SEQ_Oconvergent( tc_RealDef_Oreal, X ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_Oconvergent( X, Y
% 1.30/1.72 ), ! c_SEQ_Oconvergent( X, Z ), c_SEQ_Oconvergent( X, c_COMBS(
% 1.30/1.72 tc_Nat_Onat, X, X, c_COMBB( X, tc_fun( X, X ), tc_Nat_Onat,
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, Y ),
% 1.30/1.72 c_SEQ_OBseq( X, c_COMBB( tc_Nat_Onat, X, tc_Nat_Onat, Y, c_COMBC(
% 1.30/1.72 tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(
% 1.30/1.72 tc_Nat_Onat ), Z ) ) ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! c_SEQ_OBseq( X, c_COMBB
% 1.30/1.72 ( tc_Nat_Onat, X, tc_Nat_Onat, Y, c_COMBC( tc_Nat_Onat, tc_Nat_Onat,
% 1.30/1.72 tc_Nat_Onat, c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ) ) ),
% 1.30/1.72 c_SEQ_OBseq( X, Y ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.30/1.72 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.30/1.72 Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.30/1.72 tc_Nat_Onat ), X ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.30/1.72 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.30/1.72 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) }.
% 1.30/1.72 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), hAPP( hAPP
% 1.30/1.72 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.30/1.72 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) = Y }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ), Y ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ), Y ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ), X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ), X ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ), Y ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ) = X }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ), Y ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), X ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), Y ) = X }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) = Z, X = hAPP(
% 1.30/1.72 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! X = hAPP(
% 1.30/1.72 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) = Z }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ), Y ) = hAPP( hAPP
% 1.30/1.72 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), Z ) = hAPP(
% 1.30/1.72 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ), Y ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Z ) ), Y ) = hAPP( hAPP
% 1.30/1.72 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), Z ) }.
% 1.30/1.72 { hAPP( c_Complex_ORe, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.30/1.72 tc_Complex_Ocomplex ), Y ), X ) ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( c_Complex_ORe, Y )
% 1.30/1.72 ), hAPP( c_Complex_ORe, X ) ) }.
% 1.30/1.72 { hAPP( c_Complex_OIm, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.30/1.72 tc_Complex_Ocomplex ), Y ), X ) ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( c_Complex_OIm, Y )
% 1.30/1.72 ), hAPP( c_Complex_OIm, X ) ) }.
% 1.30/1.72 { hAPP( c_Complex_OIm, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.30/1.72 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ), hAPP(
% 1.30/1.72 hAPP( c_Complex_Ocomplex_OComplex, T ), Z ) ), hAPP( hAPP(
% 1.30/1.72 c_Complex_Ocomplex_OComplex, Y ), X ) ) = hAPP( hAPP(
% 1.30/1.72 c_Complex_Ocomplex_OComplex, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.30/1.72 tc_RealDef_Oreal ), T ), Y ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.30/1.72 tc_RealDef_Oreal ), Z ), X ) ) }.
% 1.30/1.72 { hAPP( c_Complex_ORe, c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) =
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.30/1.72 { ! hBOOL( hAPP( Z, hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat
% 1.30/1.72 ), Y ), X ) ) ), alpha2( X, Y, Z ) }.
% 1.30/1.72 { ! hBOOL( hAPP( Z, hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat
% 1.30/1.72 ), Y ), X ) ) ), alpha24( X, Y, Z ) }.
% 1.30/1.72 { ! alpha2( X, Y, Z ), ! alpha24( X, Y, Z ), hBOOL( hAPP( Z, hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) ) }.
% 1.30/1.72 { ! alpha24( X, Y, Z ), ! Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.30/1.72 tc_Nat_Onat ), X ), T ), hBOOL( hAPP( Z, T ) ) }.
% 1.30/1.72 { ! hBOOL( hAPP( Z, skol26( T, U, Z ) ) ), alpha24( X, Y, Z ) }.
% 1.30/1.72 { Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), skol26(
% 1.30/1.72 X, Y, Z ) ), alpha24( X, Y, Z ) }.
% 1.30/1.72 { ! alpha2( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X )
% 1.30/1.72 , hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.30/1.72 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), alpha2( X, Y, Z ) }.
% 1.30/1.72 { ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha2
% 1.30/1.72 ( X, Y, Z ) }.
% 1.30/1.72 { ! hBOOL( hAPP( Z, hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat
% 1.30/1.72 ), Y ), X ) ) ), ! alpha3( X, Y, Z ) }.
% 1.30/1.72 { ! hBOOL( hAPP( Z, hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat
% 1.30/1.72 ), Y ), X ) ) ), ! alpha25( X, Y, Z ) }.
% 1.30/1.72 { alpha3( X, Y, Z ), alpha25( X, Y, Z ), hBOOL( hAPP( Z, hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) ) }.
% 1.30/1.72 { ! alpha25( X, Y, Z ), ! hBOOL( hAPP( Z, skol27( T, U, Z ) ) ) }.
% 1.30/1.72 { ! alpha25( X, Y, Z ), Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.30/1.72 tc_Nat_Onat ), X ), skol27( X, Y, Z ) ) }.
% 1.30/1.72 { ! Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), T ),
% 1.30/1.72 hBOOL( hAPP( Z, T ) ), alpha25( X, Y, Z ) }.
% 1.30/1.72 { ! alpha3( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }
% 1.30/1.72 .
% 1.30/1.72 { ! alpha3( X, Y, Z ), ! hBOOL( hAPP( Z, c_Groups_Ozero__class_Ozero(
% 1.30/1.72 tc_Nat_Onat ) ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), hBOOL( hAPP( Z,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha3( X, Y, Z ) }.
% 1.30/1.72 { ! class_Rings_Olinordered__idom( X ), Z = Y,
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, Z, Y ), c_Orderings_Oord__class_Oless(
% 1.30/1.72 X, Y, Z ) }.
% 1.30/1.72 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex ), Y ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ), Y ), X ) ) ), hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex ), X ) ) ) }.
% 1.30/1.72 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal ), hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ), Y ), X ) ) ), hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex ), Y ) ), hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex ), X ) ) }.
% 1.30/1.72 { ! hAPP( hAPP( c_Complex_Ocomplex_OComplex, Y ), X ) =
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), Y =
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.30/1.72 { ! hAPP( hAPP( c_Complex_Ocomplex_OComplex, Y ), X ) =
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ), X =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.30/1.72 { ! Y = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), ! X =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.30/1.72 c_Complex_Ocomplex_OComplex, Y ), X ) = c_Groups_Oone__class_Oone(
% 1.30/1.72 tc_Complex_Ocomplex ) }.
% 1.30/1.72 { c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) = hAPP( hAPP(
% 1.30/1.72 c_Complex_Ocomplex_OComplex, c_Groups_Oone__class_Oone( tc_RealDef_Oreal
% 1.30/1.72 ) ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.30/1.72 { ! class_SEQ_Ocomplete__space( X ), ! c_SEQ_Oconvergent( X, Y ), !
% 1.30/1.72 c_SEQ_Osubseq( Z ), c_SEQ_Oconvergent( X, c_Fun_Ocomp( tc_Nat_Onat, X,
% 1.30/1.72 tc_Nat_Onat, Y, Z ) ) }.
% 1.30/1.72 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ), Y ), X )
% 1.30/1.72 = hAPP( hAPP( c_Complex_Ocomplex_OComplex, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( c_Complex_ORe, Y )
% 1.30/1.72 ), hAPP( c_Complex_ORe, X ) ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.30/1.72 ( tc_RealDef_Oreal ), hAPP( c_Complex_OIm, Y ) ), hAPP( c_Complex_OIm, X
% 1.30/1.72 ) ) ) }.
% 1.30/1.72 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Oone__class_Oone( X ) =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.72 { ! class_Rings_Ozero__neq__one( X ), ! c_Groups_Ozero__class_Ozero( X ) =
% 1.30/1.72 c_Groups_Oone__class_Oone( X ) }.
% 1.30/1.72 { ! class_Rings_Olinordered__idom( X ), hAPP( c_Groups_Oabs__class_Oabs( X
% 1.30/1.72 ), c_Groups_Oone__class_Oone( X ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.30/1.72 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.30/1.72 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless(
% 1.30/1.72 X, T, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) }.
% 1.30/1.72 { ! class_Rings_Olinordered__semidom( X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.30/1.72 c_Groups_Oone__class_Oone( X ) ) }.
% 1.30/1.72 { ! class_Rings_Olinordered__semidom( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.72 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.30/1.72 , c_Groups_Ozero__class_Ozero( X ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.30/1.72 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.30/1.72 ( X, c_Groups_Oone__class_Oone( X ), c_Groups_Ozero__class_Ozero( X ) ) }
% 1.30/1.72 .
% 1.30/1.72 { ! class_Rings_Olinordered__semidom( X ), c_Orderings_Oord__class_Oless( X
% 1.30/1.72 , Y, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ),
% 1.30/1.72 c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.30/1.72 { c_Limits_Otendsto( tc_Nat_Onat, tc_RealDef_Oreal, c_COMBB(
% 1.30/1.72 tc_Complex_Ocomplex, tc_RealDef_Oreal, tc_Nat_Onat, c_Complex_OIm,
% 1.30/1.72 c_COMBB( tc_Nat_Onat, tc_Complex_Ocomplex, tc_Nat_Onat, v_s, c_COMBB(
% 1.30/1.72 tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____, v_ga____ ) ) ), skol28,
% 1.30/1.72 c_Limits_Osequentially ) }.
% 1.30/1.72 { c_Limits_Otendsto( tc_Nat_Onat, tc_RealDef_Oreal, c_COMBB(
% 1.30/1.72 tc_Complex_Ocomplex, tc_RealDef_Oreal, tc_Nat_Onat, c_Complex_OIm,
% 1.30/1.72 c_COMBB( tc_Nat_Onat, tc_Complex_Ocomplex, tc_Nat_Onat, v_s, c_COMBB(
% 1.30/1.72 tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat, v_f____, v_ga____ ) ) ), skol29,
% 1.30/1.72 c_Limits_Osequentially ) }.
% 1.30/1.72 { c_Limits_Otendsto( tc_Nat_Onat, tc_RealDef_Oreal, c_COMBB(
% 1.30/1.72 tc_Complex_Ocomplex, tc_RealDef_Oreal, tc_Nat_Onat, c_Complex_ORe,
% 1.30/1.72 c_COMBB( tc_Nat_Onat, tc_Complex_Ocomplex, tc_Nat_Onat, v_s, v_f____ ) )
% 1.30/1.72 , skol30, c_Limits_Osequentially ) }.
% 1.30/1.72 { c_Limits_Otendsto( tc_Nat_Onat, tc_RealDef_Oreal, c_COMBB(
% 1.30/1.72 tc_Complex_Ocomplex, tc_RealDef_Oreal, tc_Nat_Onat, c_Complex_ORe,
% 1.30/1.72 c_COMBB( tc_Nat_Onat, tc_Complex_Ocomplex, tc_Nat_Onat, v_s, v_f____ ) )
% 1.30/1.72 , skol31, c_Limits_Osequentially ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! c_Limits_Otendsto( T,
% 1.30/1.72 tc_RealDef_Oreal, c_COMBB( X, tc_RealDef_Oreal, T,
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), Z ), c_Groups_Ozero__class_Ozero(
% 1.30/1.72 tc_RealDef_Oreal ), Y ), c_Limits_Otendsto( T, X, Z,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! c_Limits_Otendsto( T, X
% 1.30/1.72 , Z, c_Groups_Ozero__class_Ozero( X ), Y ), c_Limits_Otendsto( T,
% 1.30/1.72 tc_RealDef_Oreal, c_COMBB( X, tc_RealDef_Oreal, T,
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), Z ), c_Groups_Ozero__class_Ozero(
% 1.30/1.72 tc_RealDef_Oreal ), Y ) }.
% 1.30/1.72 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) = hAPP(
% 1.30/1.72 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) }.
% 1.30/1.72 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) ) }.
% 1.30/1.72 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.30/1.72 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) }.
% 1.30/1.72 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) = hAPP
% 1.30/1.72 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ), Y = X }.
% 1.30/1.72 { ! Y = X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y )
% 1.30/1.72 = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), X ) }.
% 1.30/1.72 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) = hAPP
% 1.30/1.72 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ), Z = X }.
% 1.30/1.72 { ! Z = X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y )
% 1.30/1.72 = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), Y ) }.
% 1.30/1.72 { ! c_Limits_Otendsto( T, tc_Complex_Ocomplex, Z, Y, X ), c_Limits_Otendsto
% 1.30/1.72 ( T, tc_RealDef_Oreal, c_COMBB( tc_Complex_Ocomplex, tc_RealDef_Oreal, T
% 1.30/1.72 , c_Complex_ORe, Z ), hAPP( c_Complex_ORe, Y ), X ) }.
% 1.30/1.72 { ! c_Limits_Otendsto( T, tc_Complex_Ocomplex, Z, Y, X ), c_Limits_Otendsto
% 1.30/1.72 ( T, tc_RealDef_Oreal, c_COMBB( tc_Complex_Ocomplex, tc_RealDef_Oreal, T
% 1.30/1.72 , c_Complex_OIm, Z ), hAPP( c_Complex_OIm, Y ), X ) }.
% 1.30/1.72 { ! c_Limits_Otendsto( T, tc_RealDef_Oreal, Z, Y, X ), ! c_Limits_Otendsto
% 1.30/1.72 ( T, tc_RealDef_Oreal, W, U, X ), c_Limits_Otendsto( T,
% 1.30/1.72 tc_Complex_Ocomplex, c_COMBS( T, tc_RealDef_Oreal, tc_Complex_Ocomplex,
% 1.30/1.72 c_COMBB( tc_RealDef_Oreal, tc_fun( tc_RealDef_Oreal, tc_Complex_Ocomplex
% 1.30/1.72 ), T, c_Complex_Ocomplex_OComplex, Z ), W ), hAPP( hAPP(
% 1.30/1.72 c_Complex_Ocomplex_OComplex, Y ), U ), X ) }.
% 1.30/1.72 { ! c_SEQ_Oconvergent( tc_Complex_Ocomplex, X ), c_SEQ_Oconvergent(
% 1.30/1.72 tc_RealDef_Oreal, c_COMBB( tc_Complex_Ocomplex, tc_RealDef_Oreal,
% 1.30/1.72 tc_Nat_Onat, c_Complex_ORe, X ) ) }.
% 1.30/1.72 { ! c_SEQ_Oconvergent( tc_Complex_Ocomplex, X ), c_SEQ_Oconvergent(
% 1.30/1.72 tc_RealDef_Oreal, c_COMBB( tc_Complex_Ocomplex, tc_RealDef_Oreal,
% 1.30/1.72 tc_Nat_Onat, c_Complex_OIm, X ) ) }.
% 1.30/1.72 { ! class_RealVector_Otopological__space( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Limits_Onet( T ), Z, Y ), !
% 1.30/1.72 c_Limits_Otendsto( T, X, W, U, Y ), c_Limits_Otendsto( T, X, W, U, Z ) }
% 1.30/1.72 .
% 1.30/1.72 { ! c_Limits_Otendsto( tc_Nat_Onat, tc_Complex_Ocomplex, Y, X,
% 1.30/1.72 c_Limits_Osequentially ), c_Limits_Otendsto( tc_Nat_Onat,
% 1.30/1.72 tc_RealDef_Oreal, c_COMBB( tc_Complex_Ocomplex, tc_RealDef_Oreal,
% 1.30/1.72 tc_Nat_Onat, c_Complex_ORe, Y ), hAPP( c_Complex_ORe, X ),
% 1.30/1.72 c_Limits_Osequentially ) }.
% 1.30/1.72 { ! c_Limits_Otendsto( tc_Nat_Onat, tc_Complex_Ocomplex, Y, X,
% 1.30/1.72 c_Limits_Osequentially ), c_Limits_Otendsto( tc_Nat_Onat,
% 1.30/1.72 tc_RealDef_Oreal, c_COMBB( tc_Complex_Ocomplex, tc_RealDef_Oreal,
% 1.30/1.72 tc_Nat_Onat, c_Complex_OIm, Y ), hAPP( c_Complex_OIm, X ),
% 1.30/1.72 c_Limits_Osequentially ) }.
% 1.30/1.72 { ! c_Limits_Otendsto( tc_Nat_Onat, tc_RealDef_Oreal, Y, X,
% 1.30/1.72 c_Limits_Osequentially ), ! c_Limits_Otendsto( tc_Nat_Onat,
% 1.30/1.72 tc_RealDef_Oreal, T, Z, c_Limits_Osequentially ), c_Limits_Otendsto(
% 1.30/1.72 tc_Nat_Onat, tc_Complex_Ocomplex, c_COMBS( tc_Nat_Onat, tc_RealDef_Oreal
% 1.30/1.72 , tc_Complex_Ocomplex, c_COMBB( tc_RealDef_Oreal, tc_fun(
% 1.30/1.72 tc_RealDef_Oreal, tc_Complex_Ocomplex ), tc_Nat_Onat,
% 1.30/1.72 c_Complex_Ocomplex_OComplex, Y ), T ), hAPP( hAPP(
% 1.30/1.72 c_Complex_Ocomplex_OComplex, X ), Z ), c_Limits_Osequentially ) }.
% 1.30/1.72 { ! class_RealVector_Otopological__space( X ), c_Limits_Otendsto( T, X,
% 1.30/1.72 c_COMBK( X, T, Z ), Z, Y ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! c_Limits_Otendsto( U, X
% 1.30/1.72 , T, Z, Y ), ! c_Limits_Otendsto( U, X, V0, W, Y ), c_Limits_Otendsto( U
% 1.30/1.72 , X, c_COMBS( U, X, X, c_COMBB( X, tc_fun( X, X ), U,
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), T ), V0 ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Z ), W ), Y ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! c_Limits_Otendsto( U, X
% 1.30/1.72 , T, Z, Y ), ! c_Limits_Otendsto( U, X, V0, W, Y ), c_Limits_Otendsto( U
% 1.30/1.72 , X, c_COMBS( U, X, X, c_COMBB( X, tc_fun( X, X ), U,
% 1.30/1.72 c_Groups_Ominus__class_Ominus( X ), T ), V0 ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( X ), Z ), W ), Y ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! c_Limits_Otendsto( U, X
% 1.30/1.72 , T, Z, Y ), c_Limits_Otendsto( U, tc_RealDef_Oreal, c_COMBB( X,
% 1.30/1.72 tc_RealDef_Oreal, U, c_RealVector_Onorm__class_Onorm( X ), T ), hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), Z ), Y ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! c_Limits_Otendsto( T,
% 1.30/1.72 tc_RealDef_Oreal, c_COMBB( X, tc_RealDef_Oreal, T,
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), Z ), c_Groups_Ozero__class_Ozero(
% 1.30/1.72 tc_RealDef_Oreal ), Y ), c_Limits_Otendsto( T, X, Z,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! c_Limits_Otendsto( T, X
% 1.30/1.72 , Z, c_Groups_Ozero__class_Ozero( X ), Y ), c_Limits_Otendsto( T,
% 1.30/1.72 tc_RealDef_Oreal, c_COMBB( X, tc_RealDef_Oreal, T,
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), Z ), c_Groups_Ozero__class_Ozero(
% 1.30/1.72 tc_RealDef_Oreal ), Y ) }.
% 1.30/1.72 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.30/1.72 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ),
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Y,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.72 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.30/1.72 , Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X
% 1.30/1.72 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Y ), Y ),
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.72 { ! hAPP( c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex ), X ) =
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ), X ),
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ),
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex ), X ),
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) ) ),
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Complex_Ocomplex ), X ), c_Complex_Oii )
% 1.30/1.72 ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex ), X ), c_Complex_Oii
% 1.30/1.72 ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! c_Limits_Otendsto(
% 1.30/1.72 tc_Nat_Onat, X, Z, Y, c_Limits_Osequentially ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), T ), alpha4( X, Y, Z, T
% 1.30/1.72 ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__vector( X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol32( T, U, W ) ),
% 1.30/1.72 c_Limits_Otendsto( tc_Nat_Onat, X, Z, Y, c_Limits_Osequentially ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! alpha4( X, Y, Z, skol32
% 1.30/1.72 ( X, Y, Z ) ), c_Limits_Otendsto( tc_Nat_Onat, X, Z, Y,
% 1.30/1.72 c_Limits_Osequentially ) }.
% 1.30/1.72 { ! alpha4( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat
% 1.30/1.72 , skol33( X, Y, Z, T ), U ), c_Orderings_Oord__class_Oless(
% 1.30/1.72 tc_RealDef_Oreal, hAPP( c_RealVector_Onorm__class_Onorm( X ), hAPP( hAPP
% 1.30/1.72 ( c_Groups_Ominus__class_Ominus( X ), hAPP( Z, U ) ), Y ) ), T ) }.
% 1.30/1.72 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, U, skol54( W, V0, V1, V2
% 1.30/1.72 , U ) ), alpha4( X, Y, Z, T ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( X ), hAPP( Z, skol54( X, Y, Z, T, U ) ) )
% 1.30/1.72 , Y ) ), T ), alpha4( X, Y, Z, T ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! c_Limits_Otendsto(
% 1.30/1.72 tc_Nat_Onat, X, Z, Y, c_Limits_Osequentially ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), T ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, skol34( X, Y, Z, T ), U )
% 1.30/1.72 , c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( X ), hAPP( Z, U ) ), Y ) ), T ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 1.30/1.72 ), c_Orderings_Oord__class_Oless__eq( X, T, skol35( X, U, W, T ) ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, T, V0 ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( Y ), hAPP( Z, V0 ) ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( Y ), hAPP( Z, T ) ) ) ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__vector( Y ), ! class_Orderings_Oord( X
% 1.30/1.72 ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( Y ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( Y ), hAPP( Z, T ) ), hAPP( Z, skol35( X, Y
% 1.30/1.72 , Z, T ) ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( Y ), hAPP( Z, U ) ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( Y ), hAPP( Z, T ) ) ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Limits_Onet( Z ), Y, X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Limits_Onet( Z ), Y, X ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Limits_Onet( Z ), Y, X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Limits_Onet( Z ), X, Y ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Limits_Onet( Z ), Y, X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Limits_Onet( Z ), X, Y ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Limits_Onet( Z ), Y, X ) }.
% 1.30/1.72 { ! c_Complex_Oii = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ) }.
% 1.30/1.72 { ! c_Complex_Oii = c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) }.
% 1.30/1.72 { hAPP( c_Complex_ORe, c_Complex_Oii ) = c_Groups_Ozero__class_Ozero(
% 1.30/1.72 tc_RealDef_Oreal ) }.
% 1.30/1.72 { hAPP( c_Complex_OIm, c_Complex_Oii ) = c_Groups_Oone__class_Oone(
% 1.30/1.72 tc_RealDef_Oreal ) }.
% 1.30/1.72 { c_Complex_Oii = hAPP( hAPP( c_Complex_Ocomplex_OComplex,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.30/1.72 { ! hAPP( hAPP( c_Complex_Ocomplex_OComplex, Y ), X ) = c_Complex_Oii, Y =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.30/1.72 { ! hAPP( hAPP( c_Complex_Ocomplex_OComplex, Y ), X ) = c_Complex_Oii, X =
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.30/1.72 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.30/1.72 c_Complex_Ocomplex_OComplex, Y ), X ) = c_Complex_Oii }.
% 1.30/1.72 { ! class_Groups_Olinordered__ab__group__add( X ), ! hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) = c_Groups_Ozero__class_Ozero
% 1.30/1.72 ( X ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.72 { ! class_Groups_Olinordered__ab__group__add( X ), ! Y =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.30/1.72 ( X ), Y ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.72 { ! class_RealVector_Ometric__space( X ), ! c_SEQ_Oconvergent( X, Y ),
% 1.30/1.72 c_Limits_Otendsto( tc_Nat_Onat, X, Y, c_SEQ_Olim( X, Y ),
% 1.30/1.72 c_Limits_Osequentially ) }.
% 1.30/1.72 { ! class_RealVector_Ometric__space( X ), ! c_Limits_Otendsto( tc_Nat_Onat
% 1.30/1.72 , X, Y, c_SEQ_Olim( X, Y ), c_Limits_Osequentially ), c_SEQ_Oconvergent(
% 1.30/1.72 X, Y ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), X = hAPP( hAPP
% 1.30/1.72 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), skol36( X, Y ) ) }.
% 1.30/1.72 { ! X = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), Z ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.30/1.72 c_RComplete_Onatceiling( hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.30/1.72 tc_RealDef_Oreal ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 1.30/1.72 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.30/1.72 c_RComplete_Onatceiling( X ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat )
% 1.30/1.72 ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP(
% 1.30/1.72 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal ), X ),
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), c_Limits_Otendsto(
% 1.30/1.72 tc_Nat_Onat, tc_RealDef_Oreal, hAPP( c_Power_Opower__class_Opower(
% 1.30/1.72 tc_RealDef_Oreal ), hAPP( c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal ),
% 1.30/1.72 X ) ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.30/1.72 c_Limits_Osequentially ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP(
% 1.30/1.72 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal ), X ),
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), c_Limits_Otendsto(
% 1.30/1.72 tc_Nat_Onat, tc_RealDef_Oreal, hAPP( c_Power_Opower__class_Opower(
% 1.30/1.72 tc_RealDef_Oreal ), X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 1.30/1.72 , c_Limits_Osequentially ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__algebra__1( X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), Z ), Y ) ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), Z ) ), Y ) ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__div__algebra( X ), hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( tc_RealDef_Oreal ), hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), Z ) ), Y ) }.
% 1.30/1.72 { c_RComplete_Onatceiling( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 1.30/1.72 = c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.30/1.72 { ! class_Power_Opower( X ), ! class_RealVector_Oreal__normed__algebra( X )
% 1.30/1.72 , ! c_Limits_Otendsto( tc_Nat_Onat, X, Z, Y, c_Limits_Osequentially ),
% 1.30/1.72 c_Limits_Otendsto( tc_Nat_Onat, X, c_COMBC( tc_Nat_Onat, tc_Nat_Onat, X,
% 1.30/1.72 c_COMBB( X, tc_fun( tc_Nat_Onat, X ), tc_Nat_Onat,
% 1.30/1.72 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), Y ), T ), c_Limits_Osequentially ) }.
% 1.30/1.72 { c_RComplete_Onatceiling( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 1.30/1.72 ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.30/1.72 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatceiling( X )
% 1.30/1.72 ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 1.30/1.72 Y ), c_RComplete_Onatceiling( X ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.30/1.72 c_RComplete_Onatceiling( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.30/1.72 }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling
% 1.30/1.72 ( X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 1.30/1.72 X ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), c_SEQ_Omonoseq(
% 1.30/1.72 tc_RealDef_Oreal, hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal )
% 1.30/1.72 , X ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), c_SEQ_Oconvergent(
% 1.30/1.72 tc_RealDef_Oreal, hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal )
% 1.30/1.72 , X ) ) }.
% 1.30/1.72 { ! class_RealVector_Ometric__space( X ), ! c_Limits_Otendsto( tc_Nat_Onat
% 1.30/1.72 , X, Z, Y, c_Limits_Osequentially ), c_SEQ_Olim( X, Z ) = Y }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), c_SEQ_OBseq(
% 1.30/1.72 tc_RealDef_Oreal, hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal )
% 1.30/1.72 , X ) ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__algebra__1( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), Y ), c_Groups_Oone__class_Oone(
% 1.30/1.72 tc_RealDef_Oreal ) ), c_Limits_Otendsto( tc_Nat_Onat, X, hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.30/1.72 , c_Limits_Osequentially ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X,
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), c_Limits_Otendsto(
% 1.30/1.72 tc_Nat_Onat, tc_RealDef_Oreal, hAPP( c_Power_Opower__class_Opower(
% 1.30/1.72 tc_RealDef_Oreal ), X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal )
% 1.30/1.72 , c_Limits_Osequentially ) }.
% 1.30/1.72 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.30/1.72 ( X, Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), Z ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.72 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), T ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.30/1.72 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.30/1.72 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.30/1.72 ( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 1.30/1.72 hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.30/1.72 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.30/1.72 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 1.30/1.72 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.30/1.72 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.30/1.72 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.30/1.72 ( X, c_Groups_Oone__class_Oone( X ), Y ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ) }.
% 1.30/1.72 { ! class_Rings_Olinordered__semidom( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.30/1.72 ), ! c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Oone__class_Oone
% 1.30/1.72 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.30/1.72 ( tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint )
% 1.30/1.72 , hAPP( c_Groups_Oabs__class_Oabs( tc_Int_Oint ), Y ) ), X ) ), ! Y =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.30/1.72 { Y = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.30/1.72 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 1.30/1.72 hAPP( c_Groups_Oabs__class_Oabs( tc_Int_Oint ), Y ) ), X ) ) }.
% 1.30/1.72 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.30/1.72 tc_Int_Oint ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ),
% 1.30/1.72 hAPP( c_Groups_Oabs__class_Oabs( tc_Int_Oint ), Y ) ), X ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.30/1.72 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.30/1.72 ( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Z ), hAPP( hAPP
% 1.30/1.72 ( c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.30/1.72 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.30/1.72 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), X =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.30/1.72 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.30/1.72 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.30/1.72 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.30/1.72 ), X ) ) }.
% 1.30/1.72 { ! class_Rings_Oring__1__no__zero__divisors( X ), Y =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), Y ), Z ) = c_Groups_Ozero__class_Ozero
% 1.30/1.72 ( X ) }.
% 1.30/1.72 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.30/1.72 = c_Groups_Oone__class_Oone( X ) }.
% 1.30/1.72 { ! class_Rings_Olinordered__idom( X ), hAPP( c_Groups_Oabs__class_Oabs( X
% 1.30/1.72 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP(
% 1.30/1.72 hAPP( c_Power_Opower__class_Opower( X ), hAPP( c_Groups_Oabs__class_Oabs
% 1.30/1.72 ( X ), Z ) ), Y ) }.
% 1.30/1.72 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.30/1.72 tc_Nat_Onat ) ) = Y }.
% 1.30/1.72 { ! class_Rings_Olinordered__semidom( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.30/1.72 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.30/1.72 { ! class_Rings_Olinordered__semidom( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.30/1.72 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.30/1.72 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.30/1.72 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.30/1.72 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless
% 1.30/1.72 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.30/1.72 { ! class_Rings_Olinordered__semidom( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 1.30/1.72 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.30/1.72 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.30/1.72 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.30/1.72 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.30/1.72 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.30/1.72 .
% 1.30/1.72 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.30/1.72 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.30/1.72 , ! hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero(
% 1.30/1.72 tc_Nat_Onat ) }.
% 1.30/1.72 { ! class_Power_Opower( X ), ! class_Rings_Omult__zero( X ), !
% 1.30/1.72 class_Rings_Ono__zero__divisors( X ), ! class_Rings_Ozero__neq__one( X )
% 1.30/1.72 , ! Z = c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero
% 1.30/1.72 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y )
% 1.30/1.72 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.72 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.30/1.72 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), Y ), Z ), T = Z }.
% 1.30/1.72 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.30/1.72 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! T = Z, hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), Y ), T ) = hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), Y ), Z ) }.
% 1.30/1.72 { ! class_Power_Opower( X ), hAPP( hAPP( c_Power_Opower__class_Opower( X )
% 1.30/1.72 , Y ), c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.30/1.72 c_Groups_Oone__class_Oone( X ) }.
% 1.30/1.72 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.30/1.72 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), T ), hAPP( hAPP
% 1.30/1.72 ( c_Power_Opower__class_Opower( X ), Y ), T ) ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.30/1.72 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.30/1.72 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), ! Y =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.30/1.72 ) = c_Groups_Oone__class_Oone( X ) }.
% 1.30/1.72 { ! class_Power_Opower( X ), ! class_Rings_Osemiring__0( X ), Y =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.30/1.72 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.72 { ! class_Rings_Olinordered__idom( X ), c_Orderings_Oord__class_Oless__eq(
% 1.30/1.72 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), hAPP( c_Groups_Oabs__class_Oabs( X ),
% 1.30/1.72 Z ) ), Y ) ) }.
% 1.30/1.72 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.30/1.72 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.30/1.72 c_Groups_Oone__class_Oone( X ), T ), c_Orderings_Oord__class_Oless( X,
% 1.30/1.72 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.30/1.72 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.30/1.72 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.30/1.72 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.30/1.72 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.30/1.72 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.30/1.72 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.30/1.72 ( X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP
% 1.30/1.72 ( c_Power_Opower__class_Opower( X ), Y ), Z ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, Z ) }.
% 1.30/1.72 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.30/1.72 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.30/1.72 ( tc_Nat_Onat, T, Z ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), Y ), T ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.30/1.72 { ! class_Rings_Olinordered__semidom( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), T )
% 1.30/1.72 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), T ), Z ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.30/1.72 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.30/1.72 ( tc_Nat_Onat, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 1.30/1.72 , T, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.30/1.72 hAPP( hAPP( c_Power_Opower__class_Opower( X ), T ), Y ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), T ), Z ) ) }.
% 1.30/1.72 { ! class_Rings_Olinordered__semidom( X ), ! hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), T ), Z ) = hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), Y ), Z ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.30/1.72 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.30/1.72 X ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Z ), T = Y }.
% 1.30/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Ozero__class_Ozero(
% 1.30/1.72 tc_Nat_Onat ) ) = c_Groups_Oone__class_Oone( X ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.30/1.72 c_RComplete_Onatfloor( hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.30/1.72 tc_RealDef_Oreal ), X ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) )
% 1.30/1.72 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ),
% 1.30/1.72 c_RComplete_Onatfloor( X ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) )
% 1.30/1.72 }.
% 1.30/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), Y ), c_Groups_Oone__class_Oone(
% 1.30/1.72 tc_Nat_Onat ) ) = Y }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.30/1.72 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless__eq(
% 1.30/1.72 tc_RealDef_Oreal, X, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.30/1.72 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ),
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 1.30/1.72 c_RComplete_Onatceiling( X ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.30/1.72 tc_Nat_Onat ), Y ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) }.
% 1.30/1.72 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.30/1.72 tc_Nat_Onat, X ) ) }.
% 1.30/1.72 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP(
% 1.30/1.72 c_Groups_Oabs__class_Oabs( tc_Int_Oint ), Y ) ), X ) ) }.
% 1.30/1.72 { ! X = c_RealDef_Oreal( tc_Nat_Onat, c_RComplete_Onatfloor( X ) ),
% 1.30/1.72 c_RComplete_Onatfloor( hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.30/1.72 tc_RealDef_Oreal ), X ), Y ) ) = hAPP( hAPP( c_Power_Opower__class_Opower
% 1.30/1.72 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ), Y ) }.
% 1.30/1.72 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.30/1.72 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Power_Opower__class_Opower(
% 1.30/1.72 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) }.
% 1.30/1.72 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ),
% 1.30/1.72 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), X ) = c_RealDef_Oreal( tc_Nat_Onat,
% 1.30/1.72 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.30/1.72 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ),
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), X ) = X }.
% 1.30/1.72 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) = X }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.30/1.72 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ), X ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.30/1.72 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 1.30/1.72 , c_RComplete_Onatfloor( X ) ) }.
% 1.30/1.72 { hAPP( c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.30/1.72 tc_Nat_Onat, X ) ) = c_RealDef_Oreal( tc_Nat_Onat, X ) }.
% 1.30/1.72 { c_RComplete_Onatfloor( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 1.30/1.72 { ! c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat, X ),
% 1.30/1.72 Y = X }.
% 1.30/1.72 { ! Y = X, c_RealDef_Oreal( tc_Nat_Onat, Y ) = c_RealDef_Oreal( tc_Nat_Onat
% 1.30/1.72 , X ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Y ), X ),
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Y ), X ),
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), ! Y = X }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), Y = X,
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.30/1.72 { c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X,
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Z ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), T ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Z ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), Z ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Z ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ),
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.30/1.72 tc_Int_Oint ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ),
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.30/1.72 tc_Int_Oint ) ), X ) ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) )
% 1.30/1.72 , c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.30/1.72 tc_Int_Oint ) ), X ) ), X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) )
% 1.30/1.72 }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ),
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ),
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.30/1.72 c_Groups_Oabs__class_Oabs( tc_Int_Oint ), X ), c_Groups_Oone__class_Oone
% 1.30/1.72 ( tc_Int_Oint ) ), X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.30/1.72 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.30/1.72 c_Groups_Oabs__class_Oabs( tc_Int_Oint ), X ), c_Groups_Oone__class_Oone
% 1.30/1.72 ( tc_Int_Oint ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), Y = X }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) }.
% 1.30/1.72 { ! Y = X, c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Int_Oint ), X ),
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Int_Oint ), X ),
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ),
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.30/1.72 tc_Int_Oint ), X ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.30/1.72 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_Int_Oint ), X ) }.
% 1.30/1.72 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.30/1.72 tc_Int_Oint ), c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.30/1.72 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.30/1.72 tc_Int_Oint ) ), X ) ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint )
% 1.30/1.72 }.
% 1.30/1.72 { ! c_Groups_Ozero__class_Ozero( tc_Int_Oint ) = c_Groups_Oone__class_Oone
% 1.30/1.72 ( tc_Int_Oint ) }.
% 1.30/1.72 { c_RComplete_Onatceiling( c_RealDef_Oreal( tc_Nat_Onat, X ) ) = X }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, c_RComplete_Onatfloor
% 1.30/1.72 ( X ) ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.30/1.72 c_RealDef_Oreal( tc_Nat_Onat, Y ), X ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.30/1.72 tc_Nat_Onat, Y ), X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y
% 1.30/1.72 , c_RComplete_Onatfloor( X ) ) }.
% 1.30/1.72 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.30/1.72 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ) ), c_Groups_Oone__class_Oone(
% 1.30/1.72 tc_RealDef_Oreal ) ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.30/1.72 tc_Nat_Onat, Y ), X ), c_RComplete_Onatfloor( hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal ), X ), c_RealDef_Oreal(
% 1.30/1.72 tc_Nat_Onat, Y ) ) ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus(
% 1.30/1.72 tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ), Y ) }.
% 1.30/1.72 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal ), X ),
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), c_RealDef_Oreal(
% 1.30/1.72 tc_Nat_Onat, c_RComplete_Onatfloor( X ) ) ) }.
% 1.30/1.72 { ! c_RealDef_Oreal( tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero(
% 1.30/1.72 tc_RealDef_Oreal ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.30/1.72 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RealDef_Oreal(
% 1.30/1.72 tc_Nat_Onat, X ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.30/1.72 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.30/1.72 ) = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.30/1.72 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.30/1.72 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.30/1.72 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.30/1.72 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.30/1.72 tc_Nat_Onat, Y ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 1.30/1.72 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.30/1.72 c_RComplete_Onatfloor( X ), Y ) }.
% 1.30/1.72 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.30/1.72 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.30/1.72 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal
% 1.30/1.72 ( tc_Nat_Onat, X ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.30/1.72 c_RComplete_Onatfloor( hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.30/1.72 tc_RealDef_Oreal ), X ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = hAPP(
% 1.30/1.72 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), c_RComplete_Onatfloor(
% 1.30/1.72 X ) ), Y ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), c_RComplete_Onatfloor( Y ) )
% 1.30/1.72 , c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Y, c_RealDef_Oreal(
% 1.30/1.72 tc_Nat_Onat, X ) ) }.
% 1.30/1.72 { c_RealDef_Oreal( tc_Nat_Onat, c_Groups_Oone__class_Oone( tc_Nat_Onat ) )
% 1.30/1.72 = c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.30/1.72 tc_Nat_Onat, Y ), X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal
% 1.30/1.72 , X, hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ),
% 1.30/1.72 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_Groups_Oone__class_Oone(
% 1.30/1.72 tc_RealDef_Oreal ) ) ), c_RComplete_Onatfloor( X ) = Y }.
% 1.30/1.72 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 1.30/1.72 tc_Nat_Onat, c_RComplete_Onatceiling( X ) ) ) }.
% 1.30/1.72 { c_RComplete_Onatfloor( c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) )
% 1.30/1.72 = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.30/1.72 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) )
% 1.30/1.72 }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatfloor( Y
% 1.30/1.72 ), c_RComplete_Onatfloor( X ) ) }.
% 1.30/1.72 { c_RComplete_Onatfloor( c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) =
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.30/1.72 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), X =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.30/1.72 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.30/1.72 tc_Nat_Onat, X ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), c_RealDef_Oreal
% 1.30/1.72 ( tc_Nat_Onat, hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ),
% 1.30/1.72 X ), Y ) ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal
% 1.30/1.72 ), c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_RealDef_Oreal( tc_Nat_Onat, Y
% 1.30/1.72 ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y, c_RealDef_Oreal
% 1.30/1.72 ( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.30/1.72 c_RComplete_Onatceiling( Y ), X ) }.
% 1.30/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.30/1.72 ( X ), U ), T ) ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y )
% 1.30/1.72 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), U ), Z ) ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) }.
% 1.30/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.30/1.72 ( X ), T ), Z ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ),
% 1.30/1.72 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T ), Y ) ), Z ) }.
% 1.30/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.30/1.72 ( X ), T ), Z ) ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), T
% 1.30/1.72 ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) }.
% 1.30/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.30/1.72 ( X ), T ), Z ) ), Y ) }.
% 1.30/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Z ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ) }.
% 1.30/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), c_RComplete_Onatfloor
% 1.30/1.72 ( X ) = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.30/1.72 tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.30/1.72 ( tc_Nat_Onat ), X ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.30/1.72 tc_Nat_Onat, X ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.30/1.72 tc_Nat_Onat, Y ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.30/1.72 c_RealDef_Oreal( tc_Nat_Onat, X ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.30/1.72 tc_Nat_Onat, Y ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ),
% 1.30/1.72 c_RealDef_Oreal( tc_Nat_Onat, X ) ), c_Orderings_Oord__class_Oless(
% 1.30/1.72 tc_Nat_Onat, Y, X ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.30/1.72 tc_Nat_Onat, Y ), hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.30/1.72 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.30/1.72 tc_Nat_Onat, Y ), hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.30/1.72 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, X ) ),
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_RComplete_Onatceiling(
% 1.30/1.72 X ), Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.30/1.72 c_RealDef_Oreal( tc_Nat_Onat, Y ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 1.30/1.72 tc_Nat_Onat, Y ) ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.30/1.72 c_RComplete_Onatceiling( X ), Y ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.30/1.72 tc_Nat_Onat, Y ), X ), c_RComplete_Onatceiling( hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal ), X ), c_RealDef_Oreal(
% 1.30/1.72 tc_Nat_Onat, Y ) ) ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus(
% 1.30/1.72 tc_Nat_Onat ), c_RComplete_Onatceiling( X ) ), Y ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, c_Groups_Oone__class_Oone
% 1.30/1.72 ( tc_Nat_Onat ), c_RComplete_Onatfloor( X ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.30/1.72 c_RComplete_Onatceiling( hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.30/1.72 tc_RealDef_Oreal ), X ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ) ) = hAPP(
% 1.30/1.72 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), c_RComplete_Onatceiling
% 1.30/1.72 ( X ) ), Y ) }.
% 1.30/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), c_Groups_Ozero__class_Ozero( X ) ), Y )
% 1.30/1.72 = Y }.
% 1.30/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Ozero__class_Ozero( X ) )
% 1.30/1.72 = Y }.
% 1.30/1.72 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.30/1.72 ( X ), ! Z = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ), Y ), Y =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.72 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.30/1.72 ( X ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z = hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.30/1.72 ( tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat )
% 1.30/1.72 , Y ), X ) ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.30/1.72 tc_Nat_Onat ), Y ) }.
% 1.30/1.72 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.30/1.72 tc_Nat_Onat ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_Nat_Onat ), Y
% 1.30/1.72 ), X ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.30/1.72 ( tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( tc_Nat_Onat ), Y ), X ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.30/1.72 tc_Nat_Onat, hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ),
% 1.30/1.72 skol37( X ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, X, c_RealDef_Oreal(
% 1.30/1.72 tc_Nat_Onat, skol37( X ) ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( tc_Int_Oint ), X ), Y ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ), c_Limits_Otendsto(
% 1.30/1.72 tc_Nat_Onat, tc_RealDef_Oreal, c_COMBB( tc_RealDef_Oreal,
% 1.30/1.72 tc_RealDef_Oreal, tc_Nat_Onat, hAPP( c_Rings_Oinverse__class_Odivide(
% 1.30/1.72 tc_RealDef_Oreal ), Y ), hAPP( c_Power_Opower__class_Opower(
% 1.30/1.72 tc_RealDef_Oreal ), X ) ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal
% 1.30/1.72 ), c_Limits_Osequentially ) }.
% 1.30/1.72 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.30/1.72 { ! class_Rings_Odivision__ring__inverse__zero( X ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), Y ), c_Groups_Ozero__class_Ozero( X
% 1.30/1.72 ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.72 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), c_Groups_Ozero__class_Ozero( X ) )
% 1.30/1.72 , Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__field( X ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), c_Groups_Ozero__class_Ozero( X ) )
% 1.30/1.72 , Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__field( X ), Y =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), hAPP( c_RealVector_Onorm__class_Onorm(
% 1.30/1.72 X ), hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) = hAPP
% 1.30/1.72 ( hAPP( c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal ), hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), Z ) ), hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), Y ) ) }.
% 1.30/1.72 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), Y ), c_Groups_Oone__class_Oone( X )
% 1.30/1.72 ) = Y }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__field( X ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), T ), Y ) ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.30/1.72 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), T ), Y ) ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__field( X ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), T ), Y ) ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.30/1.72 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), T ), Y ) ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.30/1.72 { ! class_Fields_Ofield__inverse__zero( X ), !
% 1.30/1.72 class_RealVector_Oreal__normed__field( X ), hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal ), hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), Z ) ), hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), Y ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ), Y = X }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Z ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, Z ) }.
% 1.30/1.72 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, Y ) }.
% 1.30/1.72 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X, X ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), Y ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), X ) ) }.
% 1.30/1.72 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) = hAPP(
% 1.30/1.72 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Y ) }.
% 1.30/1.72 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), X ) ) }.
% 1.30/1.72 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.30/1.72 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__field( X ), ! c_Limits_Otendsto( U, X,
% 1.30/1.72 T, Z, Y ), c_Limits_Otendsto( U, X, c_COMBC( U, X, X, c_COMBB( X, tc_fun
% 1.30/1.72 ( X, X ), U, c_Rings_Oinverse__class_Odivide( X ), T ), W ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), Z ), W ), Y ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__field( X ), ! c_SEQ_Oconvergent( X, Y )
% 1.30/1.72 , c_SEQ_Oconvergent( X, c_COMBC( tc_Nat_Onat, X, X, c_COMBB( X, tc_fun( X
% 1.30/1.72 , X ), tc_Nat_Onat, c_Rings_Oinverse__class_Odivide( X ), Y ), Z ) ) }.
% 1.30/1.72 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.72 , ! hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) =
% 1.30/1.72 c_Groups_Oone__class_Oone( X ), Z = Y }.
% 1.30/1.72 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.72 , ! Z = Y, hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) =
% 1.30/1.72 c_Groups_Oone__class_Oone( X ) }.
% 1.30/1.72 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.72 , hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Y ), Y ) =
% 1.30/1.72 c_Groups_Oone__class_Oone( X ) }.
% 1.30/1.72 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), Y ), Y ) =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.72 { ! class_Rings_Odivision__ring__inverse__zero( X ), Y =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), Y ), Y ) =
% 1.30/1.72 c_Groups_Oone__class_Oone( X ) }.
% 1.30/1.72 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.30/1.72 hAPP( c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), T ), Y ) ), Z ) = hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.30/1.72 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.30/1.72 hAPP( hAPP( c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), c_Groups_Oone__class_Oone( X ) ), Z
% 1.30/1.72 ) ), Y ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal ), Y ), X ) ), alpha5(
% 1.30/1.72 X, Y ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal ), Y ), X ) ), alpha26
% 1.30/1.72 ( X, Y ) }.
% 1.30/1.72 { ! alpha5( X, Y ), ! alpha26( X, Y ), c_Orderings_Oord__class_Oless__eq(
% 1.30/1.72 tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP(
% 1.30/1.72 hAPP( c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.30/1.72 { ! alpha26( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), alpha26( X, Y ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), alpha26( X, Y ) }.
% 1.30/1.72 { ! alpha5( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y
% 1.30/1.72 , c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), alpha5( X, Y ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), alpha5( X, Y ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__field( X ), ! c_Limits_Otendsto( U, X,
% 1.30/1.72 T, Z, Y ), ! c_Limits_Otendsto( U, X, V0, W, Y ), W =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), c_Limits_Otendsto( U, X, c_COMBS( U, X
% 1.30/1.72 , X, c_COMBB( X, tc_fun( X, X ), U, c_Rings_Oinverse__class_Odivide( X )
% 1.30/1.72 , T ), V0 ), hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), W ),
% 1.30/1.72 Y ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__field( X ), ! c_Limits_Otendsto(
% 1.30/1.72 tc_Nat_Onat, X, Z, Y, c_Limits_Osequentially ), c_Limits_Otendsto(
% 1.30/1.72 tc_Nat_Onat, X, c_COMBC( tc_Nat_Onat, X, X, c_COMBB( X, tc_fun( X, X ),
% 1.30/1.72 tc_Nat_Onat, c_Rings_Oinverse__class_Odivide( X ), Z ), T ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), Y ), T ), c_Limits_Osequentially )
% 1.30/1.72 }.
% 1.30/1.72 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Oone__class_Oone(
% 1.30/1.72 tc_Int_Oint ) ) }.
% 1.30/1.72 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Groups_Ozero__class_Ozero(
% 1.30/1.72 tc_Int_Oint ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), X ), Y ) ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__field( X ), ! c_Limits_Otendsto(
% 1.30/1.72 tc_Nat_Onat, X, Z, Y, c_Limits_Osequentially ), ! c_Limits_Otendsto(
% 1.30/1.72 tc_Nat_Onat, X, U, T, c_Limits_Osequentially ), T =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), c_Limits_Otendsto( tc_Nat_Onat, X,
% 1.30/1.72 c_COMBS( tc_Nat_Onat, X, X, c_COMBB( X, tc_fun( X, X ), tc_Nat_Onat,
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), Z ), U ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), Y ), T ), c_Limits_Osequentially )
% 1.30/1.72 }.
% 1.30/1.72 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), Y ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), T ) ) = hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), Y ), T ) ) }.
% 1.30/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.30/1.72 hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), hAPP(
% 1.30/1.72 c_Groups_Oabs__class_Oabs( X ), Z ) ), Y ) = hAPP(
% 1.30/1.72 c_Groups_Oabs__class_Oabs( X ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.30/1.72 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.72 X, Z, Y ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.30/1.72 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.30/1.72 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.72 X, Z, Y ), c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.30/1.72 c_Groups_Oone__class_Oone( X ) ) ) ) }.
% 1.30/1.72 { ! class_Fields_Olinordered__field( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.30/1.72 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.30/1.72 ) ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.30/1.72 X ), hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Y ), Z ) ) }.
% 1.30/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), hAPP(
% 1.30/1.72 c_Groups_Oabs__class_Oabs( X ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), hAPP( c_Groups_Oabs__class_Oabs( X
% 1.30/1.72 ), Z ) ), hAPP( c_Groups_Oabs__class_Oabs( X ), Y ) ) }.
% 1.30/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.30/1.72 hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ), alpha6( X,
% 1.30/1.72 Y, Z ), alpha27( X, Y, Z ) }.
% 1.30/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha6( X, Y, Z
% 1.30/1.72 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.30/1.72 ), hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.30/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha27( X, Y, Z
% 1.30/1.72 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.30/1.72 ), hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.30/1.72 { ! alpha27( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.72 { ! alpha27( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.30/1.72 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) ), alpha27( X, Y, Z ) }.
% 1.30/1.72 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.30/1.72 { ! alpha6( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.30/1.72 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), Y ), alpha6( X, Y, Z ) }.
% 1.30/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ),
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) ), alpha7( X, Y, Z ), alpha28( X, Y, Z )
% 1.30/1.72 }.
% 1.30/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha7( X, Y, Z
% 1.30/1.72 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ),
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha28( X, Y, Z
% 1.30/1.72 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ),
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.72 { ! alpha28( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.72 { ! alpha28( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.30/1.72 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.30/1.72 ( X ), Y ), alpha28( X, Y, Z ) }.
% 1.30/1.72 { ! alpha7( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.30/1.72 { ! alpha7( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.30/1.72 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) ), alpha7( X, Y, Z ) }.
% 1.30/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.30/1.72 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), Z ), T ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), Y ), T ) ) }.
% 1.30/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 1.30/1.72 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), Y ), T ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), Z ), T ) ) }.
% 1.30/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.30/1.72 ( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ), alpha8( X, Y, Z
% 1.30/1.72 ), alpha29( X, Y, Z ) }.
% 1.30/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha8( X, Y, Z
% 1.30/1.72 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.30/1.72 hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.30/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha29( X, Y, Z
% 1.30/1.72 ), c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.30/1.72 hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.30/1.72 { ! alpha29( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.72 { ! alpha29( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.30/1.72 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.30/1.72 ), alpha29( X, Y, Z ) }.
% 1.30/1.72 { ! alpha8( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.30/1.72 { ! alpha8( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.30/1.72 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.30/1.72 ), alpha8( X, Y, Z ) }.
% 1.30/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ),
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) ), alpha9( X, Y, Z ), alpha30( X, Y, Z )
% 1.30/1.72 }.
% 1.30/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha9( X, Y, Z
% 1.30/1.72 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ),
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha30( X, Y, Z
% 1.30/1.72 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ),
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.72 { ! alpha30( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.72 { ! alpha30( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.30/1.72 , ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.30/1.72 ), alpha30( X, Y, Z ) }.
% 1.30/1.72 { ! alpha9( X, Y, Z ), c_Orderings_Oord__class_Oless( X,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.30/1.72 { ! alpha9( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.30/1.72 , ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.30/1.72 ), alpha9( X, Y, Z ) }.
% 1.30/1.72 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.72 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.30/1.72 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 1.30/1.72 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), Y ), Z ) ) }.
% 1.30/1.72 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.72 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.30/1.72 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.30/1.72 ( X, hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Y ), Z ),
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.72 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.72 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.30/1.72 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless
% 1.30/1.72 ( X, hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Y ), Z ),
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.72 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.72 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.30/1.72 ( X, Z, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.30/1.72 ( X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), Y ), Z ) ) }.
% 1.30/1.72 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.72 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless( X,
% 1.30/1.72 hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), T ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), Y ), T ) ) }.
% 1.30/1.72 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.72 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.30/1.72 hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Y ), T ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), Z ), T ) ) }.
% 1.30/1.72 { ! class_Fields_Olinordered__field( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.30/1.72 X ), hAPP( c_Groups_Oabs__class_Oabs( X ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), hAPP( c_Groups_Oabs__class_Oabs( X
% 1.30/1.72 ), Z ) ), hAPP( c_Groups_Oabs__class_Oabs( X ), Y ) ) }.
% 1.30/1.72 { ! class_Fields_Olinordered__field( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.30/1.72 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.30/1.72 , Z ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.30/1.72 ( X ), hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Y ), Z ) ) }.
% 1.30/1.72 { ! class_Fields_Olinordered__field( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.30/1.72 ), ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.30/1.72 ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), Y ), Z ),
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.72 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.72 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.30/1.72 ! c_Orderings_Oord__class_Oless( X, T, U ), c_Orderings_Oord__class_Oless
% 1.30/1.72 ( X, hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Y ), U ), hAPP(
% 1.30/1.72 hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), T ) ) }.
% 1.30/1.72 { ! class_Fields_Olinordered__field( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.30/1.72 ), ! c_Orderings_Oord__class_Oless( X, Y, Z ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.30/1.72 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), Y ), U ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), Z ), T ) ) }.
% 1.30/1.72 { ! class_Fields_Olinordered__field( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.30/1.72 ), ! c_Orderings_Oord__class_Oless__eq( X, Y, Z ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.30/1.72 ! c_Orderings_Oord__class_Oless__eq( X, T, U ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), Y ), U ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), Z ), T ) ) }.
% 1.30/1.72 { ! class_Fields_Olinordered__field( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.30/1.72 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.30/1.72 , Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), Y ), Z ),
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__field( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), Y ), c_Groups_Oone__class_Oone(
% 1.30/1.72 tc_RealDef_Oreal ) ), c_Series_Osums( X, hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), Y ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.30/1.72 hAPP( hAPP( c_Groups_Ominus__class_Ominus( X ), c_Groups_Oone__class_Oone
% 1.30/1.72 ( X ) ), Y ) ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.30/1.72 c_Nat__Transfer_Otsub( X, Y ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus
% 1.30/1.72 ( tc_Int_Oint ), X ), Y ) }.
% 1.30/1.72 { c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.30/1.72 c_Nat__Transfer_Otsub( X, Y ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint
% 1.30/1.72 ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.30/1.72 tc_Nat_Onat ), Y ), c_RComplete_Onatfloor( hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal ), X ), c_RealDef_Oreal
% 1.30/1.72 ( tc_Nat_Onat, Y ) ) ) = c_Divides_Odiv__class_Odiv( tc_Nat_Onat,
% 1.30/1.72 c_RComplete_Onatfloor( X ), Y ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__field( X ), ! c_Series_Osums( X, Z, Y )
% 1.30/1.72 , c_Series_Osums( X, c_COMBC( tc_Nat_Onat, X, X, c_COMBB( X, tc_fun( X, X
% 1.30/1.72 ), tc_Nat_Onat, c_Rings_Oinverse__class_Odivide( X ), Z ), T ), hAPP(
% 1.30/1.72 hAPP( c_Rings_Oinverse__class_Odivide( X ), Y ), T ) ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__field( X ), ! c_Series_Osums( X, Z, Y )
% 1.30/1.72 , c_Series_Osums( X, c_COMBC( tc_Nat_Onat, X, X, c_COMBB( X, tc_fun( X, X
% 1.30/1.72 ), tc_Nat_Onat, c_Rings_Oinverse__class_Odivide( X ), Z ), T ), hAPP(
% 1.30/1.72 hAPP( c_Rings_Oinverse__class_Odivide( X ), Y ), T ) ) }.
% 1.30/1.72 { ! c_Series_Osums( tc_Complex_Ocomplex, Y, X ), c_Series_Osums(
% 1.30/1.72 tc_RealDef_Oreal, c_COMBB( tc_Complex_Ocomplex, tc_RealDef_Oreal,
% 1.30/1.72 tc_Nat_Onat, c_Complex_OIm, Y ), hAPP( c_Complex_OIm, X ) ) }.
% 1.30/1.72 { ! c_Series_Osums( tc_Complex_Ocomplex, Y, X ), c_Series_Osums(
% 1.30/1.72 tc_RealDef_Oreal, c_COMBB( tc_Complex_Ocomplex, tc_RealDef_Oreal,
% 1.30/1.72 tc_Nat_Onat, c_Complex_ORe, Y ), hAPP( c_Complex_ORe, X ) ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! c_Series_Osums( X, Z, Y
% 1.30/1.72 ), ! c_Series_Osums( X, U, T ), c_Series_Osums( X, c_COMBS( tc_Nat_Onat
% 1.30/1.72 , X, X, c_COMBB( X, tc_fun( X, X ), tc_Nat_Onat,
% 1.30/1.72 c_Groups_Ominus__class_Ominus( X ), Z ), U ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( X ), Y ), T ) ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__vector( X ), ! c_Series_Osums( X, Z, Y
% 1.30/1.72 ), ! c_Series_Osums( X, U, T ), c_Series_Osums( X, c_COMBS( tc_Nat_Onat
% 1.30/1.72 , X, X, c_COMBB( X, tc_fun( X, X ), tc_Nat_Onat,
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Z ), U ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), T ) ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__vector( X ), c_Series_Osums( X, c_COMBK
% 1.30/1.72 ( X, tc_Nat_Onat, c_Groups_Ozero__class_Ozero( X ) ),
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.72 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, c_RealDef_Oreal(
% 1.30/1.72 tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ), hAPP(
% 1.30/1.72 hAPP( c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal ),
% 1.30/1.72 c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal( tc_Nat_Onat, X ) )
% 1.30/1.72 ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Nat__Transfer_Otsub( X, Y )
% 1.30/1.72 ) }.
% 1.30/1.72 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.30/1.72 tc_Nat_Onat, Y ) ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) ),
% 1.30/1.72 c_RealDef_Oreal( tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y
% 1.30/1.72 , X ) ) ) ) }.
% 1.30/1.72 { c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.30/1.72 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.30/1.72 tc_Nat_Onat, Y ) ), c_RealDef_Oreal( tc_Nat_Onat, X ) ) ),
% 1.30/1.72 c_RealDef_Oreal( tc_Nat_Onat, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y
% 1.30/1.72 , X ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ),
% 1.30/1.72 c_Nat__Transfer_Otsub( X, Y ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus
% 1.30/1.72 ( tc_Int_Oint ), X ), Y ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Oone__class_Oone(
% 1.30/1.72 tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 1.30/1.72 tc_Nat_Onat, Y, X ), Y ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.30/1.72 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X
% 1.30/1.72 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.30/1.72 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ),
% 1.30/1.72 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, X ) ) }.
% 1.30/1.72 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.72 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.30/1.72 ( X ), Y ), Z ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ),
% 1.30/1.72 c_Divides_Odiv__class_Odiv( X, Z, Y ) ), c_Groups_Oone__class_Oone( X ) )
% 1.30/1.72 }.
% 1.30/1.72 { c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.30/1.72 tc_Int_Oint ), X ) = c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.30/1.72 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.30/1.72 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.30/1.72 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.30/1.72 tc_Int_Oint ), Y ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.30/1.72 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.30/1.72 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.30/1.72 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.30/1.72 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ),
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.30/1.72 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.30/1.72 tc_Int_Oint, Y, X ), c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.30/1.72 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.30/1.72 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, X ) =
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.30/1.72 tc_Int_Oint, X, Y ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.72 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 1.30/1.72 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.30/1.72 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.72 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, Z ),
% 1.30/1.72 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ),
% 1.30/1.72 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.30/1.72 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.30/1.72 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.72 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 1.30/1.72 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.30/1.72 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.72 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.30/1.72 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y
% 1.30/1.72 , c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.30/1.72 tc_Int_Oint, Y, X ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ),
% 1.30/1.72 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.72 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ),
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.30/1.72 tc_Int_Oint ), Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.30/1.72 Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.72 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Z ),
% 1.30/1.72 c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.30/1.72 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.30/1.72 tc_Int_Oint ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, X, Y ) ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.30/1.72 tc_Int_Oint ), Y ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.30/1.72 tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.30/1.72 tc_Int_Oint, X, Y ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.30/1.72 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.30/1.72 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 1.30/1.72 , Y ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.30/1.72 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X
% 1.30/1.72 , Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.30/1.72 tc_Int_Oint, Y, X ) ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.30/1.72 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.30/1.72 tc_Int_Oint, Y, X ) ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.30/1.72 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.30/1.72 tc_Int_Oint, Y, X ) ) }.
% 1.30/1.72 { ! c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha10( X, Y ) }.
% 1.30/1.72 { ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.30/1.72 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.30/1.72 { ! alpha10( X, Y ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) }.
% 1.30/1.72 { ! alpha10( X, Y ), alpha31( X, Y ), alpha44( X, Y ) }.
% 1.30/1.72 { ! alpha31( X, Y ), alpha10( X, Y ) }.
% 1.30/1.72 { ! alpha44( X, Y ), alpha10( X, Y ) }.
% 1.30/1.72 { ! alpha44( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.30/1.72 { ! alpha44( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ), alpha44( X, Y ) }.
% 1.30/1.72 { ! alpha31( X, Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.30/1.72 { ! alpha31( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), alpha31( X, Y ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.30/1.72 ( tc_Int_Oint ), X ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y ),
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.30/1.72 tc_Int_Oint, X, Y ), X ) }.
% 1.30/1.72 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), Y ) = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.72 }.
% 1.30/1.72 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.72 { ! class_Divides_Osemiring__div( X ), c_Divides_Odiv__class_Odiv( X, Y,
% 1.30/1.72 c_Groups_Oone__class_Oone( X ) ) = Y }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.30/1.72 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, Z ),
% 1.30/1.72 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, X, Z ) ) }.
% 1.30/1.72 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.30/1.72 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ), Y ) }.
% 1.30/1.72 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.72 , c_Divides_Odiv__class_Odiv( X, Y, Y ) = c_Groups_Oone__class_Oone( X )
% 1.30/1.72 }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ),
% 1.30/1.72 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.30/1.72 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.72 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.30/1.72 ( X ), Z ), Y ), Y ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ),
% 1.30/1.72 c_Divides_Odiv__class_Odiv( X, Z, Y ) ), c_Groups_Oone__class_Oone( X ) )
% 1.30/1.72 }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ), X ), c_Limits_Otendsto(
% 1.30/1.72 tc_Nat_Onat, tc_RealDef_Oreal, c_COMBB( tc_RealDef_Oreal,
% 1.30/1.72 tc_RealDef_Oreal, tc_Nat_Onat, c_Rings_Oinverse__class_Oinverse(
% 1.30/1.72 tc_RealDef_Oreal ), hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal
% 1.30/1.72 ), X ) ), c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ),
% 1.30/1.72 c_Limits_Osequentially ) }.
% 1.30/1.72 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), c_RealDef_Oreal(
% 1.30/1.72 tc_Nat_Onat, Y ) ), X ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal )
% 1.30/1.72 ), hAPP( hAPP( c_Power_Opower__class_Opower( tc_RealDef_Oreal ), hAPP(
% 1.30/1.72 hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), X ),
% 1.30/1.72 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) ), Y ) ) }.
% 1.30/1.72 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.30/1.72 hAPP( X, Y ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol38( Z, Y
% 1.30/1.72 ), Y ) }.
% 1.30/1.72 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.30/1.72 hAPP( X, Y ) ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.30/1.72 skol38( X, Y ) ), ! hBOOL( hAPP( X, Z ) ) }.
% 1.30/1.72 { hBOOL( hAPP( X, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), ! hBOOL(
% 1.30/1.72 hAPP( X, Y ) ), hBOOL( hAPP( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.30/1.72 tc_Nat_Onat ), skol38( X, Y ) ), c_Groups_Oone__class_Oone( tc_Nat_Onat )
% 1.30/1.72 ) ) ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__algebra( X ), ! c_Series_Osums( X, Z, Y
% 1.30/1.72 ), c_Series_Osums( X, c_COMBB( X, X, tc_Nat_Onat, hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__algebra( X ), ! c_Series_Osums( X, Z, Y
% 1.30/1.72 ), c_Series_Osums( X, c_COMBC( tc_Nat_Onat, X, X, c_COMBB( X, tc_fun( X
% 1.30/1.72 , X ), tc_Nat_Onat, c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP(
% 1.30/1.72 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__algebra( X ), ! c_Series_Osums( X, Z, Y
% 1.30/1.72 ), c_Series_Osums( X, c_COMBB( X, X, tc_Nat_Onat, hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__algebra( X ), ! c_Series_Osums( X, Z, Y
% 1.30/1.72 ), c_Series_Osums( X, c_COMBC( tc_Nat_Onat, X, X, c_COMBB( X, tc_fun( X
% 1.30/1.72 , X ), tc_Nat_Onat, c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP(
% 1.30/1.72 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__div__algebra( X ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), Y ) ), !
% 1.30/1.72 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Z ),
% 1.30/1.72 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Oinverse( X ), Y ) ), hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal ), Z ) ) }.
% 1.30/1.72 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.30/1.72 ( X ), hAPP( c_Rings_Oinverse__class_Oinverse( X ), Y ) ), hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Oinverse( X ), Z ) ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ), hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Oinverse( X ), Y ) ) ), hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Oinverse( X ), Z ) ) }.
% 1.30/1.72 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.30/1.72 hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Oinverse( X ), Y ) ), Y ) =
% 1.30/1.72 c_Groups_Oone__class_Oone( X ) }.
% 1.30/1.72 { ! class_Fields_Ofield__inverse__zero( X ), ! hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Oinverse( X ), Y ) = c_Groups_Oone__class_Oone( X
% 1.30/1.72 ), Y = c_Groups_Oone__class_Oone( X ) }.
% 1.30/1.72 { ! class_Fields_Ofield__inverse__zero( X ), ! Y =
% 1.30/1.72 c_Groups_Oone__class_Oone( X ), hAPP( c_Rings_Oinverse__class_Oinverse( X
% 1.30/1.72 ), Y ) = c_Groups_Oone__class_Oone( X ) }.
% 1.30/1.72 { hAPP( hAPP( c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal ), Y ), X )
% 1.30/1.72 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 1.30/1.72 hAPP( c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal ), X ) ) }.
% 1.30/1.72 { hAPP( hAPP( c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal ), Y ), X )
% 1.30/1.72 = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ),
% 1.30/1.72 hAPP( c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal ), X ) ) }.
% 1.30/1.72 { ! class_Fields_Ofield__inverse__zero( X ), hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Oinverse( X ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), Y ), Z ) }.
% 1.30/1.72 { ! class_Fields_Ofield( X ), hAPP( hAPP( c_Rings_Oinverse__class_Odivide(
% 1.30/1.72 X ), Z ), Y ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), hAPP
% 1.30/1.72 ( c_Rings_Oinverse__class_Oinverse( X ), Y ) ) }.
% 1.30/1.72 { ! class_Fields_Ofield__inverse__zero( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), U ), T ) ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.30/1.72 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 1.30/1.72 { ! class_Rings_Odivision__ring( X ), hAPP( hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Oinverse( X ), Y ) ) }.
% 1.30/1.72 { ! class_Fields_Ofield__inverse__zero( X ), hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Oinverse( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Oinverse( X ), Z ) ), hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Oinverse( X ), Y ) ) }.
% 1.30/1.72 { ! class_Fields_Olinordered__field__inverse__zero( X ), hAPP(
% 1.30/1.72 c_Groups_Oabs__class_Oabs( X ), hAPP( c_Rings_Oinverse__class_Oinverse( X
% 1.30/1.72 ), Y ) ) = hAPP( c_Rings_Oinverse__class_Oinverse( X ), hAPP(
% 1.30/1.72 c_Groups_Oabs__class_Oabs( X ), Y ) ) }.
% 1.30/1.72 { ! class_Fields_Ofield__inverse__zero( X ), hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Oinverse( X ), c_Groups_Ozero__class_Ozero( X ) )
% 1.30/1.72 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__algebra( X ), ! c_SEQ_Oconvergent( X, Y
% 1.30/1.72 ), ! c_SEQ_Oconvergent( X, Z ), c_SEQ_Oconvergent( X, c_COMBS(
% 1.30/1.72 tc_Nat_Onat, X, X, c_COMBB( X, tc_fun( X, X ), tc_Nat_Onat,
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__algebra( X ), ! c_SEQ_Oconvergent( X, Y
% 1.30/1.72 ), c_SEQ_Oconvergent( X, c_COMBC( tc_Nat_Onat, X, X, c_COMBB( X, tc_fun
% 1.30/1.72 ( X, X ), tc_Nat_Onat, c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__algebra( X ), ! c_SEQ_Oconvergent( X, Y
% 1.30/1.72 ), c_SEQ_Oconvergent( X, c_COMBB( X, X, tc_Nat_Onat, hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.30/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.30/1.72 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), T ), Y ) ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.30/1.72 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), Z ), Y ) ), Z ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), Z ), Y ) ) }.
% 1.30/1.72 { ! class_Rings_Odivision__ring__inverse__zero( X ), hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Oinverse( X ), hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.30/1.72 c_Power_Opower__class_Opower( X ), hAPP( c_Rings_Oinverse__class_Oinverse
% 1.30/1.72 ( X ), Z ) ), Y ) }.
% 1.30/1.72 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP( hAPP
% 1.30/1.72 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ), Z = Y }.
% 1.30/1.72 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 1.30/1.72 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) = hAPP(
% 1.30/1.72 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) }.
% 1.30/1.72 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP( hAPP
% 1.30/1.72 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ), Z = Y }.
% 1.30/1.72 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! Z = Y, hAPP( hAPP
% 1.30/1.72 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) = hAPP(
% 1.30/1.72 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) }.
% 1.30/1.72 { ! class_Rings_Olinordered__idom( X ), hAPP( c_Groups_Oabs__class_Oabs( X
% 1.30/1.72 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP(
% 1.30/1.72 hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( c_Groups_Oabs__class_Oabs
% 1.30/1.72 ( X ), Z ) ), hAPP( c_Groups_Oabs__class_Oabs( X ), Y ) ) }.
% 1.30/1.72 { ! class_Rings_Olinordered__idom( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Groups_Oabs__class_Oabs( X )
% 1.30/1.72 , Y ) ), hAPP( c_Groups_Oabs__class_Oabs( X ), Y ) ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) }.
% 1.30/1.72 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.72 , Z = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Oinverse( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Oinverse( X ), Z ) ), hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Oinverse( X ), Y ) ) }.
% 1.30/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.30/1.72 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.30/1.72 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.30/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), Y ) ) }.
% 1.30/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ) }.
% 1.30/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), Z ) }.
% 1.30/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.30/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) }.
% 1.30/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.30/1.72 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 1.30/1.72 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.30/1.72 ( X ), c_Groups_Ozero__class_Ozero( X ) ), Y ) =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.72 { ! class_Rings_Omult__zero( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.30/1.72 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.72 { ! class_Rings_Oring__no__zero__divisors( X ), ! hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.30/1.72 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.72 { ! class_Rings_Oring__no__zero__divisors( X ), ! Z =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.72 { ! class_Rings_Oring__no__zero__divisors( X ), ! Y =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.72 { ! class_Rings_Ono__zero__divisors( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.30/1.72 X ), Z = c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.72 { ! class_Rings_Ono__zero__divisors( X ), ! hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ), Y
% 1.30/1.72 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.30/1.72 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Ozero__class_Ozero( X )
% 1.30/1.72 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.30/1.72 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.30/1.72 c_Groups_Otimes__class_Otimes( X ), c_Groups_Ozero__class_Ozero( X ) ), Y
% 1.30/1.72 ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.72 { hAPP( c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal ),
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ) =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.30/1.72 { ! class_Rings_Odivision__ring( X ), ! hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Oinverse( X ), Z ) = hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Oinverse( X ), Y ), Z =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z
% 1.30/1.72 = Y }.
% 1.30/1.72 { ! class_Rings_Odivision__ring( X ), ! hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Oinverse( X ), Y ) = c_Groups_Ozero__class_Ozero
% 1.30/1.72 ( X ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.72 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.72 , hAPP( c_Rings_Oinverse__class_Oinverse( X ), hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Oinverse( X ), Y ) ) = Y }.
% 1.30/1.72 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.72 , ! hAPP( c_Rings_Oinverse__class_Oinverse( X ), Y ) =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.72 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Oinverse( X ), Y ) = c_Groups_Ozero__class_Ozero
% 1.30/1.72 ( X ), Y = c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.72 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Y =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), hAPP( c_Rings_Oinverse__class_Oinverse
% 1.30/1.72 ( X ), Y ) = c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.72 { ! class_Rings_Odivision__ring__inverse__zero( X ), hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Oinverse( X ), c_Groups_Ozero__class_Ozero( X ) )
% 1.30/1.72 = c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__div__algebra( X ), Y =
% 1.30/1.72 c_Groups_Ozero__class_Ozero( X ), hAPP( c_RealVector_Onorm__class_Onorm(
% 1.30/1.72 X ), hAPP( c_Rings_Oinverse__class_Oinverse( X ), Y ) ) = hAPP(
% 1.30/1.72 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal ), hAPP(
% 1.30/1.72 c_RealVector_Onorm__class_Onorm( X ), Y ) ) }.
% 1.30/1.72 { ! class_RealVector_Oreal__normed__algebra( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP(
% 1.30/1.73 c_RealVector_Onorm__class_Onorm( X ), Z ), Y ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP(
% 1.30/1.73 c_RealVector_Onorm__class_Onorm( X ), U ), T ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP(
% 1.30/1.73 c_RealVector_Onorm__class_Onorm( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ) ) }.
% 1.30/1.73 { ! class_RealVector_Oreal__normed__div__algebra( X ), hAPP(
% 1.30/1.73 c_RealVector_Onorm__class_Onorm( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP(
% 1.30/1.73 c_RealVector_Onorm__class_Onorm( X ), Z ) ), hAPP(
% 1.30/1.73 c_RealVector_Onorm__class_Onorm( X ), Y ) ) }.
% 1.30/1.73 { ! class_RealVector_Oreal__normed__div__algebra( X ), !
% 1.30/1.73 class_Rings_Odivision__ring__inverse__zero( X ), hAPP(
% 1.30/1.73 c_RealVector_Onorm__class_Onorm( X ), hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Y ) ) = hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal ), hAPP(
% 1.30/1.73 c_RealVector_Onorm__class_Onorm( X ), Y ) ) }.
% 1.30/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ), X ) =
% 1.30/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP
% 1.30/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.30/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) =
% 1.30/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y )
% 1.30/1.73 }.
% 1.30/1.73 { ! class_Groups_Oab__semigroup__mult( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.30/1.73 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Z ) = hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Y ), Z = Y }.
% 1.30/1.73 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Z ) = hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Y ), Z = Y }.
% 1.30/1.73 { ! class_Rings_Odivision__ring__inverse__zero( X ), ! Z = Y, hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Z ) = hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Y ) }.
% 1.30/1.73 { ! class_Rings_Odivision__ring__inverse__zero( X ), hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Y ) ) = Y }.
% 1.30/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), ! c_Limits_Otendsto( U, X
% 1.30/1.73 , T, Z, Y ), c_Limits_Otendsto( U, X, c_COMBB( X, X, U, hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), W ), T ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), W ), Z ), Y ) }.
% 1.30/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), ! c_Limits_Otendsto( U, X
% 1.30/1.73 , T, Z, Y ), c_Limits_Otendsto( U, X, c_COMBC( U, X, X, c_COMBB( X,
% 1.30/1.73 tc_fun( X, X ), U, c_Groups_Otimes__class_Otimes( X ), T ), W ), hAPP(
% 1.30/1.73 hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), W ), Y ) }.
% 1.30/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), ! c_Limits_Otendsto( U, X
% 1.30/1.73 , T, Z, Y ), ! c_Limits_Otendsto( U, X, V0, W, Y ), c_Limits_Otendsto( U
% 1.30/1.73 , X, c_COMBS( U, X, X, c_COMBB( X, tc_fun( X, X ), U,
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), V0 ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), W ), Y ) }.
% 1.30/1.73 { ! class_RealVector_Oreal__normed__algebra( X ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.30/1.73 c_RealVector_Onorm__class_Onorm( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP(
% 1.30/1.73 c_RealVector_Onorm__class_Onorm( X ), Z ) ), hAPP(
% 1.30/1.73 c_RealVector_Onorm__class_Onorm( X ), Y ) ) ) }.
% 1.30/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.30/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.30/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.30/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.30/1.73 { ! class_Rings_Osemiring( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X
% 1.30/1.73 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP(
% 1.30/1.73 hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ), Y ) ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), U ), Z ) ), T ) ), Y ) }.
% 1.30/1.73 { ! class_Rings_Ocomm__semiring( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.30/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.30/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.30/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.30/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.30/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), Z ), Y ) ), X ) = hAPP
% 1.30/1.73 ( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ) ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.30/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ),
% 1.30/1.73 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ), X ) = X }.
% 1.30/1.73 { ! class_Rings_Odivision__ring( X ), ! hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) = c_Groups_Oone__class_Oone
% 1.30/1.73 ( X ), hAPP( c_Rings_Oinverse__class_Oinverse( X ), Z ) = Y }.
% 1.30/1.73 { ! class_Rings_Odivision__ring( X ), hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), c_Groups_Oone__class_Oone( X ) ) =
% 1.30/1.73 c_Groups_Oone__class_Oone( X ) }.
% 1.30/1.73 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.30/1.73 = Y }.
% 1.30/1.73 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.30/1.73 = Y }.
% 1.30/1.73 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.30/1.73 = Y }.
% 1.30/1.73 { ! class_Groups_Ocomm__monoid__mult( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.30/1.73 = Y }.
% 1.30/1.73 { X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal ), X ) ), X ) =
% 1.30/1.73 c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) }.
% 1.30/1.73 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.73 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Y ) ) = c_Groups_Oone__class_Oone
% 1.30/1.73 ( X ) }.
% 1.30/1.73 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.73 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Y ) ), Y ) =
% 1.30/1.73 c_Groups_Oone__class_Oone( X ) }.
% 1.30/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), c_Groups_Oone__class_Oone( X ) ), Y )
% 1.30/1.73 = Y }.
% 1.30/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), c_Groups_Oone__class_Oone( X ) )
% 1.30/1.73 = Y }.
% 1.30/1.73 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.30/1.73 ( X ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ), U = Z, T = Y }.
% 1.30/1.73 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.30/1.73 ( X ), ! U = Z, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.30/1.73 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.30/1.73 ( X ), ! T = Y, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.30/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), T ), Y ) ), Z ) }.
% 1.30/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.30/1.73 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.30/1.73 ( X ), U = T, Z = Y, ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP
% 1.30/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.30/1.73 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.30/1.73 ( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), ! U = T }.
% 1.30/1.73 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.30/1.73 ( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), U ), Y ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), ! Z = Y }.
% 1.30/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.30/1.73 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.73 , Z = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( c_Rings_Oinverse__class_Oinverse
% 1.30/1.73 ( X ), Y ) ), hAPP( c_Rings_Oinverse__class_Oinverse( X ), Z ) ) = hAPP(
% 1.30/1.73 hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Y ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), Y ), Z ) ) ), hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Z ) ) }.
% 1.30/1.73 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.73 , Z = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( X ), hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Y ) ), hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Z ) ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Y ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( X ), Z ), Y ) ) ), hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Z ) ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.30/1.73 hAPP( c_Rings_Oinverse__class_Oinverse( X ), Y ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.30/1.73 ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.30/1.73 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.30/1.73 ), hAPP( c_Rings_Oinverse__class_Oinverse( X ), Y ) ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Y ), c_Groups_Ozero__class_Ozero(
% 1.30/1.73 X ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.30/1.73 ), c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Y ), c_Groups_Ozero__class_Ozero(
% 1.30/1.73 X ) ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.30/1.73 ( c_Rings_Oinverse__class_Oinverse( X ), Y ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.30/1.73 .
% 1.30/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.30/1.73 ( c_Rings_Oinverse__class_Oinverse( X ), Y ) ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, hAPP( c_Rings_Oinverse__class_Oinverse
% 1.30/1.73 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ) }
% 1.30/1.73 .
% 1.30/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, hAPP( c_Rings_Oinverse__class_Oinverse
% 1.30/1.73 ( X ), Y ), c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.73 X, c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.30/1.73 X, c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Y ) ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.73 X, c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Y ) ), Y =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.73 X, Y, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless(
% 1.30/1.73 X, hAPP( c_Rings_Oinverse__class_Oinverse( X ), Y ),
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.73 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 1.30/1.73 hAPP( c_Rings_Oinverse__class_Oinverse( X ), Y ), hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Z ) ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.73 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.30/1.73 hAPP( c_Rings_Oinverse__class_Oinverse( X ), Y ), hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Z ) ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.73 X, hAPP( c_Rings_Oinverse__class_Oinverse( X ), Y ),
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.73 , c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.30/1.73 }.
% 1.30/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.73 X, hAPP( c_Rings_Oinverse__class_Oinverse( X ), Z ), hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Y ) ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.73 X, hAPP( c_Rings_Oinverse__class_Oinverse( X ), Z ), hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Y ) ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.30/1.73 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.73 , hAPP( c_Rings_Oinverse__class_Oinverse( X ), hAPP( hAPP(
% 1.30/1.73 c_Power_Opower__class_Opower( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.30/1.73 c_Power_Opower__class_Opower( X ), hAPP( c_Rings_Oinverse__class_Oinverse
% 1.30/1.73 ( X ), Y ) ), Z ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field( X ), Y = c_Groups_Ozero__class_Ozero(
% 1.30/1.73 X ), hAPP( c_Groups_Oabs__class_Oabs( X ), hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Y ) ) = hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), hAPP( c_Groups_Oabs__class_Oabs( X
% 1.30/1.73 ), Y ) ) }.
% 1.30/1.73 { ! class_Fields_Ofield( X ), hAPP( c_Rings_Oinverse__class_Oinverse( X ),
% 1.30/1.73 Y ) = hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ),
% 1.30/1.73 c_Groups_Oone__class_Oone( X ) ), Y ) }.
% 1.30/1.73 { ! class_Rings_Odivision__ring( X ), hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Y ) = hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), c_Groups_Oone__class_Oone( X ) ), Y
% 1.30/1.73 ) }.
% 1.30/1.73 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.30/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.30/1.73 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.73 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 1.30/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.30/1.73 X ), Y ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.30/1.73 ( X ) ) }.
% 1.30/1.73 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.30/1.73 , c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.30/1.73 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.30/1.73 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.30/1.73 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.30/1.73 , Z, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.30/1.73 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.30/1.73 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.30/1.73 { ! class_Rings_Oordered__semiring( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.30/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.30/1.73 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.30/1.73 { ! class_Rings_Oordered__semiring( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.30/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.30/1.73 X ), U ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.30/1.73 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.30/1.73 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.30/1.73 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.30/1.73 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.30/1.73 , Z, Y ), ! c_Orderings_Oord__class_Oless__eq( X, T,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.30/1.73 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.30/1.73 { ! class_Rings_Oordered__comm__semiring( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.30/1.73 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.30/1.73 { ! class_Rings_Oordered__semiring( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.30/1.73 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.30/1.73 { ! class_Rings_Oordered__semiring( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.30/1.73 ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.30/1.73 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.30/1.73 , Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X )
% 1.30/1.73 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X
% 1.30/1.73 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.30/1.73 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.30/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.30/1.73 X ), Z ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.30/1.73 ( X ) ) }.
% 1.30/1.73 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.30/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.30/1.73 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ),
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.73 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.30/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.30/1.73 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ),
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.73 { ! class_Rings_Oordered__cancel__semiring( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.30/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.30/1.73 X ), Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.30/1.73 ( X ) ), alpha11( X, Y, Z ), alpha32( X, Y, Z ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha11( X, Y, Z ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.30/1.73 ( X ) ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha32( X, Y, Z ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.30/1.73 ( X ) ) }.
% 1.30/1.73 { ! alpha32( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.73 { ! alpha32( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.30/1.73 ) ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero
% 1.30/1.73 ( X ), Y ), alpha32( X, Y, Z ) }.
% 1.30/1.73 { ! alpha11( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.30/1.73 { ! alpha11( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.30/1.73 , Z ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) ), alpha11( X, Y, Z ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.30/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), alpha12( X, Y
% 1.30/1.73 , Z ), alpha33( X, Y, Z ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha12( X, Y, Z ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.30/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha33( X, Y, Z ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ),
% 1.30/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.30/1.73 { ! alpha33( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Z,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.73 { ! alpha33( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.30/1.73 ) ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) ), alpha33( X, Y, Z ) }.
% 1.30/1.73 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.30/1.73 { ! alpha12( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( X,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.30/1.73 , Z ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), Y ), alpha12( X, Y, Z ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 1.30/1.73 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.30/1.73 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.30/1.73 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.30/1.73 ( X, T, c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless
% 1.30/1.73 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Otimes__class_Otimes( X ), Z ), T ) ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__comm__semiring__strict( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.30/1.73 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.30/1.73 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.30/1.73 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.30/1.73 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.30/1.73 ( X, c_Groups_Ozero__class_Ozero( X ), T ), c_Orderings_Oord__class_Oless
% 1.30/1.73 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.30/1.73 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.30/1.73 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.30/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.30/1.73 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.30/1.73 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.30/1.73 ( X ) ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.30/1.73 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, Z, T ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.30/1.73 ! c_Orderings_Oord__class_Oless( X, Z, T ), c_Orderings_Oord__class_Oless
% 1.30/1.73 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.30/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ) }
% 1.30/1.73 .
% 1.30/1.73 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.30/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.30/1.73 .
% 1.30/1.73 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.30/1.73 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.30/1.73 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), c_Groups_Ozero__class_Ozero
% 1.30/1.73 ( X ) ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.30/1.73 ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.30/1.73 , c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), c_Groups_Ozero__class_Ozero
% 1.30/1.73 ( X ) ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.30/1.73 ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.30/1.73 , c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ),
% 1.30/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.30/1.73 ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, T, Z ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.30/1.73 ! c_Orderings_Oord__class_Oless( X, T, Z ), c_Orderings_Oord__class_Oless
% 1.30/1.73 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha13( X, Y, Z, T ),
% 1.30/1.73 alpha34( X, Y, Z, T ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha13( X, Y, Z, T ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha34( X, Y, Z, T ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.30/1.73 { ! alpha34( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.73 { ! alpha34( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, Z ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( X, T, c_Groups_Ozero__class_Ozero( X ) )
% 1.30/1.73 , ! c_Orderings_Oord__class_Oless( X, Y, Z ), alpha34( X, Y, Z, T ) }.
% 1.30/1.73 { ! alpha13( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), T ) }.
% 1.30/1.73 { ! alpha13( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T )
% 1.30/1.73 , ! c_Orderings_Oord__class_Oless( X, Z, Y ), alpha13( X, Y, Z, T ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha14( X, Y, Z, T ),
% 1.30/1.73 alpha35( X, Y, Z, T ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha14( X, Y, Z, T ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__ring__strict( X ), ! alpha35( X, Y, Z, T ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.30/1.73 { ! alpha35( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Z,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.73 { ! alpha35( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, Y, T ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.30/1.73 , ! c_Orderings_Oord__class_Oless( X, Y, T ), alpha35( X, Y, Z, T ) }.
% 1.30/1.73 { ! alpha14( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), Z ) }.
% 1.30/1.73 { ! alpha14( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.30/1.73 , ! c_Orderings_Oord__class_Oless( X, T, Y ), alpha14( X, Y, Z, T ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.30/1.73 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ),
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.73 { ! class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct
% 1.30/1.73 ( X ), Y = c_Groups_Ozero__class_Ozero( X ), ! W = U, T = Z, ! hAPP( hAPP
% 1.30/1.73 ( c_Groups_Oplus__class_Oplus( X ), W ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), U ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.30/1.73 ( X, c_Groups_Oone__class_Oone( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.30/1.73 ( X, c_Groups_Oone__class_Oone( X ), Z ), c_Orderings_Oord__class_Oless(
% 1.30/1.73 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.30/1.73 { ! class_Rings_Oring( X ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X )
% 1.30/1.73 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) = hAPP
% 1.30/1.73 ( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ), T = hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( X ), Z ), W ) ), U ) ), Y ) }.
% 1.30/1.73 { ! class_Rings_Oring( X ), ! T = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.30/1.73 X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( X ), Z ), W ) ), U ) ), Y ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) }.
% 1.30/1.73 { ! class_Rings_Oring( X ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X )
% 1.30/1.73 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) = hAPP
% 1.30/1.73 ( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( X ), W ), Z ) ), U ) ), T ) = Y }.
% 1.30/1.73 { ! class_Rings_Oring( X ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X )
% 1.30/1.73 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( X ), W ), Z ) ), U ) ), T ) = Y, hAPP(
% 1.30/1.73 hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) }.
% 1.30/1.73 { ! class_Rings_Oring( X ), hAPP( hAPP( c_Groups_Ominus__class_Ominus( X )
% 1.30/1.73 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), U ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( X ), T ), Y ) ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( X ), U ), Z ) ), Y ) ) }.
% 1.30/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), U ), T ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.30/1.73 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( X ), U ), Z ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( X ), T ), Y ) ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( X ), U ), Z ) ), Y ) ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( X ), T ), Y ) ) ) }.
% 1.30/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), Y ), Y ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), c_Groups_Oone__class_Oone( X ) ),
% 1.30/1.73 c_Groups_Oone__class_Oone( X ) ) ), Y ) }.
% 1.30/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), Z ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Oone__class_Oone( X ) ) )
% 1.30/1.73 , Z ) }.
% 1.30/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), Z ), c_Groups_Oone__class_Oone( X ) ) )
% 1.30/1.73 , Y ) }.
% 1.30/1.73 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.73 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 1.30/1.73 hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) }.
% 1.30/1.73 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.73 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), hAPP(
% 1.30/1.73 hAPP( c_Rings_Oinverse__class_Odivide( X ), T ), Y ) = Z }.
% 1.30/1.73 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.73 , ! hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), T ), Y ) = Z, T =
% 1.30/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) }.
% 1.30/1.73 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.73 , ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), hAPP(
% 1.30/1.73 hAPP( c_Rings_Oinverse__class_Odivide( X ), T ), Y ) = Z }.
% 1.30/1.73 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.73 , ! T = hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ), hAPP
% 1.30/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 1.30/1.73 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.73 , ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, T =
% 1.30/1.73 hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) }.
% 1.30/1.73 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), U ), Y ) = hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), T ), Z ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) }.
% 1.30/1.73 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), ! hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), U ), Z ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), U ), Y ) = hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), T ), Z ) }.
% 1.30/1.73 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) = hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), T ), Z ) }.
% 1.30/1.73 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), T ), Z ) }.
% 1.30/1.73 { ! class_Fields_Ofield__inverse__zero( X ), ! hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), T ), Z ) = Y, alpha36( X, Y, Z, T )
% 1.30/1.73 }.
% 1.30/1.73 { ! class_Fields_Ofield__inverse__zero( X ), ! hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), T ), Z ) = Y, alpha15( X, Y, Z ) }
% 1.30/1.73 .
% 1.30/1.73 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha36( X, Y, Z, T ), !
% 1.30/1.73 alpha15( X, Y, Z ), hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), T )
% 1.30/1.73 , Z ) = Y }.
% 1.30/1.73 { ! alpha36( X, Y, Z, T ), Z = c_Groups_Ozero__class_Ozero( X ), T = hAPP(
% 1.30/1.73 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) }.
% 1.30/1.73 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha36( X, Y, Z, T ) }.
% 1.30/1.73 { ! T = hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), alpha36(
% 1.30/1.73 X, Y, Z, T ) }.
% 1.30/1.73 { ! alpha15( X, Y, Z ), ! Z = c_Groups_Ozero__class_Ozero( X ), Y =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.73 { Z = c_Groups_Ozero__class_Ozero( X ), alpha15( X, Y, Z ) }.
% 1.30/1.73 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha15( X, Y, Z ) }.
% 1.30/1.73 { ! class_Fields_Ofield__inverse__zero( X ), ! T = hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ), alpha37( X, Y, Z, T ) }.
% 1.30/1.73 { ! class_Fields_Ofield__inverse__zero( X ), ! T = hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ), alpha16( X, Y, T ) }.
% 1.30/1.73 { ! class_Fields_Ofield__inverse__zero( X ), ! alpha37( X, Y, Z, T ), !
% 1.30/1.73 alpha16( X, Y, T ), T = hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X )
% 1.30/1.73 , Z ), Y ) }.
% 1.30/1.73 { ! alpha37( X, Y, Z, T ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z }.
% 1.30/1.73 { ! Y = c_Groups_Ozero__class_Ozero( X ), alpha37( X, Y, Z, T ) }.
% 1.30/1.73 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) = Z, alpha37(
% 1.30/1.73 X, Y, Z, T ) }.
% 1.30/1.73 { ! alpha16( X, Y, Z ), ! Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.73 { Y = c_Groups_Ozero__class_Ozero( X ), alpha16( X, Y, Z ) }.
% 1.30/1.73 { ! Z = c_Groups_Ozero__class_Ozero( X ), alpha16( X, Y, Z ) }.
% 1.30/1.73 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.73 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) =
% 1.30/1.73 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 1.30/1.73 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.73 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) =
% 1.30/1.73 c_Divides_Odiv__class_Odiv( X, T, Z ) }.
% 1.30/1.73 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.73 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) = Z }.
% 1.30/1.73 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.73 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) = Z }.
% 1.30/1.73 { ! class_Divides_Osemiring__div( X ), ! T = c_Groups_Ozero__class_Ozero( X
% 1.30/1.73 ), c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.73 { ! class_Divides_Osemiring__div( X ), T = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.73 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) =
% 1.30/1.73 c_Divides_Odiv__class_Odiv( X, Z, Y ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless( X
% 1.30/1.73 , hAPP( c_Groups_Oabs__class_Oabs( X ), Z ), Y ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, hAPP( c_Groups_Oabs__class_Oabs( X ), U
% 1.30/1.73 ), T ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Groups_Oabs__class_Oabs( X )
% 1.30/1.73 , Z ) ), hAPP( c_Groups_Oabs__class_Oabs( X ), U ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.30/1.73 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.30/1.73 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.73 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.30/1.73 c_Power_Opower__class_Opower( X ), T ), Y ) ) }.
% 1.30/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.73 c_Power_Opower__class_Opower( X ), T ), Z ) ), hAPP( hAPP(
% 1.30/1.73 c_Power_Opower__class_Opower( X ), T ), Y ) ) = hAPP( hAPP(
% 1.30/1.73 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, Z, Y ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.30/1.73 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ), hAPP(
% 1.30/1.73 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.30/1.73 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ), hAPP(
% 1.30/1.73 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.30/1.73 { ! Y = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), ! X =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.30/1.73 { ! class_RealVector_Oreal__normed__div__algebra( X ), ! c_Limits_Otendsto
% 1.30/1.73 ( U, X, T, Z, Y ), Z = c_Groups_Ozero__class_Ozero( X ),
% 1.30/1.73 c_Limits_Otendsto( U, X, c_COMBB( X, X, U,
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), T ), hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Z ), Y ) }.
% 1.30/1.73 { hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal ), hAPP( Z, Y
% 1.30/1.73 ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP
% 1.30/1.73 ( hAPP( c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal ), hAPP( Z, X ) ), hAPP(
% 1.30/1.73 Z, Y ) ) ), hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal )
% 1.30/1.73 , X ), Y ) ) ), Y ) ) = hAPP( hAPP( c_Groups_Ominus__class_Ominus(
% 1.30/1.73 tc_RealDef_Oreal ), hAPP( Z, X ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal ), hAPP( Z, X ) ), hAPP(
% 1.30/1.73 Z, Y ) ) ), hAPP( hAPP( c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal )
% 1.30/1.73 , X ), Y ) ) ), X ) ) }.
% 1.30/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), ! c_Limits_Otendsto(
% 1.30/1.73 tc_Nat_Onat, X, Z, Y, c_Limits_Osequentially ), c_Limits_Otendsto(
% 1.30/1.73 tc_Nat_Onat, X, c_COMBB( X, X, tc_Nat_Onat, hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ), c_Limits_Osequentially ) }
% 1.30/1.73 .
% 1.30/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), ! c_Limits_Otendsto(
% 1.30/1.73 tc_Nat_Onat, X, Z, Y, c_Limits_Osequentially ), c_Limits_Otendsto(
% 1.30/1.73 tc_Nat_Onat, X, c_COMBC( tc_Nat_Onat, X, X, c_COMBB( X, tc_fun( X, X ),
% 1.30/1.73 tc_Nat_Onat, c_Groups_Otimes__class_Otimes( X ), Z ), T ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ), c_Limits_Osequentially ) }
% 1.30/1.73 .
% 1.30/1.73 { ! class_RealVector_Oreal__normed__algebra( X ), ! c_Limits_Otendsto(
% 1.30/1.73 tc_Nat_Onat, X, Z, Y, c_Limits_Osequentially ), ! c_Limits_Otendsto(
% 1.30/1.73 tc_Nat_Onat, X, U, T, c_Limits_Osequentially ), c_Limits_Otendsto(
% 1.30/1.73 tc_Nat_Onat, X, c_COMBS( tc_Nat_Onat, X, X, c_COMBB( X, tc_fun( X, X ),
% 1.30/1.73 tc_Nat_Onat, c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ), c_Limits_Osequentially ) }
% 1.30/1.73 .
% 1.30/1.73 { ! class_Fields_Olinordered__field( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Z ), hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Y ) ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Z ), hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Y ) ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, Z ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Y ), hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Z ) ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Y ), hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Z ) ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Y ), c_Groups_Oone__class_Oone( X
% 1.30/1.73 ) ), c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.30/1.73 , c_Groups_Oone__class_Oone( X ), Y ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.30/1.73 ), c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Y ), c_Groups_Oone__class_Oone( X
% 1.30/1.73 ) ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ), Y )
% 1.30/1.73 , c_Orderings_Oord__class_Oless__eq( X, hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Y ), c_Groups_Oone__class_Oone( X
% 1.30/1.73 ) ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Y ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.30/1.73 .
% 1.30/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Y ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.30/1.73 ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Y ) ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.73 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.30/1.73 ( X, Y, c_Groups_Oone__class_Oone( X ) ), c_Orderings_Oord__class_Oless(
% 1.30/1.73 X, c_Groups_Oone__class_Oone( X ), hAPP( c_Rings_Oinverse__class_Oinverse
% 1.30/1.73 ( X ), Y ) ) }.
% 1.30/1.73 { ! class_Rings_Odivision__ring( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.73 , hAPP( c_Rings_Oinverse__class_Oinverse( X ), Y ) = hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), c_Groups_Oone__class_Oone( X ) ), Y
% 1.30/1.73 ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), T ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, T, Y ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.30/1.73 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.30/1.73 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.30/1.73 ), c_Orderings_Oord__class_Oless( X, Z, Y ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.30/1.73 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__semiring( X ), ! c_Orderings_Oord__class_Oless
% 1.30/1.73 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Z ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.30/1.73 ), c_Orderings_Oord__class_Oless( X, T, Y ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, U, T ), ! c_Orderings_Oord__class_Oless
% 1.30/1.73 ( X, c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.30/1.73 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, U, T ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.30/1.73 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.30/1.73 , U ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.30/1.73 ( X, U, T ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), Z ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.30/1.73 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__semiring__strict( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.30/1.73 ( X, U, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.30/1.73 ), c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), U ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.30/1.73 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, T ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.30/1.73 ! c_Orderings_Oord__class_Oless__eq( X, Z, T ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.30/1.73 ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, T, Z ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.30/1.73 ! c_Orderings_Oord__class_Oless__eq( X, T, Z ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.30/1.73 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.30/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 1.30/1.73 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), Y ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.30/1.73 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Z
% 1.30/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Oone__class_Oone
% 1.30/1.73 ( X ) ), c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), Y ) }.
% 1.30/1.73 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.30/1.73 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( X ), Z ), W ) ), U ) ), Y ) ) }.
% 1.30/1.73 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.30/1.73 , T, hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( X ), Z ), W ) ), U ) ), Y ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) }.
% 1.30/1.73 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.30/1.73 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( X ), W ), Z ) ), U ) ), T ), Y ) }.
% 1.30/1.73 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless__eq( X
% 1.30/1.73 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( X ), W ), Z ) ), U ) ), T ), Y ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) }.
% 1.30/1.73 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.30/1.73 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( X ), Z ), W ) ), U ) ), Y ) ) }.
% 1.30/1.73 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X, T
% 1.30/1.73 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( X ), Z ), W ) ), U ) ), Y ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.30/1.73 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ),
% 1.30/1.73 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) }.
% 1.30/1.73 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.30/1.73 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.30/1.73 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( X ), W ), Z ) ), U ) ), T ), Y ) }.
% 1.30/1.73 { ! class_Rings_Oordered__ring( X ), ! c_Orderings_Oord__class_Oless( X,
% 1.30/1.73 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( X ), W ), Z ) ), U ) ), T ), Y ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.30/1.73 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), W ), U ) ), T ),
% 1.30/1.73 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), U ) ), Y ) ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ), alpha38( X, Y, Z, T ) }
% 1.30/1.73 .
% 1.30/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ), alpha45( X, Y, Z, T ) }
% 1.30/1.73 .
% 1.30/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha38( X, Y, Z
% 1.30/1.73 , T ), ! alpha45( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, T, hAPP
% 1.30/1.73 ( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.30/1.73 { ! alpha45( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), Y ), alpha51( X, Y, Z, T ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.30/1.73 , alpha45( X, Y, Z, T ) }.
% 1.30/1.73 { ! alpha51( X, Y, Z, T ), alpha45( X, Y, Z, T ) }.
% 1.30/1.73 { ! alpha51( X, Y, Z, T ), alpha58( X, Y, Z, T ) }.
% 1.30/1.73 { ! alpha51( X, Y, Z, T ), alpha17( X, Y, T ) }.
% 1.30/1.73 { ! alpha58( X, Y, Z, T ), ! alpha17( X, Y, T ), alpha51( X, Y, Z, T ) }.
% 1.30/1.73 { ! alpha58( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.30/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.30/1.73 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.30/1.73 alpha58( X, Y, Z, T ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha58( X, Y, Z, T ) }.
% 1.30/1.73 { ! alpha38( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless( X,
% 1.30/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.30/1.73 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.30/1.73 alpha38( X, Y, Z, T ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha38( X, Y, Z, T )
% 1.30/1.73 }.
% 1.30/1.73 { ! alpha17( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X, Z,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.30/1.73 , alpha17( X, Y, Z ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.30/1.73 , alpha17( X, Y, Z ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), T ), Z ), Y ), alpha39( X, Y, Z, T
% 1.30/1.73 ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), T ), Z ), Y ), alpha46( X, Y, Z, T
% 1.30/1.73 ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha39( X, Y, Z
% 1.30/1.73 , T ), ! alpha46( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X, hAPP(
% 1.30/1.73 hAPP( c_Rings_Oinverse__class_Odivide( X ), T ), Z ), Y ) }.
% 1.30/1.73 { ! alpha46( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), Z ), alpha52( X, Y, Z, T ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.30/1.73 , alpha46( X, Y, Z, T ) }.
% 1.30/1.73 { ! alpha52( X, Y, Z, T ), alpha46( X, Y, Z, T ) }.
% 1.30/1.73 { ! alpha52( X, Y, Z, T ), alpha59( X, Y, Z, T ) }.
% 1.30/1.73 { ! alpha52( X, Y, Z, T ), alpha18( X, Y, Z ) }.
% 1.30/1.73 { ! alpha59( X, Y, Z, T ), ! alpha18( X, Y, Z ), alpha52( X, Y, Z, T ) }.
% 1.30/1.73 { ! alpha59( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.30/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 1.30/1.73 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 1.30/1.73 alpha59( X, Y, Z, T ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha59( X, Y, Z, T )
% 1.30/1.73 }.
% 1.30/1.73 { ! alpha39( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless( X,
% 1.30/1.73 T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.30/1.73 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.30/1.73 alpha39( X, Y, Z, T ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha39( X, Y, Z, T ) }.
% 1.30/1.73 { ! alpha18( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless( X,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.30/1.73 , alpha18( X, Y, Z ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.30/1.73 , alpha18( X, Y, Z ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.73 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.30/1.73 ( X, T, hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.73 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.30/1.73 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.73 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.30/1.73 ( X, hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), T ), Y ), Z ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.73 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.30/1.73 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), T ), Y ), Z ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.73 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.30/1.73 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), T ), Y ), Z ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.73 X, c_Groups_Ozero__class_Ozero( X ), Y ), ! c_Orderings_Oord__class_Oless
% 1.30/1.73 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.73 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.30/1.73 ( X, T, hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, Z, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.73 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.30/1.73 ( X, Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, T, hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.73 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.30/1.73 ( X, hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), T ), Y ), Z ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.73 X, Y, c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless
% 1.30/1.73 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), T ), Y ), Z ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.73 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), T ), ! c_Orderings_Oord__class_Oless( X
% 1.30/1.73 , c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), T ), Y ), hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), T ), Z ) ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.73 X, Z, Y ), ! c_Orderings_Oord__class_Oless( X, T,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) ), ! c_Orderings_Oord__class_Oless( X,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), T ), Z ), hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), T ), Y ) ) }.
% 1.30/1.73 { ! class_Rings_Oring__1( X ), hAPP( hAPP( c_Groups_Ominus__class_Ominus( X
% 1.30/1.73 ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.30/1.73 c_Groups_Oone__class_Oone( X ) ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), Y ), c_Groups_Oone__class_Oone( X ) ) )
% 1.30/1.73 , hAPP( hAPP( c_Groups_Ominus__class_Ominus( X ), Y ),
% 1.30/1.73 c_Groups_Oone__class_Oone( X ) ) ) }.
% 1.30/1.73 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.30/1.73 ( X ), hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), U ), Y ) ), hAPP
% 1.30/1.73 ( hAPP( c_Rings_Oinverse__class_Odivide( X ), T ), Z ) ) = hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.30/1.73 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.30/1.73 hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), T ), Y ) ), Z ) = hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), Y ) }.
% 1.30/1.73 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.30/1.73 ( X ), hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), T ), Y ) ), Z )
% 1.30/1.73 = hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) ), Y ) }.
% 1.30/1.73 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.30/1.73 hAPP( c_Groups_Oplus__class_Oplus( X ), T ), hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), Z ) ), Y ) }.
% 1.30/1.73 { ! class_Fields_Ofield__inverse__zero( X ), Y =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.30/1.73 ( X ), T ), hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) )
% 1.30/1.73 = hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), Z ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), Y ) }.
% 1.30/1.73 { ! class_Rings_Oordered__ring__abs( X ), alpha69( X, Z ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.30/1.73 ), hAPP( c_Groups_Oabs__class_Oabs( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Groups_Oabs__class_Oabs( X )
% 1.30/1.73 , Z ) ), hAPP( c_Groups_Oabs__class_Oabs( X ), Y ) ) }.
% 1.30/1.73 { ! class_Rings_Oordered__ring__abs( X ), alpha69( X, Z ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.30/1.73 ), hAPP( c_Groups_Oabs__class_Oabs( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Groups_Oabs__class_Oabs( X )
% 1.30/1.73 , Z ) ), hAPP( c_Groups_Oabs__class_Oabs( X ), Y ) ) }.
% 1.30/1.73 { ! alpha69( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.30/1.73 { ! alpha69( X, Y ), ! c_Orderings_Oord__class_Oless__eq( X, Y,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.73 { c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), Y
% 1.30/1.73 ), c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero
% 1.30/1.73 ( X ) ), alpha69( X, Y ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__idom( X ), ! c_Orderings_Oord__class_Oless__eq
% 1.30/1.73 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( c_Groups_Oabs__class_Oabs( X )
% 1.30/1.73 , Z ) ), Y ) = hAPP( c_Groups_Oabs__class_Oabs( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.30/1.73 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.30/1.73 X, c_Groups_Oone__class_Oone( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.30/1.73 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.30/1.73 ( X, c_Groups_Oone__class_Oone( X ), Y ), c_Orderings_Oord__class_Oless(
% 1.30/1.73 X, hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.30/1.73 c_Power_Opower__class_Opower( X ), Y ), Z ) ) ) }.
% 1.30/1.73 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), Z =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), U ), Y ) ), hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), T ), Z ) ) = hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.30/1.73 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.30/1.73 hAPP( c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), T ), Y ) ), Z ) = hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( X ), T ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) ), Y ) }.
% 1.30/1.73 { ! class_Fields_Ofield( X ), Y = c_Groups_Ozero__class_Ozero( X ), hAPP(
% 1.30/1.73 hAPP( c_Groups_Ominus__class_Ominus( X ), T ), hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) = hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), T ) ), Z ) ), Y ) }.
% 1.30/1.73 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.73 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.30/1.73 ( X ), T ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), Y
% 1.30/1.73 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ),
% 1.30/1.73 c_Divides_Odiv__class_Odiv( X, T, Y ) ) }.
% 1.30/1.73 { ! class_Divides_Osemiring__div( X ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.73 , c_Divides_Odiv__class_Odiv( X, hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.30/1.73 ( X ), T ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ), Y
% 1.30/1.73 ) = hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), Z ),
% 1.30/1.73 c_Divides_Odiv__class_Odiv( X, T, Y ) ) }.
% 1.30/1.73 { ! class_RealVector_Oreal__field( X ), hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), W ), U ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Z ) ) ), Y ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), W ), hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( X ), U ), Z ) ), Y ) ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( X ), W ), T ) ), Y ) ), Z ) ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Z, Y ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, X,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.30/1.73 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal ), Y ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), hAPP(
% 1.30/1.73 c_Groups_Oabs__class_Oabs( tc_RealDef_Oreal ), Z ) ) ), Y =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.30/1.73 { ! class_RealVector_Oreal__normed__div__algebra( X ), ! c_Limits_Otendsto
% 1.30/1.73 ( tc_Nat_Onat, X, Z, Y, c_Limits_Osequentially ), Y =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), c_Limits_Otendsto( tc_Nat_Onat, X,
% 1.30/1.73 c_COMBB( X, X, tc_Nat_Onat, c_Rings_Oinverse__class_Oinverse( X ), Z ),
% 1.30/1.73 hAPP( c_Rings_Oinverse__class_Oinverse( X ), Y ), c_Limits_Osequentially
% 1.30/1.73 ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.73 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 1.30/1.73 , c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.30/1.73 hAPP( c_Rings_Oinverse__class_Oinverse( X ), Y ) ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, hAPP( c_Rings_Oinverse__class_Oinverse
% 1.30/1.73 ( X ), Y ), c_Groups_Oone__class_Oone( X ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.30/1.73 ), c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y )
% 1.30/1.73 }.
% 1.30/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Ozero__class_Ozero( X )
% 1.30/1.73 ), c_Orderings_Oord__class_Oless( X, hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( X ), Y ), c_Groups_Oone__class_Oone( X
% 1.30/1.73 ) ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Oone__class_Oone( X ), Y ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, hAPP( c_Rings_Oinverse__class_Oinverse
% 1.30/1.73 ( X ), Y ), c_Groups_Oone__class_Oone( X ) ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.30/1.73 hAPP( c_Rings_Oinverse__class_Oinverse( X ), Y ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ) }
% 1.30/1.73 .
% 1.30/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X ),
% 1.30/1.73 hAPP( c_Rings_Oinverse__class_Oinverse( X ), Y ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X ) )
% 1.30/1.73 }.
% 1.30/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.30/1.73 ! c_Orderings_Oord__class_Oless__eq( X, Y, c_Groups_Oone__class_Oone( X )
% 1.30/1.73 ), c_Orderings_Oord__class_Oless__eq( X, c_Groups_Oone__class_Oone( X )
% 1.30/1.73 , hAPP( c_Rings_Oinverse__class_Oinverse( X ), Y ) ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__semiring__1( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, T, Y ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), U
% 1.30/1.73 ), ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero(
% 1.30/1.73 X ), W ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), U ), W ) =
% 1.30/1.73 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless__eq( X,
% 1.30/1.73 hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, T, c_Groups_Ozero__class_Ozero( X )
% 1.30/1.73 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.30/1.73 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), T ), Z ), hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), T ), Y ) ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, Y ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), T
% 1.30/1.73 ), ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X )
% 1.30/1.73 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), T ), Y ), hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), T ), Z ) ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.73 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), T ), Y ), Z ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.73 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ), T ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), T ), Y ), Z ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.73 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.73 X, Y, c_Groups_Ozero__class_Ozero( X ) ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.73 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.73 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), T ), Y ), Z ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.73 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), T ), Y ), Z ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.73 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Y ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), T ), Y ), Z ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.73 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.73 X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), T ), Z ), Y ), alpha40( X, Y, Z, T
% 1.30/1.73 ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), T ), Z ), Y ), alpha47( X, Y, Z, T
% 1.30/1.73 ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha40( X, Y, Z
% 1.30/1.73 , T ), ! alpha47( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X,
% 1.30/1.73 hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), T ), Z ), Y ) }.
% 1.30/1.73 { ! alpha47( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), Z ), alpha53( X, Y, Z, T ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z )
% 1.30/1.73 , alpha47( X, Y, Z, T ) }.
% 1.30/1.73 { ! alpha53( X, Y, Z, T ), alpha47( X, Y, Z, T ) }.
% 1.30/1.73 { ! alpha53( X, Y, Z, T ), alpha60( X, Y, Z, T ) }.
% 1.30/1.73 { ! alpha53( X, Y, Z, T ), alpha19( X, Y, Z ) }.
% 1.30/1.73 { ! alpha60( X, Y, Z, T ), ! alpha19( X, Y, Z ), alpha53( X, Y, Z, T ) }.
% 1.30/1.73 { ! alpha60( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Z,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.30/1.73 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ) }.
% 1.30/1.73 { c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) ),
% 1.30/1.73 alpha60( X, Y, Z, T ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ), T ), alpha60( X, Y, Z, T )
% 1.30/1.73 }.
% 1.30/1.73 { ! alpha40( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), Z ), c_Orderings_Oord__class_Oless__eq
% 1.30/1.73 ( X, T, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ) }.
% 1.30/1.73 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Z ),
% 1.30/1.73 alpha40( X, Y, Z, T ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Z ) ), alpha40( X, Y, Z, T ) }.
% 1.30/1.73 { ! alpha19( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Z,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.30/1.73 , c_Groups_Ozero__class_Ozero( X ), Y ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( X, Z, c_Groups_Ozero__class_Ozero( X ) )
% 1.30/1.73 , alpha19( X, Y, Z ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X )
% 1.30/1.73 , Y ), alpha19( X, Y, Z ) }.
% 1.30/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ), alpha41( X, Y, Z, T ) }
% 1.30/1.73 .
% 1.30/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, T, hAPP( hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ), alpha48( X, Y, Z, T ) }
% 1.30/1.73 .
% 1.30/1.73 { ! class_Fields_Olinordered__field__inverse__zero( X ), ! alpha41( X, Y, Z
% 1.30/1.73 , T ), ! alpha48( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( X, T,
% 1.30/1.73 hAPP( hAPP( c_Rings_Oinverse__class_Odivide( X ), Z ), Y ) ) }.
% 1.30/1.73 { ! alpha48( X, Y, Z, T ), c_Orderings_Oord__class_Oless( X,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), Y ), alpha54( X, Y, Z, T ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y )
% 1.30/1.73 , alpha48( X, Y, Z, T ) }.
% 1.30/1.73 { ! alpha54( X, Y, Z, T ), alpha48( X, Y, Z, T ) }.
% 1.30/1.73 { ! alpha54( X, Y, Z, T ), alpha61( X, Y, Z, T ) }.
% 1.30/1.73 { ! alpha54( X, Y, Z, T ), alpha20( X, Y, T ) }.
% 1.30/1.73 { ! alpha61( X, Y, Z, T ), ! alpha20( X, Y, T ), alpha54( X, Y, Z, T ) }.
% 1.30/1.73 { ! alpha61( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X, Y,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.30/1.73 , Z, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ) ) }.
% 1.30/1.73 { c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) ),
% 1.30/1.73 alpha61( X, Y, Z, T ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless__eq( X, Z, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ) ), alpha61( X, Y, Z, T ) }.
% 1.30/1.73 { ! alpha41( X, Y, Z, T ), ! c_Orderings_Oord__class_Oless( X,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), Y ), c_Orderings_Oord__class_Oless__eq
% 1.30/1.73 ( X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ) }.
% 1.30/1.73 { c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), Y ),
% 1.30/1.73 alpha41( X, Y, Z, T ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), T ), Y ), Z ), alpha41( X, Y, Z, T )
% 1.30/1.73 }.
% 1.30/1.73 { ! alpha20( X, Y, Z ), c_Orderings_Oord__class_Oless( X, Y,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) ), c_Orderings_Oord__class_Oless__eq( X
% 1.30/1.73 , Z, c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( X, Y, c_Groups_Ozero__class_Ozero( X ) )
% 1.30/1.73 , alpha20( X, Y, Z ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless__eq( X, Z, c_Groups_Ozero__class_Ozero( X
% 1.30/1.73 ) ), alpha20( X, Y, Z ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__semidom( X ), ! c_Orderings_Oord__class_Oless
% 1.30/1.73 ( X, c_Groups_Ozero__class_Ozero( X ), Y ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, Y, c_Groups_Oone__class_Oone( X ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.30/1.73 c_Power_Opower__class_Opower( X ), Y ), Z ) ), hAPP( hAPP(
% 1.30/1.73 c_Power_Opower__class_Opower( X ), Y ), Z ) ) }.
% 1.30/1.73 { ! class_RealVector_Oreal__normed__vector( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, Y,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal, hAPP(
% 1.30/1.73 c_RealVector_Onorm__class_Onorm( X ), Z ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), hAPP(
% 1.30/1.73 c_RealVector_Onorm__class_Onorm( X ), T ) ) ), Z =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.73 { ! class_RealVector_Oreal__normed__div__algebra( X ), ! c_Limits_Otendsto
% 1.30/1.73 ( tc_Nat_Onat, X, Z, Y, c_Limits_Osequentially ), Y =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), c_SEQ_OBseq( X, c_COMBB( X, X,
% 1.30/1.73 tc_Nat_Onat, c_Rings_Oinverse__class_Oinverse( X ), Z ) ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__semiring__1__strict( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, Z, Y ), ! c_Orderings_Oord__class_Oless
% 1.30/1.73 ( X, T, Y ), ! c_Orderings_Oord__class_Oless__eq( X,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), U ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, c_Groups_Ozero__class_Ozero( X ), W
% 1.30/1.73 ), ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), U ), W ) =
% 1.30/1.73 c_Groups_Oone__class_Oone( X ), c_Orderings_Oord__class_Oless( X, hAPP(
% 1.30/1.73 hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), U ), Z ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), W ), T ) ), Y ) }.
% 1.30/1.73 { ! class_Groups_Omonoid__mult( X ), ! c_Orderings_Oord__class_Oless(
% 1.30/1.73 tc_Nat_Onat, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Otimes__class_Otimes( X ), hAPP( hAPP(
% 1.30/1.73 c_Power_Opower__class_Opower( X ), Z ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ),
% 1.30/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ), Z ) = hAPP( hAPP(
% 1.30/1.73 c_Power_Opower__class_Opower( X ), Z ), Y ) }.
% 1.30/1.73 { ! class_Power_Opower( X ), ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat
% 1.30/1.73 ), hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) =
% 1.30/1.73 c_Groups_Oone__class_Oone( X ) }.
% 1.30/1.73 { ! class_Power_Opower( X ), Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat )
% 1.30/1.73 , hAPP( hAPP( c_Power_Opower__class_Opower( X ), Y ), Z ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), hAPP( hAPP(
% 1.30/1.73 c_Power_Opower__class_Opower( X ), Y ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ),
% 1.30/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), T ), hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal ), X ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal ), Y ) ) ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), T ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Z ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal ), X ) ), T ), hAPP(
% 1.30/1.73 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP(
% 1.30/1.73 c_Rings_Oinverse__class_Oinverse( tc_RealDef_Oreal ), Y ) ), Z ) ) }.
% 1.30/1.73 { c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) =
% 1.30/1.73 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, c_Divides_Odiv__class_Odiv(
% 1.30/1.73 tc_Nat_Onat, Z, Y ), X ) }.
% 1.30/1.73 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), hAPP( hAPP(
% 1.30/1.73 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.30/1.73 ( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.30/1.73 { ! class_Rings_Ocomm__semiring__1( X ), hAPP( hAPP(
% 1.30/1.73 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.30/1.73 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) = hAPP( hAPP(
% 1.30/1.73 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) }.
% 1.30/1.73 { ! class_Groups_Omonoid__mult( X ), hAPP( hAPP(
% 1.30/1.73 c_Power_Opower__class_Opower( X ), T ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ) = hAPP( hAPP(
% 1.30/1.73 c_Power_Opower__class_Opower( X ), hAPP( hAPP(
% 1.30/1.73 c_Power_Opower__class_Opower( X ), T ), Z ) ), Y ) }.
% 1.30/1.73 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.30/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), Z = X
% 1.30/1.73 , Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.30/1.73 { ! Z = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.30/1.73 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }
% 1.30/1.73 .
% 1.30/1.73 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.30/1.73 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.30/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Y = X
% 1.30/1.73 , Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.30/1.73 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.30/1.73 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.30/1.73 .
% 1.30/1.73 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.30/1.73 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.30/1.73 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.30/1.73 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.30/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.30/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ), X ) =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.30/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.30/1.73 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.30/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), X ) ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.30/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Y ), X ) ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( tc_Int_Oint ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.30/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 1.30/1.73 hAPP( c_Groups_Ominus__class_Ominus( tc_Int_Oint ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.30/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP( hAPP
% 1.30/1.73 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.30/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, Z ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), T ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.30/1.73 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) ) }.
% 1.30/1.73 { c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), X ) ) }.
% 1.30/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 1.30/1.73 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.30/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.30/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.30/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ), X ) = X }.
% 1.30/1.73 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), Y =
% 1.30/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.30/1.73 { ! c_Groups_Oone__class_Oone( tc_Nat_Onat ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X =
% 1.30/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.30/1.73 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.30/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ), c_Groups_Oone__class_Oone(
% 1.30/1.73 tc_Nat_Onat ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.30/1.73 , Y ), X ) }.
% 1.30/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ),
% 1.30/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) = X }.
% 1.30/1.73 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.30/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y = c_Groups_Oone__class_Oone(
% 1.30/1.73 tc_Nat_Onat ) }.
% 1.30/1.73 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.30/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ), X = c_Groups_Oone__class_Oone(
% 1.30/1.73 tc_Nat_Onat ) }.
% 1.30/1.73 { ! Y = c_Groups_Oone__class_Oone( tc_Nat_Onat ), ! X =
% 1.30/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.30/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.30/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.30/1.73 c_Groups_Oone__class_Oone( tc_Int_Oint ) ), X ) = X }.
% 1.30/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ),
% 1.30/1.73 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) = X }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.30/1.73 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.30/1.73 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.30/1.73 ( tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat )
% 1.30/1.73 , Y ), X ) ), c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.30/1.73 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), X ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.30/1.73 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.30/1.73 Y ), X ) ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.30/1.73 tc_Nat_Onat ), Z ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.30/1.73 ( tc_Nat_Onat ), Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X
% 1.30/1.73 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.30/1.73 tc_Nat_Onat ), Y ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.30/1.73 ( tc_Nat_Onat ), Y ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, X
% 1.30/1.73 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.30/1.73 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.30/1.73 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ) ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Y, X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.30/1.73 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP(
% 1.30/1.73 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Y, X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.30/1.73 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.30/1.73 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), X ) ) }.
% 1.30/1.73 { ! Y = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X )
% 1.30/1.73 , X = c_Groups_Oone__class_Oone( tc_Nat_Onat ), Y =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.30/1.73 { c_RealDef_Oreal( tc_Nat_Onat, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.30/1.73 tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.30/1.73 tc_RealDef_Oreal ), c_RealDef_Oreal( tc_Nat_Onat, Y ) ), c_RealDef_Oreal
% 1.30/1.73 ( tc_Nat_Onat, X ) ) }.
% 1.30/1.73 { ! hAPP( c_Groups_Oabs__class_Oabs( tc_Int_Oint ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) ) =
% 1.30/1.73 c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( c_Groups_Oabs__class_Oabs
% 1.30/1.73 ( tc_Int_Oint ), X ) = c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.30/1.73 { hAPP( hAPP( c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), Y ), X ) ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.30/1.73 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), Y ) ), hAPP( hAPP(
% 1.30/1.73 c_Power_Opower__class_Opower( tc_Int_Oint ), Z ), X ) ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.30/1.73 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X
% 1.30/1.73 ) }.
% 1.30/1.73 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.30/1.73 tc_Nat_Onat ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 1.30/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 1.30/1.73 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, X ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.30/1.73 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X
% 1.30/1.73 ) }.
% 1.30/1.73 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.30/1.73 tc_Nat_Onat ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP
% 1.30/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP(
% 1.30/1.73 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.30/1.73 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.30/1.73 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), X =
% 1.30/1.73 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.30/1.73 ( tc_Int_Oint ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.30/1.73 tc_Int_Oint ), X ), Y ) = c_Groups_Oone__class_Oone( tc_Int_Oint ), Y =
% 1.30/1.73 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.30/1.73 ( tc_Int_Oint ), X ), ! X = c_Groups_Oone__class_Oone( tc_Int_Oint ), ! Y
% 1.30/1.73 = c_Groups_Oone__class_Oone( tc_Int_Oint ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) =
% 1.30/1.73 c_Groups_Oone__class_Oone( tc_Int_Oint ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.30/1.73 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 1.30/1.73 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ), X ) = Y }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.30/1.73 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 1.30/1.73 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ), X ) = Y }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.30/1.73 ( tc_Int_Oint ), X ), c_Divides_Odiv__class_Odiv( tc_Int_Oint, Z, hAPP(
% 1.30/1.73 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) =
% 1.30/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, c_Divides_Odiv__class_Odiv(
% 1.30/1.73 tc_Int_Oint, Z, Y ), X ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.30/1.73 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ),
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.30/1.73 tc_Int_Oint ), Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ) ), Z ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ) ), X ) ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, U ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, U ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T, Y ) }.
% 1.30/1.73 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ) ), T ) = hAPP(
% 1.30/1.73 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Z ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.30/1.73 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.30/1.73 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, U, Y ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), T ) ), Z ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), U ), Y ) ), X ) ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, U, Z ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, T ) }.
% 1.30/1.73 { ! hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), W ), U ) ), T ) = hAPP(
% 1.30/1.73 hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ),
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, T, W ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.30/1.73 tc_Int_Oint ), Z ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Z,
% 1.30/1.73 W ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y, U ) }.
% 1.30/1.73 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 1.30/1.73 alpha21( X, Z ) }.
% 1.30/1.73 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ),
% 1.30/1.73 alpha42( X, Y, Z ) }.
% 1.30/1.73 { ! alpha21( X, Z ), ! alpha42( X, Y, Z ), hBOOL( hAPP( Z,
% 1.30/1.73 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) ) ) }.
% 1.30/1.73 { ! alpha42( X, Y, Z ), X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.30/1.73 alpha49( X, Y, Z ) }.
% 1.30/1.73 { ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha42( X, Y, Z ) }.
% 1.30/1.73 { ! alpha49( X, Y, Z ), alpha42( X, Y, Z ) }.
% 1.30/1.73 { ! alpha49( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, X
% 1.30/1.73 ), alpha55( X, Y, Z, T ) }.
% 1.30/1.73 { c_Orderings_Oord__class_Oless( tc_Nat_Onat, skol39( X, T, U ), X ),
% 1.30/1.73 alpha49( X, Y, Z ) }.
% 1.30/1.73 { ! alpha55( X, Y, Z, skol39( X, Y, Z ) ), alpha49( X, Y, Z ) }.
% 1.30/1.73 { ! alpha55( X, Y, Z, T ), ! Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.30/1.73 tc_Nat_Onat ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ),
% 1.30/1.73 X ), U ) ), T ), hBOOL( hAPP( Z, U ) ) }.
% 1.30/1.73 { ! hBOOL( hAPP( Z, skol40( U, W, Z, V0 ) ) ), alpha55( X, Y, Z, T ) }.
% 1.30/1.73 { Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), skol40( X, Y, Z, T ) )
% 1.30/1.73 ), T ), alpha55( X, Y, Z, T ) }.
% 1.30/1.73 { ! alpha21( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.30/1.73 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ) }.
% 1.30/1.73 { X = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), alpha21( X, Y ) }.
% 1.30/1.73 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) ) ), alpha21
% 1.30/1.73 ( X, Y ) }.
% 1.30/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), hAPP(
% 1.30/1.73 hAPP( c_Complex_Ocomplex_OComplex, T ), Z ) ), hAPP( hAPP(
% 1.30/1.73 c_Complex_Ocomplex_OComplex, Y ), X ) ) = hAPP( hAPP(
% 1.30/1.73 c_Complex_Ocomplex_OComplex, hAPP( hAPP( c_Groups_Ominus__class_Ominus(
% 1.30/1.73 tc_RealDef_Oreal ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.30/1.73 tc_RealDef_Oreal ), T ), Y ) ), hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.30/1.73 ( tc_RealDef_Oreal ), Z ), X ) ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), T ), X ) ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Z ), Y ) ) ) }.
% 1.30/1.73 { hAPP( c_Complex_OIm, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.30/1.73 tc_Complex_Ocomplex ), Y ), X ) ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( c_Complex_ORe, Y
% 1.30/1.73 ) ), hAPP( c_Complex_OIm, X ) ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( c_Complex_OIm, Y
% 1.30/1.73 ) ), hAPP( c_Complex_ORe, X ) ) ) }.
% 1.30/1.73 { hAPP( c_Complex_ORe, hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.30/1.73 tc_Complex_Ocomplex ), Y ), X ) ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( c_Complex_ORe, Y
% 1.30/1.73 ) ), hAPP( c_Complex_ORe, X ) ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( c_Complex_OIm, Y
% 1.30/1.73 ) ), hAPP( c_Complex_OIm, X ) ) ) }.
% 1.30/1.73 { ! class_RealVector_Otopological__space( X ), ! c_Limits_Otendsto(
% 1.30/1.73 tc_Nat_Onat, X, Z, Y, c_Limits_Osequentially ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero(
% 1.30/1.73 tc_Nat_Onat ), T ), c_Limits_Otendsto( tc_Nat_Onat, X, c_COMBB(
% 1.30/1.73 tc_Nat_Onat, X, tc_Nat_Onat, Z, c_COMBC( tc_Nat_Onat, tc_Nat_Onat,
% 1.30/1.73 tc_Nat_Onat, c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ) ), Y,
% 1.30/1.73 c_Limits_Osequentially ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.30/1.73 ( tc_Int_Oint ), X ), ! X = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.30/1.73 tc_Int_Oint ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.30/1.73 tc_Int_Oint ), X ), Y ) ), ! c_Orderings_Oord__class_Oless__eq(
% 1.30/1.73 tc_Int_Oint, c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, Y,
% 1.30/1.73 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.30/1.73 ( tc_Int_Oint ), X ), ! X = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.30/1.73 tc_Int_Oint ), Z ), hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.30/1.73 tc_Int_Oint ), X ), Y ) ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.30/1.73 Z, X ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.73 c_Groups_Oone__class_Oone( tc_Int_Oint ), Y ) }.
% 1.30/1.73 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 1.30/1.73 alpha22( X, Z ) }.
% 1.30/1.73 { ! hBOOL( hAPP( Z, c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ),
% 1.30/1.73 alpha43( X, Y, Z ) }.
% 1.30/1.73 { ! alpha22( X, Z ), ! alpha43( X, Y, Z ), hBOOL( hAPP( Z,
% 1.30/1.73 c_Divides_Odiv__class_Odiv( tc_Int_Oint, Y, X ) ) ) }.
% 1.30/1.73 { ! alpha43( X, Y, Z ), alpha50( X, Y, Z ) }.
% 1.30/1.73 { ! alpha43( X, Y, Z ), alpha56( X, Y, Z ) }.
% 1.30/1.73 { ! alpha50( X, Y, Z ), ! alpha56( X, Y, Z ), alpha43( X, Y, Z ) }.
% 1.30/1.73 { ! alpha56( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha62( X, Y, Z ) }.
% 1.30/1.73 { c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), alpha56( X, Y, Z ) }.
% 1.30/1.73 { ! alpha62( X, Y, Z ), alpha56( X, Y, Z ) }.
% 1.30/1.73 { ! alpha62( X, Y, Z ), ! alpha64( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 1.30/1.73 { ! hBOOL( hAPP( Z, skol41( T, U, Z ) ) ), alpha62( X, Y, Z ) }.
% 1.30/1.73 { alpha64( X, Y, skol41( X, Y, Z ) ), alpha62( X, Y, Z ) }.
% 1.30/1.73 { ! alpha64( X, Y, Z ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X,
% 1.30/1.73 skol42( X, T, U ) ) }.
% 1.30/1.73 { ! alpha64( X, Y, Z ), alpha66( X, Y, Z, skol42( X, Y, Z ) ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, X, T ), ! alpha66( X, Y, Z
% 1.30/1.73 , T ), alpha64( X, Y, Z ) }.
% 1.30/1.73 { ! alpha66( X, Y, Z, T ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.73 T, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) }.
% 1.30/1.73 { ! alpha66( X, Y, Z, T ), Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.30/1.73 tc_Int_Oint ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.30/1.73 X ), Z ) ), T ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, T,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), ! Y = hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), T ), alpha66( X
% 1.30/1.73 , Y, Z, T ) }.
% 1.30/1.73 { ! alpha50( X, Y, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha57( X, Y, Z ) }.
% 1.30/1.73 { c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero(
% 1.30/1.73 tc_Int_Oint ), X ), alpha50( X, Y, Z ) }.
% 1.30/1.73 { ! alpha57( X, Y, Z ), alpha50( X, Y, Z ) }.
% 1.30/1.73 { ! alpha57( X, Y, Z ), ! alpha63( X, Y, T ), hBOOL( hAPP( Z, T ) ) }.
% 1.30/1.73 { ! hBOOL( hAPP( Z, skol43( T, U, Z ) ) ), alpha57( X, Y, Z ) }.
% 1.30/1.73 { alpha63( X, Y, skol43( X, Y, Z ) ), alpha57( X, Y, Z ) }.
% 1.30/1.73 { ! alpha63( X, Y, Z ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), skol44( T, U, W ) ) }.
% 1.30/1.73 { ! alpha63( X, Y, Z ), alpha65( X, Y, Z, skol44( X, Y, Z ) ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), T ), ! alpha65( X, Y, Z, T )
% 1.30/1.73 , alpha63( X, Y, Z ) }.
% 1.30/1.73 { ! alpha65( X, Y, Z, T ), c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X
% 1.30/1.73 ) }.
% 1.30/1.73 { ! alpha65( X, Y, Z, T ), Y = hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.30/1.73 tc_Int_Oint ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ),
% 1.30/1.73 X ), Z ) ), T ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, T, X ), ! Y = hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Z ) ), T ), alpha65( X
% 1.30/1.73 , Y, Z, T ) }.
% 1.30/1.73 { ! alpha22( X, Y ), ! X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ),
% 1.30/1.73 hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ) }.
% 1.30/1.73 { X = c_Groups_Ozero__class_Ozero( tc_Int_Oint ), alpha22( X, Y ) }.
% 1.30/1.73 { ! hBOOL( hAPP( Y, c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ) ), alpha22
% 1.30/1.73 ( X, Y ) }.
% 1.30/1.73 { ! T = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ), alpha70
% 1.30/1.73 ( X, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Z ), Z =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.30/1.73 tc_Int_Oint, T, Z ) = Y }.
% 1.30/1.73 { ! T = hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ), alpha70
% 1.30/1.73 ( X, Z ), ! c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( tc_Int_Oint, X,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ) ), Z =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), c_Divides_Odiv__class_Odiv(
% 1.30/1.73 tc_Int_Oint, T, Z ) = Y }.
% 1.30/1.73 { ! alpha70( X, Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), Y ) }.
% 1.30/1.73 { ! alpha70( X, Y ), ! c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.30/1.73 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless__eq( tc_Int_Oint,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Int_Oint ), X ), alpha70( X, Y ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.30/1.73 ( tc_Int_Oint ), Y ), c_Orderings_Oord__class_Oless( tc_Int_Oint, X, Y )
% 1.30/1.73 , alpha70( X, Y ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( tc_RealDef_Oreal,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), Y ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), c_RComplete_Onatfloor( X )
% 1.30/1.73 ), c_RComplete_Onatfloor( Y ) ), c_RComplete_Onatfloor( hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), Y ) ) ) }.
% 1.30/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), Y ), X
% 1.30/1.73 ) = hAPP( hAPP( c_Complex_Ocomplex_OComplex, hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( c_Complex_ORe, Y
% 1.30/1.73 ) ), hAPP( c_Complex_ORe, X ) ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( c_Complex_OIm, Y
% 1.30/1.73 ) ), hAPP( c_Complex_OIm, X ) ) ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( c_Complex_ORe, Y
% 1.30/1.73 ) ), hAPP( c_Complex_OIm, X ) ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), hAPP( c_Complex_OIm, Y
% 1.30/1.73 ) ), hAPP( c_Complex_ORe, X ) ) ) ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.30/1.73 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, Z, hAPP
% 1.30/1.73 ( hAPP( c_Groups_Oplus__class_Oplus( tc_Int_Oint ), Y ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP(
% 1.30/1.73 c_Groups_Oabs__class_Oabs( tc_Int_Oint ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Y ), Z ) ) ),
% 1.30/1.73 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ) ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_Int_Oint, c_Groups_Ozero__class_Ozero
% 1.30/1.73 ( tc_Int_Oint ), X ), c_Orderings_Oord__class_Oless( tc_Int_Oint, hAPP(
% 1.30/1.73 hAPP( c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Int_Oint ), hAPP(
% 1.30/1.73 c_Groups_Oabs__class_Oabs( tc_Int_Oint ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( tc_Int_Oint ), Z ), Y ) ) ),
% 1.30/1.73 c_Groups_Oone__class_Oone( tc_Int_Oint ) ) ), X ) ), Y ) }.
% 1.30/1.73 { hAPP( hAPP( c_Rings_Oinverse__class_Odivide( tc_Complex_Ocomplex ), Y ),
% 1.30/1.73 X ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), Y
% 1.30/1.73 ), hAPP( c_Rings_Oinverse__class_Oinverse( tc_Complex_Ocomplex ), X ) )
% 1.30/1.73 }.
% 1.30/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) ), X ) = hAPP(
% 1.30/1.73 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) ) }.
% 1.30/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP
% 1.30/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) }.
% 1.30/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), Y ) ), X ) = hAPP(
% 1.30/1.73 hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Z ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) ) }.
% 1.30/1.73 { hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), Y ), X ) = hAPP
% 1.30/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Int_Oint ), X ), Y ) }.
% 1.30/1.73 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) =
% 1.30/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ) }.
% 1.30/1.73 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), Y ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.30/1.73 c_Power_Opower__class_Opower( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ),
% 1.30/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ) ) }.
% 1.30/1.73 { ! Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.30/1.73 { Y = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), X ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), Y ),
% 1.30/1.73 c_Groups_Oone__class_Oone( tc_Nat_Onat ) ) ), X ) ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__ring__strict( X ), ! hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), Z = c_Groups_Ozero__class_Ozero( X ) }
% 1.30/1.73 .
% 1.30/1.73 { ! class_Rings_Olinordered__ring__strict( X ), ! hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), Y = c_Groups_Ozero__class_Ozero( X ) }
% 1.30/1.73 .
% 1.30/1.73 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.73 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) ), Z = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.73 }.
% 1.30/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) ), Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.73 }.
% 1.30/1.73 { ! class_Rings_Olinordered__ring__strict( X ), ! Z =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.73 , c_Orderings_Oord__class_Oless__eq( X, hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__ring( X ), c_Orderings_Oord__class_Oless__eq(
% 1.30/1.73 X, c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__ring__strict( X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( X, c_Groups_Ozero__class_Ozero( X ), hAPP
% 1.30/1.73 ( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ), ! Z =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), ! Y = c_Groups_Ozero__class_Ozero( X )
% 1.30/1.73 }.
% 1.30/1.73 { ! class_Rings_Olinordered__ring__strict( X ), Z =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.30/1.73 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP(
% 1.30/1.73 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__ring__strict( X ), Y =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), c_Orderings_Oord__class_Oless( X,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ), hAPP( hAPP( c_Groups_Oplus__class_Oplus
% 1.30/1.73 ( X ), hAPP( hAPP( c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP(
% 1.30/1.73 hAPP( c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ) ) }.
% 1.30/1.73 { ! class_Rings_Olinordered__ring( X ), ! c_Orderings_Oord__class_Oless( X
% 1.30/1.73 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Z ), Z ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( X ), Y ), Y ) ),
% 1.30/1.73 c_Groups_Ozero__class_Ozero( X ) ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), Z ) ) }
% 1.30/1.73 .
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, T, hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), Z ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), T ), Z )
% 1.30/1.73 }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), T ), Z )
% 1.30/1.73 , c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) ) }.
% 1.30/1.73 { ! hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) =
% 1.30/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ), Z =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), Y = X }.
% 1.30/1.73 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ) = hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }.
% 1.30/1.73 { ! Y = X, hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y
% 1.30/1.73 ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) }
% 1.30/1.73 .
% 1.30/1.73 { hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), T ), Z ) ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), Z ) ), X ) ) = hAPP(
% 1.30/1.73 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), T ), Y ) ), Z ) ), X ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.30/1.73 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP
% 1.30/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP(
% 1.30/1.73 hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.30/1.73 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, Z, Y
% 1.30/1.73 ), c_Orderings_Oord__class_Oless( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.30/1.73 ( tc_Nat_Onat ), X ), ! hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.30/1.73 tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.30/1.73 tc_Nat_Onat ), X ), Y ), Z = Y }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.30/1.73 ( tc_Nat_Onat ), X ), ! Z = Y, hAPP( hAPP( c_Groups_Otimes__class_Otimes
% 1.30/1.73 ( tc_Nat_Onat ), X ), Z ) = hAPP( hAPP( c_Groups_Otimes__class_Otimes(
% 1.30/1.73 tc_Nat_Onat ), X ), Y ) }.
% 1.30/1.73 { ! Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.30/1.73 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ) }.
% 1.30/1.73 { Z = c_Groups_Ozero__class_Ozero( tc_Nat_Onat ),
% 1.30/1.73 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), Y ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Z ), X ) ) =
% 1.30/1.73 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Y, X ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.30/1.73 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat,
% 1.30/1.73 hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP
% 1.30/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z, Y ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.30/1.73 ( tc_Nat_Onat ), X ), ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z
% 1.30/1.73 , Y ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) = hAPP(
% 1.30/1.73 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ), T = hAPP(
% 1.30/1.73 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), Z ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! T = hAPP(
% 1.30/1.73 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), Z ),
% 1.30/1.73 hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) = hAPP(
% 1.30/1.73 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ) ), hAPP(
% 1.30/1.73 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) ) = hAPP(
% 1.30/1.73 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), T ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), Z ) ) }
% 1.30/1.73 .
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), Z ) ) }
% 1.30/1.73 .
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, T, hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), Z ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), T ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), Z ) ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) = hAPP(
% 1.30/1.73 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), T ) = Z
% 1.30/1.73 }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), ! hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), T ) = Z
% 1.30/1.73 , hAPP( hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) = hAPP(
% 1.30/1.73 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ) ), hAPP(
% 1.30/1.73 hAPP( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) ) = hAPP(
% 1.30/1.73 hAPP( c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), T ) ), Z
% 1.30/1.73 ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) ),
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), T ), Z )
% 1.30/1.73 }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Y, X ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Ominus__class_Ominus( tc_Nat_Onat ), X ), Y ) ), U ) ), T ), Z )
% 1.30/1.73 , c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, hAPP( hAPP(
% 1.30/1.73 c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), U ) ), T ), hAPP( hAPP
% 1.30/1.73 ( c_Groups_Oplus__class_Oplus( tc_Nat_Onat ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), Y ), U ) ), Z ) ) }.
% 1.30/1.73 { ! c_Orderings_Oord__class_Oless( tc_Nat_Onat, c_Groups_Ozero__class_Ozero
% 1.30/1.73 ( tc_Nat_Onat ), X ), c_Divides_Odiv__class_Odiv( tc_Nat_Onat, hAPP( hAPP
% 1.30/1.73 ( c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Z ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_Nat_Onat ), X ), Y ) ) =
% 1.30/1.73 c_Divides_Odiv__class_Odiv( tc_Nat_Onat, Z, Y ) }.
% 1.30/1.73 { X = c_Groups_Ozero__class_Ozero( tc_Complex_Ocomplex ), Y =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_Nat_Onat ), c_Orderings_Oord__class_Oless
% 1.30/1.73 ( tc_RealDef_Oreal, hAPP( c_RealVector_Onorm__class_Onorm(
% 1.30/1.73 tc_Complex_Ocomplex ), hAPP( hAPP( c_Groups_Oplus__class_Oplus(
% 1.30/1.73 tc_Complex_Ocomplex ), c_Groups_Oone__class_Oone( tc_Complex_Ocomplex ) )
% 1.30/1.73 , hAPP( hAPP( c_Groups_Otimes__class_Otimes( tc_Complex_Ocomplex ), X ),
% 1.30/1.73 hAPP( hAPP( c_Power_Opower__class_Opower( tc_Complex_Ocomplex ), skol45(
% 1.30/1.73 X, Y ) ), Y ) ) ) ), c_Groups_Oone__class_Oone( tc_RealDef_Oreal ) ) }.
% 1.30/1.73 { c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ), X =
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ) }.
% 1.30/1.73 { ! X = c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), !
% 1.30/1.73 c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.30/1.73 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), hAPP( hAPP(
% 1.30/1.73 c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), X ), X ) ) }.
% 1.30/1.73 { hAPP( hAPP( c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal ), hAPP(
% 1.30/1.73 hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), X ) ), hAPP
% 1.30/1.73 ( hAPP( c_Groups_Otimes__class_Otimes( tc_RealDef_Oreal ), Y ), Y ) ) =
% 1.30/1.73 hAPP( hAPP( c_Rings_Oinverse__class_Odivide( tc_RealDef_Oreal ), X ), Y )
% 1.30/1.73 }.
% 1.30/1.73 { ! class_Rings_Oidom( X ), class_Rings_Oidom( tc_Polynomial_Opoly( X ) ) }
% 1.30/1.73 .
% 1.30/1.73 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.30/1.73 class_Groups_Ocancel__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.73 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring__0(
% 1.30/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.73 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Ocomm__ring__1(
% 1.30/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.73 { ! class_Rings_Ocomm__ring( X ), class_Rings_Ocomm__ring(
% 1.30/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.30/1.73 { class_Rings_Oidom( tc_Complex_Ocomplex ) }.
% 1.30/1.73 { class_Groups_Ocancel__comm__monoid__add( tc_Complex_Ocomplex ) }.
% 1.30/1.73 { class_Rings_Ocomm__semiring__0( tc_Complex_Ocomplex ) }.
% 1.30/1.73 { class_Rings_Ocomm__ring__1( tc_Complex_Ocomplex ) }.
% 1.30/1.73 { class_Rings_Ocomm__ring( tc_Complex_Ocomplex ) }.
% 1.30/1.73 { class_Rings_Oidom( tc_RealDef_Oreal ) }.
% 1.30/1.73 { class_Groups_Ocancel__comm__monoid__add( tc_RealDef_Oreal ) }.
% 1.30/1.73 { class_Rings_Ocomm__semiring__0( tc_RealDef_Oreal ) }.
% 1.30/1.73 { class_Rings_Ocomm__ring__1( tc_RealDef_Oreal ) }.
% 1.30/1.73 { class_Rings_Ocomm__ring( tc_RealDef_Oreal ) }.
% 1.30/1.73 { class_Groups_Ocancel__comm__monoid__add( tc_Nat_Onat ) }.
% 1.30/1.73 { class_Rings_Ocomm__semiring__0( tc_Nat_Onat ) }.
% 1.30/1.73 { class_Rings_Oidom( tc_Int_Oint ) }.
% 1.30/1.73 { class_Groups_Ocancel__comm__monoid__add( tc_Int_Oint ) }.
% 1.30/1.73 { class_Rings_Ocomm__semiring__0( tc_Int_Oint ) }.
% 1.30/1.73 { class_Rings_Ocomm__ring__1( tc_Int_Oint ) }.
% 1.30/1.73 { class_Rings_Ocomm__ring( tc_Int_Oint ) }.
% 1.30/1.73 { ! class_Orderings_Opreorder( X ), class_Orderings_Opreorder( tc_fun( Y, X
% 1.30/1.73 ) ) }.
% 1.30/1.73 { ! class_Orderings_Oorder( X ), class_Orderings_Oorder( tc_fun( Y, X ) ) }
% 1.30/1.73 .
% 1.30/1.73 { ! class_Orderings_Oord( X ), class_Orderings_Oord( tc_fun( Y, X ) ) }.
% 1.30/1.73 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.30/1.73 tc_Int_Oint ) }.
% 1.30/1.73 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.30/1.73 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Int_Oint ) }.
% 1.30/1.73 { class_Rings_Olinordered__comm__semiring__strict( tc_Int_Oint ) }.
% 1.30/1.73 { class_Rings_Olinordered__semiring__1__strict( tc_Int_Oint ) }.
% 1.30/1.73 { class_Rings_Olinordered__semiring__strict( tc_Int_Oint ) }.
% 1.30/1.73 { class_Groups_Oordered__ab__semigroup__add( tc_Int_Oint ) }.
% 1.30/1.73 { class_Groups_Oordered__ab__group__add__abs( tc_Int_Oint ) }.
% 1.30/1.73 { class_Groups_Oordered__comm__monoid__add( tc_Int_Oint ) }.
% 1.30/1.73 { class_Groups_Olinordered__ab__group__add( tc_Int_Oint ) }.
% 1.30/1.73 { class_Groups_Ocancel__ab__semigroup__add( tc_Int_Oint ) }.
% 1.30/1.73 { class_Rings_Oring__1__no__zero__divisors( tc_Int_Oint ) }.
% 1.30/1.73 { class_Rings_Oordered__cancel__semiring( tc_Int_Oint ) }.
% 1.30/1.73 { class_Rings_Olinordered__ring__strict( tc_Int_Oint ) }.
% 1.30/1.73 { class_Rings_Oring__no__zero__divisors( tc_Int_Oint ) }.
% 1.30/1.73 { class_Rings_Oordered__comm__semiring( tc_Int_Oint ) }.
% 1.30/1.73 { class_Rings_Olinordered__semiring__1( tc_Int_Oint ) }.
% 1.30/1.73 { class_Groups_Oordered__ab__group__add( tc_Int_Oint ) }.
% 1.30/1.73 { class_Groups_Ocancel__semigroup__add( tc_Int_Oint ) }.
% 1.30/1.73 { class_Rings_Olinordered__semiring( tc_Int_Oint ) }.
% 1.30/1.73 { class_Rings_Olinordered__semidom( tc_Int_Oint ) }.
% 1.30/1.73 { class_Groups_Oab__semigroup__mult( tc_Int_Oint ) }.
% 1.30/1.73 { class_Groups_Ocomm__monoid__mult( tc_Int_Oint ) }.
% 1.30/1.73 { class_Groups_Oab__semigroup__add( tc_Int_Oint ) }.
% 1.30/1.73 { class_Rings_Oordered__semiring( tc_Int_Oint ) }.
% 1.30/1.73 { class_Rings_Oordered__ring__abs( tc_Int_Oint ) }.
% 1.30/1.73 { class_Rings_Ono__zero__divisors( tc_Int_Oint ) }.
% 1.30/1.73 { class_Groups_Ocomm__monoid__add( tc_Int_Oint ) }.
% 1.30/1.73 { class_Rings_Olinordered__ring( tc_Int_Oint ) }.
% 1.30/1.73 { class_Rings_Olinordered__idom( tc_Int_Oint ) }.
% 1.30/1.73 { class_Rings_Ocomm__semiring__1( tc_Int_Oint ) }.
% 1.30/1.73 { class_Divides_Osemiring__div( tc_Int_Oint ) }.
% 1.30/1.73 { class_Rings_Ocomm__semiring( tc_Int_Oint ) }.
% 1.30/1.73 { class_Groups_Oab__group__add( tc_Int_Oint ) }.
% 1.30/1.73 { class_Rings_Ozero__neq__one( tc_Int_Oint ) }.
% 1.30/1.73 { class_Rings_Oordered__ring( tc_Int_Oint ) }.
% 1.30/1.73 { class_Orderings_Opreorder( tc_Int_Oint ) }.
% 1.30/1.73 { class_Orderings_Olinorder( tc_Int_Oint ) }.
% 1.30/1.73 { class_Groups_Omonoid__mult( tc_Int_Oint ) }.
% 1.30/1.73 { class_Groups_Omonoid__add( tc_Int_Oint ) }.
% 1.30/1.73 { class_Rings_Osemiring__0( tc_Int_Oint ) }.
% 1.30/1.73 { class_Groups_Ogroup__add( tc_Int_Oint ) }.
% 1.30/1.73 { class_Rings_Omult__zero( tc_Int_Oint ) }.
% 1.30/1.73 { class_Orderings_Oorder( tc_Int_Oint ) }.
% 1.30/1.73 { class_Rings_Osemiring( tc_Int_Oint ) }.
% 1.30/1.73 { class_Orderings_Oord( tc_Int_Oint ) }.
% 1.30/1.73 { class_Rings_Oring__1( tc_Int_Oint ) }.
% 1.30/1.73 { class_Power_Opower( tc_Int_Oint ) }.
% 1.30/1.73 { class_Groups_Ozero( tc_Int_Oint ) }.
% 1.30/1.73 { class_Rings_Oring( tc_Int_Oint ) }.
% 1.30/1.73 { class_Groups_Oone( tc_Int_Oint ) }.
% 1.30/1.73 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.30/1.73 tc_Nat_Onat ) }.
% 1.30/1.73 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.30/1.73 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Nat_Onat ) }.
% 1.30/1.73 { class_Rings_Olinordered__comm__semiring__strict( tc_Nat_Onat ) }.
% 1.30/1.73 { class_Rings_Olinordered__semiring__strict( tc_Nat_Onat ) }.
% 1.30/1.73 { class_Groups_Oordered__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.30/1.73 { class_Groups_Oordered__comm__monoid__add( tc_Nat_Onat ) }.
% 1.30/1.73 { class_Groups_Ocancel__ab__semigroup__add( tc_Nat_Onat ) }.
% 1.30/1.73 { class_Rings_Oordered__cancel__semiring( tc_Nat_Onat ) }.
% 1.30/1.73 { class_Rings_Oordered__comm__semiring( tc_Nat_Onat ) }.
% 1.30/1.73 { class_Groups_Ocancel__semigroup__add( tc_Nat_Onat ) }.
% 1.30/1.73 { class_Rings_Olinordered__semiring( tc_Nat_Onat ) }.
% 1.30/1.73 { class_Rings_Olinordered__semidom( tc_Nat_Onat ) }.
% 1.30/1.73 { class_Groups_Oab__semigroup__mult( tc_Nat_Onat ) }.
% 1.30/1.73 { class_Groups_Ocomm__monoid__mult( tc_Nat_Onat ) }.
% 1.30/1.73 { class_Groups_Oab__semigroup__add( tc_Nat_Onat ) }.
% 1.30/1.73 { class_Rings_Oordered__semiring( tc_Nat_Onat ) }.
% 1.30/1.73 { class_Rings_Ono__zero__divisors( tc_Nat_Onat ) }.
% 1.30/1.73 { class_Groups_Ocomm__monoid__add( tc_Nat_Onat ) }.
% 1.30/1.73 { class_Rings_Ocomm__semiring__1( tc_Nat_Onat ) }.
% 1.30/1.73 { class_Divides_Osemiring__div( tc_Nat_Onat ) }.
% 1.30/1.73 { class_Rings_Ocomm__semiring( tc_Nat_Onat ) }.
% 1.30/1.73 { class_Rings_Ozero__neq__one( tc_Nat_Onat ) }.
% 1.30/1.73 { class_Orderings_Opreorder( tc_Nat_Onat ) }.
% 1.30/1.73 { class_Orderings_Olinorder( tc_Nat_Onat ) }.
% 1.30/1.73 { class_Groups_Omonoid__mult( tc_Nat_Onat ) }.
% 1.30/1.73 { class_Groups_Omonoid__add( tc_Nat_Onat ) }.
% 1.30/1.73 { class_Rings_Osemiring__0( tc_Nat_Onat ) }.
% 1.30/1.73 { class_Rings_Omult__zero( tc_Nat_Onat ) }.
% 1.30/1.73 { class_Orderings_Oorder( tc_Nat_Onat ) }.
% 1.30/1.73 { class_Rings_Osemiring( tc_Nat_Onat ) }.
% 1.30/1.73 { class_Orderings_Oord( tc_Nat_Onat ) }.
% 1.30/1.73 { class_Power_Opower( tc_Nat_Onat ) }.
% 1.30/1.73 { class_Groups_Ozero( tc_Nat_Onat ) }.
% 1.30/1.73 { class_Groups_Oone( tc_Nat_Onat ) }.
% 1.30/1.73 { class_Orderings_Opreorder( tc_HOL_Obool ) }.
% 1.30/1.73 { class_Orderings_Oorder( tc_HOL_Obool ) }.
% 1.30/1.73 { class_Orderings_Oord( tc_HOL_Obool ) }.
% 1.30/1.73 { class_Orderings_Opreorder( tc_Limits_Onet( X ) ) }.
% 1.30/1.73 { class_Orderings_Oorder( tc_Limits_Onet( X ) ) }.
% 1.30/1.73 { class_Orderings_Oord( tc_Limits_Onet( X ) ) }.
% 1.30/1.73 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.30/1.73 tc_RealDef_Oreal ) }.
% 1.30/1.73 { class_Groups_Oordered__cancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Groups_Oordered__ab__semigroup__add__imp__le( tc_RealDef_Oreal ) }
% 1.37/1.73 .
% 1.37/1.73 { class_Rings_Olinordered__comm__semiring__strict( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Fields_Olinordered__field__inverse__zero( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Rings_Olinordered__semiring__1__strict( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_RealVector_Oreal__normed__div__algebra( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Rings_Olinordered__semiring__strict( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Rings_Odivision__ring__inverse__zero( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_RealVector_Oreal__normed__algebra__1( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Groups_Oordered__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Groups_Oordered__ab__group__add__abs( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_RealVector_Oreal__normed__algebra( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Groups_Oordered__comm__monoid__add( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Groups_Olinordered__ab__group__add( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Groups_Ocancel__ab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Rings_Oring__1__no__zero__divisors( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Rings_Oordered__cancel__semiring( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_RealVector_Oreal__normed__vector( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Rings_Olinordered__ring__strict( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_RealVector_Otopological__space( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_RealVector_Oreal__normed__field( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Rings_Oring__no__zero__divisors( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Rings_Oordered__comm__semiring( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Rings_Olinordered__semiring__1( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Groups_Oordered__ab__group__add( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Groups_Ocancel__semigroup__add( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Rings_Olinordered__semiring( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Fields_Ofield__inverse__zero( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Rings_Olinordered__semidom( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Groups_Oab__semigroup__mult( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_RealVector_Ometric__space( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Groups_Ocomm__monoid__mult( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Groups_Oab__semigroup__add( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Fields_Olinordered__field( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Rings_Oordered__semiring( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Rings_Oordered__ring__abs( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Rings_Ono__zero__divisors( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Groups_Ocomm__monoid__add( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Rings_Olinordered__ring( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Rings_Olinordered__idom( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Rings_Ocomm__semiring__1( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_RealVector_Oreal__field( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Rings_Odivision__ring( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Rings_Ocomm__semiring( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Groups_Oab__group__add( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_SEQ_Ocomplete__space( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Rings_Ozero__neq__one( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Rings_Oordered__ring( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Orderings_Opreorder( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Orderings_Olinorder( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Groups_Omonoid__mult( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Groups_Omonoid__add( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Rings_Osemiring__0( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Groups_Ogroup__add( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Rings_Omult__zero( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Orderings_Oorder( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Rings_Osemiring( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Orderings_Oord( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Rings_Oring__1( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Fields_Ofield( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Power_Opower( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Groups_Ozero( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Rings_Oring( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Groups_Oone( tc_RealDef_Oreal ) }.
% 1.37/1.73 { class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.37/1.73 tc_Complex_Ocomplex ) }.
% 1.37/1.73 { class_RealVector_Oreal__normed__div__algebra( tc_Complex_Ocomplex ) }.
% 1.37/1.73 { class_Rings_Odivision__ring__inverse__zero( tc_Complex_Ocomplex ) }.
% 1.37/1.73 { class_RealVector_Oreal__normed__algebra__1( tc_Complex_Ocomplex ) }.
% 1.37/1.73 { class_RealVector_Oreal__normed__algebra( tc_Complex_Ocomplex ) }.
% 1.37/1.73 { class_Groups_Ocancel__ab__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.37/1.73 { class_Rings_Oring__1__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.37/1.73 { class_RealVector_Oreal__normed__vector( tc_Complex_Ocomplex ) }.
% 1.37/1.73 { class_RealVector_Otopological__space( tc_Complex_Ocomplex ) }.
% 1.37/1.73 { class_RealVector_Oreal__normed__field( tc_Complex_Ocomplex ) }.
% 1.37/1.73 { class_Rings_Oring__no__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.37/1.73 { class_Groups_Ocancel__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.37/1.73 { class_Fields_Ofield__inverse__zero( tc_Complex_Ocomplex ) }.
% 1.37/1.73 { class_Groups_Oab__semigroup__mult( tc_Complex_Ocomplex ) }.
% 1.37/1.73 { class_RealVector_Ometric__space( tc_Complex_Ocomplex ) }.
% 1.37/1.73 { class_Groups_Ocomm__monoid__mult( tc_Complex_Ocomplex ) }.
% 1.37/1.73 { class_Groups_Oab__semigroup__add( tc_Complex_Ocomplex ) }.
% 1.37/1.73 { class_Rings_Ono__zero__divisors( tc_Complex_Ocomplex ) }.
% 1.37/1.73 { class_Groups_Ocomm__monoid__add( tc_Complex_Ocomplex ) }.
% 1.37/1.73 { class_Rings_Ocomm__semiring__1( tc_Complex_Ocomplex ) }.
% 1.37/1.73 { class_RealVector_Oreal__field( tc_Complex_Ocomplex ) }.
% 1.37/1.73 { class_Rings_Odivision__ring( tc_Complex_Ocomplex ) }.
% 1.37/1.73 { class_Rings_Ocomm__semiring( tc_Complex_Ocomplex ) }.
% 1.37/1.73 { class_Groups_Oab__group__add( tc_Complex_Ocomplex ) }.
% 1.37/1.73 { class_SEQ_Ocomplete__space( tc_Complex_Ocomplex ) }.
% 1.37/1.73 { class_Rings_Ozero__neq__one( tc_Complex_Ocomplex ) }.
% 1.37/1.73 { class_Groups_Omonoid__mult( tc_Complex_Ocomplex ) }.
% 1.37/1.73 { class_Groups_Omonoid__add( tc_Complex_Ocomplex ) }.
% 1.37/1.73 { class_Rings_Osemiring__0( tc_Complex_Ocomplex ) }.
% 1.37/1.73 { class_Groups_Ogroup__add( tc_Complex_Ocomplex ) }.
% 1.37/1.73 { class_Rings_Omult__zero( tc_Complex_Ocomplex ) }.
% 1.37/1.73 { class_Rings_Osemiring( tc_Complex_Ocomplex ) }.
% 1.37/1.73 { class_Rings_Oring__1( tc_Complex_Ocomplex ) }.
% 1.37/1.73 { class_Fields_Ofield( tc_Complex_Ocomplex ) }.
% 1.37/1.73 { class_Power_Opower( tc_Complex_Ocomplex ) }.
% 1.37/1.73 { class_Groups_Ozero( tc_Complex_Ocomplex ) }.
% 1.37/1.73 { class_Rings_Oring( tc_Complex_Ocomplex ) }.
% 1.37/1.73 { class_Groups_Oone( tc_Complex_Ocomplex ) }.
% 1.37/1.73 { ! class_Rings_Oidom( X ),
% 1.37/1.73 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(
% 1.37/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.73 { ! class_Rings_Olinordered__idom( X ),
% 1.37/1.73 class_Groups_Oordered__cancel__ab__semigroup__add( tc_Polynomial_Opoly( X
% 1.37/1.73 ) ) }.
% 1.37/1.73 { ! class_Rings_Olinordered__idom( X ),
% 1.37/1.73 class_Groups_Oordered__ab__semigroup__add__imp__le( tc_Polynomial_Opoly(
% 1.37/1.73 X ) ) }.
% 1.37/1.73 { ! class_Rings_Olinordered__idom( X ),
% 1.37/1.73 class_Rings_Olinordered__comm__semiring__strict( tc_Polynomial_Opoly( X )
% 1.37/1.73 ) }.
% 1.37/1.73 { ! class_Rings_Olinordered__idom( X ),
% 1.37/1.73 class_Rings_Olinordered__semiring__1__strict( tc_Polynomial_Opoly( X ) )
% 1.37/1.73 }.
% 1.37/1.73 { ! class_Rings_Olinordered__idom( X ),
% 1.37/1.73 class_Rings_Olinordered__semiring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.73 { ! class_Rings_Olinordered__idom( X ),
% 1.37/1.73 class_Groups_Oordered__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.73 { ! class_Rings_Olinordered__idom( X ),
% 1.37/1.73 class_Groups_Oordered__ab__group__add__abs( tc_Polynomial_Opoly( X ) ) }
% 1.37/1.73 .
% 1.37/1.73 { ! class_Rings_Olinordered__idom( X ),
% 1.37/1.73 class_Groups_Oordered__comm__monoid__add( tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.73 { ! class_Rings_Olinordered__idom( X ),
% 1.37/1.73 class_Groups_Olinordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.73 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.37/1.73 class_Groups_Ocancel__ab__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.73 { ! class_Rings_Oidom( X ), class_Rings_Oring__1__no__zero__divisors(
% 1.37/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.73 { ! class_Rings_Olinordered__idom( X ),
% 1.37/1.73 class_Rings_Oordered__cancel__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.73 { ! class_Rings_Olinordered__idom( X ),
% 1.37/1.73 class_Rings_Olinordered__ring__strict( tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.73 { ! class_Rings_Oidom( X ), class_Rings_Oring__no__zero__divisors(
% 1.37/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.73 { ! class_Rings_Olinordered__idom( X ),
% 1.37/1.73 class_Rings_Oordered__comm__semiring( tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.73 { ! class_Rings_Olinordered__idom( X ),
% 1.37/1.73 class_Rings_Olinordered__semiring__1( tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.73 { ! class_Rings_Olinordered__idom( X ),
% 1.37/1.73 class_Groups_Oordered__ab__group__add( tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.73 { ! class_Groups_Ocancel__comm__monoid__add( X ),
% 1.37/1.73 class_Groups_Ocancel__semigroup__add( tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.73 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semiring(
% 1.37/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.73 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__semidom(
% 1.37/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.73 { ! class_Rings_Ocomm__semiring__0( X ), class_Groups_Oab__semigroup__mult
% 1.37/1.73 ( tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.73 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Ocomm__monoid__mult(
% 1.37/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.73 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Oab__semigroup__add
% 1.37/1.73 ( tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.73 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__semiring(
% 1.37/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.73 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring__abs(
% 1.37/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.73 { ! class_Rings_Oidom( X ), class_Rings_Ono__zero__divisors(
% 1.37/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.73 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Ocomm__monoid__add(
% 1.37/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.73 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__ring(
% 1.37/1.73 tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.74 { ! class_Rings_Olinordered__idom( X ), class_Rings_Olinordered__idom(
% 1.37/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.74 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ocomm__semiring__1(
% 1.37/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.74 { ! class_Fields_Ofield( X ), class_Divides_Osemiring__div(
% 1.37/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.74 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Ocomm__semiring(
% 1.37/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.74 { ! class_Groups_Oab__group__add( X ), class_Groups_Oab__group__add(
% 1.37/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.74 { ! class_Rings_Ocomm__semiring__1( X ), class_Rings_Ozero__neq__one(
% 1.37/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.74 { ! class_Rings_Olinordered__idom( X ), class_Rings_Oordered__ring(
% 1.37/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.74 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Opreorder(
% 1.37/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.74 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Olinorder(
% 1.37/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.74 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Omonoid__mult(
% 1.37/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.74 { ! class_Groups_Ocomm__monoid__add( X ), class_Groups_Omonoid__add(
% 1.37/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.74 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring__0(
% 1.37/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.74 { ! class_Groups_Oab__group__add( X ), class_Groups_Ogroup__add(
% 1.37/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.74 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Omult__zero(
% 1.37/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.74 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oorder(
% 1.37/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.74 { ! class_Rings_Ocomm__semiring__0( X ), class_Rings_Osemiring(
% 1.37/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.74 { ! class_Rings_Olinordered__idom( X ), class_Orderings_Oord(
% 1.37/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.74 { ! class_Rings_Ocomm__ring__1( X ), class_Rings_Oring__1(
% 1.37/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.74 { ! class_Rings_Ocomm__semiring__1( X ), class_Power_Opower(
% 1.37/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.74 { ! class_Groups_Ozero( X ), class_Groups_Ozero( tc_Polynomial_Opoly( X ) )
% 1.37/1.74 }.
% 1.37/1.74 { ! class_Rings_Ocomm__ring( X ), class_Rings_Oring( tc_Polynomial_Opoly( X
% 1.37/1.74 ) ) }.
% 1.37/1.74 { ! class_Rings_Ocomm__semiring__1( X ), class_Groups_Oone(
% 1.37/1.74 tc_Polynomial_Opoly( X ) ) }.
% 1.37/1.74 { hAPP( c_COMBK( T, Z, Y ), X ) = Y }.
% 1.37/1.74 { hAPP( c_COMBB( W, U, T, Z, Y ), X ) = hAPP( Z, hAPP( Y, X ) ) }.
% 1.37/1.74 { hAPP( c_COMBC( W, U, T, Z, Y ), X ) = hAPP( hAPP( Z, X ), Y ) }.
% 1.37/1.74 { hAPP( c_COMBS( W, U, T, Z, Y ), X ) = hAPP( hAPP( Z, X ), hAPP( Y, X ) )
% 1.37/1.74 }.
% 1.37/1.74 { ! c_SEQ_Osubseq( X ), c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.37/1.74 c_Groups_Ozero__class_Ozero( tc_RealDef_Oreal ), skol46( Z, T ) ) }.
% 1.37/1.74 { ! c_SEQ_Osubseq( X ), c_Orderings_Oord__class_Oless__eq( tc_Nat_Onat, Z,
% 1.37/1.74 skol55( T, U, Z ) ) }.
% 1.37/1.74 { ! c_SEQ_Osubseq( X ), ! c_Orderings_Oord__class_Oless( tc_RealDef_Oreal,
% 1.37/1.74 hAPP( c_RealVector_Onorm__class_Onorm( tc_Complex_Ocomplex ), hAPP( hAPP
% 1.37/1.74 ( c_Groups_Ominus__class_Ominus( tc_Complex_Ocomplex ), hAPP( v_s, hAPP(
% 1.37/1.74 X, skol55( X, Y, Z ) ) ) ), Y ) ), skol46( X, Y ) ) }.
% 1.37/1.74
% 1.37/1.74 *** allocated 15000 integers for clauses
% 1.37/1.74 *** allocated 22500 integers for clauses
% 1.37/1.74 *** allocated 33750 integers for clauses
% 1.37/1.74 *** allocated 50625 integers for clauses
% 1.37/1.74 *** allocated 75937 integers for clauses
% 1.37/1.74 *** allocated 113905 integers for clauses
% 1.37/1.74 percentage equality = 0.204309, percentage horn = 0.890756
% 1.37/1.74 This is a problem with some equality
% 1.37/1.74
% 1.37/1.74
% 1.37/1.74
% 1.37/1.74 Options Used:
% 1.37/1.74
% 1.37/1.74 useres = 1
% 1.37/1.74 useparamod = 1
% 1.37/1.74 useeqrefl = 1
% 1.37/1.74 useeqfact = 1
% 1.37/1.74 usefactor = 1
% 1.37/1.74 usesimpsplitting = 0
% 1.37/1.74 usesimpdemod = 5
% 1.37/1.74 usesimpres = 3
% 1.37/1.74
% 1.37/1.74 resimpinuse = 1000
% 1.37/1.74 resimpclauses = 20000
% 1.37/1.74 substype = eqrewr
% 1.37/1.74 backwardsubs = 1
% 1.37/1.74 selectoldest = 5
% 1.37/1.74
% 1.37/1.74 litorderings [0] = split
% 1.37/1.74 litorderings [1] = extend the termordering, first sorting on arguments
% 1.37/1.74
% 1.37/1.74 termordering = kbo
% 1.37/1.74
% 1.37/1.74 litapriori = 0
% 1.37/1.74 termapriori = 1
% 1.37/1.74 litaposteriori = 0
% 1.37/1.74 termaposteriori = 0
% 1.37/1.74 demodaposteriori = 0
% 1.37/1.74 ordereqreflfact = 0
% 1.37/1.74
% 1.37/1.74 litselect = negord
% 1.37/1.74
% 1.37/1.74 maxweight = 15
% 1.37/1.74 maxdepth = 30000
% 1.37/1.74 maxlength = 115
% 1.37/1.74 maxnrvars = 195
% 1.37/1.74 excuselevel = 1
% 1.37/1.74 increasemaxweight = 1
% 1.37/1.74
% 1.37/1.74 maxselected = 10000000
% 1.37/1.74 maxnrclauses = 10000000
% 1.37/1.74
% 1.37/1.74 showgenerated = 0
% 1.37/1.74 showkept = 0
% 1.37/1.74 showselected = 0
% 1.37/1.74 showdeleted = 0
% 1.37/1.74 showresimp = 1
% 1.37/1.74 showstatus = 2000
% 1.37/1.74
% 1.37/1.74 prologoutput = 0
% 1.37/1.74 nrgoals = 5000000
% 1.37/1.74 totalproof = 1
% 1.37/1.74
% 1.37/1.74 Symbols occurring in the translation:
% 1.37/1.74
% 1.37/1.74 {} [0, 0] (w:1, o:2, a:1, s:1, b:0),
% 1.37/1.74 . [1, 2] (w:1, o:243, a:1, s:1, b:0),
% 1.37/1.74 ! [4, 1] (w:0, o:142, a:1, s:1, b:0),
% 1.37/1.74 = [13, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.37/1.74 ==> [14, 2] (w:1, o:0, a:0, s:1, b:0),
% 1.37/1.74 hAPP [38, 2] (w:1, o:267, a:1, s:1, b:0),
% 1.37/1.74 v_ga____ [39, 0] (w:1, o:15, a:1, s:1, b:0),
% 1.37/1.74 c_SEQ_Osubseq [40, 1] (w:1, o:152, a:1, s:1, b:0),
% 1.37/1.74 v_f____ [41, 0] (w:1, o:14, a:1, s:1, b:0),
% 1.37/1.74 class_RealVector_Oreal__normed__vector [44, 1] (w:1, o:153, a:1, s:1
% 1.37/1.74 , b:0),
% 1.37/1.74 tc_RealDef_Oreal [45, 0] (w:1, o:30, a:1, s:1, b:0),
% 1.37/1.74 c_Groups_Ozero__class_Ozero [46, 1] (w:1, o:154, a:1, s:1, b:0),
% 1.37/1.74 c_RealVector_Onorm__class_Onorm [47, 1] (w:1, o:147, a:1, s:1, b:0),
% 1.37/1.74
% 1.37/1.74 c_Orderings_Oord__class_Oless [48, 3] (w:1, o:309, a:1, s:1, b:0),
% 1.37/1.74 class_Groups_Oordered__ab__group__add [52, 1] (w:1, o:159, a:1, s:1
% 1.37/1.74 , b:0),
% 1.37/1.74 c_Groups_Ominus__class_Ominus [53, 1] (w:1, o:160, a:1, s:1, b:0),
% 1.37/1.74 c_Orderings_Oord__class_Oless__eq [54, 3] (w:1, o:310, a:1, s:1, b:0)
% 1.37/1.74 ,
% 1.37/1.74 tc_Complex_Ocomplex [56, 0] (w:1, o:40, a:1, s:1, b:0),
% 1.37/1.74 v_s [57, 0] (w:1, o:42, a:1, s:1, b:0),
% 1.37/1.74 v_r [58, 0] (w:1, o:41, a:1, s:1, b:0),
% 1.37/1.74 class_Orderings_Opreorder [59, 1] (w:1, o:163, a:1, s:1, b:0),
% 1.37/1.74 tc_Nat_Onat [61, 0] (w:1, o:52, a:1, s:1, b:0),
% 1.37/1.74 c_Fun_Ocomp [66, 5] (w:1, o:397, a:1, s:1, b:0),
% 1.37/1.74 class_Groups_Ozero [68, 1] (w:1, o:164, a:1, s:1, b:0),
% 1.37/1.74 class_Orderings_Olinorder [70, 1] (w:1, o:165, a:1, s:1, b:0),
% 1.37/1.74 class_Orderings_Oord [72, 1] (w:1, o:161, a:1, s:1, b:0),
% 1.37/1.74 tc_fun [73, 2] (w:1, o:286, a:1, s:1, b:0),
% 1.37/1.74 class_Orderings_Oorder [75, 1] (w:1, o:162, a:1, s:1, b:0),
% 1.37/1.74 class_Groups_Oab__group__add [78, 1] (w:1, o:166, a:1, s:1, b:0),
% 1.37/1.74 class_Groups_Ogroup__add [79, 1] (w:1, o:167, a:1, s:1, b:0),
% 1.37/1.74 c_SEQ_Odecseq [82, 2] (w:1, o:289, a:1, s:1, b:0),
% 1.37/1.74 c_SEQ_OBseq [83, 2] (w:1, o:290, a:1, s:1, b:0),
% 1.37/1.74 c_SEQ_Oincseq [85, 2] (w:1, o:291, a:1, s:1, b:0),
% 1.37/1.74 c_Complex_Ocomplex_OComplex [88, 0] (w:1, o:70, a:1, s:1, b:0),
% 1.37/1.74 v_x____ [89, 0] (w:1, o:71, a:1, s:1, b:0),
% 1.37/1.74 v_y____ [90, 0] (w:1, o:72, a:1, s:1, b:0),
% 1.37/1.74 c_SEQ_Omonoseq [91, 2] (w:1, o:293, a:1, s:1, b:0),
% 1.37/1.74 hBOOL [101, 1] (w:1, o:168, a:1, s:1, b:0),
% 1.37/1.74 c_Groups_Oabs__class_Oabs [109, 1] (w:1, o:169, a:1, s:1, b:0),
% 1.37/1.74 c_Complex_OIm [110, 0] (w:1, o:101, a:1, s:1, b:0),
% 1.37/1.74 c_Fundamental__Theorem__Algebra__Mirabelle_Opsize [112, 2] (w:1, o:
% 1.37/1.74 294, a:1, s:1, b:0),
% 1.37/1.74 tc_Polynomial_Opoly [113, 1] (w:1, o:178, a:1, s:1, b:0),
% 1.37/1.74 c_Complex_Ocomplex_Ocomplex__size [116, 1] (w:1, o:179, a:1, s:1, b:0
% 1.37/1.74 ),
% 1.37/1.74 class_Groups_Oordered__ab__group__add__abs [117, 1] (w:1, o:180, a:1
% 1.37/1.74 , s:1, b:0),
% 1.37/1.74 c_Nat_Osize__class_Osize [129, 2] (w:1, o:295, a:1, s:1, b:0),
% 1.37/1.74 c_Complex_ORe [130, 0] (w:1, o:107, a:1, s:1, b:0),
% 1.37/1.74 c_Complex_Ocomplex_Ocomplex__rec [132, 3] (w:1, o:311, a:1, s:1, b:0)
% 1.37/1.74 ,
% 1.37/1.74 c_Complex_Ocomplex_Ocomplex__case [133, 3] (w:1, o:312, a:1, s:1, b:0
% 1.37/1.74 ),
% 1.37/1.74 c_COMBB [134, 5] (w:1, o:398, a:1, s:1, b:0),
% 1.37/1.74 c_Groups_Oplus__class_Oplus [135, 1] (w:1, o:182, a:1, s:1, b:0),
% 1.37/1.74 c_Groups_Oone__class_Oone [136, 1] (w:1, o:181, a:1, s:1, b:0),
% 1.37/1.74 class_Groups_Oone [139, 1] (w:1, o:183, a:1, s:1, b:0),
% 1.37/1.74 class_Groups_Oab__semigroup__add [140, 1] (w:1, o:184, a:1, s:1, b:0)
% 1.37/1.74 ,
% 1.37/1.74 class_Groups_Ocancel__semigroup__add [141, 1] (w:1, o:185, a:1, s:1
% 1.37/1.74 , b:0),
% 1.37/1.74 class_Groups_Ocancel__ab__semigroup__add [142, 1] (w:1, o:186, a:1
% 1.37/1.74 , s:1, b:0),
% 1.37/1.74 class_RealVector_Oreal__normed__algebra__1 [143, 1] (w:1, o:187, a:1
% 1.37/1.74 , s:1, b:0),
% 1.37/1.74 class_Groups_Omonoid__add [144, 1] (w:1, o:189, a:1, s:1, b:0),
% 1.37/1.74 class_Groups_Ocomm__monoid__add [145, 1] (w:1, o:190, a:1, s:1, b:0)
% 1.37/1.74 ,
% 1.37/1.74 class_Groups_Olinordered__ab__group__add [146, 1] (w:1, o:188, a:1
% 1.37/1.74 , s:1, b:0),
% 1.37/1.74 class_Groups_Oordered__ab__semigroup__add__imp__le [147, 1] (w:1, o:
% 1.37/1.74 191, a:1, s:1, b:0),
% 1.37/1.74 class_Groups_Oordered__ab__semigroup__add [148, 1] (w:1, o:192, a:1
% 1.37/1.74 , s:1, b:0),
% 1.37/1.74 class_Groups_Oordered__cancel__ab__semigroup__add [149, 1] (w:1, o:
% 1.37/1.74 193, a:1, s:1, b:0),
% 1.37/1.74 class_Groups_Oordered__comm__monoid__add [150, 1] (w:1, o:194, a:1
% 1.37/1.74 , s:1, b:0),
% 1.37/1.74 c_SEQ_Oconvergent [153, 2] (w:1, o:288, a:1, s:1, b:0),
% 1.37/1.74 class_Rings_Olinordered__idom [155, 1] (w:1, o:195, a:1, s:1, b:0),
% 1.37/1.74 class_Rings_Olinordered__semidom [156, 1] (w:1, o:198, a:1, s:1, b:0)
% 1.37/1.74 ,
% 1.37/1.74 c_Limits_Osequentially [157, 0] (w:1, o:113, a:1, s:1, b:0),
% 1.37/1.74 c_Limits_Otendsto [158, 5] (w:1, o:399, a:1, s:1, b:0),
% 1.37/1.74 class_RealVector_Ometric__space [160, 1] (w:1, o:199, a:1, s:1, b:0)
% 1.37/1.74 ,
% 1.37/1.74 c_COMBK [161, 3] (w:1, o:313, a:1, s:1, b:0),
% 1.37/1.74 class_RealVector_Otopological__space [162, 1] (w:1, o:200, a:1, s:1
% 1.37/1.74 , b:0),
% 1.37/1.74 c_COMBC [163, 5] (w:1, o:400, a:1, s:1, b:0),
% 1.37/1.74 c_COMBS [165, 5] (w:1, o:401, a:1, s:1, b:0),
% 1.37/1.74 class_SEQ_Ocomplete__space [171, 1] (w:1, o:232, a:1, s:1, b:0),
% 1.37/1.74 class_Rings_Ozero__neq__one [172, 1] (w:1, o:201, a:1, s:1, b:0),
% 1.37/1.74 tc_Limits_Onet [175, 1] (w:1, o:233, a:1, s:1, b:0),
% 1.37/1.74 c_Complex_Oii [176, 0] (w:1, o:121, a:1, s:1, b:0),
% 1.37/1.74 c_SEQ_Olim [179, 2] (w:1, o:292, a:1, s:1, b:0),
% 1.37/1.74 c_RComplete_Onatceiling [180, 1] (w:1, o:148, a:1, s:1, b:0),
% 1.37/1.74 c_Power_Opower__class_Opower [181, 1] (w:1, o:234, a:1, s:1, b:0),
% 1.37/1.74 class_RealVector_Oreal__normed__div__algebra [182, 1] (w:1, o:202, a:
% 1.37/1.74 1, s:1, b:0),
% 1.37/1.74 class_Power_Opower [183, 1] (w:1, o:235, a:1, s:1, b:0),
% 1.37/1.74 class_RealVector_Oreal__normed__algebra [184, 1] (w:1, o:203, a:1, s:
% 1.37/1.74 1, b:0),
% 1.37/1.74 tc_Int_Oint [186, 0] (w:1, o:125, a:1, s:1, b:0),
% 1.37/1.74 class_Rings_Oring__1__no__zero__divisors [187, 1] (w:1, o:204, a:1
% 1.37/1.74 , s:1, b:0),
% 1.37/1.74 class_Groups_Omonoid__mult [188, 1] (w:1, o:236, a:1, s:1, b:0),
% 1.37/1.74 class_Rings_Omult__zero [189, 1] (w:1, o:210, a:1, s:1, b:0),
% 1.37/1.74 class_Rings_Ono__zero__divisors [190, 1] (w:1, o:211, a:1, s:1, b:0)
% 1.37/1.74 ,
% 1.37/1.74 class_Rings_Osemiring__0 [191, 1] (w:1, o:215, a:1, s:1, b:0),
% 1.37/1.74 class_Rings_Ocomm__semiring__1 [192, 1] (w:1, o:219, a:1, s:1, b:0),
% 1.37/1.74
% 1.37/1.74 c_RComplete_Onatfloor [193, 1] (w:1, o:149, a:1, s:1, b:0),
% 1.37/1.74 c_RealDef_Oreal [194, 2] (w:1, o:287, a:1, s:1, b:0),
% 1.37/1.74 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct [
% 1.37/1.74 199, 1] (w:1, o:237, a:1, s:1, b:0),
% 1.37/1.74 c_Rings_Oinverse__class_Odivide [200, 1] (w:1, o:150, a:1, s:1, b:0)
% 1.37/1.74 ,
% 1.37/1.74 class_Fields_Ofield__inverse__zero [201, 1] (w:1, o:155, a:1, s:1, b:
% 1.37/1.74 0),
% 1.37/1.74 class_Rings_Odivision__ring__inverse__zero [202, 1] (w:1, o:221, a:1
% 1.37/1.74 , s:1, b:0),
% 1.37/1.74 class_Rings_Odivision__ring [203, 1] (w:1, o:222, a:1, s:1, b:0),
% 1.37/1.74 class_RealVector_Oreal__normed__field [204, 1] (w:1, o:223, a:1, s:1
% 1.37/1.74 , b:0),
% 1.37/1.74 class_Fields_Ofield [209, 1] (w:1, o:156, a:1, s:1, b:0),
% 1.37/1.74 class_Fields_Olinordered__field__inverse__zero [210, 1] (w:1, o:157
% 1.37/1.74 , a:1, s:1, b:0),
% 1.37/1.74 class_Fields_Olinordered__field [211, 1] (w:1, o:158, a:1, s:1, b:0)
% 1.37/1.74 ,
% 1.37/1.74 c_Series_Osums [212, 3] (w:1, o:314, a:1, s:1, b:0),
% 1.37/1.74 c_Nat__Transfer_Otsub [213, 2] (w:1, o:296, a:1, s:1, b:0),
% 1.37/1.74 c_Divides_Odiv__class_Odiv [214, 3] (w:1, o:315, a:1, s:1, b:0),
% 1.37/1.74 class_Divides_Osemiring__div [215, 1] (w:1, o:238, a:1, s:1, b:0),
% 1.37/1.74 c_Rings_Oinverse__class_Oinverse [218, 1] (w:1, o:151, a:1, s:1, b:0)
% 1.37/1.74 ,
% 1.37/1.74 c_Groups_Otimes__class_Otimes [219, 1] (w:1, o:239, a:1, s:1, b:0),
% 1.37/1.74 class_Groups_Ocomm__monoid__mult [224, 1] (w:1, o:240, a:1, s:1, b:0)
% 1.37/1.74 ,
% 1.37/1.74 class_Rings_Oring__no__zero__divisors [229, 1] (w:1, o:212, a:1, s:1
% 1.37/1.74 , b:0),
% 1.37/1.74 class_Groups_Oab__semigroup__mult [230, 1] (w:1, o:241, a:1, s:1, b:0
% 1.37/1.74 ),
% 1.37/1.74 class_Rings_Osemiring [233, 1] (w:1, o:224, a:1, s:1, b:0),
% 1.37/1.74 class_Rings_Ocomm__semiring [234, 1] (w:1, o:220, a:1, s:1, b:0),
% 1.37/1.74 class_Rings_Oordered__cancel__semiring [235, 1] (w:1, o:225, a:1, s:1
% 1.37/1.74 , b:0),
% 1.37/1.74 class_Rings_Oordered__ring [236, 1] (w:1, o:226, a:1, s:1, b:0),
% 1.37/1.74 class_Rings_Oordered__semiring [237, 1] (w:1, o:228, a:1, s:1, b:0),
% 1.37/1.74
% 1.37/1.74 class_Rings_Oordered__comm__semiring [238, 1] (w:1, o:229, a:1, s:1
% 1.37/1.74 , b:0),
% 1.37/1.74 class_Rings_Olinordered__ring__strict [239, 1] (w:1, o:196, a:1, s:1
% 1.37/1.74 , b:0),
% 1.37/1.74 class_Rings_Olinordered__ring [240, 1] (w:1, o:197, a:1, s:1, b:0),
% 1.37/1.74 class_Rings_Olinordered__comm__semiring__strict [241, 1] (w:1, o:205
% 1.37/1.74 , a:1, s:1, b:0),
% 1.37/1.74 class_Rings_Olinordered__semiring__strict [242, 1] (w:1, o:206, a:1
% 1.37/1.74 , s:1, b:0),
% 1.37/1.74 class_Rings_Oring [243, 1] (w:1, o:213, a:1, s:1, b:0),
% 1.37/1.74 class_Rings_Olinordered__semiring [245, 1] (w:1, o:207, a:1, s:1, b:0
% 1.37/1.74 ),
% 1.37/1.74 class_Rings_Oring__1 [246, 1] (w:1, o:214, a:1, s:1, b:0),
% 1.37/1.74 class_Rings_Oordered__ring__abs [247, 1] (w:1, o:227, a:1, s:1, b:0)
% 1.37/1.74 ,
% 1.37/1.74 class_RealVector_Oreal__field [249, 1] (w:1, o:230, a:1, s:1, b:0),
% 1.37/1.74 class_Rings_Olinordered__semiring__1 [252, 1] (w:1, o:208, a:1, s:1
% 1.37/1.74 , b:0),
% 1.37/1.74 class_Rings_Olinordered__semiring__1__strict [253, 1] (w:1, o:209, a:
% 1.37/1.74 1, s:1, b:0),
% 1.37/1.74 class_Rings_Oidom [264, 1] (w:1, o:231, a:1, s:1, b:0),
% 1.37/1.74 class_Groups_Ocancel__comm__monoid__add [265, 1] (w:1, o:242, a:1, s:
% 1.37/1.74 1, b:0),
% 1.37/1.74 class_Rings_Ocomm__semiring__0 [266, 1] (w:1, o:218, a:1, s:1, b:0),
% 1.37/1.74
% 1.37/1.74 class_Rings_Ocomm__ring__1 [267, 1] (w:1, o:216, a:1, s:1, b:0),
% 1.37/1.74 class_Rings_Ocomm__ring [268, 1] (w:1, o:217, a:1, s:1, b:0),
% 1.37/1.74 tc_HOL_Obool [270, 0] (w:1, o:124, a:1, s:1, b:0),
% 1.37/1.74 alpha1 [276, 2] (w:1, o:297, a:1, s:1, b:1),
% 1.37/1.74 alpha2 [277, 3] (w:1, o:323, a:1, s:1, b:1),
% 1.37/1.74 alpha3 [278, 3] (w:1, o:330, a:1, s:1, b:1),
% 1.37/1.74 alpha4 [279, 4] (w:1, o:372, a:1, s:1, b:1),
% 1.37/1.74 alpha5 [280, 2] (w:1, o:299, a:1, s:1, b:1),
% 1.37/1.74 alpha6 [281, 3] (w:1, o:334, a:1, s:1, b:1),
% 1.37/1.74 alpha7 [282, 3] (w:1, o:339, a:1, s:1, b:1),
% 1.37/1.74 alpha8 [283, 3] (w:1, o:341, a:1, s:1, b:1),
% 1.37/1.74 alpha9 [284, 3] (w:1, o:342, a:1, s:1, b:1),
% 2.57/2.96 alpha10 [285, 2] (w:1, o:300, a:1, s:1, b:1),
% 2.57/2.96 alpha11 [286, 3] (w:1, o:316, a:1, s:1, b:1),
% 2.57/2.96 alpha12 [287, 3] (w:1, o:317, a:1, s:1, b:1),
% 2.57/2.96 alpha13 [288, 4] (w:1, o:373, a:1, s:1, b:1),
% 2.57/2.96 alpha14 [289, 4] (w:1, o:374, a:1, s:1, b:1),
% 2.57/2.96 alpha15 [290, 3] (w:1, o:318, a:1, s:1, b:1),
% 2.57/2.96 alpha16 [291, 3] (w:1, o:319, a:1, s:1, b:1),
% 2.57/2.96 alpha17 [292, 3] (w:1, o:320, a:1, s:1, b:1),
% 2.57/2.96 alpha18 [293, 3] (w:1, o:321, a:1, s:1, b:1),
% 2.57/2.96 alpha19 [294, 3] (w:1, o:322, a:1, s:1, b:1),
% 2.57/2.96 alpha20 [295, 3] (w:1, o:324, a:1, s:1, b:1),
% 2.57/2.96 alpha21 [296, 2] (w:1, o:301, a:1, s:1, b:1),
% 2.57/2.96 alpha22 [297, 2] (w:1, o:302, a:1, s:1, b:1),
% 2.57/2.96 alpha23 [298, 2] (w:1, o:303, a:1, s:1, b:1),
% 2.57/2.96 alpha24 [299, 3] (w:1, o:325, a:1, s:1, b:1),
% 2.57/2.96 alpha25 [300, 3] (w:1, o:326, a:1, s:1, b:1),
% 2.57/2.96 alpha26 [301, 2] (w:1, o:304, a:1, s:1, b:1),
% 2.57/2.96 alpha27 [302, 3] (w:1, o:327, a:1, s:1, b:1),
% 2.57/2.96 alpha28 [303, 3] (w:1, o:328, a:1, s:1, b:1),
% 2.57/2.96 alpha29 [304, 3] (w:1, o:329, a:1, s:1, b:1),
% 2.57/2.96 alpha30 [305, 3] (w:1, o:343, a:1, s:1, b:1),
% 2.57/2.96 alpha31 [306, 2] (w:1, o:305, a:1, s:1, b:1),
% 2.57/2.96 alpha32 [307, 3] (w:1, o:344, a:1, s:1, b:1),
% 2.57/2.96 alpha33 [308, 3] (w:1, o:345, a:1, s:1, b:1),
% 2.57/2.96 alpha34 [309, 4] (w:1, o:366, a:1, s:1, b:1),
% 2.57/2.96 alpha35 [310, 4] (w:1, o:367, a:1, s:1, b:1),
% 2.57/2.96 alpha36 [311, 4] (w:1, o:368, a:1, s:1, b:1),
% 2.57/2.96 alpha37 [312, 4] (w:1, o:369, a:1, s:1, b:1),
% 2.57/2.96 alpha38 [313, 4] (w:1, o:370, a:1, s:1, b:1),
% 2.57/2.96 alpha39 [314, 4] (w:1, o:371, a:1, s:1, b:1),
% 2.57/2.96 alpha40 [315, 4] (w:1, o:375, a:1, s:1, b:1),
% 2.57/2.96 alpha41 [316, 4] (w:1, o:376, a:1, s:1, b:1),
% 2.57/2.96 alpha42 [317, 3] (w:1, o:346, a:1, s:1, b:1),
% 2.57/2.96 alpha43 [318, 3] (w:1, o:347, a:1, s:1, b:1),
% 2.57/2.96 alpha44 [319, 2] (w:1, o:298, a:1, s:1, b:1),
% 2.57/2.96 alpha45 [320, 4] (w:1, o:377, a:1, s:1, b:1),
% 2.57/2.96 alpha46 [321, 4] (w:1, o:378, a:1, s:1, b:1),
% 2.57/2.96 alpha47 [322, 4] (w:1, o:379, a:1, s:1, b:1),
% 2.57/2.96 alpha48 [323, 4] (w:1, o:380, a:1, s:1, b:1),
% 2.57/2.96 alpha49 [324, 3] (w:1, o:348, a:1, s:1, b:1),
% 2.57/2.96 alpha50 [325, 3] (w:1, o:331, a:1, s:1, b:1),
% 2.57/2.96 alpha51 [326, 4] (w:1, o:381, a:1, s:1, b:1),
% 2.57/2.96 alpha52 [327, 4] (w:1, o:382, a:1, s:1, b:1),
% 2.57/2.96 alpha53 [328, 4] (w:1, o:383, a:1, s:1, b:1),
% 2.57/2.96 alpha54 [329, 4] (w:1, o:384, a:1, s:1, b:1),
% 2.57/2.96 alpha55 [330, 4] (w:1, o:385, a:1, s:1, b:1),
% 2.57/2.96 alpha56 [331, 3] (w:1, o:332, a:1, s:1, b:1),
% 2.57/2.96 alpha57 [332, 3] (w:1, o:333, a:1, s:1, b:1),
% 2.57/2.96 alpha58 [333, 4] (w:1, o:386, a:1, s:1, b:1),
% 2.57/2.96 alpha59 [334, 4] (w:1, o:387, a:1, s:1, b:1),
% 2.57/2.96 alpha60 [335, 4] (w:1, o:388, a:1, s:1, b:1),
% 2.57/2.96 alpha61 [336, 4] (w:1, o:389, a:1, s:1, b:1),
% 2.57/2.96 alpha62 [337, 3] (w:1, o:335, a:1, s:1, b:1),
% 2.57/2.96 alpha63 [338, 3] (w:1, o:336, a:1, s:1, b:1),
% 2.57/2.96 alpha64 [339, 3] (w:1, o:337, a:1, s:1, b:1),
% 2.57/2.96 alpha65 [340, 4] (w:1, o:390, a:1, s:1, b:1),
% 2.57/2.96 alpha66 [341, 4] (w:1, o:391, a:1, s:1, b:1),
% 2.57/2.96 alpha67 [342, 3] (w:1, o:338, a:1, s:1, b:1),
% 2.57/2.96 alpha68 [343, 2] (w:1, o:306, a:1, s:1, b:1),
% 2.57/2.96 alpha69 [344, 2] (w:1, o:307, a:1, s:1, b:1),
% 2.57/2.96 alpha70 [345, 2] (w:1, o:308, a:1, s:1, b:1),
% 2.57/2.96 alpha71 [346, 3] (w:1, o:340, a:1, s:1, b:1),
% 2.57/2.96 skol1 [347, 2] (w:1, o:268, a:1, s:1, b:1),
% 2.57/2.96 skol2 [348, 1] (w:1, o:172, a:1, s:1, b:1),
% 2.57/2.96 skol3 [349, 3] (w:1, o:354, a:1, s:1, b:1),
% 2.57/2.96 skol4 [350, 2] (w:1, o:271, a:1, s:1, b:1),
% 2.57/2.96 skol5 [351, 2] (w:1, o:275, a:1, s:1, b:1),
% 2.57/2.96 skol6 [352, 2] (w:1, o:279, a:1, s:1, b:1),
% 2.57/2.96 skol7 [353, 1] (w:1, o:173, a:1, s:1, b:1),
% 2.57/2.96 skol8 [354, 2] (w:1, o:280, a:1, s:1, b:1),
% 2.57/2.96 skol9 [355, 2] (w:1, o:281, a:1, s:1, b:1),
% 2.57/2.96 skol10 [356, 2] (w:1, o:282, a:1, s:1, b:1),
% 2.57/2.96 skol11 [357, 3] (w:1, o:355, a:1, s:1, b:1),
% 2.57/2.96 skol12 [358, 4] (w:1, o:392, a:1, s:1, b:1),
% 2.57/2.96 skol13 [359, 1] (w:1, o:170, a:1, s:1, b:1),
% 2.57/2.96 skol14 [360, 1] (w:1, o:171, a:1, s:1, b:1),
% 2.57/2.96 skol15 [361, 3] (w:1, o:356, a:1, s:1, b:1),
% 2.57/2.96 skol16 [362, 3] (w:1, o:357, a:1, s:1, b:1),
% 11.21/11.60 skol17 [363, 0] (w:1, o:23, a:1, s:1, b:1),
% 11.21/11.60 skol18 [364, 0] (w:1, o:24, a:1, s:1, b:1),
% 11.21/11.60 skol19 [365, 0] (w:1, o:25, a:1, s:1, b:1),
% 11.21/11.60 skol20 [366, 2] (w:1, o:283, a:1, s:1, b:1),
% 11.21/11.60 skol21 [367, 3] (w:1, o:349, a:1, s:1, b:1),
% 11.21/11.60 skol22 [368, 3] (w:1, o:350, a:1, s:1, b:1),
% 11.21/11.60 skol23 [369, 3] (w:1, o:351, a:1, s:1, b:1),
% 11.21/11.60 skol24 [370, 2] (w:1, o:284, a:1, s:1, b:1),
% 11.21/11.60 skol25 [371, 2] (w:1, o:285, a:1, s:1, b:1),
% 11.21/11.60 skol26 [372, 3] (w:1, o:352, a:1, s:1, b:1),
% 11.21/11.60 skol27 [373, 3] (w:1, o:353, a:1, s:1, b:1),
% 11.21/11.60 skol28 [374, 0] (w:1, o:26, a:1, s:1, b:1),
% 11.21/11.60 skol29 [375, 0] (w:1, o:27, a:1, s:1, b:1),
% 11.21/11.60 skol30 [376, 0] (w:1, o:28, a:1, s:1, b:1),
% 11.21/11.60 skol31 [377, 0] (w:1, o:29, a:1, s:1, b:1),
% 11.21/11.60 skol32 [378, 3] (w:1, o:358, a:1, s:1, b:1),
% 11.21/11.60 skol33 [379, 4] (w:1, o:393, a:1, s:1, b:1),
% 11.21/11.60 skol34 [380, 4] (w:1, o:394, a:1, s:1, b:1),
% 11.21/11.60 skol35 [381, 4] (w:1, o:395, a:1, s:1, b:1),
% 11.21/11.60 skol36 [382, 2] (w:1, o:269, a:1, s:1, b:1),
% 11.21/11.60 skol37 [383, 1] (w:1, o:174, a:1, s:1, b:1),
% 11.21/11.60 skol38 [384, 2] (w:1, o:270, a:1, s:1, b:1),
% 11.21/11.60 skol39 [385, 3] (w:1, o:359, a:1, s:1, b:1),
% 11.21/11.60 skol40 [386, 4] (w:1, o:396, a:1, s:1, b:1),
% 11.21/11.60 skol41 [387, 3] (w:1, o:360, a:1, s:1, b:1),
% 11.21/11.60 skol42 [388, 3] (w:1, o:361, a:1, s:1, b:1),
% 11.21/11.60 skol43 [389, 3] (w:1, o:362, a:1, s:1, b:1),
% 11.21/11.60 skol44 [390, 3] (w:1, o:363, a:1, s:1, b:1),
% 11.21/11.60 skol45 [391, 2] (w:1, o:272, a:1, s:1, b:1),
% 11.21/11.60 skol46 [392, 2] (w:1, o:273, a:1, s:1, b:1),
% 11.21/11.60 skol47 [393, 1] (w:1, o:175, a:1, s:1, b:1),
% 11.21/11.60 skol48 [394, 2] (w:1, o:274, a:1, s:1, b:1),
% 11.21/11.60 skol49 [395, 3] (w:1, o:364, a:1, s:1, b:1),
% 11.21/11.60 skol50 [396, 2] (w:1, o:276, a:1, s:1, b:1),
% 11.21/11.60 skol51 [397, 2] (w:1, o:277, a:1, s:1, b:1),
% 11.21/11.60 skol52 [398, 2] (w:1, o:278, a:1, s:1, b:1),
% 11.21/11.60 skol53 [399, 1] (w:1, o:176, a:1, s:1, b:1),
% 11.21/11.60 skol54 [400, 5] (w:1, o:402, a:1, s:1, b:1),
% 11.21/11.60 skol55 [401, 3] (w:1, o:365, a:1, s:1, b:1),
% 11.21/11.60 skol56 [402, 1] (w:1, o:177, a:1, s:1, b:1).
% 11.21/11.60
% 11.21/11.60
% 11.21/11.60 Starting Search:
% 11.21/11.60
% 11.21/11.60 *** allocated 170857 integers for clauses
% 11.21/11.60 Resimplifying inuse:
% 11.21/11.60 Done
% 11.21/11.60
% 11.21/11.60
% 11.21/11.60 Intermediate Status:
% 11.21/11.60 Generated: 2761
% 11.21/11.60 Kept: 2001
% 11.21/11.60 Inuse: 18
% 11.21/11.60 Deleted: 0
% 11.21/11.60 Deletedinuse: 0
% 11.21/11.60
% 11.21/11.60 *** allocated 256285 integers for clauses
% 11.21/11.60 Resimplifying inuse:
% 11.21/11.60 Done
% 11.21/11.60
% 11.21/11.60 *** allocated 384427 integers for clauses
% 11.21/11.60
% 11.21/11.60 Intermediate Status:
% 11.21/11.60 Generated: 6554
% 11.21/11.60 Kept: 4004
% 11.21/11.60 Inuse: 182
% 11.21/11.60 Deleted: 2
% 11.21/11.60 Deletedinuse: 0
% 11.21/11.60
% 11.21/11.60 Resimplifying inuse:
% 11.21/11.60 Done
% 11.21/11.60
% 11.21/11.60 Resimplifying inuse:
% 11.21/11.60 Done
% 11.21/11.60
% 11.21/11.60 *** allocated 256285 integers for termspace/termends
% 11.21/11.60
% 11.21/11.60 Intermediate Status:
% 11.21/11.60 Generated: 11582
% 11.21/11.60 Kept: 6489
% 11.21/11.60 Inuse: 306
% 11.21/11.60 Deleted: 5
% 11.21/11.60 Deletedinuse: 0
% 11.21/11.60
% 11.21/11.60 Resimplifying inuse:
% 11.21/11.60 Done
% 11.21/11.60
% 11.21/11.60 *** allocated 576640 integers for clauses
% 11.21/11.60 Resimplifying inuse:
% 11.21/11.60 Done
% 11.21/11.60
% 11.21/11.60
% 11.21/11.60 Intermediate Status:
% 11.21/11.60 Generated: 15497
% 11.21/11.60 Kept: 9079
% 11.21/11.60 Inuse: 351
% 11.21/11.60 Deleted: 5
% 11.21/11.60 Deletedinuse: 0
% 11.21/11.60
% 11.21/11.60 Resimplifying inuse:
% 11.21/11.60 Done
% 11.21/11.60
% 11.21/11.60 *** allocated 384427 integers for termspace/termends
% 11.21/11.60 Resimplifying inuse:
% 11.21/11.60 Done
% 11.21/11.60
% 11.21/11.60 *** allocated 864960 integers for clauses
% 11.21/11.60
% 11.21/11.60 Intermediate Status:
% 11.21/11.60 Generated: 19442
% 11.21/11.60 Kept: 11968
% 11.21/11.60 Inuse: 381
% 11.21/11.60 Deleted: 5
% 11.21/11.60 Deletedinuse: 0
% 11.21/11.60
% 11.21/11.60 Resimplifying inuse:
% 11.21/11.60 Done
% 11.21/11.60
% 11.21/11.60 Resimplifying inuse:
% 11.21/11.60 Done
% 11.21/11.60
% 11.21/11.60
% 11.21/11.60 Intermediate Status:
% 11.21/11.60 Generated: 22769
% 11.21/11.60 Kept: 14001
% 11.21/11.60 Inuse: 427
% 11.21/11.60 Deleted: 5
% 11.21/11.60 Deletedinuse: 0
% 11.21/11.60
% 11.21/11.60 Resimplifying inuse:
% 11.21/11.60 Done
% 11.21/11.60
% 11.21/11.60 Resimplifying inuse:
% 11.21/11.60 Done
% 11.21/11.60
% 11.21/11.60
% 11.21/11.60 Intermediate Status:
% 11.21/11.60 Generated: 26074
% 11.21/11.60 Kept: 16016
% 11.21/11.60 Inuse: 457
% 11.21/11.60 Deleted: 5
% 11.21/11.60 Deletedinuse: 0
% 11.21/11.60
% 11.21/11.60 Resimplifying inuse:
% 11.21/11.60 Done
% 11.21/11.60
% 11.21/11.60 *** allocated 576640 integers for termspace/termends
% 11.21/11.60 Resimplifying inuse:
% 11.21/11.60 Done
% 11.21/11.60
% 11.21/11.60
% 11.21/11.60 Intermediate Status:
% 11.21/11.60 Generated: 28989
% 11.21/11.60 Kept: 18041
% 11.21/11.60 Inuse: 503
% 11.21/11.60 Deleted: 5
% 11.21/11.60 Deletedinuse: 0
% 11.21/11.60
% 11.21/11.60 Resimplifying inuse:
% 11.21/11.60 Done
% 11.21/11.60
% 11.21/11.60 *** allocated 1297440 integers for clauses
% 11.21/11.60 Resimplifying inuse:
% 11.21/11.60 Done
% 11.21/11.60
% 11.21/11.60 Resimplifying clauses:
% 11.21/11.60 Done
% 11.21/11.60
% 11.21/11.60
% 11.21/11.60 Intermediate Status:
% 11.21/11.60 Generated: 35003
% 11.21/11.60 Kept: 20957
% 11.21/11.60 Inuse: 526
% 11.21/11.60 Deleted: 261
% 11.21/11.60 Deletedinuse: 0
% 11.21/11.60
% 11.21/11.60 Resimplifying inuse:
% 11.21/11.60 Done
% 11.21/11.60
% 11.21/11.60 Resimplifying inuse:
% 11.21/11.60 Done
% 11.21/11.60
% 11.21/11.60
% 11.21/11.60 Intermediate Status:
% 11.21/11.60 Generated: 38927
% 37.36/37.74 Kept: 23000
% 37.36/37.74 Inuse: 571
% 37.36/37.74 Deleted: 262
% 37.36/37.74 Deletedinuse: 1
% 37.36/37.74
% 37.36/37.74 Resimplifying inuse:
% 37.36/37.74 Done
% 37.36/37.74
% 37.36/37.74 Resimplifying inuse:
% 37.36/37.74 Done
% 37.36/37.74
% 37.36/37.74
% 37.36/37.74 Intermediate Status:
% 37.36/37.74 Generated: 45159
% 37.36/37.74 Kept: 25076
% 37.36/37.74 Inuse: 606
% 37.36/37.74 Deleted: 262
% 37.36/37.74 Deletedinuse: 1
% 37.36/37.74
% 37.36/37.74 Resimplifying inuse:
% 37.36/37.74 Done
% 37.36/37.74
% 37.36/37.74 *** allocated 864960 integers for termspace/termends
% 37.36/37.74
% 37.36/37.74 Intermediate Status:
% 37.36/37.74 Generated: 50431
% 37.36/37.74 Kept: 27630
% 37.36/37.74 Inuse: 613
% 37.36/37.74 Deleted: 265
% 37.36/37.74 Deletedinuse: 1
% 37.36/37.74
% 37.36/37.74 Resimplifying inuse:
% 37.36/37.74 Done
% 37.36/37.74
% 37.36/37.74 *** allocated 1946160 integers for clauses
% 37.36/37.74 Resimplifying inuse:
% 37.36/37.74 Done
% 37.36/37.74
% 37.36/37.74
% 37.36/37.74 Intermediate Status:
% 37.36/37.74 Generated: 59457
% 37.36/37.74 Kept: 30350
% 37.36/37.74 Inuse: 626
% 37.36/37.74 Deleted: 313
% 37.36/37.74 Deletedinuse: 2
% 37.36/37.74
% 37.36/37.74 Resimplifying inuse:
% 37.36/37.74 Done
% 37.36/37.74
% 37.36/37.74 Resimplifying inuse:
% 37.36/37.74 Done
% 37.36/37.74
% 37.36/37.74
% 37.36/37.74 Intermediate Status:
% 37.36/37.74 Generated: 63944
% 37.36/37.74 Kept: 33700
% 37.36/37.74 Inuse: 629
% 37.36/37.74 Deleted: 325
% 37.36/37.74 Deletedinuse: 2
% 37.36/37.74
% 37.36/37.74 Resimplifying inuse:
% 37.36/37.74 Done
% 37.36/37.74
% 37.36/37.74 Resimplifying inuse:
% 37.36/37.74 Done
% 37.36/37.74
% 37.36/37.74
% 37.36/37.74 Intermediate Status:
% 37.36/37.74 Generated: 72246
% 37.36/37.74 Kept: 35721
% 37.36/37.74 Inuse: 646
% 37.36/37.74 Deleted: 336
% 37.36/37.74 Deletedinuse: 2
% 37.36/37.74
% 37.36/37.74 Resimplifying inuse:
% 37.36/37.74 Done
% 37.36/37.74
% 37.36/37.74
% 37.36/37.74 Intermediate Status:
% 37.36/37.75 Generated: 77776
% 37.36/37.75 Kept: 38507
% 37.36/37.75 Inuse: 663
% 37.36/37.75 Deleted: 336
% 37.36/37.75 Deletedinuse: 2
% 37.36/37.75
% 37.36/37.75 Resimplifying inuse:
% 37.36/37.75 Done
% 37.36/37.75
% 37.36/37.75 Resimplifying inuse:
% 37.36/37.75 Done
% 37.36/37.75
% 37.36/37.75 Resimplifying clauses:
% 37.36/37.75 Done
% 37.36/37.75
% 37.36/37.75 *** allocated 1297440 integers for termspace/termends
% 37.36/37.75
% 37.36/37.75 Intermediate Status:
% 37.36/37.75 Generated: 83907
% 37.36/37.75 Kept: 40605
% 37.36/37.75 Inuse: 673
% 37.36/37.75 Deleted: 502
% 37.36/37.75 Deletedinuse: 2
% 37.36/37.75
% 37.36/37.75 Resimplifying inuse:
% 37.36/37.75 Done
% 37.36/37.75
% 37.36/37.75
% 37.36/37.75 Intermediate Status:
% 37.36/37.75 Generated: 87555
% 37.36/37.75 Kept: 42936
% 37.36/37.75 Inuse: 681
% 37.36/37.75 Deleted: 531
% 37.36/37.75 Deletedinuse: 4
% 37.36/37.75
% 37.36/37.75 Resimplifying inuse:
% 37.36/37.75 Done
% 37.36/37.75
% 37.36/37.75 *** allocated 2919240 integers for clauses
% 37.36/37.75
% 37.36/37.75 Intermediate Status:
% 37.36/37.75 Generated: 91048
% 37.36/37.75 Kept: 44981
% 37.36/37.75 Inuse: 689
% 37.36/37.75 Deleted: 565
% 37.36/37.75 Deletedinuse: 6
% 37.36/37.75
% 37.36/37.75 Resimplifying inuse:
% 37.36/37.75 Done
% 37.36/37.75
% 37.36/37.75 Resimplifying inuse:
% 37.36/37.75 Done
% 37.36/37.75
% 37.36/37.75
% 37.36/37.75 Intermediate Status:
% 37.36/37.75 Generated: 94978
% 37.36/37.75 Kept: 47010
% 37.36/37.75 Inuse: 717
% 37.36/37.75 Deleted: 572
% 37.36/37.75 Deletedinuse: 7
% 37.36/37.75
% 37.36/37.75 Resimplifying inuse:
% 37.36/37.75 Done
% 37.36/37.75
% 37.36/37.75
% 37.36/37.75 Intermediate Status:
% 37.36/37.75 Generated: 98738
% 37.36/37.75 Kept: 49478
% 37.36/37.75 Inuse: 728
% 37.36/37.75 Deleted: 572
% 37.36/37.75 Deletedinuse: 7
% 37.36/37.75
% 37.36/37.75 Resimplifying inuse:
% 37.36/37.75 Done
% 37.36/37.75
% 37.36/37.75 Resimplifying inuse:
% 37.36/37.75 Done
% 37.36/37.75
% 37.36/37.75
% 37.36/37.75 Intermediate Status:
% 37.36/37.75 Generated: 104727
% 37.36/37.75 Kept: 51483
% 37.36/37.75 Inuse: 734
% 37.36/37.75 Deleted: 587
% 37.36/37.75 Deletedinuse: 8
% 37.36/37.75
% 37.36/37.75 Resimplifying inuse:
% 37.36/37.75 Done
% 37.36/37.75
% 37.36/37.75
% 37.36/37.75 Intermediate Status:
% 37.36/37.75 Generated: 108860
% 37.36/37.75 Kept: 53489
% 37.36/37.75 Inuse: 747
% 37.36/37.75 Deleted: 598
% 37.36/37.75 Deletedinuse: 8
% 37.36/37.75
% 37.36/37.75 Resimplifying inuse:
% 37.36/37.75 Done
% 37.36/37.75
% 37.36/37.75
% 37.36/37.75 Intermediate Status:
% 37.36/37.75 Generated: 120014
% 37.36/37.75 Kept: 56975
% 37.36/37.75 Inuse: 753
% 37.36/37.75 Deleted: 598
% 37.36/37.75 Deletedinuse: 8
% 37.36/37.75
% 37.36/37.75 Resimplifying inuse:
% 37.36/37.75 Done
% 37.36/37.75
% 37.36/37.75 Resimplifying inuse:
% 37.36/37.75 Done
% 37.36/37.75
% 37.36/37.75
% 37.36/37.75 Intermediate Status:
% 37.36/37.75 Generated: 126036
% 37.36/37.75 Kept: 58987
% 37.36/37.75 Inuse: 775
% 37.36/37.75 Deleted: 598
% 37.36/37.75 Deletedinuse: 8
% 37.36/37.75
% 37.36/37.75 Resimplifying inuse:
% 37.36/37.75 Done
% 37.36/37.75
% 37.36/37.75 Resimplifying inuse:
% 37.36/37.75 Done
% 37.36/37.75
% 37.36/37.75 Resimplifying clauses:
% 37.36/37.75 Done
% 37.36/37.75
% 37.36/37.75 *** allocated 1946160 integers for termspace/termends
% 37.36/37.75
% 37.36/37.75 Intermediate Status:
% 37.36/37.75 Generated: 130545
% 37.36/37.75 Kept: 61017
% 37.36/37.75 Inuse: 796
% 37.36/37.75 Deleted: 1047
% 37.36/37.75 Deletedinuse: 10
% 37.36/37.75
% 37.36/37.75 Resimplifying inuse:
% 37.36/37.75 Done
% 37.36/37.75
% 37.36/37.75 Resimplifying inuse:
% 37.36/37.75 Done
% 37.36/37.75
% 37.36/37.75
% 37.36/37.75 Intermediate Status:
% 37.36/37.75 Generated: 135975
% 37.36/37.75 Kept: 63194
% 37.36/37.75 Inuse: 818
% 37.36/37.75 Deleted: 1047
% 37.36/37.75 Deletedinuse: 10
% 37.36/37.75
% 37.36/37.75 Resimplifying inuse:
% 37.36/37.75 Done
% 37.36/37.75
% 37.36/37.75 *** allocated 4378860 integers for clauses
% 37.36/37.75 Resimplifying inuse:
% 37.36/37.75 Done
% 37.36/37.75
% 37.36/37.75
% 37.36/37.75 Intermediate Status:
% 37.36/37.75 Generated: 145287
% 37.36/37.75 Kept: 65714
% 37.36/37.75 Inuse: 833
% 37.36/37.75 Deleted: 1047
% 37.36/37.75 Deletedinuse: 10
% 37.36/37.75
% 37.36/37.75 Resimplifying inuse:
% 37.36/37.75 Done
% 37.36/37.75
% 37.36/37.75 Resimplifying inuse:
% 37.36/37.75 Done
% 37.36/37.75
% 37.36/37.75
% 37.36/37.75 Intermediate Status:
% 37.36/37.75 Generated: 158008
% 37.36/37.75 Kept: 68157
% 37.36/37.75 Inuse: 843
% 37.36/37.75 Deleted: 1047
% 37.36/37.75 Deletedinuse: 10
% 37.36/37.75
% 37.36/37.75 Resimplifying inuse:
% 37.36/37.75 Done
% 37.36/37.75
% 37.36/37.75 Resimplifying inuse:
% 37.36/37.75 Done
% 37.36/37.75
% 37.36/37.75
% 37.36/37.75 Intermediate Status:
% 37.36/37.75 Generated: 164220
% 37.36/37.75 Kept: 70182
% 37.36/37.75 Inuse: 862
% 37.36/37.75 Deleted: 1047
% 37.36/37.75 Deletedinuse: 10
% 37.36/37.75
% 37.36/37.75 Resimplifying inuse:
% 37.36/37.75 Done
% 37.36/37.75
% 37.36/37.75 Resimplifying inuse:
% 37.36/37.75 Done
% 37.36/37.75
% 37.36/37.75
% 37.36/37.75 Intermediate Status:
% 37.36/37.75 Generated: 170790
% 37.36/37.75 Kept: 72524
% 37.36/37.75 Inuse: 878
% 37.36/37.75 Deleted: 1047
% 37.36/37.75 Deletedinuse: 10
% 37.36/37.75
% 37.36/37.75 Resimplifying inuse:
% 37.36/37.75 Done
% 37.36/37.75
% 37.36/37.75 Resimplifying inuse:
% 37.36/37.75 Done
% 37.36/37.75
% 37.36/37.75
% 37.36/37.75 Intermediate Status:
% 37.36/37.75 Generated: 176755
% 37.36/37.75 Kept: 74527
% 37.36/37.75 Inuse: 901
% 37.36/37.75 Deleted: 1047
% 37.36/37.75 Deletedinuse: 10
% 37.36/37.75
% 37.36/37.75 Resimplifying inuse:
% 37.36/37.75 Done
% 37.36/37.75
% 37.36/37.75 Resimplifying inuse:
% 37.36/37.75 Done
% 37.36/37.75
% 37.36/37.75
% 37.36/37.75 Intermediate Status:
% 37.36/37.75 Generated: 182538
% 37.36/37.75 Kept: 76562
% 89.73/90.11 Inuse: 920
% 89.73/90.11 Deleted: 1047
% 89.73/90.11 Deletedinuse: 10
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 188544
% 89.73/90.11 Kept: 78586
% 89.73/90.11 Inuse: 938
% 89.73/90.11 Deleted: 1047
% 89.73/90.11 Deletedinuse: 10
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11 Resimplifying clauses:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 194520
% 89.73/90.11 Kept: 80588
% 89.73/90.11 Inuse: 959
% 89.73/90.11 Deleted: 1105
% 89.73/90.11 Deletedinuse: 10
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 208315
% 89.73/90.11 Kept: 83626
% 89.73/90.11 Inuse: 978
% 89.73/90.11 Deleted: 1105
% 89.73/90.11 Deletedinuse: 10
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 215513
% 89.73/90.11 Kept: 85807
% 89.73/90.11 Inuse: 1003
% 89.73/90.11 Deleted: 1107
% 89.73/90.11 Deletedinuse: 12
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11 *** allocated 2919240 integers for termspace/termends
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 222079
% 89.73/90.11 Kept: 87843
% 89.73/90.11 Inuse: 1021
% 89.73/90.11 Deleted: 1107
% 89.73/90.11 Deletedinuse: 12
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 230743
% 89.73/90.11 Kept: 90083
% 89.73/90.11 Inuse: 1025
% 89.73/90.11 Deleted: 1107
% 89.73/90.11 Deletedinuse: 12
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 238363
% 89.73/90.11 Kept: 92365
% 89.73/90.11 Inuse: 1038
% 89.73/90.11 Deleted: 1107
% 89.73/90.11 Deletedinuse: 12
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 248683
% 89.73/90.11 Kept: 94686
% 89.73/90.11 Inuse: 1053
% 89.73/90.11 Deleted: 1107
% 89.73/90.11 Deletedinuse: 12
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 255759
% 89.73/90.11 Kept: 96856
% 89.73/90.11 Inuse: 1083
% 89.73/90.11 Deleted: 1107
% 89.73/90.11 Deletedinuse: 12
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11 *** allocated 6568290 integers for clauses
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 262197
% 89.73/90.11 Kept: 98938
% 89.73/90.11 Inuse: 1108
% 89.73/90.11 Deleted: 1107
% 89.73/90.11 Deletedinuse: 12
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11 Resimplifying clauses:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 267946
% 89.73/90.11 Kept: 100979
% 89.73/90.11 Inuse: 1133
% 89.73/90.11 Deleted: 2235
% 89.73/90.11 Deletedinuse: 12
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 276445
% 89.73/90.11 Kept: 103770
% 89.73/90.11 Inuse: 1163
% 89.73/90.11 Deleted: 2235
% 89.73/90.11 Deletedinuse: 12
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 285214
% 89.73/90.11 Kept: 106136
% 89.73/90.11 Inuse: 1188
% 89.73/90.11 Deleted: 2235
% 89.73/90.11 Deletedinuse: 12
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 291976
% 89.73/90.11 Kept: 108580
% 89.73/90.11 Inuse: 1213
% 89.73/90.11 Deleted: 2235
% 89.73/90.11 Deletedinuse: 12
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 298101
% 89.73/90.11 Kept: 110772
% 89.73/90.11 Inuse: 1233
% 89.73/90.11 Deleted: 2235
% 89.73/90.11 Deletedinuse: 12
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 307009
% 89.73/90.11 Kept: 115360
% 89.73/90.11 Inuse: 1243
% 89.73/90.11 Deleted: 2235
% 89.73/90.11 Deletedinuse: 12
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 314663
% 89.73/90.11 Kept: 117598
% 89.73/90.11 Inuse: 1273
% 89.73/90.11 Deleted: 2235
% 89.73/90.11 Deletedinuse: 12
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11 *** allocated 4378860 integers for termspace/termends
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 326135
% 89.73/90.11 Kept: 119655
% 89.73/90.11 Inuse: 1288
% 89.73/90.11 Deleted: 2235
% 89.73/90.11 Deletedinuse: 12
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11 Resimplifying clauses:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 333671
% 89.73/90.11 Kept: 121847
% 89.73/90.11 Inuse: 1318
% 89.73/90.11 Deleted: 2371
% 89.73/90.11 Deletedinuse: 13
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 343974
% 89.73/90.11 Kept: 126481
% 89.73/90.11 Inuse: 1338
% 89.73/90.11 Deleted: 2372
% 89.73/90.11 Deletedinuse: 14
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 349034
% 89.73/90.11 Kept: 129789
% 89.73/90.11 Inuse: 1343
% 89.73/90.11 Deleted: 2372
% 89.73/90.11 Deletedinuse: 14
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 354614
% 89.73/90.11 Kept: 133162
% 89.73/90.11 Inuse: 1348
% 89.73/90.11 Deleted: 2372
% 89.73/90.11 Deletedinuse: 14
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11 Resimplifying inuse:
% 89.73/90.11 Done
% 89.73/90.11
% 89.73/90.11
% 89.73/90.11 Intermediate Status:
% 89.73/90.11 Generated: 364281
% 89.73/90.11 Kept: 135390
% 89.73/90.11 Inuse: 1378
% 89.73/90.11 Deleted: 2373
% 204.01/204.50 Deletedinuse: 15
% 204.01/204.50
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50
% 204.01/204.50 Intermediate Status:
% 204.01/204.50 Generated: 373591
% 204.01/204.50 Kept: 137440
% 204.01/204.50 Inuse: 1399
% 204.01/204.50 Deleted: 2374
% 204.01/204.50 Deletedinuse: 16
% 204.01/204.50
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50
% 204.01/204.50 Intermediate Status:
% 204.01/204.50 Generated: 379318
% 204.01/204.50 Kept: 139454
% 204.01/204.50 Inuse: 1419
% 204.01/204.50 Deleted: 2375
% 204.01/204.50 Deletedinuse: 17
% 204.01/204.50
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50 Resimplifying clauses:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50
% 204.01/204.50 Intermediate Status:
% 204.01/204.50 Generated: 385666
% 204.01/204.50 Kept: 141571
% 204.01/204.50 Inuse: 1438
% 204.01/204.50 Deleted: 2733
% 204.01/204.50 Deletedinuse: 17
% 204.01/204.50
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50
% 204.01/204.50 Intermediate Status:
% 204.01/204.50 Generated: 393659
% 204.01/204.50 Kept: 143650
% 204.01/204.50 Inuse: 1463
% 204.01/204.50 Deleted: 2733
% 204.01/204.50 Deletedinuse: 17
% 204.01/204.50
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50
% 204.01/204.50 Intermediate Status:
% 204.01/204.50 Generated: 401210
% 204.01/204.50 Kept: 145660
% 204.01/204.50 Inuse: 1490
% 204.01/204.50 Deleted: 2733
% 204.01/204.50 Deletedinuse: 17
% 204.01/204.50
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50
% 204.01/204.50 Intermediate Status:
% 204.01/204.50 Generated: 408278
% 204.01/204.50 Kept: 147683
% 204.01/204.50 Inuse: 1517
% 204.01/204.50 Deleted: 2737
% 204.01/204.50 Deletedinuse: 21
% 204.01/204.50
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50
% 204.01/204.50 Intermediate Status:
% 204.01/204.50 Generated: 416143
% 204.01/204.50 Kept: 149815
% 204.01/204.50 Inuse: 1543
% 204.01/204.50 Deleted: 2737
% 204.01/204.50 Deletedinuse: 21
% 204.01/204.50
% 204.01/204.50 *** allocated 9852435 integers for clauses
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50
% 204.01/204.50 Intermediate Status:
% 204.01/204.50 Generated: 423727
% 204.01/204.50 Kept: 151951
% 204.01/204.50 Inuse: 1567
% 204.01/204.50 Deleted: 2738
% 204.01/204.50 Deletedinuse: 21
% 204.01/204.50
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50
% 204.01/204.50 Intermediate Status:
% 204.01/204.50 Generated: 434005
% 204.01/204.50 Kept: 154289
% 204.01/204.50 Inuse: 1610
% 204.01/204.50 Deleted: 2745
% 204.01/204.50 Deletedinuse: 21
% 204.01/204.50
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50
% 204.01/204.50 Intermediate Status:
% 204.01/204.50 Generated: 440604
% 204.01/204.50 Kept: 156317
% 204.01/204.50 Inuse: 1635
% 204.01/204.50 Deleted: 2745
% 204.01/204.50 Deletedinuse: 21
% 204.01/204.50
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50
% 204.01/204.50 Intermediate Status:
% 204.01/204.50 Generated: 447528
% 204.01/204.50 Kept: 158321
% 204.01/204.50 Inuse: 1663
% 204.01/204.50 Deleted: 2745
% 204.01/204.50 Deletedinuse: 21
% 204.01/204.50
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50
% 204.01/204.50 Intermediate Status:
% 204.01/204.50 Generated: 454010
% 204.01/204.50 Kept: 160331
% 204.01/204.50 Inuse: 1698
% 204.01/204.50 Deleted: 2745
% 204.01/204.50 Deletedinuse: 21
% 204.01/204.50
% 204.01/204.50 Resimplifying clauses:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50
% 204.01/204.50 Intermediate Status:
% 204.01/204.50 Generated: 475020
% 204.01/204.50 Kept: 164673
% 204.01/204.50 Inuse: 1725
% 204.01/204.50 Deleted: 5493
% 204.01/204.50 Deletedinuse: 21
% 204.01/204.50
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50
% 204.01/204.50 Intermediate Status:
% 204.01/204.50 Generated: 486353
% 204.01/204.50 Kept: 170443
% 204.01/204.50 Inuse: 1740
% 204.01/204.50 Deleted: 5493
% 204.01/204.50 Deletedinuse: 21
% 204.01/204.50
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50
% 204.01/204.50 Intermediate Status:
% 204.01/204.50 Generated: 493416
% 204.01/204.50 Kept: 174841
% 204.01/204.50 Inuse: 1745
% 204.01/204.50 Deleted: 5493
% 204.01/204.50 Deletedinuse: 21
% 204.01/204.50
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50
% 204.01/204.50 Intermediate Status:
% 204.01/204.50 Generated: 502322
% 204.01/204.50 Kept: 177124
% 204.01/204.50 Inuse: 1775
% 204.01/204.50 Deleted: 5493
% 204.01/204.50 Deletedinuse: 21
% 204.01/204.50
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50 *** allocated 6568290 integers for termspace/termends
% 204.01/204.50
% 204.01/204.50 Intermediate Status:
% 204.01/204.50 Generated: 510435
% 204.01/204.50 Kept: 179464
% 204.01/204.50 Inuse: 1805
% 204.01/204.50 Deleted: 5493
% 204.01/204.50 Deletedinuse: 21
% 204.01/204.50
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50 Resimplifying clauses:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50
% 204.01/204.50 Intermediate Status:
% 204.01/204.50 Generated: 516948
% 204.01/204.50 Kept: 181571
% 204.01/204.50 Inuse: 1820
% 204.01/204.50 Deleted: 5588
% 204.01/204.50 Deletedinuse: 22
% 204.01/204.50
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50
% 204.01/204.50 Intermediate Status:
% 204.01/204.50 Generated: 537870
% 204.01/204.50 Kept: 185460
% 204.01/204.50 Inuse: 1845
% 204.01/204.50 Deleted: 5588
% 204.01/204.50 Deletedinuse: 22
% 204.01/204.50
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50
% 204.01/204.50 Intermediate Status:
% 204.01/204.50 Generated: 552418
% 204.01/204.50 Kept: 187642
% 204.01/204.50 Inuse: 1850
% 204.01/204.50 Deleted: 5588
% 204.01/204.50 Deletedinuse: 22
% 204.01/204.50
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50
% 204.01/204.50 Intermediate Status:
% 204.01/204.50 Generated: 565545
% 204.01/204.50 Kept: 189670
% 204.01/204.50 Inuse: 1871
% 204.01/204.50 Deleted: 5588
% 204.01/204.50 Deletedinuse: 22
% 204.01/204.50
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50
% 204.01/204.50 Intermediate Status:
% 204.01/204.50 Generated: 570850
% 204.01/204.50 Kept: 191801
% 204.01/204.50 Inuse: 1879
% 204.01/204.50 Deleted: 5621
% 204.01/204.50 Deletedinuse: 24
% 204.01/204.50
% 204.01/204.50 Resimplifying inuse:
% 204.01/204.50 Done
% 204.01/204.50
% 204.01/204.50
% 204.01/204.50 Intermediate Status:
% 204.01/204.50 Generated: 578789
% 204.01/204.50 Kept: 194177
% 204.01/204.50 Inuse: 1884
% 204.01/204.50 Deleted: 5641
% 204.01/204.50 DeletedinuseCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------