theorem Th23:
  B+^C c= B+^D implies C c= D
proof
  assume
A1: B+^C c= B+^D;
  B+^C c= B+^D & B+^C <> B+^D iff B+^C c< B+^D;
  then C = D or C in D by A1,Th21,Th22,ORDINAL1:11;
  hence thesis by ORDINAL1:def 2;
end;
