theorem Th33:
  B*^A = C*^A & A <> {} implies B = C
proof
  assume that
A1: B*^A = C*^A and
A2: A <> {} and
A3: B <> C;
  B in C or C in B by A3,ORDINAL1:14;
  then B*^A in B*^A by A1,A2,ORDINAL2:40;
  hence contradiction;
end;
