theorem
  A c= B & C c= D implies A*^C c= B*^D
proof
  assume that
A1: A c= B and
A2: C c= D;
A3: B*^C c= B*^D by A2,ORDINAL2:42;
  A*^C c= B*^C by A1,ORDINAL2:41;
  hence thesis by A3;
end;
