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,ORDINAL2:33;
  A+^C c= B+^C by A1,ORDINAL2:34;
  hence thesis by A3;
end;
