
theorem
  for R, S being non empty RelStr, x being Element of R [*] S holds x in
  the carrier of R or x in (the carrier of S) \ (the carrier of R)
proof
  let R, S be non empty RelStr, x be Element of R [*] S;
  x in the carrier of R [*] S;
  then x in (the carrier of S) \/ (the carrier of R) by Def2;
  then
  x in (the carrier of R) \/ ((the carrier of S) \ (the carrier of R)) by
XBOOLE_1:39;
  hence thesis by XBOOLE_0:def 3;
end;
