
theorem
  for x, y, A, B being set st x in A \/ B & y in A \/ B holds x in A \ B
  & y in A \ B or x in B & y in B or x in A \ B & y in B or x in B & y in A \ B
proof
  let x, y, A, B be set;
  assume
A1: x in A \/ B & y in A \/ B;
  A \/ B = (A \ B) \/ B by XBOOLE_1:39;
  hence thesis by A1,XBOOLE_0:def 3;
end;
