
theorem
  for X being non empty set,
      R being total Relation of X holds
  for S being Relation of X holds
    R \/ S is total
  proof
    let X be non empty set,
        R be total Relation of X;
    let S be Relation of X;
A1: dom R = X by PARTFUN1:def 2;
    dom (R \/ S) = X \/ dom S by A1,XTUPLE_0:23;
    hence thesis by PARTFUN1:def 2,XBOOLE_1:12;
  end;
