
theorem
  for X being non empty set,
      R being total reflexive Relation of X holds
    R~ is total
  proof
    let X be non empty set,
        R be total reflexive Relation of X;
    dom R = X by PARTFUN1:def 2; then
    dom (R~) = X by RELAT_2:12;
    hence thesis by PARTFUN1:def 2;
  end;
