
theorem Lemma7:
  for a, b being object,
      R being Relation st R = {[a, b]} holds
    R~ = {[b, a]}
  proof
    let a, b be object, R be Relation;
    assume R = {[a, b]}; then
    dom R = {a} & rng R = {b} by RELAT_1:9; then
    dom (R~) = {b} & rng (R~) = {a} by RELAT_1:20;
    hence thesis by RELAT_1:189;
  end;
