theorem
  for r being X-defined Y-valued Relation holds r is Relation of X,Y
  proof
    let r be X-defined Y-valued Relation;
    [:dom r, rng r:] c= [:X,Y:] & r c= [:dom r, rng r:]
      by RELAT_1:7,ZFMISC_1:96;
    hence r is Relation of X,Y by XBOOLE_1:1;
  end;
