reserve a,a1,a2,b,c,d for Ordinal,
  n,m,k for Nat,
  x,y,z,t,X,Y,Z for set;
reserve f,g for Function;
reserve A,B,C for array;
reserve O for connected non empty Poset;
reserve R,Q for array of O;
reserve T for non empty array of O;
reserve p,q,r,s for Element of dom T;
reserve A for array, B for permutation of A;

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;
