reserve A for set, x,y,z for object,
  k for Element of NAT;
reserve n for Nat,
  x for object;
reserve V, C for set;

theorem Th17:
  for X being set, R being Relation st field R c= X holds R is Relation of X
proof
  let X be set, R be Relation;
  assume
A1: field R c= X;
  R c= [:X,X:]
  proof
    let x,y be object;
    assume [x,y] in R;
    then x in field R & y in field R by RELAT_1:15;
    hence thesis by A1,ZFMISC_1:def 2;
  end;
  hence thesis;
end;
