reserve i,j,k,n,m for Nat,
  x,y,z,y1,y2 for object, X,Y,D for set,
  p,q for XFinSequence;

theorem Th4: ::from FINSEQ_2:14
  for p st for i st i in dom p holds p.i in D
   holds p is XFinSequence of D
proof
  let p;
  assume
A1: for i st i in dom p holds p.i in D;
  rng p c= D
  proof
    let x be object;
    assume x in rng p;
    then ex i being Element of NAT st i in dom p & p.i = x by Th3;
    hence thesis by A1;
  end;
  hence thesis by RELAT_1:def 19;
end;
