
theorem NF315:
  for D be set, p being FinSequence st
  (for i being Nat st i in dom p holds p . i in D) holds
  p is FinSequence of D
  proof
    let D be set, p be FinSequence;

    assume L000: for i being Nat st i in dom p holds p . i in D;

    for y being object st y in rng p holds y in D
    proof
      let y1 be object;

      assume L430: y1 in rng p;

      consider i being object such that
      L431: i in dom p and
      L432: y1 = p . i by L430,FUNCT_1:def 3;

      thus y1 in D by L431,L000,L432;
    end;
    then rng p c= D;
    hence p is FinSequence of D by FINSEQ_1:def 4;
  end;
