
theorem NF260:
  for a being non empty FinSequence of REAL,
  f being FinSequence of NAT st
  dom f = dom a holds
  SumBin (a, f, rng f) = Sum a
  proof
    let a be non empty FinSequence of REAL, f be FinSequence of NAT;

    assume L00: dom f = dom a;

    L200: f " (rng f) = dom f by RELAT_1:134;

    Seq (a, f " (rng f)) = Seq (a | dom a) by L200,L00
    .= a by FINSEQ_3:116;
    hence SumBin (a, f, rng f) = Sum a;
  end;
