
theorem RestrictedXFin:
  for f being sequence of REAL,
      n being Nat holds
    f | n is XFinSequence
  proof
    let f be sequence of REAL,
        n be Nat;
    dom f = NAT by FUNCT_2:def 1; then
    dom (f|Segm n) = Segm n; then
    f | n is finite Sequence-like;
    hence thesis;
  end;
