reserve n for Nat;

theorem Th15:
  for n be Nat, f be set holds f is sequence of REAL-NS
  n iff f is sequence of REAL-US n
proof
  let n be Nat, f be set;
  the carrier of REAL-NS n = REAL n by Def4
    .= the carrier of REAL-US n by Def6;
  hence thesis;
end;
