theorem Th72:
  for f being Function of NAT,R^1 st f = seq & lim_f f <> {} holds
  lim_f f = {lim seq}
  proof
    let f be Function of NAT,R^1;
    assume that
A1: f = seq and
A2: lim_f f <> {};
    [#]OrderedNAT = NAT & the carrier of R^1 = REAL by STRUCT_0:def 3;
    then reconsider f1 = f as Function of [#]OrderedNAT,R^1;
    lim_f f = lim_f f1 by CARDFIL2:54;
    hence thesis by A1,A2,Th71;
  end;
