
theorem Th22:
  for T being non empty TopStruct, x being Point of T, S being
  sequence of T holds S = (NAT --> x) implies S is_convergent_to x
proof
  let T be non empty TopStruct, x be Point of T, S be sequence of T;
  assume
A1: S = (NAT --> x);
    let U1 be Subset of T;
    assume that
    U1 is open and
A2: x in U1;
    take 0;
    let m be Nat;
      m in NAT by ORDINAL1:def 12;
    hence thesis by A1,A2,FUNCOP_1:7;
end;
