reserve n for Nat;

theorem
  for T being non empty TopSpace, F being SetSequence of the carrier of
T, A being closed Subset of T st for i being Nat holds F.i = A holds Lim_inf F
  = A
proof
  let T be non empty TopSpace, F be SetSequence of the carrier of T, A be
  closed Subset of T;
  assume for i being Nat holds F.i = A;
  then Lim_inf F = Cl A by Th23;
  hence thesis by PRE_TOPC:22;
end;
