theorem Th10:
  FX is finite implies FX is locally_finite
proof
  assume
A1: FX is finite;
  for x ex W being Subset of T st x in W & W is open & { V : V in FX & V
  meets W } is finite
  proof
    let x;
    take [#]T;
    thus x in [#]T;
    thus [#]T is open;
    thus thesis by A1,Th8,FINSET_1:1;
  end;
  hence thesis;
end;
