theorem :: Stone Theorem
  PT is metrizable implies PT is paracompact
proof
  assume PT is metrizable;
  then
  for FX being Subset-Family of PT st FX is Cover of PT & FX is open ex GX
being Subset-Family of PT st GX is open & GX is Cover of PT & GX is_finer_than
  FX & GX is locally_finite by Th6;
  hence thesis by PCOMPS_1:def 3;
end;
