reserve i for Nat;
reserve R for Relation;
reserve A for set;
reserve PT for non empty TopSpace;
reserve PM for MetrSpace;
reserve FX,GX,HX for Subset-Family of PT;
reserve Y,V,W for Subset of PT;
reserve Mn for Relation;
reserve n,k,l,q,p,q1 for Nat;

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;
