reserve PM for MetrStruct;
reserve x,y for Element of PM;
reserve r,p,q,s,t for Real;
reserve T for TopSpace;
reserve A for Subset of T;
reserve T for non empty TopSpace;
reserve x for Point of T;
reserve Z,X,V,W,Y,Q for Subset of T;
reserve FX for Subset-Family of T;
reserve a for set;
reserve x,y for Point of T;
reserve A,B for Subset of T;
reserve FX,GX for Subset-Family of T;

theorem Th8:
  for W holds { V : V in FX & V meets W} c= FX
proof
  let W;
  now
    let Y be object;
    assume Y in { V : V in FX & V meets W };
    then ex V st Y = V & V in FX & V meets W;
    hence Y in FX;
  end;
  hence thesis;
end;
