theorem Th14:
  FX c= GX implies clf FX c= clf GX
proof
  reconsider CFX = clf FX,CGX = clf GX as set;
  assume
A1: FX c= GX;
  for X be object st X in CFX holds X in CGX
  proof
    let X be object;
    assume
A2: X in CFX;
    then reconsider X as Subset of T;
    ex V st X = Cl V & V in FX by A2,Def2;
    hence thesis by A1,Def2;
  end;
  hence thesis;
end;
