
theorem Th6:
  for T being TopSpace, F, G being Subset-Family of T st F c= G
  holds Fr F c= Fr G
proof
  let T be TopSpace, F, G be Subset-Family of T;
  assume
A1: F c= G;
  Fr F c= Fr G
  proof
    let x be object;
    assume
A2: x in Fr F;
    then reconsider A = x as Subset of T;
    ex B being Subset of T st A = Fr B & B in F by A2,Def1;
    hence thesis by A1,Def1;
  end;
  hence thesis;
end;
