reserve T for TopStruct;
reserve GX for TopSpace;

theorem Th19:
  for A,B being Subset of T st A c= B holds Cl A c= Cl B
proof
  let A,B be Subset of T such that
A1: A c= B;
    let x be object;
    assume
A2: x in Cl A;
    now
      let D1 be Subset of T;
      assume
A3:   D1 is closed;
      assume B c= D1;
      then A c= D1 by A1;
      hence x in D1 by A2,A3,Th15;
    end;
    hence x in Cl B by A2,Th15;
end;
