
theorem Th25:
  for T being TopSpace holds
    Flip ClMap T = IntMap T
  proof
    let T be TopSpace;
    set f = Flip ClMap T, g = IntMap T;
    for x being Subset of T holds f.x = g.x
    proof
      let x be Subset of T;
A1:   (Int x)` = (Cl x`) by TDLAT_3:2;
      f.x = ((ClMap T).x`)` by Def14
         .= (Cl x`)` by Def15
         .= g.x by Def16,A1;
      hence thesis;
    end;
    hence thesis;
  end;
