
theorem Th27:
  for R being non empty RelStr holds
    Flip UAp R = LAp R
  proof
    let R be non empty RelStr;
    set f = Flip UAp R, g = LAp R;
    for x being Subset of R holds f.x = g.x
    proof
      let x be Subset of R;
      f.x = ((UAp R).x`)` by Def14
         .= Lap x by Def11
         .= LAp x by Th9
         .= g.x by Def10;
      hence thesis;
    end;
    hence thesis;
  end;
