theorem
  (homography(N)).P1 = (homography(N)).P2 implies P1 = P2
  proof
    assume
A1: (homography(N)).P1 = (homography(N)).P2;
    P1 = (homography(N~)).((homography(N)).P1) by Th16
      .= P2 by A1,Th16;
    hence thesis;
  end;
