theorem Th16:
  (homography(N)).((homography(N~)).P) = P &
  (homography(N~)).((homography(N)).P) = P
  proof
A1: N~ is_reverse_of N by MATRIX_6:def 4;
    thus (homography(N)).((homography(N~)).P) = (homography(N * N~)).P
                                               by Th14
                                             .= (homography(1.(F_Real,3))).P
                                               by A1,MATRIX_6:def 2
                                             .= P by Th15;
    thus (homography(N~)).((homography(N)).P) = (homography(N~ * N)).P
                                               by Th14
                                             .= (homography(1.(F_Real,3))).P
                                               by A1,MATRIX_6:def 2
                                             .= P by Th15;
  end;
