
theorem
  for P being non zero_proj1 non zero_proj2 Point of ProjectiveSpace TOP-REAL 3
  for u being non zero Element of TOP-REAL 3 st P = Dir u holds
  normalize_proj1 P = |[1, u.2/u.1, u.3/u.1]| &
  normalize_proj2 P = |[u.1/u.2, 1, u.3/u.2]| by Th11,Th14;
