reserve G for Group,
  a,b for Element of G,
  m, n for Nat,
  p for Prime;

theorem Th9:
  for G being Group, H being Subgroup of G, a,b being Element of G
  holds a * H = b * H implies ex h being Element of G st a = b * h & h in H
by GROUP_2:108,GROUP_2:103;
