reserve G for strict Group,
  a,b,x,y,z for Element of G,
  H,K for strict Subgroup of G,
  p for Element of NAT,
  A for Subset of G;

theorem
  for G being Group, H being Subgroup of G, a being Element of H
  for b being Element of G st a = b for n being Element of NAT
  holds a|^n = b|^n by GROUP_4:1;
