
theorem GRCY212:
  for G being Group, a, b being Element of G st b in gr{a}
  holds gr{b} is strict Subgroup of gr{a}
  proof
    let G be Group, a, b be Element of G;
    assume b in gr{a}; then
    reconsider b0 = b as Element of gr{a};
    gr{b0} = gr{b} by GR_CY_2:3;
    hence thesis;
  end;
