
theorem Th3:
  for G being Group for A being Subset of G for H being strict
  Subgroup of G st A = the carrier of H holds gr A = H
proof
  let G be Group;
  let A be Subset of G;
  let H be strict Subgroup of G such that
A1: A = the carrier of H;
  gr carr H = H by GROUP_4:31;
  hence thesis by A1,GROUP_2:def 9;
end;
