reserve i for Element of NAT;

theorem Th8:
  for G,H being Group, g being Homomorphism of G,H
   for A being Subgroup of G holds
    the carrier of (g.: A) = g.:(the carrier of A)
proof
  let G,H be Group;
  let g be Homomorphism of G,H;
  let A be Subgroup of G;
  thus the carrier of (g.: A)=rng (g|A) by GROUP_6:44
    .=g.:(the carrier of A) by RELAT_1:115;
end;
