
theorem
  for G1, G2 being Group for f being Function of the carrier of G1, the
  carrier of G2 for A being Subset of G1 holds f.:A c= f.:the carrier of gr A
proof
  let G1, G2 be Group;
  let f be Function of the carrier of G1, the carrier of G2;
  let A be Subset of G1;
  A c= the carrier of gr A by GROUP_4:def 4;
  hence thesis by RELAT_1:123;
end;
