 reserve I for non empty set;
 reserve i for Element of I;
 reserve F for Group-Family of I;
 reserve G for Group;
reserve S for Subgroup-Family of F;

theorem
  for G being Group
  for H being strict Subgroup of G
  holds Image (incl H) = H
proof
  let G be Group;
  let H be strict Subgroup of G;
  the carrier of H c= the carrier of H;
  then the carrier of H
   = (id the carrier of H) .: (the carrier of H) by FUNCT_1:92
  .= (incl H) .: (the carrier of H) by Def9
  .= the carrier of Image (incl H) by GROUP_6:def 10;
  hence Image(incl H) = H by GROUP_2:59;
end;
