 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 Th18:
  for H being Group
  for h being Element of H
  st H is Subgroup of G
  holds (incl (H, G)).h = h
proof
  let H be Group;
  let h be Element of H;
  assume H is Subgroup of G;
  hence (incl (H, G)).h = (id the carrier of H).h by Def9
                       .= h;
end;
