 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;
reserve f for Homomorphism-Family of G, F;

theorem Th34:
  for g being Element of product F
  for h being Element of F.i
  holds g +* (i, h) in product F
proof
  let g be Element of product F;
  let h be Element of F.i;
  g in product F;
  hence thesis by GROUP_19:24;
end;
