 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 Th29:
  for g being Element of product F
  holds g.i is Element of F.i
proof
  let g be Element of product F;
  g is Function & g in product F;
  then g.i in F.i by GROUP_19:5;
  hence thesis;
end;
