 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 ThGSubOmega:
  G is Subgroup of (Omega).G
proof
  G is Subgroup of G by GROUP_2:54;
  hence thesis by GROUP_2:57;
end;
