 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 ThS2:
  for I being non empty set
  for G being Group
  for F being Subgroup-Family of I,G
  holds F is componentwise_strict
  iff (for i being Element of I holds F.i is strict Subgroup of G);
