 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 Def4:
  for I be non empty set
  for F be Group-Family of I
  for IT be Subgroup-Family of F holds
    IT is componentwise_strict iff
    for i being Element of I holds IT.i is strict Subgroup of F.i;
