 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
  for I being set
  for J being Subset of I st J is empty
  for F being normal Subgroup-Family of I,G
  holds Carrier (F|J) = {} --> (bool the carrier of G);
