theorem
  for G,H being Group, F1 being FinSequence of the carrier of G, F2
  being FinSequence of the carrier of H, I being FinSequence of INT, f being
Homomorphism of G,H st (for k being Nat st k in dom F1 holds F2.k = f.(F1.k)) &
  len F1 = len I & len F2 = len I holds f.(Product(F1 |^ I)) = Product(F2 |^ I)
  by Lm23;
