theorem :: GROUP_9:125

for G, H being Group
for F1 being FinSequence of the carrier of G
for F2 being FinSequence of the carrier of H
for I being FinSequence of INT
for 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;