for I0, I being non empty finite set
for F0 being Group-like associative multMagma-Family of I0
for F being Group-like associative multMagma-Family of I
for H, K being Group
for q being Element of I
for k being Element of K
for g being Function st g in the carrier of (product F0) & not q in I0 & I = I0 \/ {q} & F = F0 +* (q .--> K) holds
g +* (q .--> k) in the carrier of (product F)