for G being Group
for I1, I2 being non empty set
for F1 being DirectSumComponents of G,I1
for F2 being Group-Family of I2 st I1 misses I2 & ( for i being Element of I2 holds card (F2 . i) = 1 ) holds
F1 +* F2 is DirectSumComponents of G,I1 \/ I2