theorem Th38: :: ZMODUL05:55

for R being Ring
for V, W being LeftMod of R
for l being Linear_Combination of V
for T being linear-transformation of V,W
for G being FinSequence of V st rng G = Carrier l & T | (Carrier l) is one-to-one holds
T * (l (#) G) = (T @* l) (#) (T * G)