theorem Th42: :: ZMODUL05:59

for R being Ring
for V, W being LeftMod of R
for X being Subset of V
for T being linear-transformation of V,W
for X being Subset of V
for l being Linear_Combination of T .: X
for v being Element of V st v in X & T | X is one-to-one holds
(T # l) . v = l . (T . v)