theorem Th42: :: RANKNULL:42

for F being Field
for V, W being VectSp of F
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)