theorem Th22: :: VECTSP_6:22

for GF being non empty right_complementable well-unital distributive Abelian add-associative right_zeroed associative doubleLoopStr
for V being non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed ModuleStr over GF
for v being Element of V
for L1, L2 being Linear_Combination of V holds (L1 + L2) . v = (L1 . v) + (L2 . v)