theorem Th13: :: VECTSP_6:13

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 F, G being FinSequence of V
for f being Function of V,GF holds f (#) (F ^ G) = (f (#) F) ^ (f (#) G)