theorem Th11: :: VECTSP_6:11

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 v1, v2 being Element of V
for f being Function of V,GF holds f (#) <*v1,v2*> = <*((f . v1) * v1),((f . v2) * v2)*>