:: deftheorem Def9 defines * VECTSP_6:def 9 :
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 a being Element of GF
for L, b₅ being Linear_Combination of V holds
( b₅ = a * L iff for v being Element of V holds b₅ . v = a * (L . v) );