:: deftheorem Def7 defines SubJoin VECTSP_5:def 7 :
for GF being non empty right_complementable well-unital distributive Abelian add-associative right_zeroed associative doubleLoopStr
for M being non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed ModuleStr over GF
for b₃ being BinOp of (Subspaces M) holds
( b₃ = SubJoin M iff for A1, A2 being Element of Subspaces M
for W1, W2 being Subspace of M st A1 = W1 & A2 = W2 holds
b₃ . (A1,A2) = W1 + W2 );