:: deftheorem Def3 defines Subspaces VECTSP_5:def 3 :
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 set holds
( b₃ = Subspaces M iff for x being object holds
( x in b₃ iff ex W being strict Subspace of M st W = x ) );