Section AspaceTheory.
Variables (K : fieldType) (aT : FalgType K).
Implicit Types (u v e : aT) (U V : {vspace aT}) (A B : {aspace aT}).
Definition algid U := s2val (algid_subproof U).

Lemma memv_cosetP {U v w} :
reflect (exists2 u, u\in U & w = u * v) (w \in U * <[v]>)%VS.