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 dim_cosetv_unit V u : u \is a GRing.unit -> \dim (V * <[u]>) = \dim V.