Canonical aspaceOver E := ASpace (aspaceOver_suproof E).

(* Specifications: *)
Lemma dim_vspaceOver M : (F * M <= M)%VS -> \dim (vspaceOver M) = \dim_F M.
Lemma dim_aspaceOver E : (F <= E)%VS -> \dim (vspaceOver E) = \dim_F E.
Lemma aspaceOverP (E_F : {subfield L_F}) :
{E | [/\ E_F = aspaceOver E, (F <= E)%VS & E_F =i E]}.