pply: eq_bigr => k _; rewrite -{5 6}[k](enum_valK k); case/enum_val: k.
Qed.pply/prodvP=> u v; rewrite !mem_baseVspace; apply: memvM.
Qed.Canonical baseAspace E := ASpace (baseAspace_suproof E).Fact refBaseField_key : unit. Proof. by []. Qed.

(* Specifications: *)
Lemma module_baseVspace M0 :
Lemma module_baseAspace (E0 : {subfield L0}) :
Lemma base_aspaceOver (E : {subfield L}) :