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.