Fact prodv_is_aspace E F : is_aspace (E * F).
Canonical prodv_aspace E F : {subfield L} := ASpace (prodv_is_aspace E F).
Fact field_mem_algid E F : algid E \in F. Proof. by rewrite algid1 mem1v. Qed.
Canonical capv_aspace E F : {subfield L} := aspace_cap (field_mem_algid E F).

Lemma field_module_dimS F M : (F * M <= M)%VS -> (\dim F %| \dim M)%N.
Section FadjoinPolyDefinitions.