Section FieldExtTheory.
Variables (F0 : fieldType) (L : fieldExtType F0).
Implicit Types (U V M : {vspace L}) (E F K : {subfield L}).
Canonical prodv_comoid := Monoid.ComLaw prodvC.
Canonical aimg_aspace rT f E := ASpace (@aimg_is_aspace rT f E).
Fact aspace_divr_closed K : divr_closed K.
Canonical subvs_fieldType K :=
Eval hnf in FieldType (subvs_of K) (@subvs_fieldMixin K).
Canonical subvs_fieldExtType K := Eval hnf in [fieldExtType F0 of subvs_of K].

Lemma polyOver_subvs {K} {p : {poly L}} :
reflect (exists q : {poly subvs_of K}, p = map_poly vsval q)
(p \is a polyOver K).