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].

(* Specifications: *)
Lemma polyOver_subvs {K} {p : {poly L}} :
reflect (exists q : {poly subvs_of K}, p = map_poly vsval q)
(p \is a polyOver K).
Lemma divp_polyOver K : {in polyOver K &, forall p q, p %/ q \is a polyOver K}.
Lemma modp_polyOver K : {in polyOver K &, forall p q, p %% q \is a polyOver K}.
Lemma gcdp_polyOver K :
{in polyOver K &, forall p q, gcdp p q \is a polyOver K}.