Section Irreducible.
Hypothesis irr_p : irreducible_poly p.
Let nz_p : p != 0. Proof. exact: irredp_neq0. Qed.
Definition SubfxVectMixin := VectMixin min_subfx_vectAxiom.
Definition SubfxVectType := VectType F subFExtend SubfxVectMixin.
Definition SubfxFalgType := Eval simpl in [FalgType F of SubfxVectType].
Definition SubFieldExtType := Eval simpl in [fieldExtType F of SubfxFalgType].
End Irreducible.
End SubFieldExtension.
Prenex Implicits subfx_inj.

Lemma irredp_FAdjoin (F : fieldType) (p : {poly F}) :
irreducible_poly p ->
{L : fieldExtType F & \dim {:L} = (size p).-1 &
{z | root (map_poly (in_alg L) p) z & <<1; z>>%VS = fullv}}.