Fact subfx_scalerA a b x :
subfx_scale a (subfx_scale b x) = subfx_scale (a * b) x.

(* Specifications: *)
Lemma subfx_inj_root : subfx_inj subfx_root = z.
Lemma subfx_irreducibleP :
(forall q, root q^iota z -> q != 0 -> size p <= size q) <-> irreducible_poly p.