(* Monic predicate *)
Fact monic_key : pred_key monic. Proof. by []. Qed.
Canonical monic_keyed := KeyedQualifier monic_key.

Lemma monic_comreg p :
p \is monic -> GRing.comm p (lead_coef p)%:P /\ GRing.rreg (lead_coef p).