proposition: Lemma lead_coef_Mmonic p q : q \is monic -> lead_coef (p * q) = lead_coef p.
proof: Proof. have [-> | nz_p] := eqVneq p 0; first by rewrite mul0r. by move/monicP=> mon_q; rewrite lead_coef_proper_mul mon_q mulr1 ?lead_coef_eq0. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype bigop finset tuple) mathcomp(div ssralg countalg binomial)