proposition: Lemma lead_coef_monicM p q : p \is monic -> lead_coef (p * q) = lead_coef q.
proof: Proof. have [-> | nz_q] := eqVneq q 0; first by rewrite mulr0. by move/monicP=> mon_p; rewrite lead_coef_proper_mul mon_p mul1r ?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)