proposition: Lemma lead_coefM p q : lead_coef (p * q) = lead_coef p * lead_coef q.
proof: Proof. have [-> | nz_p] := eqVneq p 0; first by rewrite !(mul0r, lead_coef0). have [-> | nz_q] := eqVneq q 0; first by rewrite !(mulr0, lead_coef0). by rewrite lead_coef_proper_mul // mulf_neq0 ?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)