proposition: Lemma divp_eq p q : p = (p %/ q) * q + (p %% q).
proof: Proof. have [-> | qn0] := eqVneq q 0; first by rewrite modp0 mulr0 add0r. by apply: IdomainUnit.divp_eq; rewrite unitfE lead_coef_eq0. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype bigop ssralg poly)