proposition: Lemma rmodpX p n : rmodp ((rmodp p d) ^+ n) d = rmodp (p ^+ n) d.
proof: Proof. elim: n => [|n IH]; first by rewrite !expr0. rewrite !exprS -rmodp_mulmr // IH rmodp_mulmr //. by rewrite mulrC rmodp_mulmr // mulrC. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype bigop ssralg poly)