proposition: Lemma scaler_int n v : n%:~R *: v = v *~ n.
proof: Proof. elim: n=> [|n ihn|n ihn]; first by rewrite scale0r. by rewrite intS !mulrzDr_tmp scalerDl ihn scale1r. by rewrite intS opprD !mulrzDr_tmp scalerDl ihn scaleN1r. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat choice seq) mathcomp(fintype finfun bigop order ssralg countalg ssrnum) mathcomp(poly)