proposition: Lemma powR_mulrn a n : 0 <= a -> a `^ n%:R = a ^+ n.
proof: Proof. move=> a_ge0; elim: n => [|n IHn]; first by rewrite powRr0 expr0. by rewrite -natr1 powRD ?natr1 ?pnatr_eq0// powRr1// IHn exprSr. Qed.
imports: mathcomp(all_ssreflect ssralg ssrint ssrnum matrix) mathcomp(interval rat) mathcomp(boolp classical_sets functions) mathcomp(mathcomp_extra) reals ereal signed topology normedtype landau sequences derive realfun itv convex