proposition: Lemma le1r_powR a r : 1 <= a -> 1 <= r -> a <= a `^ r.
proof: Proof. by move=> a1 r1; rewrite (le_trans _ (ler_powR _ r1)) ?powRr1// (le_trans _ a1). 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