proposition: Lemma poweR_gt0 x r : 0 < x -> 0 < x `^ r.
proof: Proof. by move: x => [x|_|]//=; [rewrite lte_fin; exact: powR_gt0|case: ifPn]. 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