proposition: Lemma gt0_poweR x r : (0 < r)%R -> 0 <= x -> 0 < x `^ r -> 0 < x.
proof: Proof. move=> r0; move: x => [x|//|]; rewrite ?leeNe_eq// lee_fin !lte_fin. exact: gt0_powR. 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