proposition: Lemma poweR_eq0_eq0 x r : 0 <= x -> x `^ r = 0 -> x = 0.
proof: Proof. by move=> + /eqP => /poweR_eq0-> /andP[/eqP]. 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