proposition: Lemma poweR_eq0 x r : 0 <= x -> (x `^ r == 0) = ((x == 0) && (r != 0%R)).
proof: Proof. move: x => [x _|_/=|//]; first by rewrite poweR_EFin eqe powR_eq0. by case: ifP => //; rewrite onee_eq0. 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