proposition: Lemma nneg_neq0_poweRD_def x r s : x != 0 -> (r >= 0)%R -> (s >= 0)%R -> x `^?(r +? s).
proof: Proof. move=> xN0 rge0 sge0; rewrite /poweRD_def xN0/=. by case: ltgtP rge0 => // [r_gt0|<-]; case: ltgtP sge0 => // [s_gt0|<-]//=; rewrite ?addr0 ?add0r ?implybT// gt_eqF//= ?addr_gt0. 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