proposition: Lemma continuous_ln x : 0 < x -> {for x, continuous ln}.
proof: Proof. move=> x_gt0; rewrite -[x]lnK//. apply: nbhs_singleton (near_can_continuous _ _); near=> z; first exact: expRK. by apply: continuous_expR. Unshelve. all: by end_near. 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