proposition: Lemma ln_sublinear x : 0 < x -> ln x < x.
proof: Proof. move=> x_gt0; apply: lt_le_trans (_ : ln (1 + x) <= _). by rewrite -ltr_expR !lnK ?qualifE/= ?addr_gt0 // ltrDr. by rewrite -ler_expR lnK ?qualifE/= ?addr_gt0// expR_ge1Dx // ltW. 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