proposition: Lemma le_ln1Dx x : 0 <= x -> ln (1 + x) <= x.
proof: Proof. move=> x_ge0; rewrite -ler_expR lnK ?expR_ge1Dx //. by apply: lt_le_trans (_ : 0 < 1) _; rewrite // lerDl. 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