proposition: Lemma ln_lt0 x : 0 < x < 1 -> ln x < 0.
proof: Proof. by move=> /andP[x_gt0 x_lt1]; rewrite -ltr_expR expR0 lnK. 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