proposition: Lemma ln_gt0 x : 1 < x -> 0 < ln x.
proof: Proof. by move=> x_gt1; rewrite -ltr_expR expR0 lnK // qualifE/= (lt_trans _ x_gt1). 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