proposition: Lemma ln_ge0 x : 1 <= x -> 0 <= ln x.
proof: Proof. by move=> x_ge1; rewrite -ler_expR expR0 lnK// qualifE/= (lt_le_trans _ x_ge1). 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