proposition: Fact ln0 x : x <= 0 -> ln x = 0.
proof: Proof. rewrite /ln; case: xgetP => //= y _ /eqP yx x0. by have := expR_gt0 y; rewrite yx => /(le_lt_trans x0); rewrite ltxx. 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