proposition: Lemma ln_le0 (x : R) : x <= 1 -> ln x <= 0.
proof: Proof. have [x0|x0 x1] := leP x 0; first by rewrite ln0. by rewrite -ler_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