proposition: Lemma max_1: forall n N1 N2, In n N1 -> In n (max N1 N2).
proof: Proof. unfold In, max; intros. destruct N1; auto. destruct N2; auto. lia. Qed.
imports: Coq(ZArith Psatz Bool String List FMaps) Coq(FunctionalExtensionality) CDF(Sequences IMP)