proposition: Lemma add_1: forall n1 n2 N1 N2, In n1 N1 -> In n2 N2 -> In (n1 + n2) (add N1 N2).
proof: Proof. unfold In, add; intros. destruct N1; auto. destruct N2; auto. lia. Qed.
imports: Coq(ZArith Psatz Bool String List FMaps) Coq(FunctionalExtensionality) CDF(Sequences IMP)