proposition: Lemma elim_not_In_app : forall (A : Type) (xs ys : list A) (x : A), ~ In x (xs ++ ys) -> ~ In x xs /\ ~ In x ys.
proof: Proof. split; auto using in_or_app. Qed.
imports: Coq.Lists.List Coq.Lists.SetoidList Metalib.CoqUniquenessTac