proposition: Lemma NoDup_app_in {A} (ls ls' : list A) (x : A) (H : NoDup (ls ++ ls')) : In x ls' -> In x ls -> False.
proof: Proof. intros H0 H1. induction ls as [|?? IHls]; simpl in *; trivial. destruct H1; inversion H; clear H; subst; eauto. rewrite in_app_iff in *. eauto. Qed.
imports: Fiat.Common.Coq__8_4__8_5__Compat Coq.ZArith.ZArith Coq.Lists.List Coq.Lists.SetoidList Coq.Bool.Bool Fiat.Common Fiat.Common.List.Operations Fiat.Common.Equality Fiat.Common.List.FlattenList Fiat.Common.LogicFacts