proposition: Lemma in_list_preserve_filter {A} : forall (f : A -> bool) xs x, List.In x (filter f xs) -> List.In x xs.
proof: Proof. intros; apply (filter_In f x xs) in H; tauto. 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