proposition: Lemma filter_out_filter {A} f (ls : list A) : filter_out f ls = filter (fun x => negb (f x)) ls.
proof: Proof. induction ls; simpl; trivial; rewrite !IHls; edestruct f; reflexivity. 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