proposition: Lemma permu_filter_rewrite : forall (A: Type) (l: list A) (f: A -> bool), Permutation l ((filter (fun x => negb (f x)) l) ++ (filter f l)).
proof: Proof. induction l; intros; simpl in *. - intuition. - case_eq (f a); intros; simpl in *. + rewrite <- Permutation_middle; rewrite <- IHl; reflexivity. + rewrite <- IHl; reflexivity. Qed.
imports: Fiat.Common.Coq__8_4__8_5__Compat Coq.Lists.List Coq.Program.Program Fiat.QueryStructure.Implementation.DataStructures.Bags.BagsInterface Fiat.QueryStructure.Implementation.DataStructures.Bags.CountingListBags Fiat.QueryStructure.Implementation.DataStructures.Bags.TreeBags Fiat.QueryStructure.Specification.Representation.Tuple Fiat.QueryStructure.Specification.Representation.Heading Fiat.Common.ilist Coq.Bool.Bool Coq.Strings.String Coq.Arith.Arith Coq.Structures.OrderedTypeEx Fiat.Common.String_as_OT Fiat.Common.i2list Fiat.Common.DecideableEnsembles Fiat.Common.Ensembles.IndexedEnsembles Fiat.Common.Ensembles.EnsembleListEquivalence Fiat.ADTRefinement.GeneralBuildADTTactics Fiat.Common.List.PermutationFacts Fiat.QueryStructure.Implementation.DataStructures.Bags.BagsOfTuples Fiat.QueryStructure.Implementation.Operations.General.QueryRefinements Fiat.QueryStructure.Specification.Representation.QueryStructureNotations Fiat.QueryStructure.Implementation.DataStructures.BagADT.BagADT Fiat.Common.List.ListFacts TransparentAbstract