proposition: Lemma IndexedEnsemble_Intersection_And : forall (ens : IndexedEnsemble) (P Q : Ensemble ElementType), Same_set _ (IndexedEnsemble_Intersection (IndexedEnsemble_Intersection ens P) Q) (IndexedEnsemble_Intersection ens (fun el => P el /\ Q el)).
proof: Proof. unfold Same_set, Included, IndexedEnsemble_Intersection, In; intuition. Qed.
imports: Fiat.Common.Coq__8_4__8_5__Compat Coq.Lists.List Coq.Strings.String Coq.ZArith.ZArith Coq.Logic.FunctionalExtensionality Coq.Sorting.Permutation Coq.Sets.Ensembles Fiat.Common.DecideableEnsembles Fiat.Common.List.PermutationFacts Fiat.Common.List.ListMorphisms Fiat.Common.List.ListFacts