proposition: Lemma consistency_key_eq : forall (container : IndexedBag) (key: TKey) bag item, IndexedBag_RepInv container -> MapsTo key bag container -> List.In item (benumerate bag) -> E.eq (projection item) key.
proof: Proof. intros; unfold IndexedBag_RepInv in *; eauto. eapply H; eauto. Qed.
imports: Fiat.QueryStructure.Implementation.DataStructures.Bags.BagsInterface Fiat.QueryStructure.Implementation.DataStructures.Bags.BagsProperties Coq.FSets.FMapInterface Coq.FSets.FMapFacts Coq.Arith.PeanoNat Fiat.Common Fiat.Common.List.ListFacts Fiat.Common.List.FlattenList Fiat.Common.SetEqProperties Fiat.Common.FMapExtensions Fiat.Common.List.PermutationFacts