proposition: Lemma Find_MatchingIndexesOK_Subset : forall (st : IndexSearchTermT) (MKey : KeyMapT) (MValues : ValuesMapT) item idx, MValues.MapsTo idx item (Find_MatchingIndexes MKey st MValues) -> MValues.MapsTo idx item MValues.
proof: Proof. induction st; simpl; unfold inclA; intros; intuition. - case_eq (MKeys.find a MKey); intros; rewrite H0 in H. + apply IHst in H. rewrite MValuesProperties.filter_iff in H; intuition. + apply MValues.empty_1 in H; intuition. Qed.
imports: Fiat.Common.Coq__8_4__8_5__Compat Fiat.QueryStructure.Implementation.DataStructures.Bags.BagsInterface Fiat.QueryStructure.Implementation.DataStructures.Bags.BagsProperties Coq.Arith.Peano_dec Coq.Structures.OrdersEx Coq.FSets.FMapInterface Coq.FSets.FMapFacts Coq.FSets.FMapAVL Coq.ZArith.ZArith Fiat.Common Fiat.Common.String_as_OT Fiat.Common.List.ListFacts Fiat.Common.List.FlattenList Fiat.Common.SetEqProperties Fiat.Common.FMapExtensions Fiat.Common.List.PermutationFacts Fiat.QueryStructure.Specification.SearchTerms.ListInclusion