proposition: Lemma In_Join_Lists {A B} : forall (l : list A) (l' : list B) (a : A) (b : B), List.In (a, b) (Join_Lists l l') <-> (List.In a l /\ List.In b l').
proof: Proof. unfold Join_Lists; setoid_rewrite in_flat_map; setoid_rewrite in_map_iff. firstorder; congruence. Qed.
imports: Coq.Strings.String Coq.ZArith.ZArith Coq.Lists.List Coq.Logic.FunctionalExtensionality Coq.Sets.Ensembles Coq.Sorting.Permutation Fiat.Computation Fiat.ADT Fiat.ADTRefinement Fiat.ADTNotation Fiat.ADTRefinement.GeneralBuildADTRefinements Fiat.QueryStructure.Specification.Representation.QueryStructureSchema Fiat.QueryStructure.Specification.Operations.Query Fiat.QueryStructure.Specification.Representation.QueryStructure Fiat.QueryStructure.Implementation.Operations.General.QueryRefinements Fiat.Common.SetEq Fiat.Common.Ensembles.IndexedEnsembles Fiat.Common.DecideableEnsembles Fiat.Common.List.ListMorphisms Fiat.Common.List.FlattenList Fiat.QueryStructure.Specification.Operations.FlattenCompList