proposition: Lemma map_then_map : forall {heading} (m: @RawTuple heading -> @RawTuple heading) (x: list IndexedElement), map m (map indexedElement x) = map indexedElement (map (fun t => {| indexedElement := m (indexedElement t); elementIndex := elementIndex t|}) x).
proof: Proof. intro; induction x as [| x' xs']. - simpl. reflexivity. - simpl. rewrite IHxs'. 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