proposition: Corollary refine_Join_Comp_Lists_filter_filter_search_term_snd_dep' (ResultT : Type) : forall r_o (r_n : IndexedQueryStructure qs_schema BagIndexKeys) (_ : DelegateToBag_AbsR r_o r_n) idx idx' (search_pattern : _ -> _) (resultComp : ilist2 (B:= @RawTuple) [_; _] -> Comp (list ResultT)) filter_rest st, refine (cl <- CallBagFind idx r_n st; l' <- (Join_Comp_Lists (Build_single_Tuple_list (snd cl)) (fun _ => l <- CallBagEnumerate idx' r_n ; ret (snd l))); List_Query_In (filter (fun a : ilist2 (B:= @RawTuple) [_ ; _] => BagMatchSearchTerm _ (search_pattern (ilist2_tl a)) (ilist2_hd a) && filter_rest a) l') resultComp) (cl <- CallBagFind idx r_n st; l' <- (Join_Comp_Lists (Build_single_Tuple_list (snd cl)) (fun tup => l <- CallBagFind idx' r_n (search_pattern tup); ret (snd l))); List_Query_In (filter filter_rest l') resultComp).
proof: Proof. intros; f_equiv; intro; eapply refine_Join_Comp_Lists_filter_search_term_snd_dep; eauto. Qed.
imports: Fiat.Common.Coq__8_4__8_5__Compat Coq.Lists.List Coq.Program.Program Fiat.QueryStructure.Specification.Representation.Tuple Fiat.QueryStructure.Specification.Representation.Heading Fiat.Common.ilist2 Fiat.Common.i2list Fiat.Common.ilist3 Fiat.Common.i3list Coq.Bool.Bool Coq.Strings.String Coq.Structures.OrderedTypeEx Coq.Arith.Arith Fiat.Common.String_as_OT Fiat.Common.Ensembles.IndexedEnsembles Fiat.Common.DecideableEnsembles Fiat.Common.List.ListFacts Fiat.QueryStructure.Specification.Operations.FlattenCompList Fiat.QueryStructure.Implementation.Operations.General.QueryRefinements Fiat.QueryStructure.Implementation.Operations.General.InsertRefinements Fiat.QueryStructure.Implementation.Operations.General.EmptyRefinements Fiat.QueryStructure.Specification.Representation.QueryStructureNotations Fiat.QueryStructure.Implementation.ListImplementation Fiat.Common.List.PermutationFacts Fiat.QueryStructure.Implementation.DataStructures.BagADT.BagADT Fiat.QueryStructure.Implementation.DataStructures.BagADT.QueryStructureImplementation Fiat.QueryStructure.Implementation.DataStructures.BagADT.IndexSearchTerms Fiat.QueryStructure.Implementation.Operations.General.DeleteRefinements