proposition: Lemma refine_decides_Equiv_Ensemble' {A}: forall (P P' : Ensemble A), ((forall idx : A, P idx) <-> (forall idx' : A, P' idx')) -> refine {b : bool | decides b (forall idx : A, P idx)} {b : bool | decides b (forall idx : A, P' idx)}.
proof: Proof. intros; eapply refineEquiv_pick_pick. intro; destruct x; simpl; split; intros; intuition eauto. Qed.
imports: Coq.Vectors.Vector Coq.Strings.Ascii Coq.Bool.Bool Coq.Bool.Bvector Coq.Lists.List Fiat.Computation.ListComputations Fiat.QueryStructure.Automation.AutoDB Fiat.QueryStructure.Implementation.DataStructures.BagADT.BagADT Fiat.QueryStructure.Automation.IndexSelection Fiat.QueryStructure.Specification.SearchTerms.ListPrefix Fiat.QueryStructure.Automation.SearchTerms.FindPrefixSearchTerms Fiat.QueryStructure.Automation.QSImplementation Fiat.Narcissus.Formats.DomainNameOpt Fiat.Narcissus.Examples.DNS.SimpleDnsOpt Fiat.Narcissus.Examples.DNS.SimpleDNSPacket Fiat.Examples.DnsServer.DecomposeSumField Fiat.Computation.FoldComp Fiat.Examples.DnsServer.SimpleAuthoritativeDNSSchema