proposition: Theorem FunctionalDependency_symmetry : forall A H (f : _ -> _ -> Comp A) (P : _ -> Prop) attrlist1 attrlist2 n, refine (x1 <- {b | decides b (forall tup' : @IndexedRawTuple H, P tup' -> FunctionalDependency_P attrlist1 attrlist2 n (indexedElement tup'))}; x2 <- {b | decides b (forall tup' : @IndexedRawTuple H, P tup' -> FunctionalDependency_P attrlist1 attrlist2 (indexedElement tup') n)}; f x1 x2) (x1 <- {b | decides b (forall tup' : @IndexedRawTuple H, P tup' -> FunctionalDependency_P attrlist1 attrlist2 n (indexedElement tup'))}; f x1 x1).
proof: Proof. unfold refine, FunctionalDependency_P; intros. computes_to_inv; firstorder. computes_to_inv; firstorder. repeat (computes_to_econstructor; eauto). destruct v0; simpl in *; unfold tupleAgree in *; intros; eauto. erewrite H0; eauto; intros; rewrite H2; eauto. unfold not; intros; eapply H0; intros. rewrite H1; eauto; intros; rewrite H3; eauto. Qed.
imports: Fiat.QueryStructure.Specification.Representation.QueryStructureNotations Fiat.QueryStructure.Specification.Operations.Query Coq.Lists.List Coq.Arith.Compare_dec Coq.Bool.Bool Coq.Strings.String Fiat.Common.BoolFacts Fiat.Common.List.PermutationFacts Fiat.Common.List.ListMorphisms Fiat.QueryStructure.Specification.Operations.FlattenCompList Fiat.Common.Ensembles.EnsembleListEquivalence Fiat.QueryStructure.Implementation.Operations.General.QueryRefinements Fiat.Common.IterateBoundedIndex Fiat.Common.List.ListFacts Fiat.Common.LogicFacts Fiat.Common.DecideableEnsembles Fiat.Computation.Refinements.Iterate_Decide_Comp Fiat.Computation.Refinements.General Fiat.QueryStructure.Specification.Constraints.tupleAgree Fiat.QueryStructure.Specification.Operations.Mutate