proposition: Lemma Proper_negb_KeyBasedPartitioningFunction : forall key', Proper (X.eq ==> eq ==> eq) (fun (k0 : XMap.key) (e : Trie) => negb (KeyBasedPartitioningFunction Trie key' k0 e)).
proof: Proof. unfold Proper, respectful, KeyBasedPartitioningFunction; intros. repeat find_if_inside; subst; simpl; eauto; rewrite H in *; intuition. Qed.
imports: Fiat.Common.Coq__8_4__8_5__Compat Fiat.QueryStructure.Implementation.DataStructures.Bags.BagsInterface Fiat.QueryStructure.Implementation.DataStructures.Bags.BagsProperties Coq.FSets.FMapInterface Coq.FSets.FMapFacts Coq.FSets.FMapAVL Coq.ZArith.ZArith Fiat.Common Fiat.Common.List.ListFacts Fiat.Common.List.FlattenList Fiat.Common.SetEqProperties Fiat.Common.FMapExtensions Fiat.Common.List.PermutationFacts Fiat.QueryStructure.Specification.SearchTerms.ListPrefix