proposition: Lemma KVEnsemble_EquivalentKeys_Remove {B C} : forall (ens : Ensemble (Key * B)) (ens' : Ensemble (Key * C)) (EquivKeys : KVEnsemble_EquivalentKeys ens ens') (a : Key), KVEnsemble_EquivalentKeys (EnsembleRemoveKey a ens) (EnsembleRemoveKey a ens').
proof: Proof. unfold KVEnsemble_EquivalentKeys, EnsembleRemoveKey in *; simpl in *; intuition. apply H in H3; destruct_ex; eauto. apply H0 in H3; destruct_ex; eauto. Qed.
imports: Coq.Strings.String Coq.ZArith.ZArith Coq.Lists.List Coq.Logic.FunctionalExtensionality Coq.Sets.Ensembles Computation ADT ADTRefinement ADTNotation BuildADTRefinements KVEnsembles CacheSpec