proposition: Lemma Permutation_UnIndexedEnsembleListEquivalence' : forall ensemble (l l' : list _), UnIndexedEnsembleListEquivalence ensemble l -> UnIndexedEnsembleListEquivalence ensemble l' -> Permutation l l'.
proof: Proof. simpl; intros. destruct H; destruct H0; intuition subst. setoid_rewrite H0 in H2. eapply Permutation_map. eapply NoDup_Permutation; eauto using NoDup_IndexedElement. Qed.
imports: Fiat.Common.Coq__8_4__8_5__Compat Coq.Lists.List Coq.Strings.String Coq.ZArith.ZArith Coq.Logic.FunctionalExtensionality Coq.Sorting.Permutation Coq.Sets.Ensembles Fiat.Common.DecideableEnsembles Fiat.Common.List.PermutationFacts Fiat.Common.List.ListMorphisms Fiat.Common.List.ListFacts