proposition: Lemma map_msg_fail_eq_nodup : forall h failed ns ns', NoDup ns -> Permutation (map tot_map_name ns) ns' -> Permutation (map (fun nm : name * msg => (tot_map_name (fst nm), tot_map_msg (snd nm))) (map2snd msg_fail (filter_rel adjacent_to_dec h (remove_all name_eq_dec failed ns)))) (map2snd msg_fail (filter_rel adjacent_to_dec (tot_map_name h) (remove_all name_eq_dec (map tot_map_name failed) ns'))).
proof: Proof. Proof using overlay_map_congr name_map_bijective fail_msg_map_congr. move => h failed. rewrite tot_fail_msg_fst_snd. exact: nodup_perm_map_map_pair_perm. Qed.
imports: Verdi(Verdi DynamicNetLemmas) Coq(FunctionalExtensionality) Coq(Sorting.Permutation Sumbool) Verdi(Ssrexport)