proposition: Theorem lb_step_failure_pt_mapped_simulation_1_silent : forall net net' failed failed' lb tr, tot_map_label lb = label_silent -> @lb_step_failure _ labeled_multi_fst (failed, net) lb (failed', net') tr -> @lb_step_failure _ labeled_multi_snd (List.map tot_map_name failed, pt_map_net net) label_silent (List.map tot_map_name failed', pt_map_net net') [] /\ filterMap trace_non_empty_out (filterMap pt_map_trace_occ tr) = [].
proof: Proof. Proof using multi_map_lb_congr multi_map_congr. move => net net' failed failed' lb tr H_eq H_step. invcs H_step => //=. - destruct (pt_map_packet p) eqn:?. destruct p, p0. simpl in *. break_match_hyp => //. find_injection. have H_q := @pt_net_handlers_some _ _ _ _ _ _ _ multi_map_congr pDst pSrc pBody (nwState net pDst) _ Heqo0. rewrite /pt_mapped_net_handlers /net_handlers /= /unlabeled_net_handlers in H_q. repeat break_let. repeat tuple_inversion. have H_q' := @pt_lb_net_handlers_some _ _ _ _ _ _ _ _ multi_map_lb_congr _ _ _ _ _ _ _ _ _ Heqo0 Heqp1. break_and. unfold tot_mapped_lb_net_handlers_label in *. repeat break_let. by repeat tuple_inversion. destruct p. simpl in *. break_match_hyp => //. have H_q := @pt_net_handlers_none _ _ _ _ _ _ _ multi_map_congr pDst pSrc pBody (nwState net pDst) out d l Heqo0. rewrite /net_handlers /= /unlabeled_net_handlers in H_q. repeat break_let. repeat tuple_inversion. concludes. break_and. have H_q' := @pt_lb_net_handlers_none _ _ _ _ _ _ _ _ multi_map_lb_congr pDst pSrc _ (nwState net pDst) Heqo0. rewrite /tot_mapped_lb_net_handlers_label in H_q'. repeat break_let. repeat tuple_inversion. rewrite /pt_map_net /=. rewrite filterMap_app. rewrite filterMap_pt_map_name_msg_empty_eq //=. rewrite H3. rewrite filterMap_app /=. repeat break_match => //. rewrite -filterMap_app. set s1 := fun _ => _. set s2 := fun _ => _. have H_eq_s: s1 = s2. rewrite /s1 /s2. apply functional_extensionality => n. rewrite /update. by break_if; first by rewrite H e. rewrite -H_eq_s /s1 {s1 s2 H_eq_s}. split => //. exact: LabeledStepFailure_stutter. - case H_i: (pt_map_input inp) => [inp'|]. have H_q := @pt_input_handlers_some _ _ _ _ _ _ _ multi_map_congr h _ (nwState net h) _ H_i. rewrite /pt_mapped_input_handlers /input_handlers /= /unlabeled_input_handlers in H_q. repeat break_let. repeat tuple_inversion. have H_q' := @pt_lb_input_handlers_some _ _ _ _ _ _ _ _ multi_map_lb_congr _ _ _ _ _ _ _ _ H_i Heqp1. break_and. unfold tot_mapped_lb_input_handlers_label in *. repeat break_let. by tuple_inversion. have H_q := @pt_input_handlers_none _ _ _ _ _ _ _ multi_map_congr h _ (nwState net h) out d l H_i. rewrite /input_handlers /= /unlabeled_input_handlers in H_q. repeat break_let. repeat tuple_inversion. concludes. break_and. have H_q' := @pt_lb_input_handlers_none _ _ _ _ _ _ _ _ multi_map_lb_congr h _ (nwState net h) H_i. rewrite /tot_mapped_lb_input_handlers_label in H_q'. repeat break_let. repeat tuple_inversion. rewrite /pt_map_net /=. rewrite filterMap_app. rewrite filterMap_pt_map_name_msg_empty_eq //=. set s1 := fun _ => _. set s2 := fun _ => _. have H_eq_s: s1 = s2. rewrite /s1 /s2. apply functional_extensionality => n. rewrite /update. by break_if; first by rewrite H e. rewrite -H_eq_s /s1 {s1 s2 H_eq_s}. split; first exact: LabeledStepFailure_stutter. by repeat find_rewrite. - split => //; exact: LabeledStepFailure_stutter. Qed.
imports: Verdi(Verdi LabeledNet) Verdi(TotalMapSimulations PartialMapSimulations) Verdi(TotalMapExecutionSimulations) InfSeqExt(infseq map exteq) Coq(FunctionalExtensionality) Verdi(Ssrexport) Coq(ssrbool)