Definition step_ordered_dynamic_failure_tot_s_net_handlers_eq :=
  forall net failed tr src m ms d out st' ps out' st'',
  step_ordered_dynamic_failure_star step_ordered_dynamic_failure_init (failed, net) tr ->
  odnwPackets net src me = m :: ms ->
  ~ In me failed ->
  odnwState net me = Some d ->
  net_handlers me src m d = (out, st', ps) ->
  input_handler (tot_s_map_msg me src m) (tot_s_map_data d) = (out', st'') ->
  map tot_s_map_output out = out' /\ tot_s_map_data st' = st''.

(* Specifications: *)
Theorem step_ordered_dynamic_failure_tot_one_mapped_simulation_1 : step_ordered_dynamic_failure_tot_s_net_handlers_eq -> forall net net' failed failed' tr tr', step_ordered_dynamic_failure_star step_ordered_dynamic_failure_init (failed, net) tr -> step_ordered_dynamic_failure (failed, net) (failed', net') tr' -> forall d, net.(odnwState) me = Some d -> forall d', net'.(odnwState) me = Some d' -> d = d' \/ exists tr'', @step_s _ single (tot_s_map_data d) (tot_s_map_data d') tr''.
Lemma step_ordered_dynamic_failure_tot_one_mapped_simulation_1_init : forall net net' failed failed' tr, step_ordered_dynamic_failure (failed, net) (failed', net') tr -> net.(odnwState) me = None -> forall d, net'.(odnwState) me = Some d -> tot_s_map_data d = init_handler.
Lemma step_ordered_dynamic_failure_tot_one_mapped_simulation_star_1 : step_ordered_dynamic_failure_tot_s_net_handlers_eq -> forall net failed tr, step_ordered_dynamic_failure_star step_ordered_dynamic_failure_init (failed, net) tr -> forall d, net.(odnwState) me = Some d -> exists tr', @step_s_star _ single init_handler (tot_s_map_data d) tr'.