Corollary step_failure_tot_mapped_simulation_star_1 :
  forall net failed tr,
    @step_failure_star _ _ fail_fst step_failure_init (failed, net) tr ->
    @step_failure_star _ _ fail_snd step_failure_init (map tot_map_name failed, tot_map_net net) (map tot_map_trace_occ tr).

Theorem step_failure_tot_mapped_simulation_2 : forall net net' failed failed' out mnet mfailed mfailed' mout, @step_failure _ _ fail_snd (failed, net) (failed', net') out -> tot_map_net mnet = net -> map tot_map_name mfailed = failed -> map tot_map_name mfailed' = failed' -> map tot_map_trace_occ mout = out -> exists mnet', @step_failure _ _ fail_fst (mfailed, mnet) (mfailed', mnet') mout /\ tot_map_net mnet' = net'.