Proof using.
by move => s; rewrite -map_Cons /= -{3}(recons s).
Qed.

(* Specifications: *)
Lemma lb_step_trace_execution_lb_step_failure_tot_map_net_infseq : forall s,
lb_step_execution lb_step_failure s ->
lb_step_execution lb_step_failure (map tot_map_net_event s).
Lemma lb_step_execution_lb_step_ordered_failure_tot_map_onet_infseq : forall s,
lb_step_execution lb_step_ordered_failure s ->
lb_step_execution lb_step_ordered_failure (map tot_map_onet_event s).
Lemma lb_step_execution_lb_step_ordered_dynamic_failure_tot_map_odnet_infseq : forall s,
lb_step_execution lb_step_ordered_dynamic_failure s ->
lb_step_execution lb_step_ordered_dynamic_failure (map tot_map_odnet_event s).
Lemma lb_step_execution_lb_step_ordered_failure_pt_map_onet_infseq : forall s,
lb_step_execution lb_step_ordered_failure s ->
lb_step_execution lb_step_ordered_failure (map pt_map_onet_event s).
Lemma lb_step_execution_lb_step_ordered_dynamic_failure_pt_map_odnet_infseq : forall s,
lb_step_execution lb_step_ordered_dynamic_failure s ->
lb_step_execution lb_step_ordered_dynamic_failure (map pt_map_odnet_event s).