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

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).