Proof using.
rewrite /step_star_lb_step_reachable.
case => failed net l.
case => failed' net' tr tr' H_star H_st.
invcs H_st.
- set net' := {| onwPackets := _ ; onwState := _ |}.
apply (@refl_trans_1n_trace_trans _ _ _ _ (failed', net)) => //.
rewrite (app_nil_end (map2fst _ _)).
apply: (@RT1nTStep _ _ _ _ (failed', net')); last exact: RT1nTBase.
apply: (StepOrderedFailure_deliver _ _ _ H3) => //.
rewrite /net_handlers /= /unlabeled_net_handlers /=.
repeat break_let.
by tuple_inversion.
- set net' := {| onwPackets := _ ; onwState := _ |}.
apply (@refl_trans_1n_trace_trans _ _ _ _ (failed', net)) => //.
rewrite (app_nil_end (_ :: _)).
apply: (@RT1nTStep _ _ _ _ (failed', net')); last exact: RT1nTBase.
apply: StepOrderedFailure_input => //; first by [].
rewrite /input_handlers /= /unlabeled_input_handlers /=.
repeat break_let.
by tuple_inversion.
- by have ->: tr' ++ [] = tr' by auto with datatypes.
Qed.

Lemma step_ordered_failure_star_lb_step_execution :
forall s, event_step_star step_ordered_failure step_ordered_failure_init (hd s) ->
lb_step_execution lb_step_ordered_failure s ->
always (now (event_step_star step_ordered_failure step_ordered_failure_init)) s.