Proof using.
move => net failed tr H.
remember step_ordered_dynamic_failure_init as y in *.
have ->: failed = fst (failed, net) by [].
have H_eq_o: net = snd (failed, net) by [].
rewrite {2}H_eq_o {H_eq_o}.
move: Heqy.
induction H using refl_trans_1n_trace_n1_ind => H_init /=; first by rewrite H_init.
repeat find_rewrite.
concludes => {H_init}.
match goal with
| [ H : step_ordered_dynamic_failure _ _ _ |- _ ] => invc H
end; rewrite /=.
- move => n H_in.
right.
exact: IHrefl_trans_1n_trace1.
- move => n H_in.
exact: IHrefl_trans_1n_trace1.
- move => n H_in.
exact: IHrefl_trans_1n_trace1.
- move => n H_in.
case: H_in => H_in; first by rewrite -H_in.
exact: IHrefl_trans_1n_trace1.
Qed.

Lemma ordered_dynamic_state_not_initialized_not_failed :
forall net failed tr,
step_ordered_dynamic_failure_star step_ordered_dynamic_failure_init (failed, net) tr ->
forall n, ~ In n (odnwNodes net) ->
~ In n failed.