Proof using.
intros.
apply before_func_deduplicate'; auto.
simpl. intros. discriminate.
Qed.

Lemma entries_ordered_before_log_to_IR :
forall k k' net failed tr,
step_failure_star step_failure_init (failed, net) tr ->
In (O k) (import tr) ->
k <> k' ->
entries_ordered (fst k) (snd k) (fst k') (snd k') net ->
before (IRO k) (IRI k')
(log_to_IR (get_output tr) (deduplicate_log (applied_entries (nwState net)))).