Proof using.
intros. induction l; simpl in *; intuition.
- subst. break_if; simpl in *; intuition eauto.
- break_match; simpl in *; intuition eauto.
break_if; simpl in *; intuition eauto.
Qed.

Theorem import_get_output :
forall tr k,
In (O k) (import tr) ->
exists o,
get_output tr k = Some o.