Proof using.
induction tr; simpl; auto.
destruct a, s; simpl.
- rewrite IHtr; auto.
- destruct l; auto.
Qed.

(* Specifications: *)
Lemma get_output_tr_filterMap_trace_non_empty_out :
forall tr,
get_output tr = get_output (filterMap trace_non_empty_out tr).