Proof using.
intros tr tr' l tr1 H_exp H_eq.
rewrite get_input_tr_filterMap_trace_non_empty_out in H_exp.
rewrite get_output_tr_filterMap_trace_non_empty_out in H_exp.
rewrite <- H_eq in H_exp.
rewrite <- get_input_tr_filterMap_trace_non_empty_out in H_exp.
rewrite <- get_output_tr_filterMap_trace_non_empty_out in H_exp.
auto.
Qed.

Lemma import_exported_filterMap_trace_non_empty_out :
forall tr,
import tr = import (filterMap trace_non_empty_out tr).