Proof using.
induction l; intros; simpl in *; intuition; eauto.
repeat break_match; simpl in *; eauto;
repeat find_insterU; break_exists; eexists; f_equal; eauto.
Qed.

Lemma deduplicate_log_app :
forall l l',
exists l'',
deduplicate_log (l ++ l') = deduplicate_log l ++ l''.