Proof using.
induction l1; intros; simpl in *; auto.
repeat break_match; simpl in *; eauto; try solve [f_equal; eauto].
- exfalso. do_bool.
find_erewrite_lem assoc_assoc_default. omega.
- do_bool.
find_erewrite_lem assoc_assoc_default.
rewrite assoc_set_same; eauto.
find_eapply_lem_hyp le_antisym; eauto. subst. auto.
- exfalso. do_bool.
find_erewrite_lem assoc_assoc_default_missing. omega.
Qed.

Lemma deduplicate_log'_a_equiv :
forall l ks ks',
a_equiv clientId_eq_dec ks ks' ->
deduplicate_log' l ks = deduplicate_log' l ks'.