Proof using.
induction es; simpl; intuition; repeat break_match; eauto using f_equal;
repeat find_reverse_rewrite.
- f_equal. subst. eapply deduplicate_log'_snoc_drop_keys; eauto.
now rewrite get_set_same.
- subst. do_bool. eapply deduplicate_log'_snoc_drop_keys; eauto; auto with *.
- f_equal. subst. eapply deduplicate_log'_snoc_drop_keys; eauto.
now rewrite get_set_same.
Qed.

Lemma deduplicate_log_snoc_drop :
forall es e e',
In e' es ->
eClient e = eClient e' ->
eId e <= eId e' ->
deduplicate_log (es ++ [e]) = deduplicate_log es.