Proof using.
unfold has_key.
intros.
destruct e'.
simpl in *.
do_bool. right. do_bool. auto.
Qed.

(* Specifications: *)
Lemma has_key_different_client_false :
forall e e',
eClient e <> eClient e' ->
has_key (eClient e) (eId e) e' = false.