Proof using.
intros.
destruct l; auto.
unfold a_equiv in *. simpl in *.
destruct p.
specialize (H k).
break_if; try congruence.
Qed.

Lemma assoc_set_a_equiv :
forall l l' (k : K) (v : V),
a_equiv l l' ->
a_equiv (assoc_set l k v) (assoc_set l' k v).