induction ls; intuition; simpl in *.
unfold setLet.
inversion H; clear H; subst.
destruct (in_dec eqd a u); intuition.
econstructor; intuition.
eapply H2.
eapply removePresent_in_only_if.
eauto.
Qed.

(* Specifications: *)
Theorem removePresent_correct2 :
forall (A : Set)(eqd : eq_dec A)(u ls : list A) a,
(~In a u) ->
In a ls ->
In a (removePresent eqd u ls).