induction ls; intuition; simpl in *.
unfold setLet in *.
destruct (in_dec eqd a u); intuition.
simpl in *.
intuition.
Qed.

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