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

Theorem removePresent_NoDup :
forall (A : Set)(eqd : eq_dec A)(u ls : list A),
NoDup ls ->
NoDup (removePresent eqd u ls).