Proof using.
induction l; intros; simpl in *; intuition;
pose proof remove_all_cons xs a l; subst; intuition;
repeat find_rewrite; simpl in *; intuition.
Qed.

(* Specifications: *)
Lemma NoDup_remove_all :
forall l l',
NoDup l' ->
NoDup (remove_all l l').