Proof using.
induction xs; intros; simpl in *; intuition.
- subst.
break_if; try congruence.
pose proof remove_length_le x xs eq_dec.
omega.
- specialize (IHxs ltac:(eauto) ltac:(eauto)).
break_if; subst; simpl; omega.
Qed.

(* Specifications: *)
Lemma subset_length :
forall xs ys,
NoDup xs ->
(forall x : A, In x xs -> In x ys) ->
length ys >= length xs.