intros.
inversion_clear H.
inversion_clear H0.
apply seq_set_n_element_subset; auto with algebra.
exists x.
tauto.
Qed.

Lemma has_n_elements_inj :
forall (A : Setoid) (n : Nat) (B : part_set A),
has_n_elements n B ->
forall (m : Nat) (C : part_set A),
has_n_elements m C -> B =' C in _ -> n =' m in _.