Proof
fun (A : Ens) (k : has_geq_1_elements A) =>
CHOICE_pr (fun X : Ens => IN X A) k.
Section given_an_element.
Variable A : Ens.
Variable X : Ens.
Variable k : IN X A.
Hypothesis m : has_leq_0_elements A.
Definition given_an_element_Out : False := m X k.
End given_an_element.

(* Specifications: *)
Theorem has_geq_1_elements_th1 :
forall (A X : Ens) (k : IN X A), has_geq_1_elements A.