Definition has_geq_1_elements (A : Ens) := ~ has_leq_0_elements A.
(**** this is equal to EXISTS ([X: Ens] (IN X A)) ****)
Definition Choose_an_element (A : Ens) (k : has_geq_1_elements A) : Ens :=
CHOICE (fun X : Ens => IN X A).

Theorem Choose_an_element_pr :
forall (A : Ens) (k : has_geq_1_elements A), IN (Choose_an_element A k) A.