Definition Its_nonempty (A : Ens) := ~ Its_empty A.
Section Its_nonempty_proof.
Variable X : Ens.
Variable A : Ens.
Hypothesis h : IN X A.
Hypothesis h2 : Its_empty A.
Definition Its_nonempty_proof_Out : False := h2 X h.
End Its_nonempty_proof.

Theorem Its_nonempty_th1 : forall (X A : Ens) (h : IN X A), Its_nonempty A.
Proof Its_nonempty_proof_Out.