Proof zero_different_from_one_Out.
Section one_different_from_two.
Variable X : Ens.
Variable Y : Ens.
Hypothesis m : has_leq_1_elements X.
Hypothesis n : has_geq_2_elements Y.
Hypothesis h : EQ X Y.
Let step1 : has_leq_1_elements Y :=
Big_Extensionality has_leq_1_elements X Y m h.
Definition one_different_from_two_Out : False := n step1.
End one_different_from_two.

Theorem counting_lem2 :
forall (X Y : Ens) (m : has_leq_1_elements X) (n : has_geq_2_elements Y),
~ EQ X Y.