Section zero_different_from_one.
Variable X : Ens.
Variable Y : Ens.
Hypothesis m : has_leq_0_elements X.
Hypothesis n : has_geq_1_elements Y.
Hypothesis h : EQ X Y.
Let step1 : has_leq_0_elements Y :=
Big_Extensionality has_leq_0_elements X Y m h.
Definition zero_different_from_one_Out : False := n step1.
End zero_different_from_one.

Theorem counting_lem1 :
forall (X Y : Ens) (m : has_leq_0_elements X) (n : has_geq_1_elements Y),
~ EQ X Y.