Section emptyfn_2.
Variable X Y Z : Ens.
Hypothesis i : IN (PAIR X Y) Zero.
Let step1 : False.
Proof EmptySet_th1 (PAIR X Y) i.
Proof false_implies_everything (EQ Y Z) step1.
End emptyfn_2.
Proof
fun (X Y Z : Ens) (i : IN (PAIR X Y) Zero) (j : IN (PAIR X Z) Zero) =>
emptyfn2_Out X Y Z i.

Theorem empty_function_function : is_a_function Zero.