Proof function_1_Out_F.
Definition Extensionally_equivalent (F G : Ens) :=
forall (X : Ens) (i : IN X (Domain F)) (j : IN X (Domain G)),
EQ (EV F X) (EV G X).
Section ee_symm_proof.
Variable F G : Ens.
Hypothesis e : Extensionally_equivalent F G.
Variable X : Ens.
Hypothesis i : IN X (Domain G).
Hypothesis j : IN X (Domain F).
Let step1 : EQ (EV F X) (EV G X).
Proof e X j i.

Lemma ee_symm_Out : EQ (EV G X) (EV F X).
Proof EQ_symm (EV F X) (EV G X) step1.