Proof comp_ev_1_Out.
Section comp_ev_2.
Variable F G X : Ens.
Hypothesis i : IN X (Domain F).
Hypothesis j : IN (EV F X) (Domain G).
Let Y := EV F X.
Let Z := EV G Y.
Let step1 : IN (PAIR X Y) F.
Proof EV_th1 F X i.
Let step2 : IN (PAIR Y Z) G.
Proof EV_th1 G Y j.

(* Specifications: *)
Lemma comp_ev_2_Out : IN (PAIR X Z) (COMP F G).
Proof COMP_th5 F G X Y Z step1 step2.