Section eval_in_range_proof.
Variable R X : Ens.
Hypothesis i : IN X (Domain R).
Let Y := EV R X.
Let step1 : IN (PAIR X Y) R.
Proof EV_th1 R X i.
Proof Range_th1 R X Y step1.
End eval_in_range_proof.

Theorem EV_in_range :
forall (R X : Ens) (i : IN X (Domain R)), IN (EV R X) (Range R).