simple induction E; intros A f r; simple induction E'; intros A' f' r';
simpl in |- *; simple induction 1; intros e1 e2 a.
apply e1.
Defined.

Theorem IN_EXType :
forall E E' : Ens,
IN E' E -> EXType (pi1 E) (fun a : pi1 E => EQ E' (pi2 E a)).