unfold Big in |- *; simpl in |- *; simple induction 1; intros E' HE';
exists E'; auto with zfc.
Qed.

(* Specifications: *)
Theorem IN_small_small :
forall (E : Ens) (E' : Ens'),
IN E (inj E') -> EXType' _ (fun E1 : Ens' => EQ E (inj E1)).
Theorem IN_small_small :
forall (E : Ens) (E' : Ens'),
IN E (inj E') -> EXType' _ (fun E1 : Ens' => EQ E (inj E1)).