(** In fact, our super-powerset meets a slightly stronger statement (but still classically equivalent) which is the following: *)

Theorem collection2 :
forall (X : Typ1) (A : Rel X) (a : X) (R : REL),
LCOMPAT R ->
RCOMPAT R ->
forall (X' : Typ1) (A' : Rel X') (a' : X'),
ELT X' A' a' X A a ->
exG (fun Y' B' b' => R X' A' a' Y' B' b') ->
exG_rel (coll X A a R) (COLL X A a R) (coll_rt X A a R)
(fun Y' B' b' => R X' A' a' Y' B' b').