Local Open Scope logic.
Fixpoint power_later (n:nat) P :=
match n with
| 0%nat => P
| S n' => later (power_later n' P)
end
.

Lemma power_later_exp': forall (n:nat) T (any:T) F,
power_later n (EX x:T, F x) = EX x:T, (power_later n (F x)).