Section dup.
Definition duplicable P := P |-- |==> P * P.
Hint Resolve emp_duplicable : dup.
Hint Resolve sepcon_duplicable : dup.
Hint Resolve invariant_duplicable' : dup.
Hint Resolve ghost_snap_duplicable : dup.
Hint Resolve prop_duplicable : dup.

Lemma exp_duplicable : forall {A} (P : A -> mpred), (forall x, duplicable (P x)) -> duplicable (exp P).