Definition fashionable  (P: pred nat) := # P = P.
Notation "P '>=>' Q" := (# (P --> Q)) (at level 55, right associativity) : pred.
Notation "P '<=>' Q" := (# (P <--> Q)) (at level 57, no associativity) : pred.

Lemma subp_exp {A} `{ageable A} : forall G B (X Y:B -> pred A),
(forall x:B, G |-- X x >=> Y x) ->
G |-- exp X >=> exp Y.