Definition rmap' := ((address->resource) * ghost)%type.Definition preds_fmap (f g:(pred rmap)->(pred rmap)) (x:preds) : preds :=
    match x with SomeP A ls => SomeP A (fmap (fpi _) f g ls) end.

Lemma preds_fmap_comp : forall f1 f2 g1 g2, preds_fmap g1 g2 oo preds_fmap f1 f2 = preds_fmap (g1 oo f1) (f2 oo g2).