Definition rmap' := sig valid.Definition preds_fmap (f:(pred rmap)->(pred rmap)) (x:preds) : preds :=
    match x with SomeP A ls => SomeP A (f oo ls) end.

(* Specifications: *)
Lemma preds_fmap_id : preds_fmap (id (pred rmap)) = id preds.
Lemma preds_fmap_comp : forall f g, preds_fmap g oo preds_fmap f = preds_fmap (g oo f).