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.

Lemma rmap_fmap_comp : forall f g, rmap_fmap g oo rmap_fmap f = rmap_fmap (g oo f).
Definition rmap'2pre_rmap (r: rmap') : pre_rmap (pred rmap).