Ltac do_map_arg :=
match goal with |- ?a = ?b =>
match a with context [map ?x _] =>
match b with context [map ?y _] => replace y with x; auto end end end.

Lemma preds_fmap_fmap:
forall f g pp, preds_fmap f (preds_fmap g pp) = preds_fmap (f oo g) pp.