Definition ghost_fp_update (a b : ghost) :=
forall n c, joins (ghost_fmap (approx n) (approx n) a) c ->
joins (ghost_fmap (approx n) (approx n) b) c.
Instance ghost_fp_update_preorder: RelationClasses.PreOrder ghost_fp_update.

Lemma ghost_fp_update_approx: forall a b n, ghost_fp_update a b ->
ghost_fp_update (ghost_fmap (approx n) (approx n) a) (ghost_fmap (approx n) (approx n) b).