(** Dually, the diamond modality asserts that the relation holds at
    some possible future world. Note the order of the premises in our
    intro rule: we want to first determine what [w'] should be, then
    attempt to prove [w ~> w']. *)

  Definition klr_diam {A B} (l: L) (R: klr W A B): klr W A B :=
    fun w x y => exists w', acc l w w' /\ R w' x y.

Lemma klr_diam_relim {A B} l (R: klr W A B) w x y P Q: (forall w', acc l w w' -> RElim (R w') x y P Q) -> RElim (klr_diam l R w) x y P Q.