(** For relators of higher arities, we let the original relator [RR]
    operate independently at each world [w]. *)

  Definition k1 RR (R1: klr W A1 B1): klr W A B :=
    fun w => RR (R1 w).

(* Specifications: *)
Lemma k1_rintro RR (R1: klr W A1 B1) w x y: RIntro (RR (R1 w) x y) (k1 RR R1 w) x y.
Lemma k1_relim RR (R1: klr W A1 B1) w x y P Q: RElim (RR (R1 w)) x y P Q -> RElim (k1 RR R1 w) x y P Q.