(** 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).

Lemma k1_rintro RR (R1: klr W A1 B1) w x y: RIntro (RR (R1 w) x y) (k1 RR R1 w) x y.