(** 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).
Global Instance k1_rel var1 var:
Monotonic k1 ((var1 ++> var) ++> ((- ==> var1) ++> (- ==> var))).

(* 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.