Definition k2 RR (R1: klr W A1 B1) (R2: klr W A2 B2): klr W A B :=
    fun w => RR (R1 w) (R2 w).

Lemma k2_relim RR (R1: klr W A1 B1) (R2: klr W A2 B2) w x y P Q: RElim (RR (R1 w) (R2 w)) x y P Q -> RElim (k2 RR R1 R2 w) x y P Q.