+
+definition appl_compatible_dx: predicate (relation term) ≝ λR.
+ ∀B,A1,A2. R A1 A2 → R (@B.A1) (@B.A2).
+
+lemma star_appl_compatible_dx: ∀R. appl_compatible_dx R →
+ appl_compatible_dx (star … R).
+#R #HR #B #A1 #A2 #H elim H -A2 // /3 width=3/
+qed.