(* FUNCTIONS ****************************************************************)
-definition left_identity (A:Type[0]) (f): predicate A ≝ λi. ∀a:A. a = f i a.
+definition left_identity (A) (f): predicate A ≝ λi. ∀a:A. a = f i a.
-definition right_identity (A:Type[0]) (f): predicate A ≝ λi. ∀a:A. a = f a i.
+definition right_identity (A) (f): predicate A ≝ λi. ∀a:A. a = f a i.
+
+definition compatible_3 (A) (B) (C): relation4 … (relation A) (relation B) (relation C) ≝
+ λf,Sa,Sb,Sc.
+ ∀a1,a2. Sa a1 a2 → ∀b1,b2. Sb b1 b2 → Sc (f a1 b1) (f a2 b2).