definition antisymmetric: ∀A.∀R:relation A.Prop
≝ λA.λR.∀x,y:A. R x y → ¬(R y x).
+definition singlevalued: ∀A,B. predicate (relation2 A B) ≝ λA,B,R.
+ ∀a,b1. R a b1 → ∀b2. R a b2 → b1 = b2.
+
(* Reflexive closure ************)
definition RC: ∀A:Type[0]. relation A → relation A ≝