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.
+
+definition confluent1: ∀A. relation A → predicate A ≝ λA,R,a0.
+ ∀a1. R a0 a1 → ∀a2. R a0 a2 →
+ ∃∃a. R a1 a & R a2 a.
+
+definition confluent: ∀A. predicate (relation A) ≝ λA,R.
+ ∀a0. confluent1 … R a0.
+
(* Reflexive closure ************)
definition RC: ∀A:Type[0]. relation A → relation A ≝