renaming in basics/relations

[helm.git] / matita / matita / lib / basics / relations.ma

diff --git a/matita/matita/lib/basics/relations.ma b/matita/matita/lib/basics/relations.ma
index a43ed63252a37e64c768326422f7dae3147678c4..9da779ee45db629c6994b682d7852c011e553701 100644 (file)
--- a/matita/matita/lib/basics/relations.ma
+++ b/matita/matita/lib/basics/relations.ma
@@ -10,6 +10,8 @@
       V_______________________________________________________________ *)
 
 include "basics/logic.ma".
+include "basics/core_notation/compose_2.ma".
+include "basics/core_notation/subseteq_2.ma".
 
 (********** predicates *********)
 
@@ -54,12 +56,16 @@ definition antisymmetric: ∀A.∀R:relation A.Prop
 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 pw_confluent: ∀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.
+                      ∀a0. pw_confluent … R a0.
+
+(* triangular confluence of two relations *)
+definition Conf3: ∀A,B. relation2 A B → relation A → Prop ≝ λA,B,S,R.
+                  ∀b,a1. S a1 b → ∀a2. R a1 a2 → S a2 b.
 
 (* Reflexive closure ************)