X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Flib%2Fbasics%2Frelations.ma;h=8b746ef6896d4f58bb4efa17728a27b7f8bba0e7;hb=2199f327081f49b21bdcd23d702b5e07ea4f58ce;hp=f469ddca29f72fe1eeaeea9d50752fefed34aad2;hpb=a04bfe6d381b281db15e8b432f6f221576aad439;p=helm.git

diff --git a/matita/matita/lib/basics/relations.ma b/matita/matita/lib/basics/relations.ma
index f469ddca2..8b746ef68 100644
--- a/matita/matita/lib/basics/relations.ma
+++ b/matita/matita/lib/basics/relations.ma
@@ -48,6 +48,17 @@ definition tight_apart: ∀A.∀eq,ap:relation A.Prop
 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 ≝
+               λA,R,x,y. R … x y ∨ x = y.
+
+lemma RC_reflexive: ∀A,R. reflexive A (RC … R).
+/2 width=1/ qed.
+
 (********** operations **********)
 definition Rcomp ≝ λA.λR1,R2:relation A.λa1,a2.
   ∃am.R1 a1 am ∧ R2 am a2.