more unistep

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

diff --git a/matita/matita/lib/basics/star.ma b/matita/matita/lib/basics/star.ma
index 892cff583c9b85d7deb844b8c53a5051c0a93d83..36aee8fe45465c016a6ca3709046a0c6fefd11c7 100644 (file)
--- a/matita/matita/lib/basics/star.ma
+++ b/matita/matita/lib/basics/star.ma
@@ -273,7 +273,7 @@ lemma bi_TC_strap: ∀A,B. ∀R:bi_relation A B. ∀a1,a,a2,b1,b,b2.
                    R a1 b1 a b → bi_TC … R a b a2 b2 → bi_TC … R a1 b1 a2 b2.
 #A #B #R #a1 #a #a2 #b1 #b #b2 #HR #H elim H -a2 -b2 /2 width=4/ /3 width=4/
 qed.
-
+                       
 lemma bi_TC_reflexive: ∀A,B,R. bi_reflexive A B R →
                        bi_reflexive A B (bi_TC … R).
 /2 width=1/ qed.
@@ -421,3 +421,21 @@ lemma bi_star_ind_dx: ∀A,B,R,a2,b2. ∀P:relation2 A B. P a2 b2 →
 | #H12 @(bi_TC_ind_dx ?????????? H12) -a1 -b1 /2 width=5/ -H /3 width=5/
 ]
 qed-.
+
+(* ************ confluence of star *****************)
+
+lemma star_strip: ∀A,R. confluent A R →
+                  ∀a0,a1. star … R a0 a1 → ∀a2. R a0 a2 →
+                  ∃∃a. R a1 a & star … R a2 a.
+#A #R #HR #a0 #a1 #H elim H -a1 /2 width=3/
+#a #a1 #_ #Ha1 #IHa0 #a2 #Ha02
+elim (IHa0 … Ha02) -a0 #a0 #Ha0 #Ha20
+elim (HR … Ha1 … Ha0) -a /3 width=5/
+qed-.
+
+lemma star_confluent: ∀A,R. confluent A R → confluent A (star … R).
+#A #R #HR #a0 #a1 #H elim H -a1 /2 width=3/
+#a #a1 #_ #Ha1 #IHa0 #a2 #Ha02
+elim (IHa0 … Ha02) -a0 #a0 #Ha0 #Ha20
+elim (star_strip … HR … Ha0 … Ha1) -a /3 width=5/
+qed-.