update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / reduction / dbfr.ma

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dbfr.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dbfr.ma
index b9b7246332c8d36daf376af38637e96f84313319..841baabb0c107cbcdcd5cfa25ba6eab296afeaa5 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dbfr.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dbfr.ma
@@ -19,7 +19,6 @@ include "delayed_updating/syntax/path_closed.ma".
 include "delayed_updating/syntax/path_balanced.ma".
 include "delayed_updating/syntax/path_structure.ma".
 include "delayed_updating/notation/relations/black_rightarrow_dbf_3.ma".
-include "ground/arith/nat_rplus.ma".
 include "ground/xoa/ex_6_5.ma".
 
 (* DELAYED BALANCED FOCUSED REDUCTION ***************************************)
@@ -27,10 +26,19 @@ include "ground/xoa/ex_6_5.ma".
 definition dbfr (r): relation2 prototerm prototerm ≝
            λt1,t2.
            ∃∃p,b,q,m,n. p●𝗔◗b●𝗟◗q = r &
-           â\8a\97b ϵ ð\9d\90\81 & b ϵ ð\9d\90\82â\9d¨â\93\89,mâ\9d© & q ϵ ð\9d\90\82â\9d¨â\92»,n❩ & r◖𝗱↑n ϵ t1 &
+           â\8a\97b ϵ ð\9d\90\81 & b ϵ ð\9d\90\82â\9d¨â\92»,m,ð\9d\9f\8eâ\9d© & q ϵ ð\9d\90\82â\9d¨â\92»,n,ð\9d\9f\8e❩ & r◖𝗱↑n ϵ t1 &
            t1[⋔r←𝛕↑(m+n).(t1⋔(p◖𝗦))] ⇔ t2
 .
 
 interpretation
   "balanced focused reduction with delayed updating (prototerm)"
   'BlackRightArrowDBF t1 r t2 = (dbfr r t1 t2).
+
+(* Constructions with subset_equivalence ************************************)
+
+lemma dbfr_eq_trans (t) (t1) (t2) (r):
+      t1 ➡𝐝𝐛𝐟[r] t → t ⇔ t2 → t1 ➡𝐝𝐛𝐟[r] t2.
+#t #t1 #t2 #r
+* #p #b #q #m #n #Hr #Hb #Hm #Hn #Ht1 #Ht #Ht2
+/3 width=13 by subset_eq_trans, ex6_5_intro/
+qed-.