X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fdelayed_updating%2Freduction%2Fibfr.ma;h=90b16d3de1941cf62d8bd2fcee61aa8133df92b0;hb=513c4a61f11ce03888a8a0f9d8e513de6e3a7c8b;hp=b235cb4811ebc4724d54e35a7972246ee858c92c;hpb=b1c5b3370653db6e495bbf6b3799cba592746cdd;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ibfr.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ibfr.ma
index b235cb481..90b16d3de 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ibfr.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/ibfr.ma
@@ -15,7 +15,7 @@
 include "delayed_updating/substitution/fsubst.ma".
 include "delayed_updating/substitution/lift_prototerm.ma".
 include "delayed_updating/syntax/prototerm_eq.ma".
-include "delayed_updating/syntax/path_head.ma".
+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_ibf_3.ma".
@@ -25,15 +25,22 @@ include "ground/xoa/ex_6_5.ma".
 
 (* IMMEDIATE BALANCED FOCUSED REDUCTION *************************************)
 
-(**) (* explicit ninj because we cannot declare the expectd type of k *)
 definition ibfr (r): relation2 prototerm prototerm ≝
            λt1,t2.
-           ∃∃p,b,q,h,k. p●𝗔◗b●𝗟◗q = r &
-           ⊗b ϵ 𝐁 & b = ↳[h]b &
-           (𝗟◗q) = ↳[ninj k](𝗟◗q) & r◖𝗱k ϵ t1 &
-           t1[⋔r←↑[𝐮❨k+h❩](t1⋔(p◖𝗦))] ⇔ t2
+           ∃∃p,b,q,m,n. p●𝗔◗b●𝗟◗q = r &
+           ⊗b ϵ 𝐁 & b ϵ 𝐂❨Ⓣ,m❩ & q ϵ 𝐂❨Ⓕ,n❩ & r◖𝗱↑n ϵ t1 &
+           t1[⋔r←🠡[𝐮❨↑(m+n)❩](t1⋔(p◖𝗦))] ⇔ t2
 .
 
 interpretation
   "balanced focused reduction with immediate updating (prototerm)"
   'BlackRightArrowIBF t1 r t2 = (ibfr r t1 t2).
+
+(* Constructions with subset_equivalence ************************************)
+
+lemma ibfr_eq_trans (t) (t1) (t2) (r):
+      t1 ➡𝐢𝐛𝐟[r] t → t ⇔ t2 → t1 ➡𝐢𝐛𝐟[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-.