X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fdelayed_updating%2Fsubstitution%2Flift_depth.ma;h=cefb45d49c977fd1f4fb7989ebc9fd32fd64a8fa;hb=62d0f5f2c89830ebe884e6afee91eb68b68790fc;hp=dc829088925c5831bbfbe448cd002928dbc9bff7;hpb=be152b5436a8e1e107684722be834dbe02196d53;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_depth.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_depth.ma
index dc8290889..cefb45d49 100644
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_depth.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_depth.ma
@@ -14,17 +14,28 @@
 
 include "delayed_updating/substitution/lift.ma".
 include "delayed_updating/syntax/path_depth.ma".
-include "ground/relocation/tr_pushs.ma".
+include "ground/relocation/tr_id_compose.ma".
+include "ground/relocation/tr_compose_compose.ma".
+include "ground/relocation/tr_compose_pn.ma".
+include "ground/relocation/tr_compose_eq.ma".
+include "ground/relocation/tr_pn_eq.ma".
+include "ground/lib/stream_eq_eq.ma".
 
 (* LIFT FOR PATH ***********************************************************)
 
-(* Basic constructions with depth ******************************************)
+(* Constructions with depth ************************************************)
 
-lemma pippo (p) (f):
-      (⫯*[❘p❘]f) ∘ (↑[p]𝐢) = ↑[p]f.
-#p elim p -p
-[ #f <lift_rmap_empty <lift_rmap_empty <tr_pushs_zero
-| * [ #n ] #p #IH #f //
-  <lift_rmap_d_sn <lift_rmap_d_sn <depth_d_sn
-  @(trans_eq … (IH …)) -IH
-      
+lemma lift_rmap_decompose (p) (f):
+      ↑[p]f ≗ (⫯*[❘p❘]f)∘(↑[p]𝐢).
+#p @(list_ind_rcons … p) -p
+[ #f <lift_rmap_empty <lift_rmap_empty <tr_pushs_zero //
+| #p * [ #n ] #IH #f //
+  [ <lift_rmap_d_dx <lift_rmap_d_dx <depth_d_dx
+    @(stream_eq_trans … (tr_compose_assoc …))
+    /2 width=1 by tr_compose_eq_repl/
+  | <lift_rmap_L_dx <lift_rmap_L_dx <depth_L_dx
+    <tr_pushs_succ <tr_compose_push_bi
+    /2 width=1 by tr_push_eq_repl/
+  ]
+]
+qed.