update in delayed_updating

+ improved lift

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift.ma
index 5db8fa945bed188af60940375e5d8a43e4573831..f0d5ebd58e4c1eef44ee72b128b1eecfd95b5847 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift.ma
@@ -31,7 +31,7 @@ match p with
   match l with
   [ label_node_d n ⇒
     match q with
-    [ list_empty     ⇒ lift_gen (A) (λp. k (𝗱❨f@❨n❩❩◗p)) q f
+    [ list_empty     ⇒ lift_gen (A) (λp. k (𝗱❨f@❨n❩❩◗p)) q (f∘𝐮❨n❩)
     | list_lcons _ _ ⇒ lift_gen (A) k q (f∘𝐮❨n❩)
     ]
   | label_edge_L   ⇒ lift_gen (A) (λp. k (𝗟◗p)) q (⫯f)
@@ -63,7 +63,7 @@ lemma lift_empty (A) (k) (f):
 // qed.
 
 lemma lift_d_empty_sn (A) (k) (n) (f):
-      ↑❨(λp. k (𝗱❨f@❨n❩❩◗p)), 𝐞, f❩ = ↑{A}❨k, 𝗱❨n❩◗𝐞, f❩.
+      â\86\91â\9d¨(λp. k (ð\9d\97±â\9d¨f@â\9d¨nâ\9d©â\9d©â\97\97p)), ð\9d\90\9e, fâ\88\98ð\9d\90®â\9d¨ninj nâ\9d©â\9d© = â\86\91{A}â\9d¨k, ð\9d\97±â\9d¨nâ\9d©â\97\97ð\9d\90\9e, fâ\9d©.
 // qed.
 
 lemma lift_d_lcons_sn (A) (k) (p) (l) (n) (f):
@@ -94,13 +94,9 @@ lemma lift_path_d_lcons_sn (f) (p) (l) (n):
 
 (* Basic constructions with proj_rmap ***************************************)
 
-lemma lift_rmap_d_empty_sn (f) (n):
-      f = ↑[𝗱❨n❩◗𝐞]f.
-// qed.
-
-lemma lift_rmap_d_lcons_sn (f) (p) (l) (n):
-      ↑[l◗p](f∘𝐮❨ninj n❩) = ↑[𝗱❨n❩◗l◗p]f.
-// qed.
+lemma lift_rmap_d_sn (f) (p) (n):
+      ↑[p](f∘𝐮❨ninj n❩) = ↑[𝗱❨n❩◗p]f.
+#f * // qed.
 
 lemma lift_rmap_L_sn (f) (p):
       ↑[p](⫯f) = ↑[𝗟◗p]f.
@@ -114,6 +110,16 @@ lemma lift_rmap_S_sn (f) (p):
       ↑[p]f = ↑[𝗦◗p]f.
 // qed.
 
+(* Advanced constructions with proj_rmap and path_append ********************)
+
+lemma lift_rmap_append (p2) (p1) (f):
+      ↑[p2]↑[p1]f = ↑[p1●p2]f.
+#p2 #p1 elim p1 -p1 // * [ #n ] #p1 #IH #f //
+[ <lift_rmap_A_sn <lift_rmap_A_sn //
+| <lift_rmap_S_sn <lift_rmap_S_sn //
+]
+qed.
+
 (* Advanced eliminations with path ******************************************)
 
 lemma path_ind_lift (Q:predicate …):

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_structure.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_structure.ma
index 903026e4dfd7167948257aa023b5274cf44a8ec3..4577a65b69ea451d9719d30152e3ca4865136a12 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_structure.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_structure.ma
@@ -20,9 +20,9 @@ include "delayed_updating/substitution/lift_eq.ma".
 (* Constructions with structure ********************************************)
 
 lemma lift_d_empty_dx (n) (p) (f):
-      (⊗p)◖𝗱❨(↑[p◖𝗱❨n❩]f)@❨n❩❩ = ↑[f](p◖𝗱❨n❩).
+      (⊗p)◖𝗱❨(↑[p]f)@❨n❩❩ = ↑[f](p◖𝗱❨n❩).
 #n #p @(path_ind_lift … p) -p // [ #m #l #p |*: #p ] #IH #f
-[ <lift_rmap_d_lcons_sn <lift_path_d_lcons_sn //
+[ <lift_rmap_d_sn <lift_path_d_lcons_sn //
 | <lift_rmap_L_sn <lift_path_L_sn <IH //
 | <lift_rmap_A_sn <lift_path_A_sn <IH //
 | <lift_rmap_S_sn <lift_path_S_sn <IH //