update in delayed updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / substitution / lift.ma

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift.ma
index 5db8fa945bed188af60940375e5d8a43e4573831..b1ed7662361b232de071f08b4972c6fe1cb3247d 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift.ma
@@ -26,12 +26,12 @@ definition lift_continuation (A:Type[0]) ≝
 (* Note: inner numeric labels are not liftable, so they are removed *)
 rec definition lift_gen (A:Type[0]) (k:lift_continuation A) (p) (f) on p ≝
 match p with
-[ list_empty     ⇒ k 𝐞 f
+[ list_empty     ⇒ k (𝐞) f
 | list_lcons l q ⇒
   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)
@@ -59,15 +59,15 @@ interpretation
 (* Basic constructions ******************************************************)
 
 lemma lift_empty (A) (k) (f):
-      k 𝐞 f = ↑{A}❨k, 𝐞, f❩.
+      k (𝐞) f = ↑{A}❨k, 𝐞, 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❩.
+      ↑❨(λp. k (𝗱(f@❨n❩)◗p)), 𝐞, f∘𝐮❨ninj n❩❩ = ↑{A}❨k, 𝗱n◗𝐞, f❩.
 // qed.
 
 lemma lift_d_lcons_sn (A) (k) (p) (l) (n) (f):
-      ↑❨k, l◗p, f∘𝐮❨ninj n❩❩ = ↑{A}❨k, 𝗱❨n❩◗l◗p, f❩.
+      ↑❨k, l◗p, f∘𝐮❨ninj n❩❩ = ↑{A}❨k, 𝗱n◗l◗p, f❩.
 // qed.
 
 lemma lift_L_sn (A) (k) (p) (f):
@@ -85,22 +85,18 @@ lemma lift_S_sn (A) (k) (p) (f):
 (* Basic constructions with proj_path ***************************************)
 
 lemma lift_path_d_empty_sn (f) (n):
-      𝗱❨f@❨n❩❩◗𝐞 = ↑[f](𝗱❨n❩◗𝐞).
+      𝗱(f@❨n❩)◗𝐞 = ↑[f](𝗱n◗𝐞).
 // qed.
 
 lemma lift_path_d_lcons_sn (f) (p) (l) (n):
-      ↑[f∘𝐮❨ninj n❩](l◗p) = ↑[f](𝗱❨n❩◗l◗p).
+      ↑[f∘𝐮❨ninj n❩](l◗p) = ↑[f](𝗱n◗l◗p).
 // qed.
 
 (* 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❩) = ↑[𝗱n◗p]f.
+#f * // qed.
 
 lemma lift_rmap_L_sn (f) (p):
       ↑[p](⫯f) = ↑[𝗟◗p]f.
@@ -114,12 +110,22 @@ 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 …):
-      Q 𝐞 →
-      (∀n. Q 𝐞 → Q (𝗱❨n❩◗𝐞)) →
-      (∀n,l,p. Q (l◗p) → Q (𝗱❨n❩◗l◗p)) →
+      Q (𝐞) →
+      (∀n. Q (𝐞) → Q (𝗱n◗𝐞)) →
+      (∀n,l,p. Q (l◗p) → Q (𝗱n◗l◗p)) →
       (∀p. Q p → Q (𝗟◗p)) →
       (∀p. Q p → Q (𝗔◗p)) →
       (∀p. Q p → Q (𝗦◗p)) →