update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / syntax / path_depth.ma

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_depth.ma b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_depth.ma
index a85d74ef16e4f6b1e84a62db74e0119c0fdbd6ac..a769327f65b218f655530102b435ca614b60eb22 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_depth.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_depth.ma
@@ -13,8 +13,8 @@
 (**************************************************************************)
 
 include "delayed_updating/syntax/path.ma".
+include "delayed_updating/notation/functions/flat_1.ma".
 include "ground/arith/nat_plus.ma".
-include "ground/notation/functions/verticalbars_1.ma".
 
 (* DEPTH FOR PATH ***********************************************************)
 
@@ -23,7 +23,7 @@ match p with
 [ list_empty     ⇒ 𝟎
 | list_lcons l q ⇒
   match l with
-  [ label_d _ ⇒ depth q
+  [ label_d k ⇒ depth q
   | label_m   ⇒ depth q
   | label_L   ⇒ ↑(depth q)
   | label_A   ⇒ depth q
@@ -33,38 +33,65 @@ match p with
 
 interpretation
   "depth (path)"
-  'VerticalBars p = (depth p).
+  'Flat p = (depth p).
 
 (* Basic constructions ******************************************************)
 
-lemma depth_empty: ð\9d\9f\8e = â\9d\98ð\9d\90\9eâ\9d\98.
+lemma depth_empty: ð\9d\9f\8e = â\99­ð\9d\90\9e.
 // qed.
 
-lemma depth_d_sn (q) (n): ❘q❘ = ❘𝗱n◗q❘.
+lemma depth_d_dx (p) (k):
+      ♭p = ♭(p◖𝗱k).
 // qed.
 
-lemma depth_m_sn (q): ❘q❘ = ❘𝗺◗q❘.
+lemma depth_m_dx (p):
+      ♭p = ♭(p◖𝗺).
 // qed.
 
-lemma depth_L_sn (q): ↑❘q❘ = ❘𝗟◗q❘.
+lemma depth_L_dx (p):
+      ↑♭p = ♭(p◖𝗟).
 // qed.
 
-lemma depth_A_sn (q): ❘q❘ = ❘𝗔◗q❘.
+lemma depth_A_dx (p):
+      ♭p = ♭(p◖𝗔).
 // qed.
 
-lemma depth_S_sn (q): ❘q❘ = ❘𝗦◗q❘.
+lemma depth_S_dx (p):
+      ♭p = ♭(p◖𝗦).
 // qed.
 
-(* Advanced constructions with nplus ****************************************)
-
-lemma depth_plus (p1) (p2):
-      ❘p2❘+❘p1❘ = ❘p1●p2❘.
-#p1 elim p1 -p1 //
-* [ #n ] #p1 #IH #p2 <list_append_lcons_sn
-[ <depth_d_sn <depth_d_sn //
-| <depth_m_sn <depth_m_sn //
-| <depth_L_sn <depth_L_sn //
-| <depth_A_sn <depth_A_sn //
-| <depth_S_sn <depth_S_sn //
+(* Main constructions *******************************************************)
+
+theorem depth_append (p) (q):
+        (♭p)+(♭q) = ♭(p●q).
+#p #q elim q -q //
+* [ #k ] #q #IH <list_append_lcons_sn
+[ <depth_d_dx <depth_d_dx //
+| <depth_m_dx <depth_m_dx //
+| <depth_L_dx <depth_L_dx //
+| <depth_A_dx <depth_A_dx //
+| <depth_S_dx <depth_S_dx //
 ]
 qed.
+
+(* Constructions with path_lcons ********************************************)
+
+lemma depth_d_sn (p) (k):
+      ♭p = ♭(𝗱k◗p).
+// qed.
+
+lemma depth_m_sn (p):
+      ♭p = ♭(𝗺◗p).
+// qed.
+
+lemma depth_L_sn (p):
+      ↑♭p = ♭(𝗟◗p).
+// qed.
+
+lemma depth_A_sn (p):
+      ♭p = ♭(𝗔◗p).
+// qed.
+
+lemma depth_S_sn (p):
+      ♭p = ♭(𝗦◗p).
+// qed.