update in delayed_updating

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

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_height.ma b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_height.ma
new file mode 100644 (file)
index 0000000..52e6f01
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_height.ma
@@ -0,0 +1,92 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "ground/arith/nat_plus.ma".
+include "delayed_updating/syntax/path.ma".
+include "delayed_updating/notation/functions/hash_1.ma".
+
+(* HEIGHT FOR PATH **********************************************************)
+
+rec definition height (p) on p: nat ≝
+match p with
+[ list_empty     ⇒ 𝟎
+| list_lcons l q ⇒
+  match l with
+  [ label_d n ⇒ n + height q
+  | label_m   ⇒ height q
+  | label_L   ⇒ height q
+  | label_A   ⇒ height q
+  | label_S   ⇒ height q
+  ]
+].
+
+interpretation
+  "height (path)"
+  'Hash p = (height p).
+
+(* Basic constructions ******************************************************)
+
+lemma height_empty: 𝟎 = ⧣𝐞.
+// qed.
+
+lemma height_d_sn (q) (n): ninj n+⧣q = ⧣(𝗱n◗q).
+// qed.
+
+lemma height_m_sn (q): ⧣q = ⧣(𝗺◗q).
+// qed.
+
+lemma height_L_sn (q): ⧣q = ⧣(𝗟◗q).
+// qed.
+
+lemma height_A_sn (q): ⧣q = ⧣(𝗔◗q).
+// qed.
+
+lemma height_S_sn (q): ⧣q = ⧣(𝗦◗q).
+// qed.
+
+(* Main constructions *******************************************************)
+
+theorem height_append (p1) (p2):
+        (⧣p2+⧣p1) = ⧣(p1●p2).
+#p1 elim p1 -p1 //
+* [ #n ] #p1 #IH #p2 <list_append_lcons_sn
+[ <height_d_sn <height_d_sn //
+| <height_m_sn <height_m_sn //
+| <height_L_sn <height_L_sn //
+| <height_A_sn <height_A_sn //
+| <height_S_sn <height_S_sn //
+]
+qed.
+
+(* Constructions with list_rcons ********************************************)
+
+lemma height_d_dx (p) (n):
+      (⧣p)+(ninj n) = ⧣(p◖𝗱n).
+// qed.
+
+lemma height_m_dx (p):
+      (⧣p) = ⧣(p◖𝗺).
+// qed.
+
+lemma height_L_dx (p):
+      (⧣p) = ⧣(p◖𝗟).
+// qed.
+
+lemma height_A_dx (p):
+      (⧣p) = ⧣(p◖𝗔).
+// qed.
+
+lemma height_S_dx (p):
+      (⧣p) = ⧣(p◖𝗦).
+// qed.