partial update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / etc / height / path_height.etc

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/height/path_height.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/height/path_height.etc
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/height/path_height.etc
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/sharp_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 k ⇒ height q + k
+  | label_m   ⇒ height q
+  | label_L   ⇒ height q
+  | label_A   ⇒ height q
+  | label_S   ⇒ height q
+  ]
+].
+
+interpretation
+  "height (path)"
+  'Sharp p = (height p).
+
+(* Basic constructions ******************************************************)
+
+lemma height_empty: 𝟎 = ♯𝐞.
+// qed.
+
+lemma height_d_dx (p) (k:pnat):
+      (♯p)+k = ♯(p◖𝗱k).
+// 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.
+
+(* Main constructions *******************************************************)
+
+theorem height_append (p) (q):
+        (♯p+♯q) = ♯(p●q).
+#p #q elim q -q //
+* [ #k ] #q #IH <list_append_lcons_sn
+[ <height_d_dx <height_d_dx //
+| <height_m_dx <height_m_dx //
+| <height_L_dx <height_L_dx //
+| <height_A_dx <height_A_dx //
+| <height_S_dx <height_S_dx //
+]
+qed.
+
+(* Constructions with path_lcons ********************************************)
+
+lemma height_d_sn (p) (k:pnat):
+      k+♯p = ♯(𝗱k◗p).
+// qed.
+
+lemma height_m_sn (p):
+      ♯p = ♯(𝗺◗p).
+// qed.
+
+lemma height_L_sn (p):
+      ♯p = ♯(𝗟◗p).
+// qed.
+
+lemma height_A_sn (p):
+      ♯p = ♯(𝗔◗p).
+// qed.
+
+lemma height_S_sn (p):
+      ♯p = ♯(𝗦◗p).
+// qed.