partial update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / etc / head / path_head_depth.etc

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/head/path_head_depth.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/head/path_head_depth.etc
new file mode 100644 (file)
index 0000000..6283e2c
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/head/path_head_depth.etc
@@ -0,0 +1,35 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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 "delayed_updating/syntax/path_head.ma".
+include "delayed_updating/syntax/path_height_labels.ma".
+include "delayed_updating/syntax/path_depth_labels.ma".
+
+(* HEAD FOR PATH ************************************************************)
+
+(* Constructions with depth and height **************************************)
+
+lemma path_head_depth (p) (n):
+      n + ♯(↳[n]p) = ♭↳[n]p.
+#p elim p -p // #l #p #IH
+#n @(nat_ind_succ … n) -n // #n #_
+cases l [ #k ]
+[ <path_head_d_dx <height_d_dx <depth_d_dx <IH //
+| <path_head_m_dx <height_m_dx <depth_m_dx //
+| <path_head_L_dx <height_L_dx <depth_L_dx
+  <nplus_succ_sn //
+| <path_head_A_dx <height_A_dx <depth_A_dx //
+| <path_head_S_dx <height_S_dx <depth_S_dx //
+]
+qed-. (**) (* gets in the way with auto *)