update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / unwind / unwind2_rmap_head.ma

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_rmap_head.ma b/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_rmap_head.ma
new file mode 100644 (file)
index 0000000..579cbd5
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/unwind/unwind2_rmap_head.ma
@@ -0,0 +1,40 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/unwind/unwind2_rmap_labels.ma".
+include "delayed_updating/unwind/nap.ma".
+include "delayed_updating/syntax/path_head_depth.ma".
+include "delayed_updating/syntax/path_height.ma".
+
+(* UNWIND MAP FOR PATH ******************************************************)
+
+(* Constructions with path_head *********************************************)
+
+lemma unwind2_rmap_head_push (f) (p) (n):
+      n + ♯(↳[n]p) = (▶[⫯f]↳[n]p)@↑❨n❩.
+#f #p elim p -p
+[ #n <path_head_empty <unwind2_rmap_labels_L <height_labels_L
+  >tr_pushs_swap <tr_nap_pushs_lt //
+| #l #p #IH #n @(nat_ind_succ … n) -n //
+  #n #_ cases l [ #m ]
+  [ <unwind2_rmap_d_sn <path_head_d_sn <height_d_sn
+    <nplus_assoc >IH -IH <tr_compose_nap //
+  | <unwind2_rmap_m_sn <path_head_m_sn <height_m_sn //
+  | <unwind2_rmap_L_sn <path_head_L_sn <height_L_sn
+    <tr_nap_push <npred_succ //
+  | <unwind2_rmap_A_sn <path_head_A_sn <height_A_sn //
+  | <unwind2_rmap_S_sn <path_head_S_sn <height_S_sn //
+  ]
+]
+qed.