partial update in delayed_updating

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

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/head/lift_path_head.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/head/lift_path_head.etc
new file mode 100644 (file)
index 0000000..21b70c5
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/head/lift_path_head.etc
@@ -0,0 +1,61 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/substitution/lift_path.ma".
+include "delayed_updating/syntax/path_head.ma".
+include "ground/relocation/xap.ma".
+
+(* LIFT FOR PATH ************************************************************)
+
+(* Constructions with head for path *****************************************)
+
+lemma lift_path_head_closed (f) (p) (q) (n):
+      q = ↳[n]q →
+      ↳[↑[p●q]f＠❨n❩]↑[↑[p]f]q = ↑[↑[p]f]q.
+#f #p #q elim q -q
+[ #n #H0
+  <(eq_inv_path_empty_head … H0) -H0
+  <path_head_zero //
+| #l #q #IH #n @(nat_ind_succ …n) -n [| #n #_ ]
+  [ <path_head_zero #H0 destruct
+  | cases l [ #k ]
+    [ <path_head_d_dx #H0
+      elim (eq_inv_list_lcons_bi ????? H0) -H0 #_ #H0
+      <lift_rmap_d_dx <lift_path_d_dx
+      <tr_xap_succ_nap <path_head_d_dx
+      <(IH … H0) in ⊢ (???%); -IH -H0 <tr_xap_plus //
+    | <path_head_m_dx #H0
+      elim (eq_inv_list_lcons_bi ????? H0) -H0 #_ #H0
+      <lift_rmap_m_dx <lift_path_m_dx
+      <tr_xap_succ_nap <path_head_m_dx
+      <(IH … H0) in ⊢ (???%); -IH -H0 //
+    | <path_head_L_dx #H0
+      elim (eq_inv_list_lcons_bi ????? H0) -H0 #_ #H0
+      <lift_rmap_L_dx <lift_path_L_dx
+      <tr_xap_succ_nap <path_head_L_dx
+      <(IH … H0) in ⊢ (???%); -IH -H0 //
+    | <path_head_A_dx #H0
+      elim (eq_inv_list_lcons_bi ????? H0) -H0 #_ #H0
+      <lift_rmap_A_dx <lift_path_A_dx
+      <tr_xap_succ_nap <path_head_A_dx
+      <(IH … H0) in ⊢ (???%); -IH -H0 //
+    | <path_head_S_dx #H0
+      elim (eq_inv_list_lcons_bi ????? H0) -H0 #_ #H0
+      <lift_rmap_S_dx <lift_path_S_dx
+      <tr_xap_succ_nap <path_head_S_dx
+      <(IH … H0) in ⊢ (???%); -IH -H0 //
+    ]
+  ]
+]
+qed.