update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / substitution / lift_path_head.ma

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_head.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_head.ma
index 126b691c6ff341101e2ea4a00a871d619dcecfb1..71b11f5d6d4807c35414dcc16ecc3f9cf9b0a699 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_head.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_path_head.ma
@@ -1,16 +1,25 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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_eq.ma".
 include "delayed_updating/syntax/path_head.ma".
 include "delayed_updating/syntax/path_reverse.ma".
 include "ground/relocation/xap.ma".
 
-axiom tr_xap_succ_pos (f) (n):
-      ↑↓(f＠❨↑n❩) = f＠❨↑n❩.
-
-axiom tr_xap_plus (n1) (n2) (f):
-      (⇂*[n2]f)＠❨n1❩+f＠❨n2❩ = f＠❨n1+n2❩.
+(* LIFT FOR PATH ************************************************************)
 
-axiom eq_inv_path_empty_head (p) (n):
-      (𝐞) = ↳[n]p → 𝟎 = n.
+(* Constructions with head for path *****************************************)
 
 lemma lift_path_head (f) (p) (q) (n):
       pᴿ = ↳[n](pᴿ●qᴿ) →
@@ -25,7 +34,34 @@ lemma lift_path_head (f) (p) (q) (n):
     [ <reverse_rcons <path_head_d_sn #H0
       elim (eq_inv_list_lcons_bi ????? H0) -H0 #_ #H0
       <list_append_assoc <lift_rmap_d_dx <lift_path_d_dx <reverse_rcons
-      <tr_xap_succ_pos <path_head_d_sn >tr_xap_succ_pos
-      <lift_path_d_dx >lift_rmap_append <reverse_rcons  
-      @eq_f2 // <(IH … H0) -IH -H0
-      @eq_f2 // <tr_xap_plus //
+      <tr_xap_succ_nap <path_head_d_sn >tr_xap_succ_nap
+      <lift_path_d_dx >lift_rmap_append <reverse_rcons
+      <(IH … H0) -IH -H0 <tr_xap_plus //
+    | <reverse_rcons <path_head_m_sn #H0
+      elim (eq_inv_list_lcons_bi ????? H0) -H0 #_ #H0
+      <list_append_assoc <lift_rmap_m_dx <lift_path_m_dx <reverse_rcons
+      <tr_xap_succ_nap <path_head_m_sn >tr_xap_succ_nap
+      <lift_path_m_dx <reverse_rcons
+      <(IH … H0) -IH -H0 //
+    | <reverse_rcons <path_head_L_sn #H0
+      elim (eq_inv_list_lcons_bi ????? H0) -H0 #_ #H0
+      <list_append_assoc <lift_rmap_L_dx <lift_path_L_dx <reverse_rcons
+      <tr_xap_succ_nap <path_head_L_sn >tr_xap_succ_nap
+      <lift_path_L_dx <reverse_rcons
+      <(IH … H0) -IH -H0 //
+    | <reverse_rcons <path_head_A_sn #H0
+      elim (eq_inv_list_lcons_bi ????? H0) -H0 #_ #H0
+      <list_append_assoc <lift_rmap_A_dx <lift_path_A_dx <reverse_rcons
+      <tr_xap_succ_nap <path_head_A_sn >tr_xap_succ_nap
+      <lift_path_A_dx <reverse_rcons
+      <(IH … H0) -IH -H0 //
+    | <reverse_rcons <path_head_S_sn #H0
+      elim (eq_inv_list_lcons_bi ????? H0) -H0 #_ #H0
+      <list_append_assoc <lift_rmap_S_dx <lift_path_S_dx <reverse_rcons
+      <tr_xap_succ_nap <path_head_S_sn >tr_xap_succ_nap
+      <lift_path_S_dx <reverse_rcons
+      <(IH … H0) -IH -H0 //
+    ]
+  ]
+]
+qed.