partial commit 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 6bbffaa7704293f6363ab6e139cd32a3209d3f2f..21b70c57a156b946eaf13113a3ea3421588cc7e6 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
@@ -12,49 +12,48 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "delayed_updating/substitution/lift_gen_eq.ma".
+include "delayed_updating/substitution/lift_path.ma".
 include "delayed_updating/syntax/path_head.ma".
-include "delayed_updating/syntax/path_reverse.ma".
 include "ground/relocation/xap.ma".
 
 (* LIFT FOR PATH ************************************************************)
 
 (* Constructions with head for path *****************************************)
 
-lemma lift_path_head (f) (p) (q) (n):
-      pᴿ = ↳[n](pᴿ) →
-      ↳[↑[q●p]f＠❨n❩](↑[↑[q]f]p)ᴿ = (↑[↑[q]f]p)ᴿ.
-#f #p @(list_ind_rcons … p) -p
-[ #q #n #H0
+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 //
-| #p #l #IH #q #n @(nat_ind_succ …n) -n [| #m #_ ]
-  [ <reverse_rcons <path_head_zero #H0 destruct
-  | cases l [ #n ]
-    [ <reverse_rcons <path_head_d_sn #H0
+| #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
-      <list_append_assoc <lift_rmap_d_dx <lift_path_d_dx <reverse_rcons
-      <tr_xap_succ_nap <path_head_d_sn
+      <lift_rmap_d_dx <lift_path_d_dx
+      <tr_xap_succ_nap <path_head_d_dx
       <(IH … H0) in ⊢ (???%); -IH -H0 <tr_xap_plus //
-    | <reverse_rcons <path_head_m_sn #H0
+    | <path_head_m_dx #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
+      <lift_rmap_m_dx <lift_path_m_dx
+      <tr_xap_succ_nap <path_head_m_dx
       <(IH … H0) in ⊢ (???%); -IH -H0 //
-    | <reverse_rcons <path_head_L_sn #H0
+    | <path_head_L_dx #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
+      <lift_rmap_L_dx <lift_path_L_dx
+      <tr_xap_succ_nap <path_head_L_dx
       <(IH … H0) in ⊢ (???%); -IH -H0 //
-    | <reverse_rcons <path_head_A_sn #H0
+    | <path_head_A_dx #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
+      <lift_rmap_A_dx <lift_path_A_dx
+      <tr_xap_succ_nap <path_head_A_dx
       <(IH … H0) in ⊢ (???%); -IH -H0 //
-    | <reverse_rcons <path_head_S_sn #H0
+    | <path_head_S_dx #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
+      <lift_rmap_S_dx <lift_path_S_dx
+      <tr_xap_succ_nap <path_head_S_dx
       <(IH … H0) in ⊢ (???%); -IH -H0 //
     ]
   ]