update in delayed_updating

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

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_structure.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_structure.ma
index 50b35e6547b781421dbc8a40f0c4a59d740fcd7e..903026e4dfd7167948257aa023b5274cf44a8ec3 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_structure.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_structure.ma
@@ -21,78 +21,39 @@ include "delayed_updating/substitution/lift_eq.ma".
 
 lemma lift_d_empty_dx (n) (p) (f):
       (⊗p)◖𝗱❨(↑[p◖𝗱❨n❩]f)@❨n❩❩ = ↑[f](p◖𝗱❨n❩).
-#n #p elim p -p
-[| * [ #m * [| #l ]] [|*: #p ] #IH ] #f
-[ //
-| <list_cons_shift <list_cons_comm <list_cons_comm //
-| <lift_d_lcons_sn <lift_d_lcons_sn //
-| <lift_L_sn <lift_L_sn <lift_lcons <IH //
-| <lift_A_sn <lift_A_sn <lift_lcons <IH //
-| <lift_S_sn <lift_S_sn <lift_lcons <IH //
+#n #p @(path_ind_lift … p) -p // [ #m #l #p |*: #p ] #IH #f
+[ <lift_rmap_d_lcons_sn <lift_path_d_lcons_sn //
+| <lift_rmap_L_sn <lift_path_L_sn <IH //
+| <lift_rmap_A_sn <lift_path_A_sn <IH //
+| <lift_rmap_S_sn <lift_path_S_sn <IH //
 ]
 qed.
 
 lemma lift_L_dx (p) (f):
       (⊗p)◖𝗟 = ↑[f](p◖𝗟).
-#p elim p -p
-[| * [ #m * [| #l ]] [|*: #p ] #IH ] #f
-[ //
-| //
-| <lift_d_lcons_sn //
-| <lift_L_sn <lift_lcons //
-| <lift_A_sn <lift_lcons //
-| <lift_S_sn <lift_lcons //
-]
+#p @(path_ind_lift … p) -p // #m #l #p #IH #f
+<lift_path_d_lcons_sn //
 qed.
 
 lemma lift_A_dx (p) (f):
       (⊗p)◖𝗔 = ↑[f](p◖𝗔).
-#p elim p -p
-[| * [ #m * [| #l ]] [|*: #p ] #IH ] #f
-[ //
-| //
-| <lift_d_lcons_sn //
-| <lift_L_sn <lift_lcons //
-| <lift_A_sn <lift_lcons //
-| <lift_S_sn <lift_lcons //
-]
+#p @(path_ind_lift … p) -p // #m #l #p #IH #f
+<lift_path_d_lcons_sn //
 qed.
 
 lemma lift_S_dx (p) (f):
       (⊗p)◖𝗦 = ↑[f](p◖𝗦).
-#p elim p -p
-[| * [ #m * [| #l ]] [|*: #p ] #IH ] #f
-[ //
-| //
-| <lift_d_lcons_sn //
-| <lift_L_sn <lift_lcons //
-| <lift_A_sn <lift_lcons //
-| <lift_S_sn <lift_lcons //
-]
+#p @(path_ind_lift … p) -p // #m #l #p #IH #f
+<lift_path_d_lcons_sn //
 qed.
 
 lemma structure_lift (p) (f):
       ⊗p = ⊗↑[f]p.
-#p elim p -p
-[| * [ #m * [| #l ]] [|*: #p ] #IH ] #f
-[ //
-| //
-| //
-| <lift_L_sn <lift_lcons //
-| <lift_A_sn <lift_lcons //
-| <lift_S_sn <lift_lcons //
-]
+#p @(path_ind_lift … p) -p // #p #IH #f
+<lift_path_L_sn //
 qed.
 
 lemma lift_structure (p) (f):
       ⊗p = ↑[f]⊗p.
-#p elim p -p
-[| * [ #m * [| #l ]] [|*: #p ] #IH ] #f
-[ //
-| //
-| //
-| <structure_L_sn <lift_L_sn <lift_lcons //
-| <structure_A_sn <lift_A_sn <lift_lcons //
-| <structure_S_sn <lift_S_sn <lift_lcons //
-]
+#p @(path_ind_lift … p) -p //
 qed.