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 903026e4dfd7167948257aa023b5274cf44a8ec3..961a5c435ef8b0f3d2cbd106a5bc80279ccf85db 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_structure.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift_structure.ma
@@ -12,48 +12,57 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "delayed_updating/syntax/path_structure.ma".
 include "delayed_updating/substitution/lift_eq.ma".
+include "delayed_updating/syntax/path_structure.ma".
+include "delayed_updating/syntax/path_proper.ma".
 
 (* LIFT FOR PATH ***********************************************************)
 
-(* Constructions with structure ********************************************)
+(* Basic constructions with structure **************************************)
 
-lemma lift_d_empty_dx (n) (p) (f):
-      (⊗p)◖𝗱❨(↑[p◖𝗱❨n❩]f)@❨n❩❩ = ↑[f](p◖𝗱❨n❩).
-#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 //
+lemma structure_lift (p) (f):
+      ⊗p = ⊗↑[f]p.
+#p @(path_ind_lift … p) -p // #p #IH #f
+<lift_path_L_sn //
+qed.
+
+lemma lift_structure (p) (f):
+      ⊗p = ↑[f]⊗p.
+#p @(path_ind_lift … p) -p //
+qed.
+
+(* Properties with proper condition for path ********************************)
+
+lemma lift_append_proper_dx (p2) (p1) (f): Ꝕp2 →
+      (⊗p1)●(↑[↑[p1]f]p2) = ↑[f](p1●p2).
+#p2 #p1 @(path_ind_lift … p1) -p1 //
+[ #n | #n #l #p1 |*: #p1 ] #IH #f #Hp2
+[ elim (ppc_inv_lcons … Hp2) -Hp2 #l #q #H destruct //
+| <lift_path_d_lcons_sn <IH //
+| <lift_path_L_sn <IH //
+| <lift_path_A_sn <IH //
+| <lift_path_S_sn <IH //
 ]
+qed-.
+
+(* Advanced constructions with structure ************************************)
+
+lemma lift_d_empty_dx (n) (p) (f):
+      (⊗p)◖𝗱((↑[p]f)@❨n❩) = ↑[f](p◖𝗱n).
+/3 width=3 by ppc_lcons, lift_append_proper_dx/
 qed.
 
 lemma lift_L_dx (p) (f):
       (⊗p)◖𝗟 = ↑[f](p◖𝗟).
-#p @(path_ind_lift … p) -p // #m #l #p #IH #f
-<lift_path_d_lcons_sn //
+/3 width=3 by ppc_lcons, lift_append_proper_dx/
 qed.
 
 lemma lift_A_dx (p) (f):
       (⊗p)◖𝗔 = ↑[f](p◖𝗔).
-#p @(path_ind_lift … p) -p // #m #l #p #IH #f
-<lift_path_d_lcons_sn //
+/3 width=3 by ppc_lcons, lift_append_proper_dx/
 qed.
 
 lemma lift_S_dx (p) (f):
       (⊗p)◖𝗦 = ↑[f](p◖𝗦).
-#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 @(path_ind_lift … p) -p // #p #IH #f
-<lift_path_L_sn //
-qed.
-
-lemma lift_structure (p) (f):
-      ⊗p = ↑[f]⊗p.
-#p @(path_ind_lift … p) -p //
+/3 width=3 by ppc_lcons, lift_append_proper_dx/
 qed.