update in delayed updating

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

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift.ma b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift.ma
index bfb66f1bc911e23f4b6a2b445f62fe236f6552c4..5865fe6ad67fd6349bfa53879db740140e6348d8 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift.ma
@@ -12,29 +12,23 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "ground/relocation/tr_compose.ma".
-include "ground/relocation/tr_uni.ma".
-include "delayed_updating/syntax/path.ma".
 include "delayed_updating/notation/functions/uparrow_4.ma".
 include "delayed_updating/notation/functions/uparrow_2.ma".
+include "delayed_updating/syntax/path.ma".
+include "ground/relocation/tr_id_pap.ma".
 
 (* LIFT FOR PATH ***********************************************************)
 
 definition lift_continuation (A:Type[0]) ≝
            tr_map → path → A.
 
-(* Note: inner numeric labels are not liftable, so they are removed *)
 rec definition lift_gen (A:Type[0]) (k:lift_continuation A) (f) (p) on p ≝
 match p with
 [ list_empty     ⇒ k f (𝐞)
 | list_lcons l q ⇒
   match l with
-  [ label_d n ⇒
-    match q with
-    [ list_empty     ⇒ lift_gen (A) (λg,p. k g (𝗱(f@❨n❩)◗p)) (f∘𝐮❨n❩) q
-    | list_lcons _ _ ⇒ lift_gen (A) k (f∘𝐮❨n❩) q
-    ]
-  | label_m   ⇒ lift_gen (A) k f q
+  [ label_d n ⇒ lift_gen (A) (λg,p. k g (𝗱(f@❨n❩)◗p)) (𝐢) q
+  | label_m   ⇒ lift_gen (A) (λg,p. k g (𝗺◗p)) f q
   | label_L   ⇒ lift_gen (A) (λg,p. k g (𝗟◗p)) (⫯f) q
   | label_A   ⇒ lift_gen (A) (λg,p. k g (𝗔◗p)) f q
   | label_S   ⇒ lift_gen (A) (λg,p. k g (𝗦◗p)) f q
@@ -65,16 +59,12 @@ lemma lift_empty (A) (k) (f):
       k f (𝐞) = ↑{A}❨k, f, 𝐞❩.
 // qed.
 
-lemma lift_d_empty_sn (A) (k) (n) (f):
-      ↑❨(λg,p. k g (𝗱(f@❨n❩)◗p)), f∘𝐮❨ninj n❩, 𝐞❩ = ↑{A}❨k, f, 𝗱n◗𝐞❩.
-// qed.
-
-lemma lift_d_lcons_sn (A) (k) (p) (l) (n) (f):
-      ↑❨k, f∘𝐮❨ninj n❩, l◗p❩ = ↑{A}❨k, f, 𝗱n◗l◗p❩.
+lemma lift_d_sn (A) (k) (p) (n) (f):
+      ↑❨(λg,p. k g (𝗱(f@❨n❩)◗p)), 𝐢, p❩ = ↑{A}❨k, f, 𝗱n◗p❩.
 // qed.
 
 lemma lift_m_sn (A) (k) (p) (f):
-      ↑❨k, f, p❩ = ↑{A}❨k, f, 𝗺◗p❩.
+      ↑❨(λg,p. k g (𝗺◗p)), f, p❩ = ↑{A}❨k, f, 𝗺◗p❩.
 // qed.
 
 lemma lift_L_sn (A) (k) (p) (f):
@@ -95,18 +85,6 @@ lemma lift_path_empty (f):
       (𝐞) = ↑[f]𝐞.
 // qed.
 
-lemma lift_path_d_empty_sn (f) (n):
-      𝗱(f@❨n❩)◗𝐞 = ↑[f](𝗱n◗𝐞).
-// qed.
-
-lemma lift_path_d_lcons_sn (f) (p) (l) (n):
-      ↑[f∘𝐮❨ninj n❩](l◗p) = ↑[f](𝗱n◗l◗p).
-// qed.
-
-lemma lift_path_m_sn (f) (p):
-      ↑[f]p = ↑[f](𝗺◗p).
-// qed.
-
 (* Basic constructions with proj_rmap ***************************************)
 
 lemma lift_rmap_empty (f):
@@ -114,8 +92,8 @@ lemma lift_rmap_empty (f):
 // qed.
 
 lemma lift_rmap_d_sn (f) (p) (n):
-      ↑[p](f∘𝐮❨ninj n❩) = ↑[𝗱n◗p]f.
-#f * // qed.
+      ↑[p]𝐢 = ↑[𝗱n◗p]f.
+// qed.
 
 lemma lift_rmap_m_sn (f) (p):
       ↑[p]f = ↑[𝗺◗p]f.
@@ -138,7 +116,8 @@ lemma lift_rmap_S_sn (f) (p):
 lemma lift_rmap_append (p2) (p1) (f):
       ↑[p2]↑[p1]f = ↑[p1●p2]f.
 #p2 #p1 elim p1 -p1 // * [ #n ] #p1 #IH #f //
-[ <lift_rmap_m_sn <lift_rmap_m_sn //
+[ <lift_rmap_d_sn <lift_rmap_d_sn //
+| <lift_rmap_m_sn <lift_rmap_m_sn //
 | <lift_rmap_A_sn <lift_rmap_A_sn //
 | <lift_rmap_S_sn <lift_rmap_S_sn //
 ]
@@ -147,7 +126,7 @@ qed.
 (* Advanced constructions with proj_rmap and path_rcons *********************)
 
 lemma lift_rmap_d_dx (f) (p) (n):
-      (↑[p]f)∘𝐮❨ninj n❩ = ↑[p◖𝗱n]f.
+      (𝐢) = ↑[p◖𝗱n]f.
 // qed.
 
 lemma lift_rmap_m_dx (f) (p):
@@ -166,18 +145,6 @@ lemma lift_rmap_S_dx (f) (p):
       ↑[p]f = ↑[p◖𝗦]f.
 // qed.
 
-(* Advanced eliminations with path ******************************************)
-
-lemma path_ind_lift (Q:predicate …):
-      Q (𝐞) →
-      (∀n. Q (𝐞) → Q (𝗱n◗𝐞)) →
-      (∀n,l,p. Q (l◗p) → Q (𝗱n◗l◗p)) →
-      (∀p. Q p → Q (𝗺◗p)) →
-      (∀p. Q p → Q (𝗟◗p)) →
-      (∀p. Q p → Q (𝗔◗p)) →
-      (∀p. Q p → Q (𝗦◗p)) →
-      ∀p. Q p.
-#Q #IH1 #IH2 #IH3 #IH4 #IH5 #IH6 #IH7 #p
-elim p -p [| * [ #n * ] ]
-/2 width=1 by/
-qed-.
+lemma lift_rmap_pap_d_dx (f) (p) (n) (m):
+      m = ↑[p◖𝗱n]f@❨m❩.
+// qed.