update in ground

[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 fa63286846e697621e2ac313b739825204abc2a5..ec7d9726faafe7735c84ab4caf0952c642eadd90 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift.ma
@@ -12,29 +12,24 @@
 (*                                                                        *)
 (**************************************************************************)
 
-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_uni.ma".
+include "ground/relocation/tr_pap_tls.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)) (⇂*[n]f) 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 +60,12 @@ 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)), ⇂*[n]f, 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):
@@ -95,23 +86,15 @@ 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.
+(* Basic constructions with proj_rmap ***************************************)
 
-lemma lift_path_m_sn (f) (p):
-      ↑[f]p = ↑[f](𝗺◗p).
+lemma lift_rmap_empty (f):
+      f = ↑[𝐞]f.
 // qed.
 
-(* Basic constructions with proj_rmap ***************************************)
-
 lemma lift_rmap_d_sn (f) (p) (n):
-      ↑[p](f∘𝐮❨ninj n❩) = ↑[𝗱n◗p]f.
-#f * // qed.
+      ↑[p](⇂*[ninj n]f) = ↑[𝗱n◗p]f.
+// qed.
 
 lemma lift_rmap_m_sn (f) (p):
       ↑[p]f = ↑[𝗺◗p]f.
@@ -140,18 +123,28 @@ lemma lift_rmap_append (p2) (p1) (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-.
+(* Advanced constructions with proj_rmap and path_rcons *********************)
+
+lemma lift_rmap_d_dx (f) (p) (n):
+      ⇂*[ninj n](↑[p]f) = ↑[p◖𝗱n]f.
+// qed.
+
+lemma lift_rmap_m_dx (f) (p):
+      ↑[p]f = ↑[p◖𝗺]f.
+// qed.
+
+lemma lift_rmap_L_dx (f) (p):
+      (⫯↑[p]f) = ↑[p◖𝗟]f.
+// qed.
+
+lemma lift_rmap_A_dx (f) (p):
+      ↑[p]f = ↑[p◖𝗔]f.
+// qed.
+
+lemma lift_rmap_S_dx (f) (p):
+      ↑[p]f = ↑[p◖𝗦]f.
+// qed.
+
+lemma lift_rmap_pap_d_dx (f) (p) (n) (m):
+      ↑[p]f＠⧣❨m+n❩ = ↑[p◖𝗱n]f＠⧣❨m❩+↑[p]f＠⧣❨n❩.
+// qed.