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 0dbb6043a4cb9dbe8f4571f40bff6194814547fa..fa63286846e697621e2ac313b739825204abc2a5 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/substitution/lift.ma
@@ -29,14 +29,15 @@ match p with
 [ list_empty     ⇒ k f (𝐞)
 | list_lcons l q ⇒
   match l with
-  [ label_node_d n ⇒
+  [ 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_edge_L   ⇒ lift_gen (A) (λg,p. k g (𝗟◗p)) (⫯f) q
-  | label_edge_A   ⇒ lift_gen (A) (λg,p. k g (𝗔◗p)) f q
-  | label_edge_S   ⇒ lift_gen (A) (λg,p. k g (𝗦◗p)) f q
+  | label_m   ⇒ lift_gen (A) k 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
   ]
 ].
 
@@ -72,6 +73,10 @@ lemma lift_d_lcons_sn (A) (k) (p) (l) (n) (f):
       ↑❨k, f∘𝐮❨ninj n❩, l◗p❩ = ↑{A}❨k, f, 𝗱n◗l◗p❩.
 // qed.
 
+lemma lift_m_sn (A) (k) (p) (f):
+      ↑❨k, f, p❩ = ↑{A}❨k, f, 𝗺◗p❩.
+// qed.
+
 lemma lift_L_sn (A) (k) (p) (f):
       ↑❨(λg,p. k g (𝗟◗p)), ⫯f, p❩ = ↑{A}❨k, f, 𝗟◗p❩.
 // qed.
@@ -98,12 +103,20 @@ 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_d_sn (f) (p) (n):
       ↑[p](f∘𝐮❨ninj n❩) = ↑[𝗱n◗p]f.
 #f * // qed.
 
+lemma lift_rmap_m_sn (f) (p):
+      ↑[p]f = ↑[𝗺◗p]f.
+// qed.
+
 lemma lift_rmap_L_sn (f) (p):
       ↑[p](⫯f) = ↑[𝗟◗p]f.
 // qed.
@@ -121,7 +134,8 @@ 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_A_sn <lift_rmap_A_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 //
 ]
 qed.
@@ -132,11 +146,12 @@ 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 #p
+#Q #IH1 #IH2 #IH3 #IH4 #IH5 #IH6 #IH7 #p
 elim p -p [| * [ #n * ] ]
 /2 width=1 by/
 qed-.