update in delayed updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / syntax / path_structure.ma

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_structure.ma b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_structure.ma
index 5bf678ebe01edecc6abb6e061d592e809def6711..6ba6e937b48778b995bae2d16e1ca16f326ce13f 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_structure.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_structure.ma
@@ -17,18 +17,75 @@ include "delayed_updating/notation/functions/circled_times_1.ma".
 
 (* STRUCTURE FOR PATH *******************************************************)
 
-rec definition path_structure (p) on p ≝
+rec definition structure (p) on p ≝
 match p with
 [ list_empty     ⇒ 𝐞
 | list_lcons l q ⇒
    match l with
-   [ label_node_d n ⇒ path_structure q
-   | label_edge_L   ⇒ 𝗟◗path_structure q
-   | label_edge_A   ⇒ 𝗔◗path_structure q
-   | label_edge_S   ⇒ 𝗦◗path_structure q
+   [ label_node_d n ⇒ structure q
+   | label_edge_L   ⇒ 𝗟◗structure q
+   | label_edge_A   ⇒ 𝗔◗structure q
+   | label_edge_S   ⇒ 𝗦◗structure q
    ]
 ].
 
 interpretation
   "structure (path)"
-  'CircledTimes p = (path_structure p).
+  'CircledTimes p = (structure p).
+
+(* Basic constructions ******************************************************)
+
+lemma structure_empty:
+      𝐞 = ⊗𝐞.
+// qed.
+
+lemma structure_d_sn (p) (n):
+      ⊗p = ⊗(𝗱❨n❩◗p).
+// qed.
+
+lemma structure_L_sn (p):
+      𝗟◗⊗p = ⊗(𝗟◗p).
+// qed.
+
+lemma structure_A_sn (p):
+      𝗔◗⊗p = ⊗(𝗔◗p).
+// qed.
+
+lemma structure_S_sn (p):
+      𝗦◗⊗p = ⊗(𝗦◗p).
+// qed.
+
+(* Main constructions *******************************************************)
+
+theorem structure_idem (p):
+        ⊗p = ⊗⊗p.
+#p elim p -p [| * [ #n ] #p #IH ] //
+qed.
+
+theorem structure_append (p1) (p2):
+        ⊗p1●⊗p2 = ⊗(p1●p2).
+#p1 elim p1 -p1 [| * [ #n ] #p1 #IH ] #p2
+[||*: <list_append_lcons_sn ] //
+qed.
+
+(* Constructions with list_rcons ********************************************)
+
+lemma structure_d_dx (p) (n):
+      ⊗p = ⊗(p◖𝗱❨n❩).
+#p #n <structure_append //
+qed.
+
+lemma structure_L_dx (p):
+      (⊗p)◖𝗟 = ⊗(p◖𝗟).
+#p <structure_append //
+qed.
+
+lemma structure_A_dx (p):
+      (⊗p)◖𝗔 = ⊗(p◖𝗔).
+#p <structure_append //
+qed.
+
+lemma structure_S_dx (p):
+      (⊗p)◖𝗦 = ⊗(p◖𝗦).
+#p <structure_append //
+qed.