update in delayed_updating

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

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_depth.ma b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_depth.ma
index e76c4943b704ce2729085a27fe150c8decb87448..cdf24943af922c8a47c74990fb79e92acf803231 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_depth.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_depth.ma
@@ -13,7 +13,7 @@
 (**************************************************************************)
 
 include "delayed_updating/syntax/path.ma".
-include "ground/arith/nat_succ.ma".
+include "ground/arith/nat_plus.ma".
 include "ground/notation/functions/verticalbars_1.ma".
 
 (* DEPTH FOR PATH ***********************************************************)
@@ -23,10 +23,11 @@ match p with
 [ list_empty     ⇒ 𝟎
 | list_lcons l q ⇒
   match l with
-  [ label_node_d _ ⇒ depth q
-  | label_edge_L   ⇒ ↑(depth q)
-  | label_edge_A   ⇒ depth q
-  | label_edge_S   ⇒ depth q
+  [ label_d _ ⇒ depth q
+  | label_m   ⇒ depth q
+  | label_L   ⇒ ↑(depth q)
+  | label_A   ⇒ depth q
+  | label_S   ⇒ depth q
   ]
 ].
 
@@ -39,14 +40,53 @@ interpretation
 lemma depth_empty: 𝟎 = ❘𝐞❘.
 // qed.
 
-lemma depth_d (q) (n): ❘q❘ = ❘𝗱❨n❩◗q❘.
+lemma depth_d_sn (q) (n): ❘q❘ = ❘𝗱n◗q❘.
 // qed.
 
-lemma depth_L (q): ↑❘q❘ = ❘𝗟◗q❘.
+lemma depth_m_sn (q): ❘q❘ = ❘𝗺◗q❘.
 // qed.
 
-lemma depth_A (q): ❘q❘ = ❘𝗔◗q❘.
+lemma depth_L_sn (q): ↑❘q❘ = ❘𝗟◗q❘.
 // qed.
 
-lemma depth_S (q): ❘q❘ = ❘𝗦◗q❘.
+lemma depth_A_sn (q): ❘q❘ = ❘𝗔◗q❘.
+// qed.
+
+lemma depth_S_sn (q): ❘q❘ = ❘𝗦◗q❘.
+// qed.
+
+(* Main constructions *******************************************************)
+
+theorem depth_append (p1) (p2):
+        ❘p2❘+❘p1❘ = ❘p1●p2❘.
+#p1 elim p1 -p1 //
+* [ #n ] #p1 #IH #p2 <list_append_lcons_sn
+[ <depth_d_sn <depth_d_sn //
+| <depth_m_sn <depth_m_sn //
+| <depth_L_sn <depth_L_sn //
+| <depth_A_sn <depth_A_sn //
+| <depth_S_sn <depth_S_sn //
+]
+qed.
+
+(* Constructions with list_rcons ********************************************)
+
+lemma depth_d_dx (p) (n):
+      ❘p❘ = ❘p◖𝗱n❘.
+// qed.
+
+lemma depth_m_dx (p):
+      ❘p❘ = ❘p◖𝗺❘.
+// qed.
+
+lemma depth_L_dx (p):
+      ↑❘p❘ = ❘p◖𝗟❘.
+// qed.
+
+lemma depth_A_dx (p):
+      ❘p❘ = ❘p◖𝗔❘.
+// qed.
+
+lemma depth_S_dx (p):
+      ❘p❘ = ❘p◖𝗦❘.
 // qed.