partial update in delayed_updating

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

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_closed_structure.ma b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_closed_structure.ma
new file mode 100644 (file)
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "delayed_updating/syntax/path_closed_height.ma".
+include "delayed_updating/syntax/path_structure.ma".
+
+(* CLOSED CONDITION FOR PATH ************************************************)
+
+(* Constructions with structure *********************************************)
+
+lemma path_closed_structure_height (p) (n):
+      p ϵ 𝐂❨n❩ → ⊗p ϵ 𝐂❨♯p+n❩.
+#p #n #Hn elim Hn -Hn //
+#p #n #_ #IH [ <nplus_succ_dx ]
+/2 width=1 by pcc_L_dx, pcc_A_dx, pcc_S_dx/
+qed.
+
+lemma path_closed_structure_depth (p) (n):
+      p ϵ 𝐂❨n❩ → ⊗p ϵ 𝐂❨♭p❩.
+#p #n #Hp <path_closed_depth
+/2 width=3 by path_closed_structure_height/
+qed.