update in delayed_updating

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

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_closed.ma b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_closed.ma
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_closed.ma
@@ -0,0 +1,48 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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.ma".
+include "delayed_updating/notation/functions/class_c_1.ma".
+include "ground/lib/subset.ma".
+
+include "delayed_updating/syntax/path_depth.ma".
+include "delayed_updating/syntax/path_height.ma".
+
+(* CLOSED CONDITION FOR PATH ************************************************)
+
+axiom pcc: relation2 nat path.
+
+interpretation
+  "closed condition (path)"
+  'ClassC n = (pcc n).
+
+(* Basic destructions *******************************************************)
+
+axiom pcc_empty:
+      (𝐞) ϵ 𝐂❨𝟎❩.
+
+axiom pcc_d (p) (d) (n:pnat):
+      p ϵ 𝐂❨d+n❩ → p◖𝗱n ϵ 𝐂❨d❩.
+
+axiom pcc_L (p) (d):
+      p ϵ 𝐂❨d❩ → p◖𝗟 ϵ 𝐂❨↑d❩.
+
+axiom pcc_A (p) (d):
+      p ϵ 𝐂❨d❩ → p◖𝗔 ϵ 𝐂❨d❩.
+
+axiom pcc_S (p) (d):
+      p ϵ 𝐂❨d❩ → p◖𝗦 ϵ 𝐂❨d❩.
+
+axiom pcc_des_gen (p) (d):
+      p ϵ 𝐂❨d❩ → d + ♯p = ❘p❘.