update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / etc / lift_i / lift_path_proper.etc

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/etc/lift_i/lift_path_proper.etc b/matita/matita/contribs/lambdadelta/delayed_updating/etc/lift_i/lift_path_proper.etc
new file mode 100644 (file)
index 0000000..0eef978
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/etc/lift_i/lift_path_proper.etc
@@ -0,0 +1,42 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/substitution/lift_eq.ma".
+include "delayed_updating/syntax/path_proper.ma".
+
+(* LIFT FOR PATH ************************************************************)
+
+(* Constructions with proper condition for path *****************************)
+
+lemma lift_path_proper (f) (p):
+      p ϵ 𝐏 → ↑[f]p ϵ 𝐏.
+#f *
+[ #H0 elim (ppc_inv_empty … H0)
+| * [ #n ] #p #_
+  [ <lift_path_d_sn /2 width=3 by ppc_lcons/
+  | <lift_path_m_sn /2 width=3 by ppc_lcons/
+  | <lift_path_L_sn /2 width=3 by ppc_lcons/
+  | <lift_path_A_sn /2 width=3 by ppc_lcons/
+  | <lift_path_S_sn /2 width=3 by ppc_lcons/
+  ]
+]
+qed.
+
+(* Inversions with proper condition for path ********************************)
+
+lemma lift_path_inv_proper (f) (p):
+      ↑[f]p ϵ 𝐏 → p ϵ 𝐏.
+#f * //
+#H0 elim (ppc_inv_empty … H0)
+qed-.