update in delayed_updating

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

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_inner.ma b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_inner.ma
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+++ b/matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_inner.ma
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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.ma".
+include "delayed_updating/notation/functions/class_i_0.ma".
+include "ground/lib/subset.ma".
+
+(* INNER CONDITION FOR PATH *************************************************)
+
+definition pic: predicate path ≝
+           λp. ∀q,n. q◖𝗱n = p → ⊥
+.
+
+interpretation
+  "inner condition (path)"
+  'ClassI = (pic).
+
+(* Basic constructions ******************************************************)
+
+lemma pic_empty: 𝐞 ϵ 𝐈.
+#q #n #H0
+elim (eq_inv_list_empty_rcons ??? (sym_eq … H0))
+qed.
+
+lemma pic_m_dx (p): p◖𝗺 ϵ 𝐈.
+#p #q #n #H0
+elim (eq_inv_list_rcons_bi ????? H0) -H0 #_ #H0 destruct
+qed.
+
+lemma pic_L_dx (p): p◖𝗟 ϵ 𝐈.
+#p #q #n #H0
+elim (eq_inv_list_rcons_bi ????? H0) -H0 #_ #H0 destruct
+qed.
+
+lemma pic_A_dx (p): p◖𝗔 ϵ 𝐈.
+#p #q #n #H0
+elim (eq_inv_list_rcons_bi ????? H0) -H0 #_ #H0 destruct
+qed.
+
+lemma pic_S_dx (p): p◖𝗦 ϵ 𝐈.
+#p #q #n #H0
+elim (eq_inv_list_rcons_bi ????? H0) -H0 #_ #H0 destruct
+qed.
+
+(* Basic inversions ********************************************************)
+
+lemma pic_inv_d_dx (p) (n):
+      p◖𝗱n ϵ 𝐈 → ⊥.
+#p #n #H0 @H0 -H0 //
+qed-.