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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 "pointer_list.ma".
+include "pointer_order.ma".
+
+(* STANDARD POINTER LIST ****************************************************)
+
+(* Note: to us, a "normal" computation contracts redexes in non-decreasing positions *)
+definition is_standard: predicate ptrl ≝ Allr … ple.
+
+lemma is_standard_compatible: ∀c,s. is_standard s → is_standard (c:::s).
+#c #s elim s -s // #p * //
+#q #s #IHs * /3 width=1/
+qed.
+
+lemma is_standard_cons: ∀p,s. is_standard s → is_standard ((dx::p)::sn:::s).
+#p #s elim s -s // #q1 * /2 width=1/
+#q2 #s #IHs * /4 width=1/
+qed.
+
+lemma is_standard_append: ∀r. is_standard r → ∀s. is_standard s → is_standard ((dx:::r)@sn:::s).
+#r elim r -r /3 width=1/ #p * /2 width=1/
+#q #r #IHr * /3 width=1/
+qed.
+
+theorem is_head_is_standard: ∀s. is_head s → is_standard s.
+#s elim s -s // #p * //
+#q #s #IHs * /3 width=1/
+qed.
+
+lemma is_standard_in_head: ∀p. in_head p → ∀s. is_standard s → is_standard (p::s).
+#p #Hp * // /3 width=1/
+qed.
+
+theorem is_head_is_standard_trans: ∀r. is_head r → ∀s. is_standard s → is_standard (r@s).
+#r elim r -r // #p *
+[ #_ * /2 width=1/
+| #q #r #IHr * /3 width=1/
+]
+qed.