update in ground

[helm.git] / matita / matita / contribs / lambdadelta / ground / relocation / pr_ist.ma

diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/pr_ist.ma b/matita/matita/contribs/lambdadelta/ground/relocation/pr_ist.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 "ground/notation/relations/predicate_t_1.ma".
+include "ground/relocation/pr_pat.ma".
+
+(* TOTALITY CONDITION FOR PARTIAL RELOCATION MAPS ***************************)
+
+(*** istot *)
+definition pr_ist: predicate pr_map ≝
+           λf. ∀i. ∃j. @❪i,f❫ ≘ j.
+
+interpretation
+  "totality condition (partial relocation maps)"
+  'PredicateT f = (pr_ist f).
+
+(* Basic inversions *********************************************************)
+
+(*** istot_inv_push *)
+lemma pr_ist_inv_push (g): 𝐓❪g❫ → ∀f. ⫯f = g → 𝐓❪f❫.
+#g #Hg #f #H #i elim (Hg (↑i)) -Hg
+#j #Hg elim (pr_pat_inv_succ_push … Hg … H) -Hg -H /2 width=3 by ex_intro/
+qed-.
+
+(*** istot_inv_next *)
+lemma pr_ist_inv_next (g): 𝐓❪g❫ → ∀f. ↑f = g → 𝐓❪f❫.
+#g #Hg #f #H #i elim (Hg i) -Hg
+#j #Hg elim (pr_pat_inv_next … Hg … H) -Hg -H /2 width=2 by ex_intro/
+qed-.
+
+(* Constructions with pr_tl *************************************************)
+
+(*** istot_tl *)
+lemma pr_ist_tl (f): 𝐓❪f❫ → 𝐓❪⫰f❫.
+#f cases (pr_map_split_tl f) *
+/2 width=3 by pr_ist_inv_next, pr_ist_inv_push/
+qed.