milestone update in ground

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

diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/gr_isf.ma b/matita/matita/contribs/lambdadelta/ground/relocation/gr_isf.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_f_1.ma".
+include "ground/relocation/gr_fcla.ma".
+
+(* FINITE COLENGTH CONDITION FOR GENERIC RELOCATION MAPS *)
+
+(*** isfin *)
+definition gr_isf: predicate gr_map ≝
+           λf. ∃n. 𝐂❪f❫ ≘ n.
+
+interpretation
+  "finite colength condition (generic relocation maps)"
+  'PredicateF f = (gr_isf f).
+
+(* Basic eliminators ********************************************************)
+
+(*** isfin_ind *)
+lemma gr_isf_ind (Q:predicate …):
+      (∀f.  𝐈❪f❫ → Q f) →
+      (∀f. 𝐅❪f❫ → Q f → Q (⫯f)) →
+      (∀f. 𝐅❪f❫ → Q f → Q (↑f)) →
+      ∀f. 𝐅❪f❫ → Q f.
+#Q #IH1 #IH2 #IH3 #f #H elim H -H
+#n #H elim H -f -n /3 width=2 by ex_intro/
+qed-.
+
+(* Basic inversion lemmas ***************************************************)
+
+(*** isfin_inv_push *)
+lemma gr_isf_inv_push (g): 𝐅❪g❫ → ∀f. ⫯f = g → 𝐅❪f❫.
+#g * /3 width=4 by gr_fcla_inv_push, ex_intro/
+qed-.
+
+(*** isfin_inv_next *)
+lemma gr_isf_inv_next (g): 𝐅❪g❫ → ∀f. ↑f = g → 𝐅❪f❫.
+#g * #n #H #f #H0 elim (gr_fcla_inv_next … H … H0) -g
+/2 width=2 by ex_intro/
+qed-.
+
+(* Basic properties *********************************************************)
+
+(*** isfin_isid *)
+lemma gr_isf_isi (f): 𝐈❪f❫ → 𝐅❪f❫.
+/3 width=2 by gr_fcla_isi, ex_intro/ qed.
+
+(*** isfin_push *)
+lemma gr_isf_push (f): 𝐅❪f❫ → 𝐅❪⫯f❫.
+#f * /3 width=2 by gr_fcla_push, ex_intro/
+qed.
+
+(*** isfin_next *)
+lemma gr_isf_next (f): 𝐅❪f❫ → 𝐅❪↑f❫.
+#f * /3 width=2 by gr_fcla_next, ex_intro/
+qed.