milestone update in ground

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

diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/gr_isi.ma b/matita/matita/contribs/lambdadelta/ground/relocation/gr_isi.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_i_1.ma".
+include "ground/relocation/gr_map.ma".
+
+(* IDENTITY CONDITION FOR GENERIC RELOCATION MAPS ***********************************************************)
+
+(*** isid *)
+coinductive gr_isi: predicate gr_map ≝
+(*** isid_push *)
+| gr_isi_push (f) (g):
+  gr_isi f → ⫯f = g → gr_isi g
+.
+
+interpretation
+  "identity condition (generic relocation maps)"
+  'PredicateI f = (gr_isi f).
+
+(* Basic inversion lemmas ***************************************************)
+
+(*** isid_inv_gen *)
+lemma gr_isi_inv_gen (g): 𝐈❪g❫ → ∃∃f. 𝐈❪f❫ & ⫯f = g.
+#g * -g
+#f #g #Hf /2 width=3 by ex2_intro/
+qed-.
+
+(* Advanced inversion lemmas ************************************************)
+
+(*** isid_inv_push *)
+lemma gr_isi_inv_push (g): 𝐈❪g❫ → ∀f. ⫯f = g → 𝐈❪f❫.
+#g #H
+elim (gr_isi_inv_gen … H) -H #f #Hf
+* -g #g #H
+>(eq_inv_gr_push_bi … H) -H //
+qed-.
+
+(*** isid_inv_next *)
+lemma gr_isi_inv_next (g): 𝐈❪g❫ → ∀f. ↑f = g → ⊥.
+#g #H
+elim (gr_isi_inv_gen … H) -H #f #Hf
+* -g #g #H elim (eq_inv_gr_next_push … H)
+qed-.