update in ground

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

diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/pr_isd.ma b/matita/matita/contribs/lambdadelta/ground/relocation/pr_isd.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_omega_1.ma".
+include "ground/relocation/pr_map.ma".
+
+(* DIVERGENCE CONDITION FOR PARTIAL RELOCATION MAPS *************************)
+
+(*** isdiv *)
+coinductive pr_isd: predicate pr_map ≝
+(*** isdiv_next *)
+| pr_isd_next (f) (g):
+  pr_isd f → ↑f = g → pr_isd g
+.
+
+interpretation
+  "divergence condition (partial relocation maps)"
+  'PredicateOmega f = (pr_isd f).
+
+(* Basic inversions *********************************************************)
+
+(*** isdiv_inv_gen *)
+lemma pr_isd_inv_gen (g): 𝛀❪g❫ → ∃∃f. 𝛀❪f❫ & ↑f = g.
+#g * -g
+#f #g #Hf * /2 width=3 by ex2_intro/
+qed-.
+
+(* Advanced inversions ******************************************************)
+
+(*** isdiv_inv_next *)
+lemma pr_isd_inv_next (g): 𝛀❪g❫ → ∀f. ↑f = g → 𝛀❪f❫.
+#g #H elim (pr_isd_inv_gen … H) -H
+#f #Hf * -g #g #H >(eq_inv_pr_next_bi … H) -H //
+qed-.
+
+(*** isdiv_inv_push *)
+lemma pr_isd_inv_push (g): 𝛀❪g❫ → ∀f. ⫯f = g → ⊥.
+#g #H elim (pr_isd_inv_gen … H) -H
+#f #Hf * -g #g #H elim (eq_inv_pr_push_next … H)
+qed-.