update in ground

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

diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/pr_isd_eq.ma b/matita/matita/contribs/lambdadelta/ground/relocation/pr_isd_eq.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/relocation/pr_tl_eq_eq.ma".
+include "ground/relocation/pr_isd.ma".
+
+(* DIVERGENCE CONDITION FOR PARTIAL RELOCATION MAPS *************************)
+
+(* Constructions with pr_eq *************************************************)
+
+(*** isdiv_eq_repl_back *)
+corec lemma pr_isd_eq_repl_back:
+            pr_eq_repl_back … pr_isd.
+#f1 #H cases (pr_isd_inv_gen … H) -H
+#g1 #Hg1 #H1 #f2 #Hf cases (pr_eq_inv_next_sn … Hf … H1) -f1
+/3 width=3 by pr_isd_next/
+qed-.
+
+(*** isdiv_eq_repl_fwd *)
+lemma pr_isd_eq_repl_fwd:
+      pr_eq_repl_fwd … pr_isd.
+/3 width=3 by pr_isd_eq_repl_back, pr_eq_repl_sym/ qed-.
+
+(* Main inversions with pr_eq ***********************************************)
+
+(*** isdiv_inv_eq_repl *)
+corec theorem pr_isd_inv_eq_repl (g1) (g2): 𝛀❪g1❫ → 𝛀❪g2❫ → g1 ≡ g2.
+#H1 #H2
+cases (pr_isd_inv_gen … H1) -H1
+cases (pr_isd_inv_gen … H2) -H2
+/3 width=5 by pr_eq_next/
+qed-.
+
+(* Alternative definition with pr_eq ****************************************)
+
+(*** eq_next_isdiv *)
+corec lemma pr_eq_next_isd (f): ↑f ≡ f → 𝛀❪f❫.
+#H cases (pr_eq_inv_next_sn … H) -H
+/4 width=3 by pr_isd_next, pr_eq_trans/
+qed.
+
+(*** eq_next_inv_isdiv *)
+corec lemma pr_eq_next_inv_isd (g): 𝛀❪g❫ → ↑g ≡ g.
+* -g #f #g #Hf *
+/3 width=5 by pr_eq_next/
+qed-.