milestone update in ground

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

diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/gr_id_eq.ma b/matita/matita/contribs/lambdadelta/ground/relocation/gr_id_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/gr_tl_eq.ma".
+include "ground/relocation/gr_id.ma".
+
+(* IDENTITY ELEMENT FOR GENERIC RELOCATION MAPS  ******************************************************)
+
+(* Properties with gr_eq *)
+
+corec lemma gr_id_eq (f): ⫯f ≡ f → 𝐢 ≡ f.
+cases gr_id_unfold #Hf
+cases (gr_eq_inv_push_sn … Hf) [|*: // ] #_ #H
+cases H in Hf; -H #Hf
+@gr_eq_push [3:|*: // ]
+/3 width=5 by gr_eq_inv_push_bi/
+qed.
+
+(* Inversions with gr_eq *)
+
+(* Note: this has the same proof of the previous *)
+corec lemma gr_id_inv_eq (f): 𝐢 ≡ f → ⫯f ≡ f.
+cases gr_id_unfold #Hf
+cases (gr_eq_inv_push_sn … Hf) [|*: // ] #_ #H
+cases H in Hf; -H #Hf
+@gr_eq_push [3:|*: // ]
+/3 width=5 by gr_eq_inv_push_bi/
+qed-.