update in ground

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

diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/pr_isu_uni.ma b/matita/matita/contribs/lambdadelta/ground/relocation/pr_isu_uni.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_isi_uni.ma".
+include "ground/relocation/pr_isu.ma".
+
+(* UNIFORMITY CONDITION FOR PARTIAL RELOCATION MAPS *************************)
+
+(* Constructions with pr_uni ************************************************)
+
+(*** isuni_uni *)
+lemma pr_isu_uni (n): 𝐔❪𝐮❨n❩❫.
+#n @(nat_ind_succ … n) -n
+/3 width=3 by pr_isu_isi, pr_isu_next/
+qed.
+
+(*** uni_inv_isuni *)
+lemma pr_isu_eq_repl_back:
+      pr_eq_repl_back … pr_isu.
+#f1 #H elim H -f1
+[ /3 width=3 by pr_isu_isi, pr_isi_eq_repl_back/
+| #f1 #_ #g1 * #IH #f2 #H -g1
+  elim (pr_eq_inv_next_sn … H) -H
+  /3 width=3 by pr_isu_next/
+]
+qed-.
+
+lemma pr_isu_eq_repl_fwd:
+      pr_eq_repl_fwd … pr_isu.
+/3 width=3 by pr_isu_eq_repl_back, pr_eq_repl_sym/ qed-.
+
+(* Inversions with pr_uni ***************************************************)
+
+(*** uni_isuni *)
+lemma pr_isu_inv_uni (f): 𝐔❪f❫ → ∃n. 𝐮❨n❩ ≡ f.
+#f #H elim H -f
+[ /3 width=2 by pr_isi_inv_uni, ex_intro/
+| #f #_ #g #H * /3 width=6 by pr_eq_next, ex_intro/
+]
+qed-.