update in ground

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

diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/pr_uni_eq.ma b/matita/matita/contribs/lambdadelta/ground/relocation/pr_uni_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/arith/nat_pred_succ.ma".
+include "ground/relocation/pr_tl_eq.ma".
+include "ground/relocation/pr_uni.ma".
+
+(* UNIFORM ELEMENTS FOR PARTIAL RELOCATION MAPS *****************************)
+
+(* Inversions with pr_eq ****************************************************)
+
+(*** uni_inv_push_dx *)
+lemma pr_eq_inv_uni_push (n) (g):  𝐮❨n❩ ≡ ⫯g → ∧∧ 𝟎 = n & 𝐢 ≡ g.
+#n @(nat_ind_succ … n) -n 
+[ /3 width=5 by pr_eq_inv_push_bi, conj/
+| #n #_ #f <pr_uni_succ #H elim (pr_eq_inv_next_push … H) -H //
+]
+qed-.
+
+(*** uni_inv_push_sn *)
+lemma pr_eq_inv_push_uni (n) (g): ⫯g ≡ 𝐮❨n❩ → ∧∧ 𝟎 = n & 𝐢 ≡ g.
+/3 width=1 by pr_eq_inv_uni_push, pr_eq_sym/ qed-.
+
+(*** uni_inv_next_dx *)
+lemma pr_eq_inv_uni_next (n) (g): 𝐮❨n❩ ≡ ↑g → ∧∧ 𝐮❨↓n❩ ≡ g & ↑↓n = n.
+#n @(nat_ind_succ … n) -n
+[ #g <pr_uni_zero <pr_id_unfold #H elim (pr_eq_inv_push_next … H) -H //
+| #n #_ #g <pr_uni_succ /3 width=5 by pr_eq_inv_next_bi, conj/
+]
+qed-.
+
+(*** uni_inv_next_sn *)
+lemma pr_eq_inv_next_uni (n) (g): ↑g ≡ 𝐮❨n❩ → ∧∧ 𝐮❨↓n❩ ≡ g & ↑↓n = n.
+/3 width=1 by pr_eq_inv_uni_next, pr_eq_sym/ qed-.
+
+(* Inversions with pr_id and pr_eq ******************************************)
+
+(*** uni_inv_id_dx *)
+lemma pr_eq_inv_uni_id (n): 𝐮❨n❩ ≡ 𝐢 → 𝟎 = n.
+#n <pr_id_unfold #H elim (pr_eq_inv_uni_push … H) -H //
+qed-.
+
+(*** uni_inv_id_sn *)
+lemma pr_eq_inv_id_uni (n):  𝐢 ≡ 𝐮❨n❩ → 𝟎 = n.
+/3 width=1 by pr_eq_inv_uni_id, pr_eq_sym/ qed-.