update in ground

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

diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/gr_nat_basic.ma b/matita/matita/contribs/lambdadelta/ground/relocation/gr_nat_basic.ma
deleted file mode 100644 (file)
index a9c9cae..0000000
--- a/matita/matita/contribs/lambdadelta/ground/relocation/gr_nat_basic.ma
+++ /dev/null
@@ -1,51 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||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_basic.ma".
-include "ground/relocation/gr_nat_uni.ma".
-
-(* NON-NEGATIVE APPLICATION FOR GENERIC RELOCATION MAPS *********************)
-
-(* Constructions with gr_basic **********************************************)
-
-lemma gr_nat_basic_lt (m) (n) (l):
-      l < m → @↑❪l, 𝐛❨m,n❩❫ ≘ l.
-#m @(nat_ind_succ … m) -m
-[ #n #i #H elim (nlt_inv_zero_dx … H)
-| #m #IH #n #l @(nat_ind_succ … l) -l
-  [ #_ /2 width=2 by refl, gr_pat_refl/
-  | #l #_ #H
-    lapply (nlt_inv_succ_bi … H) -H #Hlm
-    /3 width=7 by refl, gr_pat_push/
-  ]
-]
-qed.
-
-lemma gr_nat_basic_ge (m) (n) (l):
-      m ≤ l → @↑❪l, 𝐛❨m,n❩❫ ≘ l+n.
-#m @(nat_ind_succ … m) -m //
-#m #IH #n #l #H
-elim (nle_inv_succ_sn … H) -H #Hml #H >H -H
-/3 width=7 by gr_nat_push/
-qed.
-
-(* Inversions with gr_basic *************************************************)
-
-lemma gr_nat_basic_inv_lt (m) (n) (l) (k):
-      l < m → @↑❪l, 𝐛❨m,n❩❫ ≘ k → l = k.
-/3 width=4 by gr_nat_basic_lt, gr_nat_mono/ qed-.
-
-lemma gr_nat_basic_inv_ge (m) (n) (l) (k):
-      m ≤ l → @↑❪l, 𝐛❨m,n❩❫ ≘ k → l+n = k.
-/3 width=4 by gr_nat_basic_ge, gr_nat_mono/ qed-.