update in ground

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

diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/gr_nexts.ma b/matita/matita/contribs/lambdadelta/ground/relocation/gr_nexts.ma
deleted file mode 100644 (file)
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--- a/matita/matita/contribs/lambdadelta/ground/relocation/gr_nexts.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/notation/functions/uparrowstar_2.ma".
-include "ground/arith/nat_succ_iter.ma".
-include "ground/relocation/gr_map.ma".
-
-(* ITERATED NEXT FOR GENERIC RELOCATION MAPS ********************************)
-
-(*** nexts *)
-definition gr_nexts (f:gr_map) (n:nat) ≝
-           (gr_next^n) f.
-
-interpretation
-  "iterated next (generic relocation maps)"
-  'UpArrowStar n f = (gr_nexts f n).
-
-(* Basic constructions ******************************************************)
-
-(*** nexts_O *)
-lemma gr_nexts_zero:
-      ∀f. f = ↑*[𝟎] f.
-// qed.
-
-(*** nexts_swap *)
-lemma gr_nexts_next (n):
-      ∀f. ↑↑*[n] f = ↑*[n] ↑f.
-#f #n @(niter_appl … gr_next)
-qed.
-
-(*** nexts_S *)
-lemma gr_nexts_succ (n):
-      ∀f. ↑↑*[n] f = ↑*[↑n] f.
-#f #n @(niter_succ … gr_next)
-qed.
-
-(*** nexts_xn *)
-lemma gr_nexts_swap (n):
-      ∀f. ↑*[n] ↑f = ↑*[↑n] f.
-// qed.