matita/matita/contribs/lambdadelta/ground/relocation/rtmap_basic_at.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "ground/arith/nat_plus_rplus.ma".
  16 include "ground/relocation/rtmap_basic_nat.ma".
  17
  18 (* RELOCATION MAP ***********************************************************)
  19
  20 (* Prioerties with application **********************************************)
  21
  22 lemma at_basic_lt (m) (n) (i):
  23       ninj i ≤ m → @❪i, 𝐁❨m,n❩❫ ≘ i.
  24 #m #n #i >(npsucc_pred i) #Hmi
  25 /2 width=1 by rm_nat_basic_lt/
  26 qed.
  27
  28 lemma at_basic_ge (m) (n) (i):
  29       m < ninj i → @❪i, 𝐁❨m,n❩❫ ≘ i+n.
  30 #m #n #i >(npsucc_pred i) #Hmi <nrplus_npsucc_sn
  31 /3 width=1 by rm_nat_basic_ge, nlt_inv_succ_dx/
  32 qed.
  33
  34 (* Inversion lemmas with application ****************************************)
  35
  36 lemma at_basic_inv_lt (m) (n) (i) (j):
  37       ninj i ≤ m → @❪i, 𝐁❨m,n❩❫ ≘ j → i = j.
  38 /3 width=4 by at_basic_lt, at_mono/ qed-.
  39
  40 lemma at_basic_inv_ge (m) (n) (i) (j):
  41       m < ninj i → @❪i, 𝐁❨m,n❩❫ ≘ j → i+n = j.
  42 /3 width=4 by at_basic_ge, at_mono/ qed-.