matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_basic_after.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "ground_2/relocation/rtmap_after.ma".
  16 include "ground_2/relocation/rtmap_basic.ma".
  17
  18 (* RELOCATION MAP ***********************************************************)
  19
  20 (* Properties with composition **********************************************)
  21
  22 lemma after_basic_rc (m2,m1,n2,n1):
  23                      m1 ≤ m2 → m2 ≤ m1+n1 → 𝐁❴m2,n2❵ ⊚ 𝐁❴m1,n1❵ ≘ 𝐁❴m1,n2+n1❵.
  24 #m2 elim m2 -m2
  25 [ #m1 #n2 #n1 #Hm21 #_
  26   <(le_n_O_to_eq … Hm21) -m1 //
  27 | #m2 #IH *
  28   [ #n2 #n1 #_ < plus_O_n #H
  29     elim (le_inv_S1 … H) -H #x #Hx #H destruct
  30     <plus_n_Sm
  31     @after_push [4:|*: // ]
  32     @(IH 0 … Hx) -IH -n2 -x //
  33   | #m1 #n2 #n1 #H1 #H2
  34     lapply (le_S_S_to_le … H1) -H1 #H1
  35     lapply (le_S_S_to_le … H2) -H2 #H2
  36     /3 width=7 by after_refl/
  37   ]
  38 ]
  39 qed.