matita/matita/contribs/lambdadelta/ground/relocation/pr_tls_pushs_eq.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/relocation/pr_tls_eq.ma".
  16 include "ground/relocation/pr_pushs.ma".
  17
  18 (* ITERATED TAIL FOR PARTIAL RELOCATION MAPS ********************************)
  19
  20 (* Inversions with pr_pushs and pr_eq ***************************************)
  21
  22 (*** eq_inv_pushs_sn *)
  23 lemma pr_eq_inv_pushs_sn (n):
  24       ∀f1,g2. ⫯*[n] f1 ≡ g2 →
  25       ∧∧ f1 ≡ ⫰*[n]g2 & ⫯*[n]⫰*[n]g2 = g2.
  26 #n @(nat_ind_succ … n) -n /2 width=1 by conj/
  27 #n #IH #f1 #g2 #H
  28 elim (pr_eq_inv_push_sn … H) -H [|*: // ] #Hf10 *
  29 elim (IH … Hf10) -IH -Hf10 #Hf12 #H1
  30 <pr_tls_succ /2 width=1 by conj/
  31 qed-.
  32
  33 (*** eq_inv_pushs_dx *)
  34 lemma pr_eq_inv_pushs_dx (n):
  35       ∀f2,g1. g1 ≡ ⫯*[n] f2 →
  36       ∧∧ ⫰*[n]g1 ≡ f2 & ⫯*[n]⫰*[n]g1 = g1.
  37 #n @(nat_ind_succ … n) -n /2 width=1 by conj/
  38 #n #IH #f2 #g1 #H
  39 elim (pr_eq_inv_push_dx … H) -H [|*: // ] #Hf02 *
  40 elim (IH … Hf02) -IH -Hf02 #Hf12 #H2
  41 <pr_tls_succ /2 width=1 by conj/
  42 qed-.