matita/matita/contribs/lambdadelta/ground/relocation/pr_after_pat_tls.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.ma".
  16 include "ground/relocation/pr_pat.ma".
  17 include "ground/relocation/pr_after.ma".
  18
  19 (* RELATIONAL COMPOSITION FOR PARTIAL RELOCATION MAPS ***********************)
  20
  21 (* Constructions with pr_pat and pr_tls *************************************)
  22
  23 (* Note: this requires ↑ on first n *)
  24 (*** after_tls *)
  25 lemma pr_after_tls_sn_tls (n):
  26       ∀f1,f2,f. @❨𝟏, f1❩ ≘ ↑n →
  27       f1 ⊚ f2 ≘ f → ⫰*[n]f1 ⊚ f2 ≘ ⫰*[n]f.
  28 #n @(nat_ind_succ … n) -n //
  29 #n #IH #f1 #f2 #f #Hf1 #Hf
  30 cases (pr_pat_inv_unit_succ … Hf1) -Hf1 [ |*: // ] #g1 #Hg1 #H1
  31 cases (pr_after_inv_next_sn … Hf … H1) -Hf #g #Hg #H0 destruct
  32 <pr_tls_swap <pr_tls_swap /2 width=1 by/
  33 qed.