matita/matita/contribs/lambdadelta/ground/relocation/pr_after_ist_isi.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_ist_isi.ma".
  16 include "ground/relocation/pr_after_ist.ma".
  17
  18 (* RELATIONAL COMPOSITION FOR PARTIAL RELOCATION MAPS ***********************)
  19
  20 (* Destructions with pr_ist and pr_isi **************************************)
  21
  22 (*** after_fwd_isid_sn *)
  23 lemma pr_after_des_ist_eq_sn:
  24       ∀f2,f1,f. 𝐓❨f❩ → f2 ⊚ f1 ≘ f → f1 ≡ f → 𝐈❨f2❩.
  25 #f2 #f1 #f #H #Hf elim (pr_after_inv_ist … Hf H) -H
  26 #Hf2 #Hf1 #H @pr_isi_pat_total // -Hf2
  27 #i2 #i #Hf2 elim (Hf1 i2) -Hf1
  28 #i0 #Hf1 lapply (pr_pat_increasing … Hf1)
  29 #Hi20 lapply (pr_after_des_pat_sn … i0 … Hf1 … Hf) -Hf
  30 /3 width=7 by pr_pat_eq_repl_back, pr_pat_mono, pr_pat_id_le/
  31 qed-.
  32
  33 (*** after_fwd_isid_dx *)
  34 lemma pr_after_des_ist_eq_dx:
  35       ∀f2,f1,f.  𝐓❨f❩ → f2 ⊚ f1 ≘ f → f2 ≡ f → 𝐈❨f1❩.
  36 #f2 #f1 #f #H #Hf elim (pr_after_inv_ist … Hf H) -H
  37 #Hf2 #Hf1 #H2 @pr_isi_pat_total // -Hf1
  38 #i1 #i2 #Hi12 elim (pr_after_des_ist_pat … Hi12 … Hf) -f1
  39 /3 width=8 by pr_pat_inj, pr_pat_eq_repl_back/
  40 qed-.