matita/matita/contribs/lambdadelta/ground/relocation/tr_compose_pn.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/tr_pn_tls.ma".
  16 include "ground/relocation/tr_pap_pn.ma".
  17 include "ground/relocation/tr_compose.ma".
  18
  19 (* COMPOSITION FOR PARTIAL RELOCATION MAPS **********************************)
  20
  21 (* Constructions with tr_push anf tr_next ***********************************)
  22
  23 (*** compose_next *)
  24 lemma tr_compose_next_sn (f2) (f1):
  25       ∀f. f2∘f1 = f → (↑f2)∘f1 = ↑f.
  26 #f2 * #p1 #f1 #f
  27 <tr_compose_unfold <tr_compose_unfold * -f
  28 <tr_pap_next
  29 /3 width=1 by compose_repl_fwd_dx/
  30 qed.
  31
  32 (* Inversions with tr_push anf tr_next **************************************)
  33
  34 (*** compose_inv_O2 *)
  35 lemma tr_compose_inv_push_dx (f2) (f1):
  36       ∀f,p2,p. (p2⨮f2)∘(⫯f1) = p⨮f →
  37       ∧∧ p2 = p & f2∘f1 = f.
  38 #f2 #f1 #f #p2 #p
  39 <tr_compose_unfold #H destruct
  40 /2 width=1 by conj/
  41 qed-.
  42
  43 (*** compose_inv_S1 *)
  44 lemma tr_compose_inv_next_sn (f2) (f1):
  45       ∀f,p1,p. (↑f2)∘(p1⨮f1) = p⨮f →
  46       ∧∧ ↑(f2@❨p1❩) = p & f2∘(p1⨮f1) = f2@❨p1❩⨮f.
  47 #f2 #f1 #f #p1 #p
  48 <tr_compose_unfold #H destruct
  49 /2 width=1 by conj/
  50 qed-.