matita/matita/contribs/lambdadelta/ground/relocation/pr_sdj_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_tl_eq.ma".
  16 include "ground/relocation/pr_sdj.ma".
  17
  18 (* DISJOINTNESS FOR PARTIAL RELOCATION MAPS *********************************)
  19
  20 (* Constructions with pr_eq *************************************************)
  21
  22 (*** sdj_eq_repl_back1 *)
  23 corec lemma pr_sdj_eq_repl_back_sn:
  24             ∀f2. pr_eq_repl_back … (λf1. f1 ∥ f2).
  25 #f2 #f1 * -f2 -f1
  26 #f1 #f2 #g1 #g2 #Hf #H1 #H2 #g #H0
  27 [ cases (pr_eq_inv_push_sn …  H0 …  H1) -g1 /3 width=5 by pr_sdj_push_bi/
  28 | cases (pr_eq_inv_next_sn …  H0 …  H1) -g1 /3 width=5 by pr_sdj_next_push/
  29 | cases (pr_eq_inv_push_sn …  H0 …  H1) -g1 /3 width=5 by pr_sdj_push_next/
  30 ]
  31 qed-.
  32
  33 (*** sdj_eq_repl_fwd1 *)
  34 lemma pr_sdj_eq_repl_fwd_sn:
  35       ∀f2. pr_eq_repl_fwd … (λf1. f1 ∥ f2).
  36 #f2 @pr_eq_repl_sym /2 width=3 by pr_sdj_eq_repl_back_sn/
  37 qed-.
  38
  39 (*** sdj_eq_repl_back2 *)
  40 corec lemma pr_sdj_eq_repl_back_dx:
  41             ∀f1. pr_eq_repl_back … (λf2. f1 ∥ f2).
  42 #f1 #f2 * -f1 -f2
  43 #f1 #f2 #g1 #g2 #Hf #H1 #H2 #g #H0
  44 [ cases (pr_eq_inv_push_sn …  H0 …  H2) -g2 /3 width=5 by pr_sdj_push_bi/
  45 | cases (pr_eq_inv_push_sn …  H0 …  H2) -g2 /3 width=5 by pr_sdj_next_push/
  46 | cases (pr_eq_inv_next_sn …  H0 …  H2) -g2 /3 width=5 by pr_sdj_push_next/
  47 ]
  48 qed-.
  49
  50 (*** sdj_eq_repl_fwd2 *)
  51 lemma pr_sdj_eq_repl_fwd_dx:
  52       ∀f1. pr_eq_repl_fwd … (λf2. f1 ∥ f2).
  53 #f1 @pr_eq_repl_sym /2 width=3 by pr_sdj_eq_repl_back_dx/
  54 qed-.