matita/matita/contribs/lambdadelta/ground/relocation/gr_coafter_nat_tls_pushs.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/gr_pushs.ma".
  16 include "ground/relocation/gr_tls.ma".
  17 include "ground/relocation/gr_nat.ma".
  18 include "ground/relocation/gr_coafter.ma".
  19
  20 (* RELATIONAL CO-COMPOSITION FOR GENERIC RELOCATION MAPS ********************)
  21
  22 (* Destructions with gr_nat and gr_tls and gr_pushs *************************)
  23
  24 (*** coafter_fwd_pushs *)
  25 lemma gr_coafter_des_pushs_dx (n) (m):
  26       ∀g2,f1,g. g2 ~⊚ ⫯*[m]f1 ≘ g → @↑❪m, g2❫ ≘ n →
  27       ∃∃f. ⫱*[n]g2 ~⊚ f1 ≘ f & ⫯*[n] f = g.
  28 #n @(nat_ind_succ … n) -n
  29 [ #m #g2 #f1 #g #Hg #H
  30   elim (gr_nat_inv_zero_dx … H) -H [|*: // ] #f2 #H1 #H2 destruct
  31   /2 width=3 by ex2_intro/
  32 | #n #IH * [| #m ] #g2 #f1 #g #Hg #H
  33   [ elim (gr_nat_inv_zero_succ … H) -H [|*: // ] #f2 #Hmn #H destruct
  34     elim (gr_coafter_inv_next_sn … Hg) -Hg [|*: // ] #f #Hf #H destruct
  35     elim (IH … Hf Hmn) -IH -Hf -Hmn /2 width=3 by ex2_intro/
  36   | elim (gr_nat_inv_succ_bi … H) -H [1,4: * |*: // ] #f2 #Hmn #H destruct
  37     [ elim (gr_coafter_inv_push_bi … Hg) -Hg [|*: // ] #f #Hf #H destruct
  38       elim (IH … Hf Hmn) -IH -Hf -Hmn /2 width=3 by ex2_intro/
  39     | elim (gr_coafter_inv_next_sn … Hg) -Hg [|*: // ] #f #Hf #H destruct
  40       elim (IH … Hf Hmn) -IH -Hf -Hmn /2 width=3 by ex2_intro/
  41     ]
  42   ]
  43 ]
  44 qed-.