matita/matita/contribs/lambdadelta/ground/relocation/gr_coafter_nat_tls.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  13 (**************************************************************************)
  14
  15 include "ground/relocation/gr_tls.ma".
  16 include "ground/relocation/gr_nat.ma".
  17 include "ground/relocation/gr_coafter.ma".
  18
  19 (* RELATIONAL CO-COMPOSITION FOR GENERIC RELOCATION MAPS ********************)
  20
  21 (* Constructions with gr_nat and gr_tls *************************************)
  22
  23 (*** coafter_tls *)
  24 lemma gr_coafter_tls_bi_tls (n2) (n1):
  25       ∀f1,f2,f. @↑❪n1, f1❫ ≘ n2 →
  26       f1 ~⊚ f2 ≘ f → ⫰*[n2]f1 ~⊚ ⫰*[n1]f2 ≘ ⫰*[n2]f.
  27 #n2 @(nat_ind_succ … n2) -n2 [ #n1 | #n2 #IH * [| #n1 ] ] #f1 #f2 #f #Hf1 #Hf
  28 [ elim (gr_nat_inv_zero_dx … Hf1) -Hf1 [ |*: // ] #g1 #Hg1 #H1 destruct //
  29 | elim (gr_nat_inv_zero_succ … Hf1) -Hf1 [ |*: // ] #g1 #Hg1 #H1
  30   elim (gr_coafter_inv_next_sn … Hf … H1) -Hf #g #Hg #H0 destruct
  31   lapply (IH … Hg1 Hg) -IH -Hg1 -Hg //
  32 | elim (gr_nat_inv_succ_dx … Hf1) -Hf1 [1,3: * |*: // ] #g1 [ #n1 ] #Hg1 [ #H ] #H1
  33   [ elim (gr_coafter_inv_push_sn … Hf … H1) -Hf * #g2 #g #Hg #H2 #H0 destruct
  34     lapply (IH … Hg1 Hg) -IH -Hg1 -Hg #H //
  35   | elim (gr_coafter_inv_next_sn … Hf … H1) -Hf #g #Hg #H0 destruct
  36     lapply (IH … Hg1 Hg) -IH -Hg1 -Hg #H //
  37   ]
  38 ]
  39 qed.
  40
  41 (*** coafter_tls_O *)
  42 lemma gr_coafter_tls_sn_tls:
  43       ∀n,f1,f2,f. @↑❪𝟎, f1❫ ≘ n →
  44       f1 ~⊚ f2 ≘ f → ⫰*[n]f1 ~⊚ f2 ≘ ⫰*[n]f.
  45 /2 width=1 by gr_coafter_tls_bi_tls/ qed.