]> matita.cs.unibo.it Git - helm.git/blob - matita/matita/contribs/lambdadelta/ground/relocation/pr_after_pat_tls.ma
update in delayed_updating
[helm.git] / matita / matita / contribs / lambdadelta / ground / relocation / pr_after_pat_tls.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_tls.ma".
16 include "ground/relocation/pr_pat.ma".
17 include "ground/relocation/pr_after.ma".
18
19 (* RELATIONAL COMPOSITION FOR PARTIAL RELOCATION MAPS ***********************)
20
21 (* Constructions with pr_pat and pr_tls *************************************)
22
23 (* Note: this requires ↑ on first n *)
24 (*** after_tls *)
25 lemma pr_after_tls_sn_tls (n):
26       ∀f1,f2,f. @❨𝟏, f1❩ ≘ ↑n →
27       f1 ⊚ f2 ≘ f → ⫰*[n]f1 ⊚ f2 ≘ ⫰*[n]f.
28 #n @(nat_ind_succ … n) -n //
29 #n #IH #f1 #f2 #f #Hf1 #Hf
30 cases (pr_pat_inv_unit_succ … Hf1) -Hf1 [ |*: // ] #g1 #Hg1 #H1
31 cases (pr_after_inv_next_sn … Hf … H1) -Hf #g #Hg #H0 destruct
32 <pr_tls_swap <pr_tls_swap /2 width=1 by/
33 qed.