1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 include "ground/relocation/gr_tls.ma".
16 include "ground/relocation/gr_pat.ma".
17 include "ground/relocation/gr_after.ma".
19 (* RELATIONAL COMPOSITION FOR GENERIC RELOCATION MAPS ***********************************************************)
21 (* Properties on pat and tls ********************************************************)
23 (* Note: this requires ↑ on first n *)
25 lemma gr_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 (gr_pat_inv_unit_succ … Hf1) -Hf1 [ |*: // ] #g1 #Hg1 #H1
31 cases (gr_after_inv_next_sn … Hf … H1) -Hf #g #Hg #H0 destruct
32 <gr_tls_swap <gr_tls_swap /2 width=1 by/