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/tr_pn_tls.ma".
16 include "ground/relocation/tr_pap_pn.ma".
17 include "ground/relocation/tr_compose.ma".
19 (* COMPOSITION FOR PARTIAL RELOCATION MAPS **********************************)
21 (* Constructions with tr_push anf tr_next ***********************************)
24 lemma tr_compose_next_sn (f2) (f1):
25 ∀f. f2∘f1 = f → (↑f2)∘f1 = ↑f.
27 <tr_compose_unfold <tr_compose_unfold * -f
29 /3 width=1 by compose_repl_fwd_dx/
32 (* Inversions with tr_push anf tr_next **************************************)
34 (*** compose_inv_O2 *)
35 lemma tr_compose_inv_push_dx (f2) (f1):
36 ∀f,p2,p. (p2⨮f2)∘(⫯f1) = p⨮f →
37 ∧∧ p2 = p & f2∘f1 = f.
39 <tr_compose_unfold #H destruct
43 (*** compose_inv_S1 *)
44 lemma tr_compose_inv_next_sn (f2) (f1):
45 ∀f,p1,p. (↑f2)∘(p1⨮f1) = p⨮f →
46 ∧∧ ↑(f2@❨p1❩) = p & f2∘(p1⨮f1) = f2@❨p1❩⨮f.
48 <tr_compose_unfold #H destruct