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 TOTAL RELOCATION MAPS ************************************)
21 (* Constructions with tr_push and tr_next ***********************************)
23 lemma tr_compose_push_bi (f2) (f1):
24 (⫯(f2∘f1)) = (⫯f2)∘(⫯f1).
29 lemma tr_compose_push_next (f2) (f1):
30 ↑(f2∘f1) = (⫯f2)∘(↑f1).
32 <tr_next_unfold <tr_compose_unfold <tr_compose_unfold <tr_next_unfold
33 <tr_pap_push >nsucc_inj //
36 (* Note: to be removed *)
38 fact tr_compose_next_sn_aux (f2) (f1):
39 ∀f. f2∘f1 = f → (↑f2)∘f1 = ↑f.
41 <tr_compose_unfold <tr_compose_unfold * -f
43 /3 width=1 by compose_repl_fwd_dx/
46 lemma tr_compose_next_sn (f2) (f1):
48 /2 width=1 by tr_compose_next_sn_aux/ qed.
50 (* Inversions with tr_push and tr_next **************************************)
52 (*** compose_inv_O2 *)
53 lemma tr_compose_inv_push_dx (f2) (f1):
54 ∀f,p2,p. (p2⨮f2)∘(⫯f1) = p⨮f →
55 ∧∧ p2 = p & f2∘f1 = f.
57 <tr_compose_unfold #H destruct
61 (*** compose_inv_S1 *)
62 lemma tr_compose_inv_next_sn (f2) (f1):
63 ∀f,p1,p. (↑f2)∘(p1⨮f1) = p⨮f →
64 ∧∧ ↑(f2@⧣❨p1❩) = p & f2∘(p1⨮f1) = f2@⧣❨p1❩⨮f.
66 <tr_compose_unfold #H destruct