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_uni_pap.ma".
16 include "ground/relocation/tr_id_compose.ma".
17 include "ground/relocation/tr_compose_pn.ma".
18 include "ground/lib/stream_hdtl_eq.ma".
20 (* UNIFORM ELEMENTS FOR TOTAL RELOCATION MAPS *******************************)
22 (* Constructions with tr_compose and tr_next ********************************)
24 lemma tr_compose_uni_unit_sn (f):
25 āf ā š®āØšā©āf.
26 #f >nsucc_zero <tr_uni_succ //
29 (* Constructions with tr_compose and tr_tl **********************************)
31 lemma tr_tl_compose_uni_sn (n) (f):
32 āf ā ā(š®āØnā©āf).
33 #n @(nat_ind_succ ā¦ n) -n //
34 /2 width=1 by stream_tl_eq_repl/
37 (* Constructions with tr_compose and tr_tls *********************************)
39 lemma tr_tls_compose_uni_sn (f) (n) (p:pnat):
40 ā*[p]f ā ā*[p](š®āØnā©āf).
42 #p #IH /2 width=1 by stream_tl_eq_repl/
45 lemma tr_tl_compose_uni_dx (f) (n):
46 ā*[ān]f ā ā(fāš®āØnā©).
49 lemma tr_tls_compose_uni_dx (f) (p) (n):
50 ā*[p+n]f ā ā*[p](fāš®āØnā©).
51 #f #p elim p -p [| #p #IH ] #n
53 | <nrplus_succ_sn >nsucc_inj >nsucc_inj
54 /2 width=3 by stream_tl_eq_repl/
58 (* Main constructions with tr_compose and tr_tls ****************************)
60 theorem tr_compose_uni_dx_pap (f) (p):
61 (š®āØfļ¼ ā§£āØpā©ā©āā*[p]f) ā fāš®āØpā©.
63 @nstream_eq_inv_ext #q
64 <tr_compose_pap <tr_compose_pap
65 <tr_uni_pap <tr_uni_pap