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_tl **********************************)
24 lemma tr_tl_compose_uni_sn (n) (f):
25 āf ā ā(š®āØnā©āf).
26 #n @(nat_ind_succ ā¦ n) -n //
27 /2 width=1 by stream_tl_eq_repl/
30 (* Constructions with tr_compose and tr_tls *********************************)
32 lemma tr_tls_compose_uni_sn (f) (n) (p:pnat):
33 ā*[p]f ā ā*[p](š®āØnā©āf).
35 #p #IH /2 width=1 by stream_tl_eq_repl/
38 lemma tr_tl_compose_uni_dx (f) (n):
39 ā*[ān]f ā ā(fāš®āØnā©).
42 lemma tr_tls_compose_uni_dx (f) (p) (n):
43 ā*[p+n]f ā ā*[p](fāš®āØnā©).
44 #f #p elim p -p [| #p #IH ] #n
46 | <nrplus_succ_sn >nsucc_inj >nsucc_inj
47 /2 width=3 by stream_tl_eq_repl/
51 (* Main constructions with tr_compose and tr_tls ****************************)
53 theorem tr_compose_uni_dx (f) (p):
54 (š®āØfļ¼ ā§£āØpā©ā©āā*[p]f) ā fāš®āØpā©.
56 @nstream_eq_inv_ext #q
57 <tr_compose_pap <tr_compose_pap
58 <tr_uni_pap <tr_uni_pap