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 "delayed_updating/syntax/path_tail.ma".
16 include "delayed_updating/syntax/path_depth.ma".
17 include "delayed_updating/syntax/path_height.ma".
19 include "ground/arith/nat_plus.ma".
20 include "ground/arith/nat_pred_succ.ma".
22 (* TAIL FOR PATH ************************************************************)
24 (* Constructions with depth and height **************************************)
26 axiom depth_lablels_L (n):
29 axiom height_lablels_L (n):
32 lemma tail_depth (p) (n):
33 n + ♯(↳[n]p) = ♭↳[n]p.
34 #p elim p -p // #l #p #IH
35 #n @(nat_ind_succ … n) -n // #n #_
37 [ <tail_d_sn <height_d_sn <depth_d_sn //
38 | <tail_m_sn <height_m_sn <depth_m_sn //
39 | <tail_L_sn <height_L_sn <depth_L_sn
41 | <tail_A_sn <height_A_sn <depth_A_sn //
42 | <tail_S_sn <height_S_sn <depth_S_sn //