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_head_depth.ma".
16 include "delayed_updating/syntax/path_structure_labels.ma".
18 (* HEAD FOR PATH ************************************************************)
20 (* Constructions with structure *********************************************)
22 lemma path_head_structure_height (p) (m):
23 ⊗↳[m]p = ↳[m+♯↳[m]p]⊗p.
25 #l #p #IH #m @(nat_ind_succ … m) -m //
27 [ <height_d_sn <structure_d_sn //
30 | <height_A_sn <structure_A_sn <nplus_succ_sn <path_head_A_sn //
31 | <height_S_sn <structure_S_sn <nplus_succ_sn <path_head_S_sn //
35 lemma path_head_structure_depth (p) (m):