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_closed.ma".
16 include "delayed_updating/syntax/path_height.ma".
17 include "delayed_updating/syntax/path_depth.ma".
19 (* CLOSED CONDITION FOR PATH ************************************************)
21 (* Constructions with height and depth **************************************)
23 lemma path_closed_depth (p) (n):
24 p ϵ 𝐂❨n❩ → ♯p + n = ♭p.
25 #p #n #Hn elim Hn -Hn //
26 #p #n #_ #IH <nplus_succ_dx //