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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 *)
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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 (* Destructions with height and depth ***************************************)
23 lemma path_closed_des_depth (o) (e) (q) (n):
24 q ϵ 𝐂❨o,n,e❩ → ♯q + n = ♭q + e.
25 #o #e #q #n #Hq elim Hq -q -n //
27 <nplus_succ_dx <nplus_succ_sn //
30 lemma path_closed_des_succ_zero_depth (o) (q) (n):
31 q ϵ 𝐂❨o,↑n,𝟎❩ → ♭q = ↑↓♭q.
34 <(path_closed_des_depth … Hq) -Hq
35 <nplus_succ_dx <npred_succ //