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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_height.ma".
16 include "delayed_updating/syntax/path_structure.ma".
18 (* CLOSED CONDITION FOR PATH ************************************************)
20 (* Constructions with structure *********************************************)
22 lemma path_closed_structure_height (p) (n):
23 p ϵ 𝐂❨n❩ → ⊗p ϵ 𝐂❨♯p+n❩.
24 #p #n #Hn elim Hn -Hn //
25 #p #n #_ #IH [ <nplus_succ_dx ]
26 /2 width=1 by pcc_L_dx, pcc_A_dx, pcc_S_dx/
29 lemma path_closed_structure_depth (p) (n):
30 p ϵ 𝐂❨n❩ → ⊗p ϵ 𝐂❨♭p❩.
31 #p #n #Hp <path_closed_depth
32 /2 width=3 by path_closed_structure_height/