+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||M|| *)
-(* ||A|| A project by Andrea Asperti *)
-(* ||T|| *)
-(* ||I|| Developers: *)
-(* ||T|| The HELM team. *)
-(* ||A|| http://helm.cs.unibo.it *)
-(* \ / *)
-(* \ / This file is distributed under the terms of the *)
-(* v GNU General Public License Version 2 *)
-(* *)
-(**************************************************************************)
-
-include "delayed_updating/syntax/path_closed.ma".
-include "delayed_updating/syntax/path_height.ma".
-include "delayed_updating/syntax/path_depth.ma".
-
-(* CLOSED CONDITION FOR PATH ************************************************)
-
-(* Destructions with height and depth ***************************************)
-
-lemma path_closed_des_depth (o) (q) (n):
- q ϵ 𝐂❨o,n❩ → ♯q + n = ♭q.
-#o #q #n #Hq elim Hq -q -n //
-#q #n #_ #IH <nplus_succ_dx //
-qed-.
-
-lemma path_closed_des_succ_depth (o) (q) (n):
- q ϵ 𝐂❨o,↑n❩ → ♭q = ↑↓♭q.
-#o #q #n #Hq
-<(path_closed_des_depth … Hq) -Hq
-<nplus_succ_dx <npred_succ //
-qed-.