+++ /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_head_depth.ma".
-include "delayed_updating/syntax/path_structure_labels.ma".
-
-(* HEAD FOR PATH ************************************************************)
-
-(* Constructions with structure *********************************************)
-
-lemma path_head_structure_height (p) (n):
- ⊗↳[n]p = ↳[n+♯↳[n]p]⊗p.
-#p elim p -p //
-#l #p #IH #n @(nat_ind_succ … n) -n //
-#n #_ cases l [ #k ]
-[ <height_d_dx <structure_d_dx //
-| <structure_m_dx //
-| <structure_L_dx //
-| <height_A_dx <structure_A_dx <nplus_succ_sn <path_head_A_dx //
-| <height_S_dx <structure_S_dx <nplus_succ_sn <path_head_S_dx //
-]
-qed.
-
-lemma path_head_structure_depth (p) (n):
- ⊗↳[n]p = ↳[♭↳[n]p]⊗p.
-#p #n
-<path_head_depth //
-qed.