(**************************************************************************)
include "delayed_updating/syntax/path_head.ma".
-include "delayed_updating/syntax/path_depth_labels.ma".
include "delayed_updating/syntax/path_height_labels.ma".
+include "delayed_updating/syntax/path_depth_labels.ma".
(* HEAD FOR PATH ************************************************************)
n + ♯(↳[n]p) = ♭↳[n]p.
#p elim p -p // #l #p #IH
#n @(nat_ind_succ … n) -n // #n #_
-cases l [ #m ]
-[ <path_head_d_sn <height_d_sn <depth_d_sn //
-| <path_head_m_sn <height_m_sn <depth_m_sn //
-| <path_head_L_sn <height_L_sn <depth_L_sn
+cases l [ #k ]
+[ <path_head_d_dx <height_d_dx <depth_d_dx <IH //
+| <path_head_m_dx <height_m_dx <depth_m_dx //
+| <path_head_L_dx <height_L_dx <depth_L_dx
<nplus_succ_sn //
-| <path_head_A_sn <height_A_sn <depth_A_sn //
-| <path_head_S_sn <height_S_sn <depth_S_sn //
+| <path_head_A_dx <height_A_dx <depth_A_dx //
+| <path_head_S_dx <height_S_dx <depth_S_dx //
]
-qed.
+qed-. (**) (* gets in the way with auto *)