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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.ma".
16 include "delayed_updating/notation/functions/flat_1.ma".
17 include "ground/arith/nat_plus.ma".
19 (* DEPTH FOR PATH ***********************************************************)
21 rec definition depth (p) on p: nat ≝
28 | label_L ⇒ ↑(depth q)
38 (* Basic constructions ******************************************************)
40 lemma depth_empty: 𝟎 = ♭𝐞.
43 lemma depth_d_dx (p) (k):
63 (* Main constructions *******************************************************)
65 theorem depth_append (p) (q):
68 * [ #k ] #q #IH <list_append_lcons_sn
69 [ <depth_d_dx <depth_d_dx //
70 | <depth_m_dx <depth_m_dx //
71 | <depth_L_dx <depth_L_dx //
72 | <depth_A_dx <depth_A_dx //
73 | <depth_S_dx <depth_S_dx //
77 (* Constructions with path_lcons ********************************************)
79 lemma depth_d_sn (p) (k):