1 (**************************************************************************)
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 *)
13 (**************************************************************************)
15 include "ground/arith/nat_plus.ma".
16 include "delayed_updating/syntax/path.ma".
17 include "delayed_updating/notation/functions/sharp_1.ma".
19 (* HEIGHT FOR PATH **********************************************************)
21 rec definition height (p) on p: nat ≝
26 [ label_d k ⇒ height q + k
36 'Sharp p = (height p).
38 (* Basic constructions ******************************************************)
40 lemma height_empty: 𝟎 = ♯𝐞.
43 lemma height_d_dx (p) (k:pnat):
47 lemma height_m_dx (p):
51 lemma height_L_dx (p):
55 lemma height_A_dx (p):
59 lemma height_S_dx (p):
63 (* Main constructions *******************************************************)
65 theorem height_append (p) (q):
68 * [ #k ] #q #IH <list_append_lcons_sn
69 [ <height_d_dx <height_d_dx //
70 | <height_m_dx <height_m_dx //
71 | <height_L_dx <height_L_dx //
72 | <height_A_dx <height_A_dx //
73 | <height_S_dx <height_S_dx //
77 (* Constructions with path_lcons ********************************************)
79 lemma height_d_sn (p) (k:pnat):
83 lemma height_m_sn (p):
87 lemma height_L_sn (p):
91 lemma height_A_sn (p):
95 lemma height_S_sn (p):