matita/matita/contribs/lambdadelta/delayed_updating/syntax/path_depth.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "delayed_updating/syntax/path.ma".
  16 include "ground/arith/nat_succ.ma".
  17 include "ground/notation/functions/verticalbars_1.ma".
  18
  19 (* DEPTH FOR PATH ***********************************************************)
  20
  21 rec definition depth (p) on p: nat ≝
  22 match p with
  23 [ list_empty     ⇒ 𝟎
  24 | list_lcons l q ⇒
  25   match l with
  26   [ label_node_d _ ⇒ depth q
  27   | label_edge_L   ⇒ ↑(depth q)
  28   | label_edge_A   ⇒ depth q
  29   | label_edge_S   ⇒ depth q
  30   ]
  31 ].
  32
  33 interpretation
  34   "depth (path)"
  35   'VerticalBars p = (depth p).
  36
  37 (* Basic constructions ******************************************************)
  38
  39 lemma depth_empty: 𝟎 = ❘𝐞❘.
  40 // qed.
  41
  42 lemma depth_d (q) (n): ❘q❘ = ❘𝗱n◗q❘.
  43 // qed.
  44
  45 lemma depth_L (q): ↑❘q❘ = ❘𝗟◗q❘.
  46 // qed.
  47
  48 lemma depth_A (q): ❘q❘ = ❘𝗔◗q❘.
  49 // qed.
  50
  51 lemma depth_S (q): ❘q❘ = ❘𝗦◗q❘.
  52 // qed.