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

   1 (**************************************************************************)
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   3 (*      ||M||                                                             *)
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  11 (*        v         GNU General Public License Version 2                  *)
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  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_d _ ⇒ depth q
  27   | label_m   ⇒ depth q
  28   | label_L   ⇒ ↑(depth q)
  29   | label_A   ⇒ depth q
  30   | label_S   ⇒ depth q
  31   ]
  32 ].
  33
  34 interpretation
  35   "depth (path)"
  36   'VerticalBars p = (depth p).
  37
  38 (* Basic constructions ******************************************************)
  39
  40 lemma depth_empty: 𝟎 = ❘𝐞❘.
  41 // qed.
  42
  43 lemma depth_d (q) (n): ❘q❘ = ❘𝗱n◗q❘.
  44 // qed.
  45
  46 lemma depth_m (q): ❘q❘ = ❘𝗺◗q❘.
  47 // qed.
  48
  49 lemma depth_L (q): ↑❘q❘ = ❘𝗟◗q❘.
  50 // qed.
  51
  52 lemma depth_A (q): ❘q❘ = ❘𝗔◗q❘.
  53 // qed.
  54
  55 lemma depth_S (q): ❘q❘ = ❘𝗦◗q❘.
  56 // qed.