matita/matita/contribs/lambdadelta/static_2/syntax/term_weight.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 "ground/arith/pnat_lt_plus.ma".
  16 include "static_2/notation/functions/weight_1.ma".
  17 include "static_2/syntax/term.ma".
  18
  19 (* WEIGHT OF A TERM *********************************************************)
  20
  21 rec definition tw T ≝ match T with
  22 [ TAtom _     ⇒ 𝟏
  23 | TPair _ V T ⇒ ↑(tw V + tw T)
  24 ].
  25
  26 interpretation "weight (term)" 'Weight T = (tw T).
  27
  28 (* Basic properties *********************************************************)
  29
  30 lemma tw_atom_unfold (I): 𝟏 = ♯❨⓪[I]❩.
  31 // qed.
  32
  33 lemma tw_pair_unfold (I) (V) (T): ↑(♯❨V❩ + ♯❨T❩) = ♯❨②[I]V.T❩.
  34 // qed.
  35
  36 lemma tw_le_pair_dx (I): ∀V,T. ♯❨T❩ < ♯❨②[I]V.T❩.
  37 /2 width=1 by plt_succ_dx_trans/
  38 qed.
  39
  40 (* Basic_1: removed theorems 12:
  41             tweight_lt
  42             wadd_le wadd_lt wadd_O weight_le weight_eq weight_add_O
  43             weight_add_S tlt_trans tlt_head_sx tlt_head_dx tlt_wf_ind
  44 *)
  45 (* Basic_1: removed local theorems 1: q_ind *)