matita/matita/contribs/lambdadelta/static_2/syntax/term_weight.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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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 "static_2/notation/functions/weight_1.ma".
  16 include "static_2/syntax/term.ma".
  17
  18 (* WEIGHT OF A TERM *********************************************************)
  19
  20 rec definition tw T ≝ match T with
  21 [ TAtom _     ⇒ 1
  22 | TPair _ V T ⇒ ↑(tw V + tw T)
  23 ].
  24
  25 interpretation "weight (term)" 'Weight T = (tw T).
  26
  27 (* Basic properties *********************************************************)
  28
  29 (* Basic_1: was: tweight_lt *)
  30 lemma tw_pos: ∀T. 1 ≤ ♯❨T❩.
  31 #T elim T -T //
  32 qed.
  33
  34 lemma tw_le_pair_dx (I): ∀V,T. ♯❨T❩ < ♯❨②[I]V.T❩.
  35 #I #V #T /2 width=1 by le_S_S/
  36 qed.
  37
  38 (* Basic_1: removed theorems 11:
  39             wadd_le wadd_lt wadd_O weight_le weight_eq weight_add_O
  40             weight_add_S tlt_trans tlt_head_sx tlt_head_dx tlt_wf_ind
  41 *)
  42 (* Basic_1: removed local theorems 1: q_ind *)