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

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
   7 (*      ||T||         The HELM team.                                      *)
   8 (*      ||A||         http://helm.cs.unibo.it                             *)
   9 (*      \   /                                                             *)
  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/syntax/bind_weight.ma".
  16 include "static_2/syntax/lenv.ma".
  17
  18 (* WEIGHT OF A LOCAL ENVIRONMENT ********************************************)
  19
  20 rec definition lw L ≝ match L with
  21 [ LAtom     ⇒ 𝟏
  22 | LBind L I ⇒ lw L + ♯❨I❩
  23 ].
  24
  25 interpretation "weight (local environment)" 'Weight L = (lw L).
  26
  27 (* Basic properties *********************************************************)
  28
  29 lemma lw_atom_unfold: 𝟏 = ♯❨⋆❩.
  30 // qed.
  31
  32 lemma lw_bind_unfold (I) (L): ♯❨L❩ + ♯❨I❩ = ♯❨L.ⓘ[I]❩.
  33 // qed.
  34
  35 (* Basic_2A1: uses: lw_pair *)
  36 lemma lw_bind: ∀I,L. ♯❨L❩ < ♯❨L.ⓘ[I]❩.
  37 // qed.
  38
  39 (* Basic_1: removed theorems 4: clt_cong clt_head clt_thead clt_wf_ind *)
  40 (* Basic_1: removed local theorems 1: clt_wf__q_ind *)
  41 (* Basic_1: note: clt_thead should be renamed clt_ctail *)