matita/matita/contribs/lambdadelta/basic_2/grammar/cl_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 "basic_2/notation/functions/weight_3.ma".
  16 include "basic_2/grammar/genv.ma". (**) (* including genv after lenv shows a disambiguation bug: only the last interpretation is considered *)
  17 include "basic_2/grammar/lenv_weight.ma".
  18 include "basic_2/grammar/cl_shift.ma".
  19
  20 (* WEIGHT OF A CLOSURE ******************************************************)
  21
  22 (* activate genv *)
  23 definition fw: genv → lenv → term → ? ≝ λG,L,T. ♯{L} + ♯{T}.
  24
  25 interpretation "weight (closure)" 'Weight G L T = (fw G L T).
  26
  27 (* Basic properties *********************************************************)
  28
  29 (* Basic_1: was: flt_shift *)
  30 lemma fw_shift: ∀a,I,G,K,V,T. ♯{G, K.ⓑ{I}V, T} < ♯{G, K, ⓑ{a,I}V.T}.
  31 normalize //
  32 qed.
  33
  34 lemma fw_tpair_sn: ∀I,G,L,V,T. ♯{G, L, V} < ♯{G, L, ②{I}V.T}.
  35 normalize in ⊢ (?→?→?→?→?→?%%); //
  36 qed.
  37
  38 lemma fw_tpair_dx: ∀I,G,L,V,T. ♯{G, L, T} < ♯{G, L, ②{I}V.T}.
  39 normalize in ⊢ (?→?→?→?→?→?%%); //
  40 qed.
  41
  42 lemma fw_lpair_sn: ∀I,G,L,V,T. ♯{G, L, V} < ♯{G, L.ⓑ{I}V, T}.
  43 normalize /3 width=1 by monotonic_lt_plus_l, monotonic_le_plus_r/ (**) (* auto too slow without trace *)
  44 qed.
  45
  46 (* Basic_1: removed theorems 7:
  47             flt_thead_sx flt_thead_dx flt_trans
  48             flt_arith0 flt_arith1 flt_arith2 flt_wf_ind
  49 *)
  50 (* Basic_1: removed local theorems 1: q_ind *)