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

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   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                  *)
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  13 (**************************************************************************)
  14
  15 include "static_2/notation/functions/weight_3.ma".
  16 include "static_2/syntax/lenv_weight.ma".
  17 include "static_2/syntax/genv.ma".
  18
  19 (* WEIGHT OF A CLOSURE ******************************************************)
  20
  21 (* activate genv *)
  22 definition fw: genv → lenv → term → ? ≝ λG,L,T. ♯❨L❩ + ♯❨T❩.
  23
  24 interpretation "weight (closure)" 'Weight G L T = (fw G L T).
  25
  26 (* Basic properties *********************************************************)
  27
  28 (* Basic_1: was: flt_shift *)
  29 lemma fw_shift: ∀p,I,G,K,V,T. ♯❨G,K.ⓑ[I]V,T❩ < ♯❨G,K,ⓑ[p,I]V.T❩.
  30 normalize /2 width=1 by monotonic_le_plus_r/
  31 qed.
  32
  33 lemma fw_clear: ∀p,I1,I2,G,K,V,T. ♯❨G,K.ⓤ[I1],T❩ < ♯❨G,K,ⓑ[p,I2]V.T❩.
  34 normalize /4 width=1 by monotonic_le_plus_r, le_S_S/
  35 qed.
  36
  37 lemma fw_tpair_sn: ∀I,G,L,V,T. ♯❨G,L,V❩ < ♯❨G,L,②[I]V.T❩.
  38 normalize in ⊢ (?→?→?→?→?→?%%); //
  39 qed.
  40
  41 lemma fw_tpair_dx: ∀I,G,L,V,T. ♯❨G,L,T❩ < ♯❨G,L,②[I]V.T❩.
  42 normalize in ⊢ (?→?→?→?→?→?%%); //
  43 qed.
  44
  45 lemma fw_lpair_sn: ∀I,G,L,V,T. ♯❨G,L,V❩ < ♯❨G,L.ⓑ[I]V,T❩.
  46 normalize /3 width=1 by monotonic_lt_plus_l, monotonic_le_plus_r/
  47 qed.
  48
  49 (* Basic_1: removed theorems 7:
  50             flt_thead_sx flt_thead_dx flt_trans
  51             flt_arith0 flt_arith1 flt_arith2 flt_wf_ind
  52 *)
  53 (* Basic_1: removed local theorems 1: q_ind *)