matita/matita/contribs/lambdadelta/basic_2/grammar/lenv.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 "basic_2/grammar/term.ma".
  16
  17 (* LOCAL ENVIRONMENTS *******************************************************)
  18
  19 (* local environments *)
  20 inductive lenv: Type[0] ≝
  21 | LAtom: lenv                       (* empty *)
  22 | LPair: lenv → bind2 → term → lenv (* binary binding construction *)
  23 .
  24
  25 interpretation "sort (local environment)"
  26    'Star = LAtom.
  27
  28 interpretation "environment construction (binary)"
  29    'DxItem2 L I T = (LPair L I T).
  30
  31 interpretation "environment binding construction (binary)"
  32    'DxBind2 L I T = (LPair L I T).
  33
  34 interpretation "abbreviation (local environment)"
  35    'DxAbbr L T = (LPair L Abbr T).
  36
  37 interpretation "abstraction (local environment)"
  38    'DxAbst L T = (LPair L Abst T).
  39
  40 (* Basic properties *********************************************************)
  41
  42 axiom lenv_eq_dec: ∀L1,L2:lenv. Decidable (L1 = L2).
  43
  44 (* Basic inversion lemmas ***************************************************)
  45
  46 lemma destruct_lpair_lpair: ∀I1,I2,L1,L2,V1,V2. L1.ⓑ{I1}V1 = L2.ⓑ{I2}V2 →
  47                             ∧∧L1 = L2 & I1 = I2 & V1 = V2.
  48 #I1 #I2 #L1 #L2 #V1 #V2 #H destruct /2 width=1/
  49 qed-.
  50
  51 lemma discr_lpair_x_xy: ∀I,V,L. L = L.ⓑ{I}V → ⊥.
  52 #I #V #L elim L -L
  53 [ #H destruct
  54 | #L #J #W #IHL #H
  55   elim (destruct_lpair_lpair … H) -H #H1 #H2 #H3 destruct /2 width=1/ (**) (* destruct lemma needed *)
  56 ]
  57 qed-.
  58
  59 (* Basic_1: removed theorems 2: chead_ctail c_tail_ind *)