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

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  11 (*        v         GNU General Public License Version 2                  *)
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  13 (**************************************************************************)
  14
  15 include "static_2/syntax/lenv.ma".
  16
  17 (* SHIFT FOR RESTRICTED CLOSURES ********************************************)
  18
  19 rec definition shift L T on L ≝ match L with
  20 [ LAtom     ⇒ T
  21 | LBind L I ⇒ match I with
  22   [ BUnit _   ⇒ shift L (-ⓛ⋆0.T)
  23   | BPair I V ⇒ shift L (-ⓑ{I}V.T)
  24   ]
  25 ].
  26
  27 interpretation "shift (restricted closure)" 'plus L T = (shift L T).
  28
  29 (* Basic properties *********************************************************)
  30
  31 lemma shift_atom: ∀T. ⋆ + T = T.
  32 // qed.
  33
  34 lemma shift_unit: ∀I,L,T. L.ⓤ{I}+T = L+(-ⓛ⋆0.T).
  35 // qed.
  36
  37 lemma shift_pair: ∀I,L,V,T. (L.ⓑ{I}V)+T = L+(-ⓑ{I}V.T).
  38 // qed.