matita/matita/contribs/lambdadelta/basic_2/syntax/voids.ma

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  11 (*        v         GNU General Public License Version 2                  *)
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  14
  15 include "basic_2/notation/functions/voidstar_2.ma".
  16 include "basic_2/syntax/lenv.ma".
  17
  18 (* EXTENSION OF A LOCAL ENVIRONMENT WITH EXCLUSION BINDERS ******************)
  19
  20 rec definition voids (L:lenv) (n:nat) on n: lenv ≝ match n with
  21 [ O ⇒ L | S m ⇒ (voids L m).ⓧ ].
  22
  23 interpretation "extension with exclusion binders (local environment)"
  24    'VoidStar n L = (voids L n).
  25
  26 (* Basic properties *********************************************************)
  27
  28 lemma voids_zero: ∀L. L = ⓧ*[0]L.
  29 // qed.
  30
  31 lemma voids_succ: ∀L,n. (ⓧ*[n]L).ⓧ = ⓧ*[⫯n]L.
  32 // qed.
  33
  34 (* Advanced properties ******************************************************)
  35
  36 lemma voids_next: ∀n,L. ⓧ*[n](L.ⓧ) = ⓧ*[⫯n]L.
  37 #n elim n -n //
  38 qed.
  39
  40 (* Main inversion properties ************************************************)
  41
  42 theorem voids_inj: ∀n. injective … (λL. ⓧ*[n]L).
  43 #n elim n -n //
  44 #n #IH #L1 #L2
  45 <voids_succ <voids_succ #H
  46 elim (destruct_lbind_lbind_aux … H) -H (**) (* destruct lemma needed *)
  47 /2 width=1 by/
  48 qed-.