update in ground_2 and basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / syntax / voids.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/syntax/voids.ma b/matita/matita/contribs/lambdadelta/basic_2/syntax/voids.ma
deleted file mode 100644 (file)
index 854737b..0000000
--- a/matita/matita/contribs/lambdadelta/basic_2/syntax/voids.ma
+++ /dev/null
@@ -1,91 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||M||                                                             *)
-(*      ||A||       A project by Andrea Asperti                           *)
-(*      ||T||                                                             *)
-(*      ||I||       Developers:                                           *)
-(*      ||T||         The HELM team.                                      *)
-(*      ||A||         http://helm.cs.unibo.it                             *)
-(*      \   /                                                             *)
-(*       \ /        This file is distributed under the terms of the       *)
-(*        v         GNU General Public License Version 2                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-include "basic_2/notation/functions/voidstar_2.ma".
-include "basic_2/syntax/lenv.ma".
-
-(* EXTENSION OF A LOCAL ENVIRONMENT WITH EXCLUSION BINDERS ******************)
-
-rec definition voids (L:lenv) (n:nat) on n: lenv ≝ match n with
-[ O ⇒ L | S m ⇒ (voids L m).ⓧ ].
-
-interpretation "extension with exclusion binders (local environment)"
-   'VoidStar n L = (voids L n).
-
-(* Basic properties *********************************************************)
-
-lemma voids_zero: ∀L. L = ⓧ*[0]L.
-// qed.
-
-lemma voids_succ: ∀L,n. (ⓧ*[n]L).ⓧ = ⓧ*[⫯n]L.
-// qed.
-
-(* Advanced properties ******************************************************)
-
-lemma voids_next: ∀n,L. ⓧ*[n](L.ⓧ) = ⓧ*[⫯n]L.
-#n elim n -n //
-qed.
-
-(* Basic inversion lemmas ***************************************************)
-
-lemma voids_atom_inv: ∀K,n. ⓧ*[n]K = ⋆ → ∧∧ ⋆ = K & 0 = n.
-#K * /2 width=1 by conj/
-#n <voids_succ #H destruct
-qed-.
-
-lemma voids_pair_inv: ∀I,K1,K2,V,n. ⓧ*[n]K1 = K2.ⓑ{I}V →
-                      ∧∧ K2.ⓑ{I}V = K1 & 0 = n.
-#I #K1 #K2 #V * /2 width=1 by conj/
-#n <voids_succ #H destruct
-qed-.
-
-(* Advanced inversion lemmas ************************************************)
-
-lemma voids_inv_atom_sn: ∀n1,K2,n2. ⓧ*[n1]⋆ = ⓧ*[n2]K2 →
-                         ∧∧ ⓧ*[n1-n2]⋆ = K2 & n2 ≤ n1.
-#n1 elim n1 -n1
-[ #K2 <voids_zero * /2 width=1 by conj/
-  #n1 <voids_succ #H destruct
-| #n1 #IH #K2 *
-  [ <voids_zero #H destruct /2 width=1 by conj/
-  | #n2 <voids_succ <voids_succ >minus_S_S #H
-    elim (destruct_lbind_lbind_aux … H) -H #HK #_ (**) (* destruct lemma needed *)
-    elim (IH … HK) -IH -HK #H #Hn destruct /3 width=1 by conj, le_S_S/
-  ]
-]
-qed-.
-
-lemma voids_inv_pair_sn: ∀I,V,n1,K1,K2,n2. ⓧ*[n1]K1.ⓑ{I}V = ⓧ*[n2]K2 →
-                         ∧∧ ⓧ*[n1-n2]K1.ⓑ{I}V = K2 & n2 ≤ n1.
-#I #V #n1 elim n1 -n1
-[ #K1 #K2 <voids_zero * /2 width=1 by conj/
-  #n1 <voids_succ #H destruct
-| #n1 #IH #K1 #K2 *
-  [ <voids_zero #H destruct /2 width=1 by conj/
-  | #n2 <voids_succ <voids_succ >minus_S_S #H
-    elim (destruct_lbind_lbind_aux … H) -H #HK #_ (**) (* destruct lemma needed *)
-    elim (IH … HK) -IH -HK #H #Hn destruct /3 width=1 by conj, le_S_S/
-  ]
-]
-qed-.
-
-(* Main inversion properties ************************************************)
-
-theorem voids_inj: ∀n. injective … (λL. ⓧ*[n]L).
-#n elim n -n //
-#n #IH #L1 #L2
-<voids_succ <voids_succ #H
-elim (destruct_lbind_lbind_aux … H) -H (**) (* destruct lemma needed *)
-/2 width=1 by/
-qed-.