update in ground_2 and basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc / voids / voids_length.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/voids/voids_length.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/voids/voids_length.etc
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/basic_2/etc/voids/voids_length.etc
@@ -0,0 +1,46 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/syntax/lenv_length.ma".
+include "basic_2/syntax/voids.ma".
+
+(* EXTENSION OF A LOCAL ENVIRONMENT WITH EXCLUSION BINDERS ******************)
+
+(* Properties with length for local environments ****************************)
+
+lemma length_void: ∀L,n. n+|L| = |ⓧ*[n]L|.
+#L #n elim n -n //
+#n #IH <voids_succ >length_bind <IH -IH //
+qed.
+
+lemma length_void_le: ∀L,n. |L| ≤ |ⓧ*[n]L|.
+// qed.
+
+(* Main forward properties with length for local environments ***************)
+
+theorem voids_inj_length: ∀n1,n2,L1,L2. ⓧ*[n1]L1 = ⓧ*[n2]L2 →
+                          |L1| = |L2| → n1 = n2 ∧ L1 = L2.
+#n1 elim n1 -n1
+[ * /2 width=1 by conj/ #n2 #L1 #L2 | #n1 #IH * [ | #n2 ] #L1 #L2 ]
+[ <voids_zero #H destruct
+  <length_void <commutative_plus #H
+  elim (plus_xSy_x_false … H)
+| <voids_zero #H destruct
+  <length_void <commutative_plus #H
+  elim (plus_xSy_x_false … (sym_eq … H))
+| <voids_succ <voids_succ #H #HL12
+  elim (destruct_lbind_lbind_aux … H) -H (**) (* destruct lemma needed *)
+  #H #_ elim (IH … H HL12) -IH -H -HL12 /2 width=1 by conj/
+]
+qed-.