ground_2 released and permanently renamed as ground

[helm.git] / matita / matita / contribs / lambdadelta / ground_2 / lib / list_length.ma

diff --git a/matita/matita/contribs/lambdadelta/ground_2/lib/list_length.ma b/matita/matita/contribs/lambdadelta/ground_2/lib/list_length.ma
deleted file mode 100644 (file)
index 64aaac3..0000000
--- a/matita/matita/contribs/lambdadelta/ground_2/lib/list_length.ma
+++ /dev/null
@@ -1,53 +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 "ground_2/lib/arith.ma".
-include "ground_2/lib/list.ma".
-
-(* LENGTH OF A LIST *********************************************************)
-
-rec definition length A (l:list A) on l ≝ match l with
-[ nil      ⇒ 0
-| cons _ l ⇒ ↑(length A l)
-].
-
-interpretation "length (list)"
-   'card l = (length ? l).
-
-(* Basic properties *********************************************************)
-
-lemma length_nil (A:Type[0]): |nil A| = 0.
-// qed.
-
-lemma length_cons (A:Type[0]) (l:list A) (a:A): |a⨮l| = ↑|l|.
-// qed.
-
-(* Basic inversion lemmas ***************************************************)
-
-lemma length_inv_zero_dx (A:Type[0]) (l:list A): |l| = 0 → l = Ⓔ.
-#A * // #a #l >length_cons #H destruct
-qed-.
-
-lemma length_inv_zero_sn (A:Type[0]) (l:list A): 0 = |l| → l = Ⓔ.
-/2 width=1 by length_inv_zero_dx/ qed-.
-
-lemma length_inv_succ_dx (A:Type[0]) (l:list A) (x): |l| = ↑x →
-                         ∃∃tl,a. x = |tl| & l = a ⨮ tl.
-#A * /2 width=4 by ex2_2_intro/
->length_nil #x #H destruct
-qed-.
-
-lemma length_inv_succ_sn (A:Type[0]) (l:list A) (x): ↑x = |l| →
-                         ∃∃tl,a. x = |tl| & l = a ⨮ tl.
-/2 width=1 by length_inv_succ_dx/ qed.