ground_2 released and permanently renamed as ground

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

diff --git a/matita/matita/contribs/lambdadelta/ground_2/lib/list_eq.ma b/matita/matita/contribs/lambdadelta/ground_2/lib/list_eq.ma
deleted file mode 100644 (file)
index d1b2be4..0000000
--- a/matita/matita/contribs/lambdadelta/ground_2/lib/list_eq.ma
+++ /dev/null
@@ -1,57 +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/notation/relations/ringeq_3.ma".
-include "ground_2/lib/list.ma".
-
-(* EXTENSIONAL EQUIVALENCE OF LISTS *****************************************)
-
-rec definition eq_list A (l1,l2:list A) on l1 ≝
-match l1 with
-[ nil        ⇒
-  match l2 with
-  [ nil      ⇒ ⊤
-  | cons _ _ ⇒ ⊥
-  ]
-| cons a1 l1 ⇒
-  match l2 with
-  [ nil        ⇒ ⊥
-  | cons a2 l2 ⇒ a1 = a2 ∧ eq_list A l1 l2
-  ]
-].
-
-interpretation "extensional equivalence (list)"
-   'RingEq A l1 l2 = (eq_list A l1 l2).
-
-(* Basic properties *********************************************************)
-
-lemma eq_list_refl (A): reflexive … (eq_list A).
-#A #l elim l -l /2 width=1 by conj/
-qed.
-
-(* Main properties **********************************************************)
-
-theorem eq_eq_list (A,l1,l2): l1 = l2 → l1 ≗{A} l2.
-// qed.
-
-(* Main inversion propertiess ***********************************************)
-
-theorem eq_list_inv_eq (A,l1,l2): l1 ≗{A} l2 → l1 = l2.
-#A #l1 elim l1 -l1 [| #a1 #l1 #IH ] *
-[ //
-| #a2 #l2 #H elim H
-| #H elim H
-| #a2 #l2 * #Ha #Hl /3 width=1 by eq_f2/
-]
-qed-.