Imported Upstream version 8.1~gammaupstream/8.1.gamma

1 files changed, 0 insertions, 44 deletions

diff --git a/contrib/ring/NArithRing.v b/contrib/ring/NArithRing.v
deleted file mode 100644
index 878346ba..00000000
--- a/contrib/ring/NArithRing.v
+++ /dev/null
@@ -1,44 +0,0 @@
-(************************************************************************)
-(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
-(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
-(*   \VV/  **************************************************************)
-(*    //   *      This file is distributed under the terms of the       *)
-(*         *       GNU Lesser General Public License Version 2.1        *)
-(************************************************************************)
-
-(* $Id: NArithRing.v 6295 2004-11-12 16:40:39Z gregoire $ *)
-
-(* Instantiation of the Ring tactic for the binary natural numbers *)
-
-Require Export Ring.
-Require Export ZArith_base.
-Require Import NArith.
-Require Import Eqdep_dec.
-
-Unboxed Definition Neq (n m:N) :=
-  match (n ?= m)%N with
-  | Datatypes.Eq => true
-  | _ => false
-  end.
-
-Lemma Neq_prop : forall n m:N, Is_true (Neq n m) -> n = m.
-  intros n m H; unfold Neq in H.
-  apply Ncompare_Eq_eq.
-  destruct (n ?= m)%N; [ reflexivity | contradiction | contradiction ].
-Qed.
-
-Definition NTheory : Semi_Ring_Theory Nplus Nmult 1%N 0%N Neq.
-  split.
-    apply Nplus_comm.
-    apply Nplus_assoc.
-    apply Nmult_comm.
-    apply Nmult_assoc.
-    apply Nplus_0_l.
-    apply Nmult_1_l.
-    apply Nmult_0_l.
-    apply Nmult_plus_distr_r.
-    apply Nplus_reg_l.
-    apply Neq_prop.
-Qed.
-
-Add Semi Ring N Nplus Nmult 1%N 0%N Neq NTheory [ Npos 0%N xO xI 1%positive ].