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Diffstat (limited to 'plugins/ring/LegacyNArithRing.v')
-rw-r--r-- | plugins/ring/LegacyNArithRing.v | 43 |
1 files changed, 0 insertions, 43 deletions
diff --git a/plugins/ring/LegacyNArithRing.v b/plugins/ring/LegacyNArithRing.v deleted file mode 100644 index b358251a..00000000 --- a/plugins/ring/LegacyNArithRing.v +++ /dev/null @@ -1,43 +0,0 @@ -(************************************************************************) -(* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2014 *) -(* \VV/ **************************************************************) -(* // * This file is distributed under the terms of the *) -(* * GNU Lesser General Public License Version 2.1 *) -(************************************************************************) - -(* Instantiation of the Ring tactic for the binary natural numbers *) - -Require Import Bool. -Require Export LegacyRing. -Require Export ZArith_base. -Require Import NArith. -Require Import Eqdep_dec. - -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 N.compare_eq. - destruct (n ?= m)%N; [ reflexivity | contradiction | contradiction ]. -Qed. - -Definition NTheory : Semi_Ring_Theory N.add N.mul 1%N 0%N Neq. - split. - apply N.add_comm. - apply N.add_assoc. - apply N.mul_comm. - apply N.mul_assoc. - apply N.add_0_l. - apply N.mul_1_l. - apply N.mul_0_l. - apply N.mul_add_distr_r. - apply Neq_prop. -Qed. - -Add Legacy Semi Ring - N N.add N.mul 1%N 0%N Neq NTheory [ Npos 0%N xO xI 1%positive ]. |