diff options
author | Samuel Mimram <samuel.mimram@ens-lyon.org> | 2004-07-28 21:54:47 +0000 |
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committer | Samuel Mimram <samuel.mimram@ens-lyon.org> | 2004-07-28 21:54:47 +0000 |
commit | 6b649aba925b6f7462da07599fe67ebb12a3460e (patch) | |
tree | 43656bcaa51164548f3fa14e5b10de5ef1088574 /contrib7/ring/NArithRing.v |
Imported Upstream version 8.0pl1upstream/8.0pl1
Diffstat (limited to 'contrib7/ring/NArithRing.v')
-rw-r--r-- | contrib7/ring/NArithRing.v | 44 |
1 files changed, 44 insertions, 0 deletions
diff --git a/contrib7/ring/NArithRing.v b/contrib7/ring/NArithRing.v new file mode 100644 index 00000000..f4548bbb --- /dev/null +++ b/contrib7/ring/NArithRing.v @@ -0,0 +1,44 @@ +(************************************************************************) +(* 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,v 1.1.2.1 2004/07/16 19:30:18 herbelin Exp $ *) + +(* Instantiation of the Ring tactic for the binary natural numbers *) + +Require Export Ring. +Require Export ZArith_base. +Require NArith. +Require Eqdep_dec. + +Definition Neq := [n,m:entier] + Cases (Ncompare n m) of + EGAL => true + | _ => false + end. + +Lemma Neq_prop : (n,m:entier)(Is_true (Neq n m)) -> n=m. + Intros n m H; Unfold Neq in H. + Apply Ncompare_Eq_eq. + NewDestruct (Ncompare n m); [Reflexivity | Contradiction | Contradiction ]. +Save. + +Definition NTheory : (Semi_Ring_Theory Nplus Nmult (Pos xH) Nul 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. +Save. + +Add Semi Ring entier Nplus Nmult (Pos xH) Nul Neq NTheory [Pos Nul xO xI xH]. |