diff options
author | Stephane Glondu <steph@glondu.net> | 2012-01-12 16:02:20 +0100 |
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committer | Stephane Glondu <steph@glondu.net> | 2012-01-12 16:02:20 +0100 |
commit | 97fefe1fcca363a1317e066e7f4b99b9c1e9987b (patch) | |
tree | 97ec6b7d831cc5fb66328b0c63a11db1cbb2f158 /theories/NArith/Ndiv_def.v | |
parent | 300293c119981054c95182a90c829058530a6b6f (diff) |
Imported Upstream version 8.4~betaupstream/8.4_beta
Diffstat (limited to 'theories/NArith/Ndiv_def.v')
-rw-r--r-- | theories/NArith/Ndiv_def.v | 31 |
1 files changed, 31 insertions, 0 deletions
diff --git a/theories/NArith/Ndiv_def.v b/theories/NArith/Ndiv_def.v new file mode 100644 index 00000000..559f01f1 --- /dev/null +++ b/theories/NArith/Ndiv_def.v @@ -0,0 +1,31 @@ +(************************************************************************) +(* v * The Coq Proof Assistant / The Coq Development Team *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010 *) +(* \VV/ **************************************************************) +(* // * This file is distributed under the terms of the *) +(* * GNU Lesser General Public License Version 2.1 *) +(************************************************************************) + +Require Import BinNat. +Local Open Scope N_scope. + +(** Obsolete file, see [BinNat] now, + only compatibility notations remain here. *) + +Definition Pdiv_eucl a b := N.pos_div_eucl a (Npos b). + +Definition Pdiv_eucl_correct a b : + let (q,r) := Pdiv_eucl a b in Npos a = q * Npos b + r + := N.pos_div_eucl_spec a (Npos b). + +Lemma Pdiv_eucl_remainder a b : + snd (Pdiv_eucl a b) < Npos b. +Proof. now apply (N.pos_div_eucl_remainder a (Npos b)). Qed. + +Notation Ndiv_eucl := N.div_eucl (only parsing). +Notation Ndiv := N.div (only parsing). +Notation Nmod := N.modulo (only parsing). + +Notation Ndiv_eucl_correct := N.div_eucl_spec (only parsing). +Notation Ndiv_mod_eq := N.div_mod' (only parsing). +Notation Nmod_lt := N.mod_lt (only parsing). |