diff options
author | letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2007-11-10 23:26:12 +0000 |
---|---|---|
committer | letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2007-11-10 23:26:12 +0000 |
commit | aba2c731d3ef27adcb28c505e99dce3fc1f41e69 (patch) | |
tree | 23e28669ceec9cdf86891763c274a84da658e86d /theories/ZArith/Zdiv.v | |
parent | d79c32b352e8df2380eed4dde4253dd3530e94e4 (diff) |
A result about Zsgn(a/b), both for Zdiv and ZOdiv
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@10313 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/ZArith/Zdiv.v')
-rw-r--r-- | theories/ZArith/Zdiv.v | 8 |
1 files changed, 8 insertions, 0 deletions
diff --git a/theories/ZArith/Zdiv.v b/theories/ZArith/Zdiv.v index 85eac3c30..e28acb4a6 100644 --- a/theories/ZArith/Zdiv.v +++ b/theories/ZArith/Zdiv.v @@ -604,6 +604,14 @@ Proof. auto with zarith. Qed. +Theorem Zdiv_sgn: forall a b, + 0 <= Zsgn (a/b) * Zsgn a * Zsgn b. +Proof. + destruct a as [ |a|a]; destruct b as [ |b|b]; simpl; auto with zarith; + generalize (Z_div_pos (Zpos a) (Zpos b)); unfold Zdiv, Zdiv_eucl; + destruct Zdiv_eucl_POS as (q,r); destruct r; omega with *. +Qed. + (** * Relations between usual operations and Zmod and Zdiv *) Lemma Z_mod_plus_full : forall a b c:Z, (a + b * c) mod c = a mod c. |