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| author |  letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2010-11-02 19:30:57 +0000 |
|---|---|---|
| committer | letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2010-11-02 19:30:57 +0000 |
| commit | 2a7a989025a5dde9a6f34792e1e1f2b4e3ad3108 (patch) | |
| tree | 63b6bf19f0cf27bfc4a2d77381eef5a0cb403c85 /theories/QArith/Qround.v | |
| parent | c5eea71cebc0fd1553196598e6b88af482dbffe5 (diff) | |
Add small utility lemmas about nat/P/Z/Q arithmetic.
Initial patch by Eelis van der Weegen, minor adaptations by myself
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@13613 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/QArith/Qround.v')
| -rw-r--r-- | theories/QArith/Qround.v | 13 |
1 files changed, 12 insertions, 1 deletions
diff --git a/theories/QArith/Qround.v b/theories/QArith/Qround.v index 58a7967ed..ce363a33b 100644 --- a/theories/QArith/Qround.v +++ b/theories/QArith/Qround.v @@ -136,4 +136,15 @@ intros x y H. apply Zle_antisym. auto with *. symmetry in H; auto with *. -Qed.
\ No newline at end of file +Qed. + +Lemma Zdiv_Qdiv (n m: Z): (n / m)%Z = Qfloor (n / m). +Proof. + unfold Qfloor. intros. simpl. + destruct m as [?|?|p]; simpl. + now rewrite Zdiv_0_r, Zmult_0_r. + now rewrite Zmult_1_r. + rewrite <- Zopp_eq_mult_neg_1. + rewrite <- (Zopp_involutive (Zpos p)). + now rewrite Zdiv_opp_opp. +Qed. |