diff options
author | Russell O'Connor <roconnor@blockstream.io> | 2017-06-29 15:17:06 -0400 |
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committer | Russell O'Connor <roconnor@blockstream.io> | 2017-06-29 15:17:06 -0400 |
commit | f4f609f598fb4804acf272209782b60d4647cad4 (patch) | |
tree | 9c5b298fd555708716cccca99dec6982d3f2a9f8 /theories/ZArith | |
parent | 6d7c392b73eaa021083ab03c9042d271fb4c28c0 (diff) |
Add Z.mod_div lemma to standard library.
Diffstat (limited to 'theories/ZArith')
-rw-r--r-- | theories/ZArith/Zdiv.v | 6 |
1 files changed, 6 insertions, 0 deletions
diff --git a/theories/ZArith/Zdiv.v b/theories/ZArith/Zdiv.v index 2ba865bd0..509384104 100644 --- a/theories/ZArith/Zdiv.v +++ b/theories/ZArith/Zdiv.v @@ -508,6 +508,12 @@ Qed. (** Unfortunately, the previous result isn't always true on negative numbers. For instance: 3/(-2)/(-2) = 1 <> 0 = 3 / (-2*-2) *) +Lemma Zmod_div (a b : Z) : a mod b / b = 0. +Proof. + zero_or_not b. + auto using Z.mod_div. +Qed. + (** A last inequality: *) Theorem Zdiv_mult_le: |