diff options
| author | letouzey | 2008-05-28 18:17:30 +0000 |
|---|---|---|
| committer | letouzey | 2008-05-28 18:17:30 +0000 |
| commit | 836cf5e7ea5a83845cd70e3ba3a03db3f736e555 (patch) | |
| tree | fd242f063f7c382955212c40a71f0754187d80a6 /theories/Numbers/Cyclic/ZModulo/ZModulo.v | |
| parent | 8afb2a8fee5da2e290a3a32964d29868e005ae62 (diff) | |
Cyclic31: no more Admitted, but I've cheated: sqrt31 and sqrt312 are
now dumb wrappers around Zsqrt_plain. Wanted (dead or alive): better
implemntations _and_ their proofs.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@11013 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Numbers/Cyclic/ZModulo/ZModulo.v')
| -rw-r--r-- | theories/Numbers/Cyclic/ZModulo/ZModulo.v | 11 |
1 files changed, 0 insertions, 11 deletions
diff --git a/theories/Numbers/Cyclic/ZModulo/ZModulo.v b/theories/Numbers/Cyclic/ZModulo/ZModulo.v index 77f1a57b4a..de7e4c6e89 100644 --- a/theories/Numbers/Cyclic/ZModulo/ZModulo.v +++ b/theories/Numbers/Cyclic/ZModulo/ZModulo.v @@ -587,17 +587,6 @@ Section ZModulo. generalize (Z_mod_lt [|x|] 2); omega. Qed. - Lemma Zsquare_le : forall x, x <= x*x. - Proof. - intros. - destruct (Z_lt_le_dec 0 x). - pattern x at 1; rewrite <- (Zmult_1_l x). - apply Zmult_le_compat; auto with zarith. - apply Zle_trans with 0; auto with zarith. - rewrite <- Zmult_opp_opp. - apply Zmult_le_0_compat; auto with zarith. - Qed. - Definition znz_sqrt x := Zsqrt_plain [|x|]. Lemma spec_sqrt : forall x, [|znz_sqrt x|] ^ 2 <= [|x|] < ([|znz_sqrt x|] + 1) ^ 2. |