diff options
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. |