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| author |  Jason Gross <jgross@mit.edu> | 2017-03-31 20:06:24 -0400 |
|---|---|---|
| committer | Jason Gross <jgross@mit.edu> | 2017-03-31 20:06:24 -0400 |
| commit | 0e0a73376a4c602b7e26ddae045a7c0884670a5a (patch) | |
| tree | 0778f576c90cba2e902c21adccd38232481d7e2d /src/Util/ZUtil.v | |
| parent | 4d11f709fb93e7dd3dd1320cec945cc0dca55fec (diff) | |
Add Z.log2_up_le_pow2_full
Diffstat (limited to 'src/Util/ZUtil.v')
| -rw-r--r-- | src/Util/ZUtil.v | 9 |
1 files changed, 9 insertions, 0 deletions
diff --git a/src/Util/ZUtil.v b/src/Util/ZUtil.v index 88370e533..e8cf62ce0 100644 --- a/src/Util/ZUtil.v +++ b/src/Util/ZUtil.v @@ -2192,6 +2192,15 @@ Module Z. | rewrite Z.log2_up_eqn0 by omega; simpl; omega ]. Qed. + Lemma log2_up_le_pow2_full : forall a b : Z, (0 <= b)%Z -> (a <= 2 ^ b)%Z <-> (Z.log2_up a <= b)%Z. + Proof. + intros a b H. + destruct (Z_lt_le_dec 0 a); [ apply Z.log2_up_le_pow2; assumption | ]. + split; transitivity 0%Z; try omega; auto with zarith. + rewrite Z.log2_up_eqn0 by omega. + reflexivity. + Qed. + Lemma ones_lt_pow2 x y : 0 <= x <= y -> Z.ones x < 2^y. Proof. rewrite Z.ones_equiv, Z.lt_pred_le. |