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| author |  Jason Gross <jgross@mit.edu> | 2016-11-08 10:54:37 -0500 |
|---|---|---|
| committer | Jason Gross <jgross@mit.edu> | 2016-11-08 10:54:37 -0500 |
| commit | f929cd20f82206be0bdf40b91c179dcb346408e1 (patch) | |
| tree | e2fe0af52f9c1c9ea9a2349280708739fef9a609 /src/Util/ZUtil.v | |
| parent | 7060f490f21c52d77b8985bf3388d9964d52a60f (diff) | |
Add log2_lt_pow2_alt
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 53179b44f..17e8d62bf 100644 --- a/src/Util/ZUtil.v +++ b/src/Util/ZUtil.v @@ -2128,6 +2128,15 @@ Module Z. Qed. Hint Resolve log2_ones_lt_nonneg : zarith. + Lemma log2_lt_pow2_alt a b : 0 < b -> a < 2^b <-> Z.log2 a < b. + Proof. + destruct (Z_lt_le_dec 0 a); auto using Z.log2_lt_pow2; []. + rewrite Z.log2_nonpos by omega. + split; auto with zarith; []. + intro; eapply le_lt_trans; [ eassumption | ]. + auto with zarith. + Qed. + Lemma simplify_twice_sub_sub x y : 2 * x - (x - y) = x + y. Proof. lia. Qed. Hint Rewrite simplify_twice_sub_sub : zsimplify. |