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| author | Xavier Leroy <xavier.leroy@college-de-france.fr> | 2021-06-07 11:27:44 +0200 |
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| committer | Xavier Leroy <xavier.leroy@college-de-france.fr> | 2021-07-26 16:01:48 +0200 |
| commit | 88589fa168a0b73f7d82c4ad2dcf9fde9d17f439 (patch) | |
| tree | f347f9fd738d5d5c4995b2a46e61620c275a71b2 /lib | |
| parent | fd68e9d37164871cdcb4ee83ab649c5054b0f1cc (diff) | |
| download | compcert-kvx-88589fa168a0b73f7d82c4ad2dcf9fde9d17f439.tar.gz compcert-kvx-88589fa168a0b73f7d82c4ad2dcf9fde9d17f439.zip | |
More lemmas about `align`
Diffstat (limited to 'lib')
| -rw-r--r-- | lib/Coqlib.v | 17 |
1 files changed, 17 insertions, 0 deletions
diff --git a/lib/Coqlib.v b/lib/Coqlib.v index 361ae924..706a5d49 100644 --- a/lib/Coqlib.v +++ b/lib/Coqlib.v @@ -525,6 +525,23 @@ Proof. intros. unfold align. apply Z.divide_factor_r. Qed. +Lemma align_lt: forall x y, y > 0 -> align x y < x + y. +Proof. + intros. unfold align. + generalize (Z_div_mod_eq (x + y - 1) y H); intro. + generalize (Z_mod_lt (x + y - 1) y H); intro. + lia. +Qed. + +Lemma align_same: + forall x y, y > 0 -> (y | x) -> align x y = x. +Proof. + unfold align; intros. destruct H0 as [k E]. + replace (x + y - 1) with (x + (y - 1)) by lia. + rewrite E, Z.div_add_l, Z.div_small by lia. + lia. +Qed. + (** * Definitions and theorems on the data types [option], [sum] and [list] *) Set Implicit Arguments. |