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Diffstat (limited to 'lib/Coqlib.v')
| -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. |