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| author | xleroy <xleroy@fca1b0fc-160b-0410-b1d3-a4f43f01ea2e> | 2009-11-19 13:32:09 +0000 |
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| committer | xleroy <xleroy@fca1b0fc-160b-0410-b1d3-a4f43f01ea2e> | 2009-11-19 13:32:09 +0000 |
| commit | ef40c6d36f1c3125f3aa78ea4eaa61dcc7bcae67 (patch) | |
| tree | 7bd176bb0dbf60617954fabadd8aedc64b4cf647 /lib/Coqlib.v | |
| parent | cdf83055d96e2af784a97c783c94b83ba2032ae1 (diff) | |
| download | compcert-kvx-ef40c6d36f1c3125f3aa78ea4eaa61dcc7bcae67.tar.gz compcert-kvx-ef40c6d36f1c3125f3aa78ea4eaa61dcc7bcae67.zip | |
Revised lib/Integers.v to make it parametric w.r.t. word size.
Introduced Int.iwordsize and used it in place of "Int.repr 32" or
"Int.repr (Z_of_nat wordsize)".
git-svn-id: https://yquem.inria.fr/compcert/svn/compcert/trunk@1182 fca1b0fc-160b-0410-b1d3-a4f43f01ea2e
Diffstat (limited to 'lib/Coqlib.v')
| -rw-r--r-- | lib/Coqlib.v | 28 |
1 files changed, 23 insertions, 5 deletions
diff --git a/lib/Coqlib.v b/lib/Coqlib.v index 0c58da09..5375c044 100644 --- a/lib/Coqlib.v +++ b/lib/Coqlib.v @@ -357,6 +357,13 @@ Proof. rewrite two_power_nat_S. omega. Qed. +Lemma two_power_nat_two_p: + forall x, two_power_nat x = two_p (Z_of_nat x). +Proof. + induction x. auto. + rewrite two_power_nat_S. rewrite inj_S. rewrite two_p_S. omega. omega. +Qed. + Lemma two_p_monotone: forall x y, 0 <= x <= y -> two_p x <= two_p y. Proof. @@ -369,11 +376,12 @@ Proof. assert (two_p x > 0). apply two_p_gt_ZERO. omega. omega. Qed. -Lemma two_power_nat_two_p: - forall x, two_power_nat x = two_p (Z_of_nat x). +Lemma two_p_monotone_strict: + forall x y, 0 <= x < y -> two_p x < two_p y. Proof. - induction x. auto. - rewrite two_power_nat_S. rewrite inj_S. rewrite two_p_S. omega. omega. + intros. assert (two_p x <= two_p (y - 1)). apply two_p_monotone; omega. + assert (two_p (y - 1) > 0). apply two_p_gt_ZERO. omega. + replace y with (Zsucc (y - 1)) by omega. rewrite two_p_S. omega. omega. Qed. Lemma two_p_strict: @@ -385,6 +393,16 @@ Proof. omega. Qed. +Lemma two_p_strict_2: + forall x, x >= 0 -> 2 * x - 1 < two_p x. +Proof. + intros. assert (x = 0 \/ x - 1 >= 0) by omega. destruct H0. + subst. vm_compute. auto. + replace (two_p x) with (2 * two_p (x - 1)). + generalize (two_p_strict _ H0). omega. + rewrite <- two_p_S. decEq. omega. omega. +Qed. + (** Properties of [Zmin] and [Zmax] *) Lemma Zmin_spec: @@ -522,7 +540,7 @@ Qed. Lemma Zdiv_interval_2: forall lo hi a b, - lo <= a <= hi -> lo <= 0 -> hi > 0 -> b > 0 -> + lo <= a <= hi -> lo <= 0 -> hi >= 0 -> b > 0 -> lo <= a/b <= hi. Proof. intros. |