diff options
| author | letouzey | 2010-01-08 14:44:56 +0000 |
|---|---|---|
| committer | letouzey | 2010-01-08 14:44:56 +0000 |
| commit | 5db31bb0333810ccdd0a79e9855ae9d2fcdbf2d3 (patch) | |
| tree | dd8cd4a8b4453d96fdcd8fea56c9a56a4f766087 /theories/Numbers/Integer/BigZ | |
| parent | c630fdf04db508d5d877a6b1fd93145893377287 (diff) | |
Numbers: axiomatization + generic properties of abs and sgn.
This allow to really finish files about division.
An abs and sgn is added to BigZ.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12644 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Numbers/Integer/BigZ')
| -rw-r--r-- | theories/Numbers/Integer/BigZ/ZMake.v | 16 |
1 files changed, 16 insertions, 0 deletions
diff --git a/theories/Numbers/Integer/BigZ/ZMake.v b/theories/Numbers/Integer/BigZ/ZMake.v index 615b8d1396..827877fc5b 100644 --- a/theories/Numbers/Integer/BigZ/ZMake.v +++ b/theories/Numbers/Integer/BigZ/ZMake.v @@ -488,4 +488,20 @@ Module Make (N:NType) <: ZType. case N.to_Z; simpl; auto with zarith. Qed. + Definition sgn x := + match compare zero x with + | Lt => one + | Eq => zero + | Gt => minus_one + end. + + Lemma spec_sgn : forall x, to_Z (sgn x) = Zsgn (to_Z x). + Proof. + intros. unfold sgn. generalize (spec_compare zero x). + destruct compare. + rewrite spec_0. intros <-; auto. + rewrite spec_0, spec_1. symmetry. rewrite Zsgn_pos; auto. + rewrite spec_0, spec_m1. symmetry. rewrite Zsgn_neg; auto with zarith. + Qed. + End Make. |