diff options
| author |  letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2009-02-10 23:53:02 +0000 |
|---|---|---|
| committer | letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2009-02-10 23:53:02 +0000 |
| commit | 6afa8653207732d3cd0e9d5a2d77665369036bf0 (patch) | |
| tree | ad2070da739d7ce3175f7edd880291c65ee2271a /theories | |
| parent | 65d027ba5ffcec61e66b1a047b135bea2f281c44 (diff) | |
Cyclic31: proof of a forgotten admit
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@11906 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories')
| -rw-r--r-- | theories/Numbers/Cyclic/Int31/Cyclic31.v | 7 |
1 files changed, 6 insertions, 1 deletions
diff --git a/theories/Numbers/Cyclic/Int31/Cyclic31.v b/theories/Numbers/Cyclic/Int31/Cyclic31.v index c6ad14740..3835c6cde 100644 --- a/theories/Numbers/Cyclic/Int31/Cyclic31.v +++ b/theories/Numbers/Cyclic/Int31/Cyclic31.v @@ -1637,7 +1637,12 @@ Section Int31_Spec. apply Zplus_eq_compat. ring. assert ((2*[|y|]) mod wB = 2*[|y|] - wB). - admit. + clear - H. symmetry. apply Zmod_unique with 1; [ | ring ]. + generalize (phi_lowerbound _ H) (phi_bounded y). + set (wB' := 2^Z_of_nat (pred size)). + replace wB with (2*wB'); [ omega | ]. + unfold wB'. rewrite <- Zpower_Zsucc, <- inj_S by (auto with zarith). + f_equal. rewrite H1. replace wB with (2^(Z_of_nat n)*2^(31-Z_of_nat n)) by (rewrite <- Zpower_exp; auto with zarith; f_equal; unfold size; ring). |