diff options
Diffstat (limited to 'theories/Numbers')
| -rw-r--r-- | theories/Numbers/Cyclic/Int31/Cyclic31.v | 9 |
1 files changed, 7 insertions, 2 deletions
diff --git a/theories/Numbers/Cyclic/Int31/Cyclic31.v b/theories/Numbers/Cyclic/Int31/Cyclic31.v index 4d655eac..6da1c6ec 100644 --- a/theories/Numbers/Cyclic/Int31/Cyclic31.v +++ b/theories/Numbers/Cyclic/Int31/Cyclic31.v @@ -6,7 +6,7 @@ (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(*i $Id: Cyclic31.v 11034 2008-06-02 08:15:34Z thery $ i*) +(*i $Id: Cyclic31.v 11907 2009-02-10 23:54:28Z letouzey $ i*) (** * Int31 numbers defines indeed a cyclic structure : Z/(2^31)Z *) @@ -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). |