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-rw-r--r--theories/Numbers/Cyclic/Int31/Cyclic31.v9
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).