diff options
| author |  letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2010-02-09 17:45:06 +0000 |
|---|---|---|
| committer | letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2010-02-09 17:45:06 +0000 |
| commit | c4b5c7ebd6f316bb53e1a53f94c367f4f0129dae (patch) | |
| tree | c7c1c9e7f381923ab04b0ba01a14d803e2b3eb71 /theories/Numbers/Natural/BigN/NMake.v | |
| parent | bf90d39cec401f5daad2eb26c915ceba65e1a5cc (diff) | |
Numbers: properties of min/max with respect to 0,S,P,add,sub,mul
With these properties, we can kill Arith/MinMax, NArith/Nminmax,
and leave ZArith/Zminmax as a compatibility file only. Now
the instanciations NPeano.Nat, NBinary.N, ZBinary.Z, BigZ, BigN
contains all theses facts.
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@12718 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Numbers/Natural/BigN/NMake.v')
| -rw-r--r-- | theories/Numbers/Natural/BigN/NMake.v | 8 |
1 files changed, 4 insertions, 4 deletions
diff --git a/theories/Numbers/Natural/BigN/NMake.v b/theories/Numbers/Natural/BigN/NMake.v index b3f7befc8..e9b3d8cc8 100644 --- a/theories/Numbers/Natural/BigN/NMake.v +++ b/theories/Numbers/Natural/BigN/NMake.v @@ -807,13 +807,13 @@ Module Make (W0:CyclicType) <: NType. assert (H2 := ZnZ.spec_to_Z (ZnZ.zdigits (dom_op n))). assert (H3 := head0_zdigits n x). rewrite Zmod_small by auto with zarith. - rewrite (ZBinary.ZBinPropMod.mul_lt_mono_pos_l (2^(ZnZ.to_Z (ZnZ.head0 x)))); + rewrite (Z.mul_lt_mono_pos_l (2^(ZnZ.to_Z (ZnZ.head0 x)))); auto with zarith. - rewrite (ZBinary.ZBinPropMod.mul_le_mono_pos_l _ _ (2^(ZnZ.to_Z (ZnZ.head0 x)))); + rewrite (Z.mul_le_mono_pos_l _ _ (2^(ZnZ.to_Z (ZnZ.head0 x)))); auto with zarith. rewrite <- 2 Zpower_exp; auto with zarith. - rewrite ZBinary.ZBinPropMod.add_sub_assoc, Zplus_minus. - rewrite ZBinary.ZBinPropMod.sub_simpl_r, Zplus_minus. + rewrite Z.add_sub_assoc, Zplus_minus. + rewrite Z.sub_simpl_r, Zplus_minus. rewrite ZnZ.spec_zdigits. rewrite pow2_pos_minus_1 by (red; auto). apply ZnZ.spec_head0; auto with zarith. |