diff options
| author | letouzey | 2011-07-01 17:38:17 +0000 |
|---|---|---|
| committer | letouzey | 2011-07-01 17:38:17 +0000 |
| commit | d2204e78c2d8bfc4f46ba541749b07dedd5e7969 (patch) | |
| tree | d2c9de4d986dc2f37744fad6f434ddac1506a8e0 /theories/Numbers/Natural/Peano | |
| parent | ae95b79d0912a7b1a5370854cb6fb1aadb1db6b2 (diff) | |
Cleanup of files related with power over Z.
- Zpow_def, Zpower, Zpow_facts shortened thanks to stuff in BinInt.Z
- The alternative Zpower_alt is now in a separate file Zpow_alt.v,
not loaded by default.
- Some more injection lemmas in Znat (pow, div, mod, quot, rem)
- Btw, added a "square" function in Z, N, Pos, ... (instead of
Zpow_facts.Zsquare).
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@14253 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Numbers/Natural/Peano')
| -rw-r--r-- | theories/Numbers/Natural/Peano/NPeano.v | 8 |
1 files changed, 8 insertions, 0 deletions
diff --git a/theories/Numbers/Natural/Peano/NPeano.v b/theories/Numbers/Natural/Peano/NPeano.v index b6b26363ec..d5df6329a2 100644 --- a/theories/Numbers/Natural/Peano/NPeano.v +++ b/theories/Numbers/Natural/Peano/NPeano.v @@ -53,6 +53,11 @@ Proof. reflexivity. Qed. Lemma pow_succ_r : forall a b, 0<=b -> a^(S b) = a * a^b. Proof. reflexivity. Qed. +Definition square n := n * n. + +Lemma square_spec n : square n = n * n. +Proof. reflexivity. Qed. + Definition Even n := exists m, n = 2*m. Definition Odd n := exists m, n = 2*m+1. @@ -737,6 +742,9 @@ Definition pow_succ_r := pow_succ_r. Lemma pow_neg_r : forall a b, b<0 -> a^b = 0. inversion 1. Qed. Definition pow := pow. +Definition square := square. +Definition square_spec := square_spec. + Definition log2_spec := log2_spec. Definition log2_nonpos := log2_nonpos. Definition log2 := log2. |