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/SpecViaZ | |
| 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/SpecViaZ')
| -rw-r--r-- | theories/Numbers/Natural/SpecViaZ/NSig.v | 2 | ||||
| -rw-r--r-- | theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v | 11 |
2 files changed, 10 insertions, 3 deletions
diff --git a/theories/Numbers/Natural/SpecViaZ/NSig.v b/theories/Numbers/Natural/SpecViaZ/NSig.v index cfe842b9d2..aaf44ca649 100644 --- a/theories/Numbers/Natural/SpecViaZ/NSig.v +++ b/theories/Numbers/Natural/SpecViaZ/NSig.v @@ -83,7 +83,7 @@ Module Type NType. Parameter spec_pred: forall x, [pred x] = Z.max 0 ([x] - 1). Parameter spec_sub: forall x y, [sub x y] = Z.max 0 ([x] - [y]). Parameter spec_mul: forall x y, [mul x y] = [x] * [y]. - Parameter spec_square: forall x, [square x] = [x] * [x]. + Parameter spec_square: forall x, [square x] = [x] * [x]. Parameter spec_pow_pos: forall x n, [pow_pos x n] = [x] ^ Zpos n. Parameter spec_pow_N: forall x n, [pow_N x n] = [x] ^ Z.of_N n. Parameter spec_pow: forall x n, [pow x n] = [x] ^ [n]. diff --git a/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v b/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v index adbd8223ae..a0ad7643de 100644 --- a/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v +++ b/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v @@ -15,8 +15,8 @@ Module NTypeIsNAxioms (Import NN : NType'). Hint Rewrite spec_0 spec_1 spec_2 spec_succ spec_add spec_mul spec_pred spec_sub spec_div spec_modulo spec_gcd spec_compare spec_eqb spec_ltb spec_leb - spec_sqrt spec_log2 spec_max spec_min spec_pow_pos spec_pow_N spec_pow - spec_even spec_odd spec_testbit spec_shiftl spec_shiftr + spec_square spec_sqrt spec_log2 spec_max spec_min spec_pow_pos spec_pow_N + spec_pow spec_even spec_odd spec_testbit spec_shiftl spec_shiftr spec_land spec_lor spec_ldiff spec_lxor spec_div2 spec_of_N : nsimpl. Ltac nsimpl := autorewrite with nsimpl. @@ -256,6 +256,13 @@ Proof. intros. now zify. Qed. +(** Square *) + +Lemma square_spec n : square n == n * n. +Proof. + now zify. +Qed. + (** Sqrt *) Lemma sqrt_spec : forall n, 0<=n -> |