From d2204e78c2d8bfc4f46ba541749b07dedd5e7969 Mon Sep 17 00:00:00 2001
From: letouzey
Date: Fri, 1 Jul 2011 17:38:17 +0000
Subject: 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
---
 theories/Numbers/Integer/SpecViaZ/ZSigZAxioms.v | 9 ++++++++-
 1 file changed, 8 insertions(+), 1 deletion(-)

(limited to 'theories/Numbers/Integer/SpecViaZ')

diff --git a/theories/Numbers/Integer/SpecViaZ/ZSigZAxioms.v b/theories/Numbers/Integer/SpecViaZ/ZSigZAxioms.v
index 5a0f590ba0..bfbc063ced 100644
--- a/theories/Numbers/Integer/SpecViaZ/ZSigZAxioms.v
+++ b/theories/Numbers/Integer/SpecViaZ/ZSigZAxioms.v
@@ -14,7 +14,7 @@ Module ZTypeIsZAxioms (Import ZZ : ZType').
 
 Hint Rewrite
  spec_0 spec_1 spec_2 spec_add spec_sub spec_pred spec_succ
- spec_mul spec_opp spec_of_Z spec_div spec_modulo spec_sqrt
+ spec_mul spec_opp spec_of_Z spec_div spec_modulo spec_square spec_sqrt
  spec_compare spec_eqb spec_ltb spec_leb spec_max spec_min
  spec_abs spec_sgn spec_pow spec_log2 spec_even spec_odd spec_gcd
  spec_quot spec_rem spec_testbit spec_shiftl spec_shiftr
@@ -303,6 +303,13 @@ Proof.
  intros a b. red. now rewrite spec_pow_N, spec_pow_pos.
 Qed.
 
+(** Square *)
+
+Lemma square_spec n : square n == n * n.
+Proof.
+ now zify.
+Qed.
+
 (** Sqrt *)
 
 Lemma sqrt_spec : forall n, 0<=n ->
-- 
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