3 files changed, 13 insertions, 2 deletions
diff --git a/theories/Numbers/Integer/Abstract/ZBits.v b/theories/Numbers/Integer/Abstract/ZBits.v
index 92afbcb537..7c3a99215b 100644
--- a/theories/Numbers/Integer/Abstract/ZBits.v
+++ b/theories/Numbers/Integer/Abstract/ZBits.v
@@ -292,7 +292,7 @@ Proof.
 Qed.
 
 (** Hence the number of bits of [a] is [1+log2 a]
-    (see [Psize] and [Psize_pos]).
+    (see [Pos.size_nat] and [Pos.size]).
 *)
 
 (** For negative numbers, things are the other ways around:
diff --git a/theories/Numbers/Integer/Abstract/ZDivFloor.v b/theories/Numbers/Integer/Abstract/ZDivFloor.v
index 14003d8926..24c8dc8b07 100644
--- a/theories/Numbers/Integer/Abstract/ZDivFloor.v
+++ b/theories/Numbers/Integer/Abstract/ZDivFloor.v
@@ -16,7 +16,7 @@ Require Import ZAxioms ZMulOrder ZSgnAbs NZDiv.
 
     [a = bq+r /\ 0 <= |r| < |b| /\ Sign(r) = Sign(b)]
 
-    This is the convention followed historically by [Zdiv] in Coq, and
+    This is the convention followed historically by [Z.div] in Coq, and
     corresponds to convention "F" in the following paper:
 
     R. Boute, "The Euclidean definition of the functions div and mod",
diff --git a/theories/Numbers/Integer/Abstract/ZPow.v b/theories/Numbers/Integer/Abstract/ZPow.v
index 53d84dce1c..c9c98b1e5c 100644
--- a/theories/Numbers/Integer/Abstract/ZPow.v
+++ b/theories/Numbers/Integer/Abstract/ZPow.v
@@ -18,6 +18,17 @@ Module Type ZPowProp
 
  Include NZPowProp A A B.
 
+(** A particular case of [pow_add_r], with no precondition *)
+
+Lemma pow_twice_r a b : a^(2*b) == a^b * a^b.
+Proof.
+ rewrite two_succ. nzsimpl.
+ destruct (le_gt_cases 0 b).
+ - now rewrite pow_add_r.
+ - rewrite !pow_neg_r. now nzsimpl. trivial.
+   now apply add_neg_neg.
+Qed.
+
 (** Parity of power *)
 
 Lemma even_pow : forall a b, 0<b -> even (a^b) = even a.