diff --git a/CHANGELOG.md b/CHANGELOG.md
index 4fc86cd739c769e9b432b92bc1f8198fae374f67..74ade33e41757339dc4b13d5a6c8a41692aad2b2 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -9,10 +9,10 @@ Changes in and extensions of the theory:
* [#] Add new modality: ■ ("plainly").
* [#] Camera morphisms have to be homomorphisms, not just monotone functions.
-* [#] Add a proof that `f` has a fixed point if `f^k` is contractive.
+* Add a proof that `f` has a fixed point if `f^k` is contractive.
* Constructions for least and greatest fixed points over monotone predicates
(defined in the logic of Iris using impredicative quantification).
-* A proof of the inverse of `wp_bind`.
+* Add a proof of the inverse of `wp_bind`.
Changes in Coq:
diff --git a/docs/algebra.tex b/docs/algebra.tex
index b5050387cb9299a45f6fa1066d4e3a39e90402c3..972778a8217596cd47a8057cd0941ac803bf4fa9 100644
--- a/docs/algebra.tex
+++ b/docs/algebra.tex
@@ -75,6 +75,7 @@ The function space $\ofe \nfn \cofeB$ is a COFE if $\cofeB$ is a COFE (\ie the d
Completeness is necessary to take fixed-points.
For once, every \emph{contractive function} $f : \ofe \to \cofeB$ where $\cofeB$ is a COFE and inhabited has a \emph{unique} fixed-point $\fix(f)$ such that $\fix(f) = f(\fix(f))$.
+This also holds if $f^k$ is contractive for an arbitrary $k$.
Furthermore, by America and Rutten's theorem~\cite{America-Rutten:JCSS89,birkedal:metric-space}, every contractive (bi)functor from $\COFEs$ to $\COFEs$ has a unique\footnote{Uniqueness is not proven in Coq.} fixed-point.