diff --git a/algebra/cofe.v b/algebra/cofe.v
index 9742a09158804010373d7f6640faf3f7f60b3ae5..da126ca99a9fa35ba1b94cb84d083f44072c4a42 100644
--- a/algebra/cofe.v
+++ b/algebra/cofe.v
@@ -188,12 +188,21 @@ Definition fixpoint_eq : @fixpoint = @fixpoint_def := proj2_sig fixpoint_aux.
Section fixpoint.
Context {A : cofeT} `{Inhabited A} (f : A → A) `{!Contractive f}.
+
Lemma fixpoint_unfold : fixpoint f ≡ f (fixpoint f).
Proof.
apply equiv_dist=>n.
rewrite fixpoint_eq /fixpoint_def (conv_compl n (fixpoint_chain f)) //.
induction n as [|n IH]; simpl; eauto using contractive_0, contractive_S.
Qed.
+
+ Lemma fixpoint_unique (x : A) : x ≡ f x → x ≡ fixpoint f.
+ Proof.
+ rewrite !equiv_dist=> Hx n. induction n as [|n IH]; simpl in *.
+ - rewrite Hx fixpoint_unfold; eauto using contractive_0.
+ - rewrite Hx fixpoint_unfold. apply (contractive_S _), IH.
+ Qed.
+
Lemma fixpoint_ne (g : A → A) `{!Contractive g} n :
(∀ z, f z ≡{n}≡ g z) → fixpoint f ≡{n}≡ fixpoint g.
Proof.
diff --git a/docs/algebra.tex b/docs/algebra.tex
index 494fb54c752674b296412c1368063186d2d6b2b5..e9b3208e454bd5e1316827bbea1a5be8f0b3c999 100644
--- a/docs/algebra.tex
+++ b/docs/algebra.tex
@@ -39,7 +39,7 @@ In order to solve the recursive domain equation in \Sref{sec:model} it is also e
\end{defn}
Intuitively, applying a non-expansive function to some data will not suddenly introduce differences between seemingly equal data.
Elements that cannot be distinguished by programs within $n$ steps remain indistinguishable after applying $f$.
-The reason that contractive functions are interesting is that for every contractive $f : \cofe \to \cofe$ with $\cofe$ inhabited, there exists a \emph{unique}\footnote{Uniqueness is not proven in Coq.} fixed-point $\fix(f)$ such that $\fix(f) = f(\fix(f))$.
+The reason that contractive functions are interesting is that for every contractive $f : \cofe \to \cofe$ with $\cofe$ inhabited, there exists a \emph{unique} fixed-point $\fix(f)$ such that $\fix(f) = f(\fix(f))$.
\begin{defn}
The category $\COFEs$ consists of COFEs as objects, and non-expansive functions as arrows.