more CHANGELOG

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:
 

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.