docs: banach: make f^k part of the theorem, nut just a remark; extend ref to america-rutten

docs/algebra.tex

@@ -90,10 +90,9 @@ Completeness is necessary to take fixed-points.
 \begin{thm}[Banach's fixed-point]
 \label{thm:banach}
 Given an inhabited COFE $\ofe$ and a contractive function $f : \ofe \to \ofe$, there exists a unique fixed-point $\fixp_T f$ such that $f(\fixp_T f) = \fixp_T f$.
+Moreover, this theorem also holds if $f$ is just non-expansive, and $f^k$ is contractive for an arbitrary $k$.
 \end{thm}
 
-The above theorem also holds if $f^k$ is contractive for an arbitrary $k$.
-
 \begin{thm}[America and Rutten~\cite{America-Rutten:JCSS89,birkedal:metric-space}]
 \label{thm:america_rutten}
 Let $1$ be the discrete COFE on the unit type: $1 \eqdef \Delta \{ () \}$.

docs/program-logic.tex

@@ -36,7 +36,7 @@ Furthermore, since the $\iFunc_i$ are locally contractive, so is $\textdom{ResF}
 
 Now we can write down the recursive domain equation:
 \[ \iPreProp \cong \UPred(\textdom{ResF}(\iPreProp, \iPreProp)) \]
-Here, $\iPreProp$ is a COFE defined as the fixed-point of a locally contractive bifunctor, which exists by \thmref{thm:america_rutten}.
+Here, $\iPreProp$ is a COFE defined as the fixed-point of a locally contractive bifunctor, which exists and is unique up to isomorphism by \thmref{thm:america_rutten}.
 We do not need to consider how the object $\iPreProp$ is constructed, we only need the isomorphism, given by:
 \begin{align*}
   \Res &\eqdef \textdom{ResF}(\iPreProp, \iPreProp) \\