cor

draft/draft.tex

@@ -1943,6 +1943,9 @@ Since $\subseteq$ is a liftable order, we have the following lemma. The liftabil
 	\end{gather*}
 	Since $\powf p_1\comp\sigma=\alpha\comp p_1$ by precomposing $s$ to the both sides of the equation we get $\powf p_2\comp(\powf s\comp\sigma\comp s)=\alpha\comp p_2$. So, $\sigma\join(\powf s\comp\sigma\comp s)$ is a witness for $R$ to be a bisimulation.\qed
 \end{proof}
+\begin{cor}
+	Considering~\autoref{lem:alph-prod}, assuming that $R$ is a symmetric relation and it is an AM simulation, then $R$ is an AM bisimulation as well.
+\end{cor}
 
 \section{Relators}
 \subsection{Two-way similarity in Hughes-Jacobs}