diff --git a/main.tex b/main.tex
index 7496aecac6ec7d380262b94c406b84deea2fe045..3aa93d5bf23ba7336f1cf213cf21abc1e5e82517 100644
--- a/main.tex
+++ b/main.tex
@@ -793,12 +793,15 @@ The following lemma considers two vertices $v,w$ that are never ``crossed'' so t
 \end{proof}
 
 	\begin{definition}[Connected patches]
-		Let $P$ be an interval $[a,b]$. We say that $P$ is a patch of a particular run of the process if $P$ is a maximal connected component of the vertices that have ever become $0$ before termination. We denote the set of patches of a run by $\mathcal{P}$. For a patch $P$ let $P\in \mathcal{P}$ denote the event that one of the patches is equal to $P$. 
+		Let $P\subseteq V$ be a connected component of $G$. We say that $P$ is a patch of a particular run of the process if $P$ is a maximal connected component of the vertices that have ever become $0$ before termination. We denote the set of patches of a run by $\mathcal{P}$. For a patch $P$ let $P\in \mathcal{P}$ denote the event that one of the patches is equal to $P$. 
 		In other words
 		\begin{align*}
-		P\in\mathcal{P} := \NZ{a-1} \cap \Z{a} \cap \Z{a+1} \cap \cdots \cap \Z{b-1} \cap \Z{b} \cap \NZ{b+1} .
+		P\in\mathcal{P} := \NZ{\overline{\partial}P} \cap \Z{P}.
+		\end{align*}
+		For $\mathcaP{I}'\subseteq 2^{2^V}$ a set of patches we denote by $\mathcal{P}'\in \mathcal{P}$ the event that $\mathcal{P}'$ is a subset of the patches, i.e.,
+		\begin{align*}
+			\mathcal{P}'\in \mathcal{P} := \bigcup_{P\in \mathcal{P}'}\NZ{\overline{\partial}P} \cap \Z{P}.
 		\end{align*}
-		(In the extreme case when $P$ covers the whole cycle $[n]$, then instead $P\in\mathcal{P}:= \bigcap_{v\in[n]}\Z{v}$.)
 	\end{definition} 
 
 	We are often going to use the observation that we can partition the event $\Z{v}$ using patches: