More changes to OnIncrementTx

spec/offchain.tex

@@ -223,10 +223,11 @@ \subsubsection{Processing transactions off-chain}
   snapshot signatures $\hpRS$ containing the increment UTxO $U'_\omega$ is sent.} \\
 
 \red{\dparagraph{$\mathtt{incrementTx}$.}\quad Upon observing the \mtxIncrement{}
-	transaction, which adds it's outputs to the confirmed UTxO in the Head, the corresponding
-	pending increment UTxO is cleared and the observed version is used for future
-	snapshots by setting $\hatv = v$. The version of the open head state
-  	is incremented on each \mtxIncrement{} transaction as described in Section~\ref{sec:increment-tx}
+	transaction which outputs are added to the confirmed UTxO in the Head, we include
+  the outputs to the \emph{local} ledger state. Finally the corresponding pending increment
+  UTxO is cleared and the observed version is used for future snapshots by setting
+  $\hatv = v$. The version of the open head state is incremented on each \mtxIncrement{}
+  transaction as described in Section~\ref{sec:increment-tx}
 }
 \todo{missing to mention the multicast of $\hpRS$} \\