From 727c2ea8f94b30a1d1d15d077de7df4ad4d80464 Mon Sep 17 00:00:00 2001
From: James Ray <16969914+jamesray1@users.noreply.github.com>
Date: Thu, 8 Feb 2018 14:52:58 +1100
Subject: [PATCH] \hyperlink{ell}{\ell}

---
 Paper.tex | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Paper.tex b/Paper.tex
index 63f02da4..25efb240 100644
--- a/Paper.tex
+++ b/Paper.tex
@@ -608,11 +608,11 @@ \subsection{Execution}
 \linkdest{transaction_nonce}{}T_{\mathrm{n}} & = & \boldsymbol{\sigma}[S(T)]_{\mathrm{n}} \quad \wedge \\
 g_0 & \leqslant & T_{\mathrm{g}} \quad \wedge \\
 v_0 & \leqslant & \boldsymbol{\sigma}[S(T)]_{\mathrm{b}} \quad \wedge \\
-T_{\mathrm{g}} & \leqslant & {B_{H}}_{\mathrm{l}} - \ell(B_{\mathbf{R}})_{\mathrm{u}}
+T_{\mathrm{g}} & \leqslant & {B_{H}}_{\mathrm{l}} - \hyperlink{ell}{\ell}(B_{\mathbf{R}})_{\mathrm{u}}
 \end{array}
 \end{equation}
 
-Note the final condition; the sum of the transaction's gas limit, $T_{\mathrm{g}}$, and the gas utilised in this block prior, given by $\ell(B_{\mathbf{R}})_{\mathrm{u}}$, must be no greater than the block's \textbf{gasLimit}, ${B_{H}}_{\mathrm{l}}$.
+Note the final condition; the sum of the transaction's gas limit, $T_{\mathrm{g}}$, and the gas utilised in this block prior, given by $\hyperlink{ell}{\ell}(B_{\mathbf{R}})_{\mathrm{u}}$, must be no greater than the block's \textbf{gasLimit}, ${B_{H}}_{\mathrm{l}}$.
 
 The execution of a valid transaction begins with an irrevocable change made to the state: the nonce of the account of the sender, $S(T)$, is incremented by one and the balance is reduced by part of the up-front cost, $T_{\mathrm{g}}T_{\mathrm{p}}$. The gas available for the proceeding computation, $g$, is defined as $T_{\mathrm{g}} - g_0$. The computation, whether contract creation or a message call, results in an eventual state (which may legally be equivalent to the current state), the change to which is deterministic and never invalid: there can be no invalid transactions from this point.