remove RB for crash algorithms + some syntaxes fix in BFT algo

Recherche/BFT-ARBover/3_ARB_Def/index.tex

@@ -1,6 +1,11 @@
 
-Processes export \ABbroadcast$(m)$ and $m = \ABdeliver()$. \ARB requires total order:
-\begin{equation*}
-  \forall m_1,m_2,\ \forall p_i,p_j:\ \ (m_1 = \ABdeliver_i()) \prec (m_2 = \ABdeliver_i()) \Rightarrow (m_1 = \ABdeliver_j()) \prec (m_2 = \ABdeliver_j())
-\end{equation*}
-plus Integrity/No-duplicates/Validity (inherited from \RB and the construction).
+Processes export \ABbroadcast$(m)$ and $m = \ABdeliver()$. \ARB requires the following properties:
+\begin{itemize}[leftmargin=*]
+  \item \textbf{Total Order}: 
+  \begin{equation*}
+    \forall m_1,m_2,\ \forall p_i,p_j:\ \ (m_1 = \ABdeliver_i()) \prec (m_2 = \ABdeliver_i()) \Rightarrow (m_1 = \ABdeliver_j()) \prec (m_2 = \ABdeliver_j())
+  \end{equation*}
+  \item \textbf{Integrity}: Every message delivered was previously broadcast. $\forall p_i:\ m = \ABdeliver_i() \Rightarrow \exists p_j:\ \ABbroadcast_j(m)$.
+  \item \textbf{No-duplicates}: No message is delivered more than once at any process.
+  \item \textbf{Validity}: If a correct process broadcasts $m$, every correct process eventually delivers $m$.
+\end{itemize}