deletions | additions       diff --git a/This_example_shows_that_direction__.tex b/This_example_shows_that_direction__.tex  index 539f38e..0abbc25 100644  --- a/This_example_shows_that_direction__.tex  +++ b/This_example_shows_that_direction__.tex 
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Let us first show that that direction $2)\Rightarrow 1)$ of Theorem \ref{theorem:opinion} does hold for resistant BDPs, that is, resistant BDPs without disagreement in their cycles always stabilize:  \begin{theorem}\label{theorem:resistantsufficient}  Let $\G$ be an influence profile, $\O$ be an opinion profile, and $\C$ a set of constraints. Then the following holds:  \begin{enumerate}  \item[] If all $p\in \Atoms$, for all $C\subseteq\N$ such that $C$ is a cycle in $G_{p}$, for and  all $i,j\in C$: $\O_i(p)=\O_j(p)$, then \item[] The resistant BDP for $\O$, $\G$ and $\C$ converges.  \end{enumerate}  \end{theorem}