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@ -386,7 +386,7 @@ An ``ideal adversary'' returns an ``attack'', a future protocol state $\sigma'$
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If we can detect \emph{only some} of the circumstances in which the ideal adversary fails to find an attack, then we can construct a safety oracle which is able to detect safety in some of the states with estimate safety. Due to efficiency considerations, the cases may be available enough for it to be useful in an implementation even though it may not be an ideal safety oracle.
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We identify such a set of circumstances. To discuss more generally, we denote ``agreement'' between estimate $e$ and estimate $e'$ as $e \equiv e'$. This correspond to $e = e'$ in the binary consensus, and $e \downarrow e'$ in the blockchain consensus. Disagreement will be denoted with $\not\equiv$.
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We identify such a set of circumstances. To discuss more generally, we denote ``agreement'' between estimate $e$ and estimate $e'$ as $e \equiv e'$. This corresponds to $e = e'$ in the binary consensus, and $e \downarrow e'$ in the blockchain consensus. Disagreement will be denoted with $\not\equiv$.
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We say that validator $v_i$ ``sees validator $v_j$ agreeing with estimate $e$ in a set of protocol messages $M$'' if:
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\begin{itemize}
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