Make double pending Exculpability section about prevention
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@ -1407,7 +1407,7 @@ protocol is never used.
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\subsection{Exculpability arguments}
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\subsection{Exculpability arguments}
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\begin{lemma}\label{lemma:double-spending}
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\begin{lemma}\label{lemma:double-spending}
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The exchange can detect and prove double-spending.
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The exchange can detect, prevent, and prove double-spending.
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\end{lemma}
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\end{lemma}
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\begin{proof}
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\begin{proof}
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@ -1417,13 +1417,15 @@ obtains either a deposit-permission or a refresh-record, both of which
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contain a signature made with the public key of coin to authorizing the
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contain a signature made with the public key of coin to authorizing the
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respective operation. If the exchange has a set of refresh-records and
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respective operation. If the exchange has a set of refresh-records and
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deposit-permissions whose total value exceed the value of the coin, the
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deposit-permissions whose total value exceed the value of the coin, the
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exchange can show this set to prove that double-spending was attempted.
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exchange can show this set to prove that double-spending is being
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attempted and justify rejecting the operation.
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\end{proof}
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\end{proof}
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\begin{corollary}
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\begin{corollary}
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Merchants and customers can verify double-spending proofs by verifying that the
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Merchants and customers can verify proofs of double-spending attempts
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signatures in the set of refresh-records and deposit-permissions are correct and
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by verifying that the signatures in the set of refresh-records and
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that the total value exceeds the coin's value.
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deposit-permissions are correct and that the total value would exceed
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the coin's value.
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\end{corollary}
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\end{corollary}
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\begin{lemma}
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\begin{lemma}
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