Double spending is detected only if it present
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@ -671,7 +671,7 @@ $\widetilde{C} := S_K(C_p)$:
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\item The merchant gives $(\mathcal{D}, p, r)$ to the mint, revealing his
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payment information.
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\item The mint validates $\mathcal{D}$ and detects double spending.
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\item The mint validates $\mathcal{D}$ and checks for double spending.
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If the coin has been involved in previous transactions, it sends an error
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with the records from the previous transactions back to the merchant.
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