Prove that in DBSCAN*, for a fixed Min Pts value and two neighborhood thresholds, (epsilon_{1}

Question:

Prove that in DBSCAN*, for a fixed Min Pts value and two neighborhood thresholds, $\epsilon_{1}<\epsilon_{2}$, a cluster $C$ with respect to $\epsilon_{1}$ and MinPts must be a subset of a cluster $C^{\prime}$ with respect to $\epsilon_{2}$ and MinPts.

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