Choose $\pi _1, \ldots , \pi _ d \in \mathfrak p$ which map to a regular system of parameters of $k[y_1, \ldots , y_ m]_\mathfrak p$.
Choose $\pi _1, \ldots , \pi _ d \in \mathfrak p$ which map to a regular system of parameters of $k[y_1, \ldots , y_ m]_\mathfrak p$.
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