• for every $a \in I$ there exist $f_1, \ldots , f_ r \in J$ and $c \geq 0$ such that

1. $\det _{1 \leq i, j \leq r}(\partial f_ j/\partial x_ i)$ divides $a^ c$ in $B$, and

2. $a^ c J \subset (f_1, \ldots , f_ r) + J^2$.

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