If $T$ is a set, $P(x)$ denotes x is a hard worker and $D(x)$ denotes that $x$ is a worker, how to translate the following to English sentence?

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So $T$ is a set of workers and materials in a tower, $P(x)$ denotes that $x$ is a hard worker and $D(x)$ denotes that $x$ is a worker

$\forall x \in T: [D(x) \rightarrow [\exists y \in T: P(y)]]$

This is my translation: For all material and workers in the tower, if the unit is a worker, then there exists another worker such that he or she is a hard worker.

However I felt my translation awkward and incorrect and I have few confusions here:

$1$. How can we be determined that $y$ is a worker and why?

$2$. Is saying "For all" ok for a English sentence?

Someone please help with the translation.