Embedding of Sobolev Space $W^{n, \infty}(\Omega)$ into $C^{n-1}(\Omega)$

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In a paper I was studying it was used that $W^{n, \infty}([0,1]^d)\subset C^{n-1}([0,1]^d)$. I have searched for hours but I cannot seem to find a reference or proof of that. I suppose that it follows from some Sobolev embedding theorem but they usually only consider the case $p<\infty$.

Can someone help me out and explain why the result is true and/or provide a reference?

Thank you and best regards!