Could 'not having' be a good synonym for 'without' in the following sentence?

Hi teachers,
Could 'not having' be a good synonym for 'without' in the following sentence?
You can't arrive at work without a tie.

Thanks in advance.

learning54 said:

Hi teachers,
Could 'not having' be a good synonym for 'without' in the following sentence?
You can't arrive at work without a tie.

Thanks in advance.

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No, it's not good English to say "You can't arrive at work not having a tie."

Raymott said:

No, it's not good English to say "You can't arrive at work not having a tie."

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Hi Raymott,
Thank you for your reply. What about 'with no'? Could it be better?

learning54 said:

Hi Raymott,
Thank you for your reply. What about 'with no'? Could it be better?

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Better than 'without'? No. What's wrong with 'without'?
Or "You have to wear a tie to work."

Raymott said:

Better than 'without'? No. What's wrong with 'without'?
Or "You have to wear a tie to work."

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Hi Raymott,
Thank you for your reply. There's nothing wrong with 'without', of course. I'm just saying if 'with no' could be a good synonym for 'without'.

With no would work, though I prefer without, but I would change the verb:
You can't come to work with no tie.

Tdol said:

With no would work, though I prefer without, but I would change the verb:
You can't come to work with no tie.

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Hi Tdol,
Thank you for your reply.
I guess, I have explained myself really badly. The thing is that the original sentence is this one, 'You can't arrive at work without a tie'. My question on saying if 'with no' could be a good synonym for 'without', it is just to explain it to the students, not to change 'without' for 'with no'.
On the other hand, I have a book that says that two synonyms for 'without' can be 'not having' and 'lacking'; and it gives this example, 'Jerry got to the park two hours late without the picnic basket'. That's why I assumed that 'not having' was a good one.
The name of the book is 'Prepositions Illustrated By Gloria Wahlen. Publisher: Michigan.