Underground cave men dig path up (4,3,3)

I believe the answer is:

mind the gap

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'underground cave' is the definition.
I know nothing about this answer so I cannot judge whether it can be defined by this definition.

'men dig path up' is the wordplay.
'up' indicates an anagram.
'men'+'dig'+'path'='mendigpath'
'mendigpath' anagrammed gives 'MIND THE GAP'.

Can you help me to learn more?

(Another definition for mind the gap that I've seen is " Warning to those leaving train".)

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