Of course it is required (within the computational limits of your computer, of course)
If p(x) means 'x is an integer', you could use the regex /^1$/ since it matches integers only (in particular, the integer 1). That's not sufficient, you need to match all integers.
Comments
If a regex is required to only match x if p(x), is the regex required to match ALL x such that p(x)?
Although this is probably just pointless nitpicking on my part.
Of course it is required (within the computational limits of your computer, of course)
If p(x) means 'x is an integer', you could use the regex /^1$/ since it matches integers only (in particular, the integer 1). That's not sufficient, you need to match all integers.
edited:format
It's required to match all such x, otherwise the empty regex "" trivially satisfies the requirement.