Translating math words to Mathematica, an example, an experiment

Questions
1

A textbook has this:

For any two integers (positive, negative, or zero) n and m >= n

I tried to translate into Mathematica thusly:

Given Element[n | m, Integers] && { n > 0 | n < 0 | n = 0} && { 
  m > 0 | m < 0 | m = 0} && m >= n

Does that make sense and work in Mathematica or only to human readers? :wink: I am conducting some experiments how far and well translating from an ordinary math textbook into live Mathematica code. I am understanding more about the hidden assumptions Mathematica makes that would need to be spelled out.
Thanks.

2

Beware the difference between | and ||, between = and ==, and between {} and (). The following is closer to the textbook phrase:

ForAll[{n, m},
 Element[n | m, Integers]
  && (n > 0 || n < 0 || n == 0)
  && (m > 0 || m < 0 || m == 0)
  && m >= n,
 predicate]

For example

ForAll[{n, m},
  Element[n | m, Integers]
   && (n > 0 || n < 0 || n == 0)
   && (m > 0 || m < 0 || m == 0)
   && m >= n,
  2^m >= 2^n] // Reduce
3

Wonderful, now I have a template to use/edit going forward in my translating textbook text into live Mathematica code experiments. Since there are definitions and assumptions that are stated before giving the formula or function.
Thank you!