-----Description-----
This task requires writing a Lean 4 function that finds the single number in a non-empty list of integers, where every element appears exactly twice except for one element that appears only once. The function 
should return the integer that appears only once.

-----Input-----
The input is a non-empty list of integers:
- nums: A list in which each integer appears exactly twice except for one element that appears only once.

-----Output-----
The output is a single integer:
Returns the unique integer that appears exactly once in the list.

