-----Description-----
This task requires implementing the "Longest Increasing Subsequence" problem in Lean 4.
Given a list of integers, the function should compute the length of the longest strictly increasing
subsequence. A subsequence is formed by deleting zero or more elements without changing the order.
If the list is empty, the function should return 0.

-----Input-----
- nums: A list of integers.

-----Output-----
- A natural number representing the length of the longest strictly increasing subsequence.
- If there is no increasing subsequence, return 0.

