-----Description----- 
This task requires implementing a Lean 4 method that finds the length of the longest strictly increasing subsequence in an array of integers. A subsequence is a sequence that can be derived from an array by deleting some or no elements without changing the order of the remaining elements.

-----Input-----
The input consists of one parameter:
nums: A list of integers representing the input array.

-----Output-----
The output is an integer:
Returns the length of the longest strictly increasing subsequence in the input array. 

