-----Description----- 
This task requires writing a Lean 4 method that finds the length of the longest increasing sequence in a given array. The method should return the length of the longest increasing subsequence, in which every element is strictly less than the latter element.

-----Input-----
The input consists of an arrat:
a: The input array.

-----Output-----
The output is an integer:
Returns the length of the longest increasing subsequence, assuring that it is a subsequence of the input sequence and that every element in it is strictly less than the latter one.

