-----Description----- 
This task requires writing a Lean 4 method that computes the sum of the fourth power of the first n odd natural numbers. In other words, given a non-negative integer n, the method should calculate the sum: 1⁴ + 3⁴ + 5⁴ + ... for the first n odd numbers.

-----Input-----
The input consists of:
n: A non-negative natural number representing the number of odd natural numbers to consider.

-----Output----- 
The output is a natural number:
Returns the sum of the fourth power of the first n odd natural numbers.

-----Note----- 
The input n is assumed to be a non-negative integer.
The correctness of the result is established by a theorem that relates the computed sum to a specific formula.