-----Description-----
This task requires writing a Lean 4 method that takes two sorted (non-decreasing) integer lists and merges them into a single sorted list. The output must preserve order and include all elements from both input lists.

-----Input-----
The input consists of:
a: A list of integers sorted in non-decreasing order.
b: Another list of integers sorted in non-decreasing order.

-----Output-----
The output is a list of integers:
Returns a merged list that contains all elements from both input lists, sorted in non-decreasing order.

