-----Description----- 
This task requires writing a Lean 4 method that searches an array of integers to locate the first odd number. The method should return a pair where the first element is a Boolean indicating whether an odd number was found, and the second element is the index of that odd number if found, or -1 if no odd number exists. When an odd number is found, the method should return the smallest index at which an odd number occurs.

-----Input-----
The input consists of:
a: An array of integers.

-----Output-----
The output is a pair (Bool, Int):
- If the Boolean is true, then the integer represents the smallest index of an odd number in the array.
- If the Boolean is false, then there are no odd numbers in the array, and the accompanying integer is -1.

-----Note-----
- The input array is assumed to be non-null.
- If multiple odd numbers are present, the index returned should correspond to the first occurrence.