Design a data structure that supports insert, delete, and get-minimum operations, all in O(1) time complexity.
Assume delete(value) may remove any existing value, including the current minimum. Explain whether the requirement is achievable for arbitrary comparable values, and implement process_operations(operations) using the closest practical design if it is not.
Each operation is ['insert', value], ['delete', value], or ['get-min']; return the results of all get-min operations, using None when the structure is empty.
def process_operations(operations):