```python
def is_nested(string):
    '''
    Create a function that takes a string as input which contains only square brackets.
    The function should return True if and only if there is a valid subsequence of brackets 
    where at least one bracket in the subsequence is nested.

    is_nested('[[]]') ➞ True
    is_nested('[]]]]]]][[[[[]') ➞ False
    is_nested('[][]') ➞ False
    is_nested('[]') ➞ False
    is_nested('[[][]]') ➞ True
    is_nested('[[]][[') ➞ True
    '''
    # We need to find a valid subsequence where at least one bracket is nested.
    # A nested bracket means there is a pair of brackets that contains another pair inside it.
    # Essentially, we need to find a pattern like '[...]' where inside the brackets there is at least one '[]' pair.
    # So we need to find a substring (subsequence, but since it's contiguous in the original string for valid bracket matching, we can think of it as a substring) that has a nested structure.
    
    # Let's think about what constitutes a valid subsequence with nesting.
    # A valid subsequence of brackets means the brackets form a valid bracket sequence.
    # For nesting, we need at least one pair of brackets that contains another pair.
    # So we need to find a valid bracket sequence that has depth >= 2.
    
    # We can scan through the string and track the depth of brackets.
    # If we ever reach depth >= 2, that means we have a nested structure.
    # But we need to ensure that the brackets form a valid sequence.
    
    # Let's use a stack-based approach to find valid bracket sequences.
    # We'll track the depth. If at any point the depth reaches 2, we have found a nested structure.
    
    depth = 0
    for char in string:
        if char == '[':
            depth += 1
            if depth >= 2:
                return True
        elif char == ']':
            depth -= 1
            if depth < 0:
                # Invalid sequence, but we can continue looking for other valid subsequences
                # Actually, we need to be careful. A subsequence doesn't have to be contiguous.
                # But for bracket matching, we typically consider contiguous substrings.
                # Let me reconsider.
                pass
    
    return False
```