------
## 最终结论
```python
def valid_date(date):
    """You have to write a function which validates a given date string and
    returns True if the date is valid otherwise False.
    The date is valid if all of the following rules are satisfied:
    1. The date string is not empty.
    2. The number of days is not less than 1 or higher than 31 days for months 1,3,5,7,8,10,12. And the number of days is not less than 1 or higher than 30 days for months 4,6,9,11. And, the number of days is not less than 1 or higher than 29 for the month 2.
    3. The months should not be less than 1 or higher than 12.
    4. The date should be in the format: mm-dd-yyyy
    """
    
    # Check if the date string is empty
    if not date:
        return False
    
    # Check if the format is correct using '-' as separator
    parts = date.split('-')
    if len(parts) != 3:
        return False
    
    # Extract month, day and year from parts
    try:
        month = int(parts[0])
        day = int(parts[1])
        year = int(parts[2])
    except ValueError:
        return False
    
    # Check month validity
    if month < 1 or month > 12:
        return False
    
    # Check day validity based on month
    if month in {1, 3, 5, 7, 8, 10, 12}:
        if day < 1 or day > 31:
            return False
    elif month in {4, 6, 9, 11}:
        if day < 1 or day > 30:
            return False
    elif month == 2:
        if day < 1 or day > 29: # Simplified check for February without considering leap years
            return False
    
    return True
```