```python
def base_amount(amount: int, unit: str, defs: dict, base: str) -> int:
    """
    Convert amount of given unit into its corresponding amount in the base unit.
    
    :param amount: non-negative integer representing the amount of the unit
    :param unit: string representing the unit name
    :param defs: dictionary mapping unit names to a pair [factor, finer]
                indicating how many finer units fit in one unit
    :param base: string representing the base unit name
    :return: integer representing the equivalent amount in the base unit
    :raises ValueError: if the input is invalid
    """
    if not isinstance(amount, int) or amount < 0:
        raise ValueError("Amount must be a non-negative integer.")
    
    if not isinstance(unit, str):
        raise ValueError("Unit must be a string.")
    
    if not isinstance(defs, dict):
        raise ValueError("Defs must be a dictionary.")
    
    if not isinstance(base, str):
        raise ValueError("Base must be a string.")
    
    if unit not in defs:
        raise ValueError(f"Unknown unit: {unit}")
    
    if base not in defs or defs[base] != (0, None):
        raise ValueError(f"Invalid base unit definition for: {base}")
    
    factor, finer = defs[unit]
    
    if not isinstance(factor, int) or factor <= 0:
        raise ValueError("Factor must be a positive integer.")
    
    if finer is not None and finer not in defs:
        raise ValueError(f"Unknown finer unit: {finer}")
    
    def convert(amount, unit):
        if unit == base:
            return amount
        if unit in defs:
            factor, finer = defs[unit]
            return amount * factor + convert(amount // factor, finer)
        else:
            raise ValueError(f"Unknown unit: {unit}")
    
    try:
        result = convert(amount, unit)
    except OverflowError:
        raise ValueError("Amount is too large to convert.")
    
    return result
```