```python
def base_amount(amount: int, unit: str, defs: dict, base: str) -> int:
    if isinstance(amount, bool) or not isinstance(amount, int) or amount < 0:
        raise ValueError("amount must be a non-negative integer")
    
    if unit not in defs:
        raise ValueError(f"unit '{unit}' is not defined in defs")
    
    if base not in defs:
        raise ValueError(f"base '{base}' is not defined in defs")
    
    def get_factor(unit):
        if unit == base:
            return 1
        elif unit in defs:
            return defs[unit][0]
        else:
            raise ValueError(f"unit '{unit}' is not defined in defs")
    
    def convert(amount, unit):
        if unit == base:
            return amount
        else:
            factor = get_factor(unit)
            finer_unit = defs[unit][1]
            return convert(amount // factor, finer_unit) * factor
    
    try:
        return convert(amount, unit)
    except ValueError as e:
        raise ValueError(f"Error converting amount: {e}")
```