```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")

    def get_factor(unit):
        if unit == base:
            return 1
        for parent, [factor, finer] in defs.items():
            if parent == unit:
                return factor
        raise ValueError(f"unit '{unit}' is not defined in the defs")

    if unit not in defs or not isinstance(defs[unit], list) or len(defs[unit]) != 2:
        raise ValueError(f"invalid unit definition for '{unit}'")

    factor, finer = defs[unit]

    if not isinstance(factor, int) or factor <= 0:
        raise ValueError("factor must be a positive whole number")

    if not isinstance(finer, str) or finer not in defs:
        raise ValueError(f"finer unit '{finer}' is not defined in the defs")

    if amount == 0:
        return 0

    current_unit = unit
    total_factor = 1
    while current_unit != base:
        factor = get_factor(current_unit)
        total_factor *= factor
        current_unit = finer

    return total_factor * amount
```