```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 or base not in defs:
        raise ValueError("unknown unit or base")
    if not isinstance(defs[unit][0], int) or defs[unit][0] <= 0:
        raise ValueError("bad factor")
    if unit == base:
        return amount
    chain = [unit]
    while chain[-1] != base:
        if chain[-1] not in defs:
            raise ValueError("unknown unit in chain")
        chain.append(defs[chain[-1]][1])
    factor = 1
    for unit in chain:
        factor *= defs[unit][0]
    return amount * factor
```