```python
def warm_up(readings: list, floor: int) -> list:
    """
    Discard readings from the start that are below the floor,
    and return everything from the first reading that reaches the floor.
    If no reading reaches the floor, return an empty list.
    """
    for i, reading in enumerate(readings):
        if reading >= floor:
            return readings[i:]
    return []
```