The Court was still,in theory,under a duty to enquire into the facts alleged.

The Court was still,in theory,under a duty to enquire into the facts alleged.
The pillars that hold up the roof broke in the earthquake,leading to the collapse of the house.
请帮忙解释这两个句子,另外想问第二个句子中为何不是held up 而是原形?
改为holding可以吗？