Since he has contributed generously, we are able to open the library

-> Had it not been for his generous contribution, we couldn't have opened the library.

⇔ Had it not been for+N/V-ing, S+would /could/might+(not)+Vpp

It was not until he pulled out his badge that I knew he was a cop

-> Not until he pulled out his badge did I know he was a cop

⇔ Not until + thời gian + trợ động từ + S + V (nguyên thể)

The fire alarm suddenly went off just as I reached my office on the fifteenth floor

-> No sooner had I reached my office on the fifteenth floor than the fire alarm suddenly went off

⇔ Công thức: No sooner + had + S1 + Ved/V3 than S2 + Ved/V2 (…vừa mới...thì…)