1.prove:普通用词,指通过某种手段或方式提供证据以证实或证明某事物真实与否,某结论正确与否等情况.

I'll prove to the world that he was right.

2.certify:较正式用词,多指有签字盖章的、合符法律程序的书面证明.

Two witnesses must certify that this is your signature.