这些动词均含有“证明、证实”之意。
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。
- They hope this new evidence will prove her innocence.
他们希望这一新证据能证明她无罪。 - I certainly don't have anything to prove ─my record speaks for itself.
我当然不用证明什么——我的纪录就可说明一切。
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。
- He handed her a piece of paper certifying (that) she was in good health.
他递给她一份她的健康证明书。 - He was certified dead on arrival.
他送到时被证实已死亡。 - The accounts were certified (as) correct by the finance department.
账目经财务部门证实无误。
demonstrate : 指通过推理、辩论、实验或以实例来证明事物的正确与否。常用于理论、学说、定律等的证明上。
- These results demonstrate convincingly that our campaign is working.
这些结果有力地证明，我们的运动正在发挥作用。 - It has been demonstrated that this drug is effective.
这药已证实是有效的。
establish : 指证实事实或理论的真实性与正确性，使其能长期存在或为人们所接受。
- We need to establish where she was at the time of the shooting.
我们需要查实枪击发生时她在何处。 - It has since been established that the horse was drugged.
此后便证实马被注射了麻醉药。 - Medical tests established that she was not their own child.
医学化验证实她不是他们的亲骨肉。
testify : 较正式用词，既指出庭作证，提供证据，又指为某人或某事的是否真实提供证据或证明。
- She refused to testify against her husband.
她拒绝出庭作证指控丈夫。 - Several eyewitnesses testified that they saw the officers hit Miller in the face.
几位目击证人证明他们看见那几个警官打了米勒的脸。 - Too many young people are unable to write or spell well, as employers will testify.
写作或拼写不好的年轻人太多了，这一点雇主都会证明。 - Recent excavations testify to the presence of cultivated inhabitants on the hill during the Arthurian period.
最近几次发掘证实了亚瑟王时期这座山上有农耕人口居住过。
