A. proof 用于证明某件事是真实的，即"证明"：
I believe what you say; I don't need any proof. 我相信你所说的话；我不需要任何证明。
Have you got any proof that you own this car?
We still have no proof that he is innocent.
As a proof of his love, he spent all his money on a ring for her.
scientific proof 科学证明；a proof of carelessness 粗心的证明
B. evidence 多用于指法律方面的"证据"；另外还表示迹象 (sign, indication)"，这时常用于there is (some) evidence that…的结构：
My teacher was never called on to give evidence.
Have you enough evidence(of his guilt) to arrest him?
The supposed murder weapon was produced in evidence at his trial.
Anything you say may be used in evidence against you.
When the police arrived, he had already destroyed the evidence of his guilt.
There is some evidence that dishonesty may ebb and flow.
There is evidence that high school cheating may be on the rise.
There was some evidence that the documents had been tampered with.
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