proof

The police found DNA proof that linked the suspect to the crime scene.

(Chinese) 警方发现了将嫌疑人与犯罪现场联系起来的DNA证据。

You must show proof of identification, such as a passport, to enter the building.

(Chinese) 你必须出示身份证件（如护照）才能进入大楼。

The student wrote out a step-by-step mathematical proof for the Pythagorean theorem.

(Chinese) 学生写出了勾股定理的详细数学证明过程。

This complex logical proof was first discovered by an ancient Greek philosopher.

(Chinese) 这个复杂的逻辑证明最早是由一位古希腊哲学家发现的。