Zorn's lemma

例句：

1. 1. The theorem states that the sum of the squares of the lengths of the sides of a triangle is always greater than the square of the length of the hypotenuse.
   这个定理表明，三角形边长的平方和总是大于斜边的平方。
2. 2. In mathematics, this theorem is used to prove that a line can be extended beyond the edge of a plane figure withoutintersecting it.
   在数学中，这个定理被用来证明一条线可以延伸到平面图形的边缘之外而不与它相交。
3. 3. The lemma is often used in proofs involving triangles and their properties, such as the Pythagorean theorem.
   这个定理经常用于涉及三角形及其性质的证明中，例如毕达哥拉斯定理。