What is a rule that is proven true?

A rule that is proven true is often referred to as a theorem in mathematics. For example, the Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. This theorem has been rigorously proven through various methods and is universally accepted as true within Euclidean geometry. Such proven rules provide a foundation for further exploration and application in mathematics and related fields.