====== Theorem Name ======

===== Statement =====

**Theorem:** [Formal statement of the theorem]

===== Prerequisites =====

To understand this proof, you should be familiar with:
  * [[path:to:prerequisite1|Prerequisite 1]]
  * [[path:to:prerequisite2|Prerequisite 2]]

===== Intuition =====

[Brief explanation of the intuitive meaning of the theorem and why it matters]

===== Proof =====

**Lemma 1:** [If needed, state any supporting lemmas]

[Proof of supporting lemma]

**Main Proof:**

[Step-by-step proof using LaTeX for mathematical notation]

Let $X$ be a set such that $X = \{x \in \mathbb{R} : x > 0\}$.

We wish to prove that $\forall x \in X, \exists y \in \mathbb{R}$ such that $y^2 = x$.

Step 1: [First step of proof]

$$
\text{Mathematical expression here}
$$

Step 2: [Second step of proof]

Step n: [Final step of proof]

Therefore, [conclusion]. ■

===== Alternative Proofs =====

**Alternative Proof 1:** [If applicable]

[Details of alternative approach]

===== Applications =====

[Discussion of important applications or consequences]

===== Historical Notes =====

[Brief historical context about the theorem and its development]

===== References =====

  * [1] Author, A. (Year). *Title of Book*. Publisher.
  * [2] Author, B. (Year). "Title of Paper." *Journal*, Volume(Issue), Pages.

===== Related Theorems =====

  * [[path:to:related1|Related Theorem 1]]
  * [[path:to:related2|Related Theorem 2]]

~~DISCUSSION~~