---
name: Theorem and Proof
category: math
description: Theorem/lemma/definition with proof using amsthm
packages:
  - amsthm
  - amsmath
preamble:
  - \newtheorem{theorem}{Theorem}[section]
  - \newtheorem{lemma}[theorem]{Lemma}
  - \newtheorem{definition}[theorem]{Definition}
---
\begin{theorem}[Optional Name]
  % State your theorem here
  For all $n \geq 1$, the inequality holds.
\end{theorem}

\begin{proof}
  % Write your proof here
  By induction on $n$. The base case $n = 1$ is trivial.
  For the inductive step, assume the result holds for $n = k$.
  Then for $n = k + 1$, we have\ldots
\end{proof}
