> ## Documentation Index
> Fetch the complete documentation index at: https://resources.latex-cloud-studio.com/llms.txt
> Use this file to discover all available pages before exploring further.

# Theorems and Proof Environments in LaTeX

> Define theorem-like environments in LaTeX with amsthm and create clean proof structures for academic writing.

Use `amsthm` to build consistent theorem, lemma, and proof sections.

## Setup

```latex amsthm-setup.tex theme={null}
\usepackage{amsthm}

\newtheorem{theorem}{Theorem}[section]
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{corollary}[theorem]{Corollary}

\theoremstyle{definition}
\newtheorem{definition}[theorem]{Definition}

\theoremstyle{remark}
\newtheorem{remark}[theorem]{Remark}
```

## Usage

```latex theorem-usage.tex theme={null}
\begin{theorem}[Convergence]
Let $f_n$ be a Cauchy sequence in a complete normed space. Then $f_n$ converges.
\end{theorem}

\begin{proof}
Apply completeness and standard norm arguments.
\end{proof}
```

## Related Pages

* [Align and multline environments](/learn/latex/mathematics/align-and-multline-environments)
* [Writing a research paper](/learn/latex/how-to/writing-research-paper)