Basics

Declare the environments under amsthm in the metadata, grouped by style, and use each one as the class of a fenced div.

Definition 1. A group is a set with an associative operation, an identity element, and an inverse for each element.

A definition has a bold heading and an upright body. A theorem, in the plain style, has an italic body, in which emphasis turns upright:

Theorem 1 (Lagrange). The order of a subgroup of a finite group divides the order of the group.

The info attribute is the note in parentheses, and may contain Markdown. Lemma is listed under Theorem, so it shares its counter:

Lemma 2. A group of prime order is cyclic.

A trailing * makes an environment unnumbered. A name with a space is written with an underscore as a class:

Main Theorem. Every finite group of prime order \(p\) is isomorphic to \(\mathbb{Z}/p\mathbb{Z}\).

Remark 1. The remark style has an italic heading and an upright body.

proof is always defined, and ends with an open box:

Proof. By Lagrange’s theorem, the subgroup generated by any element other than the identity is the whole group.\(\quad\Box\)

Its info replaces the heading:

Proof of the Main Theorem. Map a generator to \(1\).\(\quad\Box\)

Source

This page is made from the Markdown below, and LaTeX output gets the LaTeX beside it. The PDF under Other Formats is that LaTeX, typeset by amsthm.

Markdown

---
title: Basics
amsthm:
  plain:
    - Theorem:
        - Lemma
    - Main Theorem\*
  definition:
    - Definition
  remark:
    - Remark
---

Declare the environments under `amsthm` in the metadata, grouped by
style, and use each one as the class of a fenced div.

::: Definition
A *group* is a set with an associative operation, an identity element,
and an inverse for each element.
:::

A definition has a bold heading and an upright body. A theorem, in the
`plain` style, has an italic body, in which *emphasis* turns upright:

::: {.Theorem info="Lagrange"}
The order of a subgroup of a finite group *divides* the order of the
group.
:::

The `info` attribute is the note in parentheses, and may contain
Markdown. Lemma is listed under Theorem, so it shares its counter:

::: Lemma
A group of prime order is cyclic.
:::

A trailing `*` makes an environment unnumbered. A name with a space is
written with an underscore as a class:

::: Main_Theorem
Every finite group of prime order $p$ is isomorphic to
$\mathbb{Z}/p\mathbb{Z}$.
:::

::: Remark
The `remark` style has an italic heading and an upright body.
:::

`proof` is always defined, and ends with an open box:

::: proof
By Lagrange's theorem, the subgroup generated by any element other than
the identity is the whole group.
:::

Its `info` replaces the heading:

::: {.proof info="Proof of the Main Theorem"}
Map a generator to $1$.
:::

LaTeX

\usepackage{amsthm}
\theoremstyle{plain}
\newtheorem{Theorem}{Theorem}
\newtheorem{Lemma}[Theorem]{Lemma}
\newtheorem*{Main Theorem}{Main Theorem}
\theoremstyle{definition}
\newtheorem{Definition}{Definition}
\theoremstyle{remark}
\newtheorem{Remark}{Remark}
Declare the environments under \texttt{amsthm} in the metadata, grouped
by style, and use each one as the class of a fenced div.

\begin{Definition}
A \emph{group} is a set with an associative operation, an identity
element, and an inverse for each element.
\end{Definition}

A definition has a bold heading and an upright body. A theorem, in the
\texttt{plain} style, has an italic body, in which \emph{emphasis} turns
upright:

\begin{Theorem}[Lagrange]
The order of a subgroup of a finite group \emph{divides} the order of
the group.
\end{Theorem}

The \texttt{info} attribute is the note in parentheses, and may contain
Markdown. Lemma is listed under Theorem, so it shares its counter:

\begin{Lemma}
A group of prime order is cyclic.
\end{Lemma}

A trailing \texttt{*} makes an environment unnumbered. A name with a
space is written with an underscore as a class:

\begin{Main Theorem}
Every finite group of prime order \(p\) is isomorphic to
\(\mathbb{Z}/p\mathbb{Z}\).
\end{Main Theorem}

\begin{Remark}
The \texttt{remark} style has an italic heading and an upright body.
\end{Remark}

\texttt{proof} is always defined, and ends with an open box:

\begin{proof}
By Lagrange's theorem, the subgroup generated by any element other than
the identity is the whole group.
\end{proof}

Its \texttt{info} replaces the heading:

\begin{proof}[Proof of the Main Theorem]
Map a generator to \(1\).
\end{proof}