Writing Theorems, Proofs, and Definitions on Dev.to

If you're writing a math-heavy article — explaining an algorithm's correctness, proving a complexity bound, or walking through a cryptographic protocol — you need a way to clearly distinguish theorems, proofs, definitions, and examples from the surrounding text.

Standard LaTeX has dedicated environments for this (\begin{theorem}, \begin{proof}). Dev.to doesn't. But with some markdown techniques, you can get close.

Method 1: Blockquotes (Simplest)

Markdown blockquotes (>) give a visual distinction from body text:

> **Theorem 1 (Lagrange's Theorem).**
> For a finite group G and subgroup H,
> the order of H divides the order of G:
> {% katex %} |G| = [G : H] \cdot |H| {% endkatex %}

Theorem 1 (Lagrange's Theorem).
For a finite group G and subgroup H, the order of H divides the order of G:

$$|G| = [G : H] \cdot |H|$$

Simple, reliable, and works everywhere.

Method 2: Collapsible Proofs

Long proofs can overwhelm readers. Use <details> to make them collapsible:

<details>
<summary><b>Proof</b></summary>

Consider the set of left cosets of H in G.
Each coset gH contains |H| elements,
and distinct cosets are disjoint.
Since G is the disjoint union of its cosets:

{% katex %}
|G| = (\text{number of cosets}) \times |H| = [G:H] \cdot |H|
{% endkatex %}

{% katex inline %} \square {% endkatex %}
</details>

Proof Consider the set of left cosets of H in G. Each coset gH contains |H| elements, and distinct cosets are disjoint. Since G is the disjoint union of its cosets:

$$|G| = (\text{number of cosets}) \times |H| = [G:H] \cdot |H|$$

$\square$

This lets readers see the theorem statement first and expand the proof only if they want the details.

Method 3: Horizontal Rules

Use --- to create visual boundaries:

---

**Theorem 2 (Euler's Formula).**

For any real number θ:

{% katex %}
e^{i\theta} = \cos\theta + i\sin\theta
{% endkatex %}

---

---

Theorem 2 (Euler's Formula).

For any real number θ:

$$e^{i\theta} = \cos\theta + i\sin\theta$$

---

QED Marks

In LaTeX, \begin{proof} automatically adds a QED mark. On Dev.to, add it manually:

Style	Code	Result
White square	{% katex inline %} \square {% endkatex %}	□
Black square	{% katex inline %} \blacksquare {% endkatex %}	■
Text	■	■

Place it at the end of your proof, typically on the last line.

Numbering Conventions

Option 1: Sequential numbering (recommended)

Theorem 1, Lemma 2, Theorem 3, Corollary 4 ...

Sequential numbering makes it easy to find referenced items — "Lemma 2 comes before Theorem 3" is immediately clear from the numbers.

Option 2: Section-based numbering

Theorem 2.1, Lemma 2.2, Theorem 3.1 ...

Better for longer articles with clear sections.

Option 3: Type-based numbering

Theorem 1, Theorem 2, Lemma 1, Lemma 2 ...

Avoid this — it's confusing when referencing ("Lemma 1 is used in the proof of Theorem 2" doesn't tell you the ordering).

Distinguishing Types

In math writing, different statement types serve different roles:

Type	Purpose	When to use
Definition	Introduces a term	Before first use
Theorem	Major result	Central claims
Lemma	Helper result	Building blocks for theorems
Proposition	Medium result	Less central than a theorem
Corollary	Direct consequence	Immediately after a theorem
Example	Concrete instance	After definitions or theorems
Remark	Commentary	Supplementary notes

Full Example: The First Isomorphism Theorem

Here's a complete example combining everything:

---

Definition 1 (Group Homomorphism).
A map $\varphi: G \to H$ between groups is a homomorphism if

$$\varphi(ab) = \varphi(a)\varphi(b)$$

for all $a, b \in G$ .

Definition 2 (Kernel and Image).
For a homomorphism $\varphi: G \to H$ :

$$\begin{aligned} \ker\varphi &= { g \in G \mid \varphi(g) = e_H } \ \operatorname{Im}\varphi &= { \varphi(g) \mid g \in G } \end{aligned}$$

Lemma 3. The kernel $\ker\varphi$ is a normal subgroup of G.

Proof

The subgroup property is straightforward. For normality: for any

$g \in G$

and

$n \in \ker\varphi$

:

$$\begin{aligned} \varphi(gng^{-1}) &= \varphi(g)\varphi(n)\varphi(g^{-1}) \\ &= \varphi(g) \cdot e_H \cdot \varphi(g)^{-1} = e_H \end{aligned}$$

So

$gng^{-1} \in \ker\varphi$

, proving

$\ker\varphi \trianglelefteq G$

.

$\square$

Theorem 4 (First Isomorphism Theorem).
For any group homomorphism $\varphi: G \to H$ :

$$G / \ker\varphi \cong \operatorname{Im}\varphi$$

Proof

Let

$N = \ker\varphi$

. Define

$\bar{\varphi}: G/N \to \operatorname{Im}\varphi$

by

$\bar{\varphi}(gN) = \varphi(g)$

.

Well-defined: If

$gN = g'N$

, then

$g^{-1}g' \in N$

, so

$\varphi(g) = \varphi(g')$

.

Homomorphism:

$\bar{\varphi}(gN \cdot g'N) = \varphi(gg') = \varphi(g)\varphi(g') = \bar{\varphi}(gN)\bar{\varphi}(g'N)$

.

Injective:

$\bar{\varphi}(gN) = e_H$

implies

$g \in N$

, so

$gN = N$

.

Surjective: By definition of

$\operatorname{Im}\varphi$

.

Hence

$\bar{\varphi}$

is an isomorphism.

$\square$

Corollary 5. If $\varphi$ is surjective, then $G/\ker\varphi \cong H$ .

---

Templates

Copy-paste these to get started:

Theorem:

> **Theorem N (Name).**
> Statement here.
> {% katex %} equation {% endkatex %}

Proof (collapsible):

<details>
<summary><b>Proof</b></summary>

Proof body here.

{% katex inline %} \square {% endkatex %}
</details>

Definition:

> **Definition N (Term).**
> Definition here.

Summary

• Blockquotes for theorems/definitions, <details> for proofs
• Sequential numbering for easy referencing
• QED mark: $\square$ at the end of proofs
• Collapsible proofs keep articles scannable
• No auto-numbering or cross-references — manage manually