## Section15.1Theorem-Like Elements

The tags <theorem>, <algorithm>, <claim>, <corollary>, <fact>, <identity>, <lemma>, and <proposition> have the same structure in PreTeXt, so we will just illustrate <theorem> here.

The code in Listing 15.1.1 produces the following output:

You don't actually need a proof, but put it inside the theorem. You can actually put another proof right after this one if you want to.

The <title> is optional and typically used for theorems with names. To give an attribution, one can use the optional <creator> tag. Cross references (see Section 22.1) can be made using the name or the number, depending on how the author codes them.

A theorem-like element can contain multipe <proof> elements. In such instances, it would be useful to use the <title> tag within your proof. By default, a <proof> is hidden in a knowl when using HTML output. Click the “Proof.” heading to expand the proof. Click it again to hide the proof. A <proof> can also be divided into <case>s, each of which can have a title. Although it has not always been so, you can author a <proof> all on its own within a division. The structure of such a detached <proof> is the same as for a <proof> contained within a theorem-like element.

You can use <definition> essentially like <theorem>, but a <definition> does not have a proof. You are encouraged to use the <term> tag to set off the word being defined. If you wish to include a list of notation as an appendix as your document, you might also add a <notation> tag such as shown in Listing 15.1.3. A <notation> tag has no effect unless you have an <appendix> with a <notation-list/> in it.

The code in Listing 15.1.3 produces the following output:

### Definition15.1.4.

The binomial coefficient $$\binom{n}{k}$$ is the number of $$k$$-element subsets of an $$n$$-element set.