Definitions, theorems, corollaries, etc. are supported by the tags: <theorem>, <corollary>, <lemma>, <algorithm>, <proposition>, <claim>, <fact>, <definition>, <conjecture>, <axiom>, and <principle>. Each may have a <title> (strongly encouraged), and then contains a <statement> which is a sequence of paragraphs and other elements. As appropriate, some of these elements (such as a <lemma>) may contain an optional <proof> (or several), while other elements may not have a <proof> (such as a <conjecture>).
A <definition> is a natural place to define notation as well (see Section 3.22), and to use the <term> tag to identify the terminology being defined.
In order to assist readers locating numbered items, these items are all numbered consecutively in a group that includes <example>s, <remark>s and inline <exercise>s.