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Escaping
Generally, if you add text inside quotes " " (e.g. in Hint) you need to escape
backslashes, but if you provide text inside a doc comment
/-- -/ (e.g. in the Statement description) you do not!
Furthermore, inside Hint you need to escape all opening curly brackets as \{ since {h} is syntax for inserting a variable name h.
Example
Inside strings, you need to escape backslashes, but not inside doc-strings, therefore you
would write Introduction "some latex here: $\\iff$." , but
/-- some latex here: $\iff$. -/ Statement ...
Support
It is important to mention that KateX supports most but not all of latex and its packages. See supported.