thymeleaf check if user is logged in or not

I'm using Spring boot with Thymeleaf and Spring security. I have got a simple view with login link. When user logs in, I'd like to change login link to logout link.

I tried:

<div sec:authorize="#{isAuthenticated()}">
  <a th:href="@{/logout}">Log out</a>
</div>
<div sec:authorize="#{isAnonymous()}">
  <a th:href="@{/login}">Log in</a>
</div>

but it's not working - it displays both links.

Best regards.