It is semantically correct to use <header> inside <section>?

Question

All examples I found on internet refers to using <h1> inside <section>, but nothing related to the use of <header> element.

It's valid HTML5, but what about semantics?

Maybe I'm misusing the <section> element, for the completeness here is my use case:

<main role="main">
  <header>page header</header>
  <section id="cookiesPolicy>
    <header>
      <h1>Cookies Policiy</h1>
    </header>
    <div>Bla bla bla bla bla bla bla</div>   
  </section>    
  <footer>page footer</footer>
</main>

Answer 1

Yes it is semantically correct to use header inside section

header – There is a crucial difference between the header element and the general accepted usage of header (or masthead). There’s usually only one header or ‘masthead’ in a page. In HTML5 you can have as many as you want. The spec defines it as “a group of introductory or navigational aids”. You can use a header in any section on your site. In fact, you probably should use a header within most of your sections. The spec describes the section element as “a thematic grouping of content, typically with a heading.”

Source

You can also check header W3 specs here

Answer 2

header is:

introductory content for its nearest ancestor sectioning content or sectioning root element.

section is a valid sectioning content, so header is semantically correct - even encouraged - in this position.

Quote taken from this HTML5 Doctor page, which actually quotes the HTML5 spec directly.