How to add link rel tags on paginated posts?

I'm using the following code in functions.php to add rel prev/next tags to paginated contents:

function add_rel_nextprev_to_paginated_content()
{
global $paged;
if ( get_previous_posts_link() ) { ?link rel="prev" href="?php echo get_pagenum_link( $paged - 1 ); ?"?php }
if ( get_next_posts_link() ) { ?link rel="next" href="?php echo get_pagenum_link( $paged + 1 ); ?"?php }
}
remove_action('wp_head', 'adjacent_posts_rel_link_wp_head');
add_action('wp_head', 'add_rel_nextprev_to_paginated_content');

This works well for categories, tags and other content, but not the posts that were split into multiple pages by WP's tag.

However, I can't find the right function to call the next page of a paginated post.

Any help is highly appreciated.