How to configure htaccess correctly if RewriteBase is used?

Question

Apache HTTP Server

Good evening!
I've got a problem that I can't solve. At the root of the site is htaccess and it redirects to the version without www.

RewriteBase / 
RewriteCond %{HTTP_HOST} ^www\.(.*)$
RewriteRule ^(.*)$ http://%1/$1 [L,R=301]

And everything seems to be fine, but one directory has its own htaccess that does not redirect to the version without www.
And I can’t defeat him in any way ..... Help me understand how ..

RewriteEngine On 
  RewriteBase /gallery 
  RewriteCond %{REQUEST_FILENAME} -f [OR]
  RewriteCond %{REQUEST_FILENAME} -d
  RewriteRule ^.*$ - [L]
  RewriteRule ^.*/?$                        index.php [L,QSA]

Answer 1

rewrite base should not interfere
well, just put your redirect to www at the beginning of the file