Check my .htaccess code please

My goal is to add the www and enable HTTPS in all URLs, does this setup look fine?

Code:

RewriteCond %{HTTPS} off
# First rewrite to HTTPS:
# Don't put www. here. If it is already there it will be included, if not
# the subsequent rule will catch it.
RewriteRule .* https://%{HTTP_HOST}%{REQUEST_URI} [L,R=301]
# Now, rewrite any request to the wrong domain to use www.
RewriteCond %{HTTP_HOST} !^www\.
RewriteRule .* https://www.%{HTTP_HOST}%{REQUEST_URI} [L,R=301]

#Checks to see if the user is attempting to access a valid file,
#such as an image or css document, if this isn't true it sends the
#request to index.php
RewriteCond %{REQUEST_FILENAME} !-f
RewriteCond %{REQUEST_FILENAME} !-d
RewriteCond $1 !^(index\.php|public|images|robots\.txt|css)
RewriteRule ^(.*)$ index.php/$1 [L]