Includeing "general-template.php" in child theme?

I’m building a WP website using theme “twenty twelve.”
I want to modify the look of search box and button. The code is in “wp-includes/general-template.php”

I don’t want my changes to be overwritten when I update wp, so I want to put the file in my child theme. I tried simply putting a copy of the file in my child theme folder, but it didn’t work. Is there any way to include “general-template.php” in child theme? or way to avoid overwriting it when update.

Thanks,

Yong