Updation frequently fails on MIUI 8.2.5
Install Xiaomi PC suit from this link: pcsuite.mi.com/
Go to fastboot mode (Turn Off phone turn on using power and volume down 
button) and connect device to computer and turn on PC suit
Here is process to install rom from PC suit
en.miui.com/thread-95630-1-1.html
Select a Global option and click on the flash device.It will install China Stable Rom.
After that download Global Stable Rom from the following link 
http://en.miui.com/download-303.html Flash it from updater app 


Note: Please take the backup before doing any steps. It will wipe out your staorage