I.OS 5 doesn't want to update to iOS 6.1.3?

I recently got an iPhone 4 but it has the older version of iOS 5. I want to update it to iOS 7 but first i have to update it to iOS 6.1.3. I tried to do that amd it says 'verifying update' and then after a while it says, 'veryfying the update could not be done because you are no longer connected to the internet'. But i'm connected to the Wi-Fi that i have at home. Any help please?

Why don't you just call apple support?