Can i downgrade from iOS 7 to 6.1.3 for my iphone 4?

Hi I have an iPhone 4 and since upgrade to iOS 7 its frustrating how slow it is. I can't do any normal tasks fast on my phone such as music listening or messaging. When I message i am a fast typer but on iOS7, it lags and delays my typing because everything is so slow. When I'm listening to music when my screen is locked, when i unlock it the song skips to some other random part for no reason. iOS 7.0.2 is so sloppy and slow for me I want to swtich to Android real soon. I don't understand why you let iPhone 4 be included in the supported devices for iOS 7 because it isnt! Is their a way to downgrade back to iOS 6 so i can use my phone properly again? thank u for ur consideration