You cant prove that your 'red' exists anywhere except in your own mind, because you cant communicate what you see or think. The fact that an overwhelming number of people do agree on what red is, is a consensus of evidence, not proof of 'red'. This is called 'consensus reality.' Youd read up where I quoted myself for more info on that.
Or try thinking of it where in english we'd call that 'red' and think of it as such. If you thought in hungarian, medium red would be piros and dark red voros. Distinct colours the way pink and red are in english. This is the problem of language. (Hungarian info provided by my brother)