Logical Proof That Reality Is A Dream

this has had me in a tizz. mainly because I have been experiencing very powerul vivid and unusual dreams. I will give you a bit of background. My mother passed away 4 years ago; and though I have been through the grieving process, I am still wounded by it. My mother died, I would say  a very happy woman, having achived  something that she always wanted to: managerial status. However, In the last two years of her life, during this period of happiness, she became a very different person than the one I knew. This had an impact upon everyone. especially my father, who didn't like the person mum became: eg, despite the fact it was a small antiques bric a bracesque shop, she was the owner and part manager, which gave her a purpose and a means to carry on. In sum, she had become sucsessful. 
succsess hasn't been something that our family -or I for that matter- specialise in. In fact I would go so far to state that I have -on nuerous occasions- deliberately screwed my life up to fail, to justify my own sense of permenent failure. that's the background.
Recently I have been having nihtmares  that are -essentally- terrifying. Usually, when I have dreams I write them out.  (see Jake a story of mine) however, these dreams are so personal and so powerfully vivid, that I think I am losing hold of reality.  The point is that there is a message to them. They involve my mother fighting violently with both her father, and myself, as if she is demonically possessed. It is troubling, however, the theme of the dreams is a terrifying fear of succsess.  That being said, I will analyse your philosophical notion. 
 

Premise 1: If a thing cannot logically be said to be different to something then it must be the same as that thing. 
(This is lovely by the way  x)
to breakdown premise one, I would like to consider a thing. A leaf.
 A leaf, on a tree -for instance- is generally termed as a leaf. So, in general terms, it cannot be seen as any different from another leaf. However, each leaf is seperate from another, as each tree vaiety is different from one another. Furhermore, each leaf changes colour, at a different rate of time in their own unique space, and some leaves stay on the tree far longer than others; so though each leaf, from each tree, can be generally termed as "a leaf" each leaf is very different.  So it is with things. It is a question of terminology. We all are very different, despite our general sameness. So though I agree with the premise in general terms, analysis shows that each thing is different, however slight that difference might be. 
(this is the beauty of philosophy, for there are never any real answers,simply more questions. See Socrates ) 

Premise 2 Dreams must be real because if they are not real then they must be something I imagined and if they are something I imagined then they are a dream.

Premise 2. if we accept that Kant is correct, "that the human mind creates the structure of the human experience", then the world of our dreams,however vivid or not, (as the case maybe)  is real.
Kant however had  his critics Arthur Schopenhour (spelling Hunt) for one, who pointed out that the world we live in, has its own rules that we as a species have to abide by. Therfore, though our dreams are unique to each of us, they must, in some small way, have a connection to the world we physically exist  in. But this also  depends of course upon the context of the dream. For instance, you might have a dream about bringing an axe to work and cleaving your boss's head in two, (possibly to the song of  "when I'm cleaning windows" ) however, you will not react on that dream. Furthermore if you go to work and saw your boss at your work station with his head split open, just because you dreamed it; it  does not necesserily mean that you a. did it or b. would do it. (that is where  the  realm of the dream and the world we are in are so different. There are no rules in the dream realm. We can chop him up as many times as we like;to any song we want.) 
Taking this further and adding my own personal take, I do belive that the dream world is real to each of us, however,we have to utilise it to suit ourselves. (see my own short dreamwars, which was a dream that I experienced and wrote up. In fact read any peice of my fiction. they alll came from the land of dreams. Testament is one huge dream that has been coming to me in parts.)

Premise 3: If dreams are real then they are part of reality. If they are part of reality then they cannot be logically said to be different to reality.

premise 3. in looking at my analysis of premise one and  two and my own understanding of it, I would say that as each person is unique that each person therefore feels real as real as possible, theofore  the dreams that they experience are real to them. However, the dreams themelves are inner messages that we either listen to,or not. They rarely have an impact upon the physical world, (see shopenhour) therefore the dream world and the physical world are different and abide by very different rules. 

Conclusion: Dreams are not different to reality, they are the same thing as reality.

my conclusion thefore leads me away from accepting that dreams are no different from reality. They are, very different and perhaps I would go further to say that dreams augment our reality. (a very old idea and a new one, especially in the age of the robot and the AI) they do have an impact upon how we feel during the day and that has an impact with how we relate to our friends and family. so though there is an impact, its an indirect one. 

I would also add to this, by stating that though each of us, like the leaf  is unique, and has their own understanding of their position in reality, (whether that is based upon a philosophy of words or science or politics or art (I could go on) ) each person interprets each dream differently, and theofore, their own personal connection to the dream world is different. As shopenhour states "both inner and outer exeriences are not without merit" Therefore one has to consider both realms together but seperate, because each persons understanding of the dream realm is different, just as each person is different. 

This is of course when it gets messy. For instance, you didn't expect this sort of reply and I fully expect you to disagree with my conclusions. So let me recap. 

does the dream world exist? 
 1. it must exist; because we have experienced it. It also exists even if we haven't experienced it, because others, (like I have done prior to considering your phliosphical notion have given you details of dreams I have expereinced.) share their experiences too. 
2. Is this thefore real?
That's the issue. It is real for each individual, for they each experience it differently. 
however, it does not seem to or  cannot have a direct impact upon the physical, world unless it becomes a general effect; eg other's share that dream and do things to either prevent the dream from  occurring,or working together to make the dream occur. 
Then of course I am a writer of fiction. I play with the theatre of the mind. People read my work and my images come alive inside people's minds. I do this because it is cathartic; but more importanty I do it becuse I find the world I live in a horrible place and I would rather be anywhere other than here.  However, my dream world is more horrible than the real real world, that is stagnant and devoid of any exitement. So perhaps I create a horrible place in my mind because at least there is some action going on? I don't know the answer to that. 
My personal conclusion is that dreams are messages, they are our subconcious attempting to get our conscous minds to wake up. To defeat our own personal demons that strike us down, they are messages that we sometimes see clearly,however, mostly we do not; because if we did, the world would be a very different place 
as an aside, the dreamworld (as you know) was considered sacred by many ancient tribes. (the natives of Australia for one) who belived that there wqa a conduit between both worlds. Perhas we shoukd get back to that. However, to do so, would lead to a full on revolution, especially as those who have the money are in a better position to make their dreams come true. 

I hope that has hepled.  Thank you very much for the excecise. You have made an old man very happy. 
 

my email account is huntandrewdavid@gmail.com. This is not connected to myabctales account.

what if you could make the dreamworld real, though some form of AI emmersive technology? this gets into the realm of existensialism.