Dream is necessary to distinguish from deep sleep, as one cannot know the presence of an object without knowing its absence.

By analyzing the mind one becomes aware of the fact that whatever seen in dream as mountain and ocean are mind . Hence none of it could have been lost, because of the entire mountain and ocean was the mind and lapses back as   mind, and as matter is only mind, having been proved to be so, the whole waking or dream is mind. But mind is not the ego, my individual mind, which can create this waking or dream. It is the common One Universal Mind, which is the soul/Atman. 

Seeker must know that it is   important and he has to understand the fact that the Waking objects, on account of their being similar to dream objects, are unreal because they are perceived objects.

What is it that perceives?

It is the Formless Witness.

What is it that the Formless Witness has in it when it sees an object?  

An idea which is mere mirage.

Suppose anything existed outside or different from the mind, one becomes aware of it because of the Formless witness, because nothing can exit without the formless witness. Since, everything within the waking/dream is powered by the formless Witness. 

As the dream appears the self is involved in witnessing the dream. When the dream disappears and when there is noting to witness it remains in its formless non dual true state. When the waking appears it is again start witnessing. The individual experiences happening within the waking or dream are mere mirage witnessed by the formless witness or soul. Thus the individual experiences or birth, life and death have no meaning on the standpoint of soul or Atman as self. Hence three states are mental states. They do not exist in reality. 

The relativity of the three states: one could not know man as man if woman did not exist. If only man existed he would never be aware of that fact. Only by existence of another opposite or contrasting thing does one know it. Similarly one would not know waking as waking if life were always waking experience. One knows waking experience exists because of existence of dream by way of contrast and of deep sleep. Therefore the three states are present together and are always present. 

Dream is necessary to distinguish from deep sleep, as one cannot know the presence of an object without knowing its absence. Everyone is given the three states; therefore everyone can realize non dual Truth.