If you want proof than exchanging a pssword and all things reported exactly the same by two dreamers who have never met.
If you just want to believe: same time both occur, same theme on location, any events that happen, and weather. add in a common theme discussed that need not be exact.
Example: Me and Sageous both report dreaming at the same time.
His dream: He calls out sivason and a giant furry spider appears and starts trying to drink off Sagous' cocktail. He asks"sivason?' and the spider becomes a human dc looking however sageous imagines me. He notices a parade is now going by is front porch, and an elephant is painted pink. Sivason complains that he has not drank nearly enough to see pink elephants.
My dream: I am looking for something and shrink down to tiny to dart through a mouse hole. I see a guy drinking what looks like a masterful cocktail. I float up and stick my whole head in it and guzzle. I hear 'sivason?' I see the DC is different and called me by name, so I enlarge to full size. It is sageous as I picture him. Suddenly a handful of pot belly pigs and cats start marching by, Monkeys start riding them. I say :I am not so drunk as to warrant monkey riding anything.
That would be enough eveidence for the two who had the dream, but would be meaningless to any who want 'proof'