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The point is:
"есть" is used in possession constructions when the existence is emphasized, and "есть" is omitted when the subject of possession is emphasized.
So, we say "У меня есть велосипед"...

That is not my theory after all. I wrote: "I can try to explain some rules where to use "есть" and where to omit it, but I'm afraid it can be a bit complicated for the beginner."

So, I tried to...

OK, and what is you question? I cannot see it.



You cannot say "У меня книгу". You can say "У меня книга". Note that "книга" is grammatically a subject here! (Lit.: At me is a book).

If your...