wondering,
Just to clarify, it has been a while since I delved into the subject of the books, but after posting to you yesterday
I tried to recall my prior understanding of it. After a brief review, the following perceptions came to mind. I hope I've recalled all of the germane points now.
And I hope by this post that I haven't confused the topic more for you.
There are two books of life: One with only the names of those whom God chose to salvation, the other containing everyone ever to be born. I believe the first book - the one in heaven - is named the Lamb's book of life.
The existence of the first book, the one containing only those whom God has chosen, is established by these verses:
[Luk 10:20 KJV]
20 Notwithstanding in this rejoice not, that the spirits are subject unto you; but rather rejoice, because your names are written in heaven.
[Heb 12:23 KJV] 23 To the general assembly and church of the firstborn, which are written in heaven, and to God the Judge of all, and to the spirits of just men made perfect,
The names "written in heaven" are ONLY those chosen to salvation by God
The second book is the book of life, AKA the book of the living. Everyone's name to ever be born, are in this book: both the chosen and not chosen. However, and this is a big however, those chosen were written into it first - one time for all, at the foundation of the world, the other names written into to it afterwards. Therefore, I think we can almost, in a sense, perceive it as consisting of two subsets of names in the one book: the chosen and not chosen. This, I believe, can be observed If we look very closely at the verses which follow.
In the below verse, we can see that that the kingdom that is to come was prepared for those who are to inherit it from the foundation of the world, when their names were written into the book of life
[Mat 25:34 KJV]
34 Then shall the King say unto them on his right hand, Come, ye blessed of my Father, inherit the kingdom prepared for you from the foundation of the world:
Those whose names are not in the book of life of the Lamb, shall worship the beast and so will be blotted out of the book of life (BTW "with the righteous" means that their names cannot be left in the book of life, sometimes referred to as the book of the living)
[Psa 69:28 KJV] 28 Let them be blotted out of the book of the living, and not be written with the righteous.
[Rev 13:8 KJV]
8 And all that dwell upon the earth shall worship him, whose names are not written in the book of life of the Lamb slain from the foundation of the world.
[Rev 21:27 KJV] 27 And there shall in no wise enter into it any thing that defileth, neither [whatsoever] worketh abomination, or [maketh] a lie: but they which are written in the Lamb's book of life.
Those whose names NOT WRITTEN into the book of life from the foundation of the world, (i.e., afterwards)
shall be enticed by and follow the beast and will be blotted out. Those whose names were written into it from the foundation of the world, because they were written into it from the foundation of the world, will NOT wonder after or follow the beast nor be blotted out. In the below verse, please observe, that it's not that their names weren't/aren't in the book of life that they are blotted out, but because they are not of those who were written into it "from the foundation of the world". By that, this verse gives to us clear distinction between those written into it from the foundation of the world, and those who weren't.
[Rev 17:8 KJV]
8 The beast that thou sawest was, and is not; and shall ascend out of the bottomless pit, and go into perdition: and they that dwell on the earth shall wonder, whose names were not written in the book of life from the foundation of the world, when they behold the beast that was, and is not, and yet is.