You’re all over the place. The Book of Life has the names of all the saved ppl in it. All those whose names are not found written in it are to be cast into the lake of fire.I think it is a lack of knowledge of logical statements.
It is conjecture that the Book Of Life is only a book of created beings, no biblical scripture.
so follow this:
If you are created being, your name is there.
I do not limit this to a salvation book, as you seem to be, It is the Book of Life , a list who has eternal (spiritual) life.
Why does one need to be saved if they never sinned? Are angels and cherubim in the book, they were created and have life,
If this Book applied to all of creation, then only those whose names are blotted out are missing.
Names are never mentioned to be added but blotted out. The blotted out names do not have eternal life , another word for lost or doomed.
So all creations is listed there, some are condemned, and if they do overcome, their names are not removed. This implies some names ARE blotted out,
This about all we know, scripturally.
Which brings us right back to where the Christ, in the day of Judgment, will tell them who had done many things in His name, “Depart from Me, you evil doers. I NEVER knew you!” He didn’t say, “I once knew you, but now I don’t!” He NEVER knew them in an intimate relationship. So the lost never have their name in the Book of Life. God doesn’t need white-out.