Whether the book of life is the same as predestination?

Objections

Objection 1 : It seems that the book of life is not the same thing as pre-destination. For it is said, "All things are the book of life" (Ecclus. 4:32)---i.e. the Old and New Testament according to a gloss. This, however, is not predestination. Therefore the book of life is not predestination.
Objection 2 : Further, Augustine says (De Civ. Dei xx, 14) that "the book of life is a certain divine energy, by which it happens that to each one his good or evil works are recalled to memory." But divine energy belongs seemingly, not to predestination, but rather to divine power. Therefore the book of life is not the same thing as predestination.
Objection 3 : Further, reprobation is opposed to predestination. So, if the book of life were the same as predestination, there should also be a book of death, as there is a book of life.