John Bunyan's "The Pilgrim's Progress" and "The Lamb's book of Life" (Revelation 3:5; 13:8; 17:8) or "The Book of Remembrances" (Malachi 3:16)?

Regarding *The Pilgrim's Progress* by John Bunyan from Chapter 2 (“The Way of the World or the Narrow Way”), pages 52–53. A quote starting on page 52, the last paragraph at the bottom: > “Then Christian asked. ”May we go into the palace?” The Interpreter took him and led him up toward the door of the palace. There Christian saw a great company of men standing at the palace door, all desiring to go in, but few daring to. A little distance from the door there was a man sitting at a table with a [book open] before him. He was writing the names of those who wished to enter the palace. **My Question**: is the book Bunyan referred to "The Lamb's Book of Life" (Revelation 3:5; 13:8; 17:8) or some other book, possibly "The Book of Remembrances" (Malachi 3:16)?