This is the conclusion to Frame’s discussion about historical/covenantal election in his The Doctrine of God (pp. 329-30):
Historical election and eternal election are distinct, but they cannot be entirely separated. Note the following:
1. Both historical and eternal election are aspects of God’s saving purpose. The election of Israel and the temporary election of individuals in history are means by which God gathers together those who will receive his final blessing.
2. As we have seen, the “remnant” of historical election is no less than Jesus Christ. Jesus himself is eternally elected by God (1 Pet. 1:20), together with those God has chosen to be in him. So in the end, historical and eternal election coincide . In history, they do not; for historical election is a temporal process and eternal election is forever settled before creation.
All of the eternally elect are historically elect, but not vice versa. Historical election is the process in time by which God executes his decree to save the eternally elect. As God judges the reprobate through history, the difference narrows between the historically elect and the eternally elect. In the end, the outcome of historical election is the same as that of eternal election.
3. As such, historical election is a mirror of eternal election. God elects Israel by grace, as he elects believers eternally by grace. He promises blessings to them which are essentially the blessings of salvation, ultimately the presence with them of the living God. God’s covenant presence with Israel in the tabernacle and temple is an image of his presence with eternally elect believers in Christ. The chief difference, of course, is that among the historically elect there are some who will not be finally saved. But even the historical rejection of unbelievers from the covenant images eternal election, for it pictures the final separation between the elect and the reprobate.
4. We may think of historical election as the visible and temporal form of eternal election. We cannot see another’s heart to know for sure whether he is eternally elect. But we can see whom God has led to unite with his visible body, the church. We can see who has given a credible profession of faith in Christ. By observing the process of historical election in the light of Scripture we gain a limited knowledge of eternal election—the best knowledge possible for us today.
5. Those who join the church are historically elect, in the way that Israel was historically elect. It is possible for people in the church to apostatize, to renounce their profession. Church membership, therefore, does not guarantee membership in the new covenant. But the church is a new covenant institution in that it proclaims God’s eternal election in Christ and the forgiveness of sins through Jesus’ atonement. In that sense, Israel also was a new covenant institution. So the Book of Hebrews reminds its Jewish Christian readers of the new covenant to which they are called, and it also warns them not to fall away as did Israel in the wilderness.
 Note that in Rev. 20:15, those whose names are “not found written in the book of life” are thrown into the lake of fire. Is this the historical book of life, from which names can be blotted out? Or is it the eternal book of life, written before the creation? We cannot tell. For by the day of judgment, all blotting will be done, and the names in the historical book will be the same as the names in the eternal book.