Christ as the seed of the woman has dealt with Satan, sin, death, and the old man. The first stanza and chorus of Hymns, #890 express the fact that Christ is the Victor over Satan, sin, and death:
Sin and death are the product of Satan. Sin came from Satan and issues in death (Rom. 5:12). However, Satan was destroyed by Christ, sin was taken away through Christ's death, and death was nullified by Christ's appearing in the flesh. Moreover, our old man, which was corrupted by Satan, sin, and death, was terminated by being crucified with Christ. All these items are included in the bruising of the serpent's head by the seed of the woman. These are the achievements of Christ as the seed of the woman.
Christ as the seed of Abraham, the last Adam, the God-man, has become the life-giving Spirit, the Spirit of Christ, the consummated and indwelling Spirit, the divine Spirit processed and compounded with Christ's humanity, His death and its effectiveness, and His resurrection and its power, the unique and all-inclusive Spirit, the Spirit (as the aggregate of the blessing of the full gospel of God in Christ), to impart Himself as God's embodiment and life into us that we may be regenerated and transformed and conformed to the glorious image of Christ as the firstborn Son of God (1 Cor. 15:45b; Rom. 8:9b, 11; Rev. 22:17a; John 3:5-6; 2 Cor. 3:17-18; Rom. 8:29).