How do we know that Satan is defeated?

Satan's defeat is confirmed in Revelation 12, where the great accuser is ultimately cast out of heaven, no longer able to stand before God to accuse the brethren. This is coalesced with the truth of Christ’s accomplishment at the cross. When Jesus declared that the prince of this world would be cast out, He was signifying that the power of sin and death had been broken, thanks to His redemptive work. Therefore, believers can live in confidence knowing that although Satan continues to roam, he does so as a defeated foe, realizing his end has been determined by God.