Peter, Sin and Forgiveness

We know that the apostle Peter was of the elect of God.  He was a true Christian; however, we see him sin against our Lord in Matthew 16:22-23.  This was after he gave his undying confession of Jesus in Matthew 16:16.  He called Jesus "the Christ, the Son of the Living God."  Peter proclaimed the deity of Jesus Christ.  It was what Nathanael proclaimed of Christ in John 1:49.  Scholars say that Peter is "a" rock or "the" rock.  I would say that Christ is "the" Rock but Peter is "a" rock.  We are called to be a little Jesus to the world.  I think Christ built the church upon Himself.  Here are the verses that speak of Peter's betrayal of Christ before His atoning death:

Matthew 16:22 KJV
Then Peter took him, and began to rebuke him, saying, Be it far from thee, Lord: this shall not be unto thee.
Matthew 16:23 KJV
But he turned, and said unto Peter, Get thee behind me, Satan: thou art an offence unto me: for thou savourest not the things that be of God, but those that be of men.

Jesus in the Gospel accounts mentions someone who is a devil and it was Judas.  Someone may think it could mean Peter as well by these verses; however, I think we can say with assurance that Peter is a true Christian.  We can learn that God forgives the greatest of sins, because Peter became an "incarnation of Satan."  Such a thing is a great sin but Jesus forgave him no doubt.  Peter also wrote epistles and instructed the Christian brethren.   We can learn that with God forgiveness is possible and actual for the worst offense.