What deal does Aslan make with the white witch?

The White Witch is given the right to a kill because of the treachery of Edmund. Normally it would be the traitor who is killed, but Aslan gets her to agree to renounce her claim on Edmunds life and kill him instead. Theologically, this represents the substitutionary character of the atonement of Jesus in that He takes upon himself the punishment for sin that should have fallen on us.