okay so just showing like this really is the update rule for that particular energy function okay now as as itself it's not super duper interesting yet but um now we get to theorem two so theorem two for the iteration that's the update rule that we just looked at we have we have that um this convergence holds as t goes to infinity for some stationary point furthermore this quantity here goes to zero so that means this is the um the update at t plus one and this is the update at t and the difference between them