Abstract: 
Working in the context of the category of representations for a Dynkin quiver $Q$, we will use Auslander-Reiten theory to show that for a stability function to be totally stable, it suffices to check inequalities corresponding to Auslander-Reiten sequences with indecomposable middle term, rather than checking inequalities on all possible Auslander-Reiten sequences for our quiver $Q$.