A class of causal principles

Take the principle that an infinite regress of causes is impossible. It's an instance of a class of principles Pt := 'An infinite regress of t-causes is impossible' where t stands for simpliciter, efficient, sustaining, composite and so on. For each t we can ask whether Pt holds. If Pt holds for some t, and if t is not equal to 'simpliciter', then all t-causal series are finite and have a first member. But this first member might not be uncaused. For it might have an s-cause where s is not equal to t.