Infinite bodies and the prime mover in 'Aristotle''s 'Physics 8.10'

In Phys. 8.10, Aristotle proves three lemmas on account of which he will conclude that the prime mover lacks parts and is not, therefore, a material body. At the end of Phys. 8.10 he invokes the first two lemmas to show that the prime mover cannot be a finite divisible body on the strength of the third lemma but instead he simply points out that, as has been shown in the physics, there are no infinite bodies. Scholars have, therefore, dismissed the third lemma, in whose proof the existence of an infinite body is inexplicably assumed, as an irrelevant adjunct to Phys. 8.10. Since, however, the proof of the third lemma actually establishes by reductio ad absurdum a conclusion which in De Caelo (275a14-24), a treatise Aristotle includes in the physics, precludes the existence of infinite bodies on kinematic grounds, the lemma in question cannot but be pertinent to the second horn of the conclusion in Phys. 8.10, namely that the prime mover cannot be an infinite divisible body.