proof of the decomposition of a fibration by a trivial fibration followed by a minimal fibration

Question

In Hovey's book theorem 3.5.9 asserts that any fibration $p:X\rightarrow Y$ can be factored as a trivial fibration followed by a minimal fibration. The proofs begins by defining a set T of simplices of $X$. Hovey asserts that every degenerate simplex is in T by lemma 3.5.8. But I'm a bit confused since lemma 3.5.8 asserts that there is at most one degenerate simplex in the p-equivalence class of a given degenerate simplex. I don't see why it implies that every degenerate simplex is in T. Do you have an explanation ?

Thanks

Answer 1

Oups I see, Hovey means that we can always choose T such that it contains all degenerate simplices of $X$ and this choice is made possible thanks to lemma 3.5.8.