Why is $c(t_i) ≥ c(t_p)$ in this matroid theorem proof?

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In the proof of theorem 5.2 here https://math.mit.edu/~goemans/18453S17/matroid-notes.pdf ,

Since $c(t_i) ≥ c(t_p) > c(s_p)$, ti should have been selected when it was considered

Why is $c(t_i) ≥ c(t_p)$?

Thanks!

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So I was being stupid and it is simple because $T_k$ is ordered non-increasing