0NYP Proof. The result follows from an inductive application of Theorem 4.7 and Corollary 4.12 to the Cartesian diagrams XSn\textstyle{X^{S^{n}}\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces\ignorespaces}X\textstyle{X\ignorespaces\ignorespaces\ignorespaces\ignorespaces}X\textstyle{X\ignorespaces\ignorespaces\ignorespaces\ignorespaces}XSn−1\textstyle{X^{S^{n-1}}} where the two maps X→XSn−1X\to X^{S^{n-1}} assign to a point of XX the corresponding constant map. ∎