Proof. The spectrum \(\KU [-2]\) is the colimit of the diagram defining \(\KU \) with its first term omitted: \[ \ku [-2] \xrightarrow {b[-2]} \ku [-4] \to \cdots . \] This subdiagram is cofinal in the original sequential diagram, so \(\KU [-2]\simeq \KU \). Applying \(\Sigma ^2\) gives the desired equivalence. □
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