0NQZ Proof. By theorem 6.10, we can describe the additive invariants KK and EE as elements of FunL(ℳadd,𝒮∞)\mathrm{Fun}^{\mathrm{L}}({\mathcal{M}}_{\mathrm{add}},{\mathcal{S}}_{\infty}). The equivalence Nat(Map(𝒰add(𝒮∞ω),−),E)≃E(𝒮∞ω)\Nat(\mathrm{Map}({\mathcal{U}}_{\mathrm{add}}({\mathcal{S}}_{\infty}^{\omega}),-),E)\simeq E({\mathcal{S}}_{\infty}^{\omega}) follows from 7.13 and the spectral Yoneda lemma. ∎