Nonexpansive bijections from balls between c₀₀ and c₀ onto balls between c₀₀ and ℓ∞ are signed permutations, wherever the target matches signs

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Nonexpansive bijections from balls between c₀₀ and c₀ onto balls between c₀₀ and ℓ∞ are signed permutations, wherever the target matches signs · Prove2Me