δ = β - β^{0}

in the Lasso cone condition. Keeping the prediction-error term in the same argument gives

\frac{1}{n} ∥ X δ ∥_{2}^{2} \leq \frac{3 λ}{2} ∥ δ_{S} ∥_{1} \leq \frac{3 λ ∣ S ∣}{2} ∥ δ ∥_{2},

\frac{1}{n} ∥ X δ ∥_{2}^{2} > γ ∥ δ ∥_{2}^{2}

for nonzero

δ

in this cone. Division by

∥ δ ∥_{2}

proves

∥ β - β^{0} ∥_{2} \leq \frac{3 λ ∣ S ∣}{2 γ} .

The result is immediate when

δ = 0

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