Solution
= Solution
On the same event, the <Lasso cone condition> and the coordinatewise bound from part a give
$$
\|\widehat\beta-\beta^0\|_1
=\|\delta_S\|_1+\|\delta_N\|_1
\leq4\|\delta_S\|_1
\leq4s\|\delta_S\|_\infty
\leq\frac{6s\lambda}{\psi}.
$$
With $\lambda=A\sqrt{\log p/n}$ this is exactly
$$
\|\widehat\beta-\beta^0\|_1
\leq\frac{6sA}{\psi}\sqrt{\frac{\log p}{n}}.
$$