= Solution
For a real boundary point $x\ne0$, the <Boundary-point Bessel flow for SLE> says that $V_t^x/\sqrt\kappa$ is a Bessel process of dimension
$$
d=1+\frac4\kappa.
$$
When $\kappa\leq4$, one has $d\geq2$, so part 2(b), including its logarithmic $d=2$ case, shows that no fixed boundary point is swallowed.
If the trace touched the real line away from its starting point, or if a later segment crossed an earlier segment, the resulting hull would disconnect from infinity a nonempty real interval, which contains a <rational number>. Applying the preceding argument after every rational time and using the <Conformal Markov property of SLE> rules this out on a countable probability-one event. Continuity of the trace then shows that no two distinct times have the same image. Thus $\operatorname{SLE}_\kappa$ is simple for $0<\kappa\leq4$.
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