# Exercise 13.4.6

Professors Skelton and Baron are concerned that at the start of case 1 of RB-DELETE-FIXUP, the node $x.p$ might not be black. If the professors are correct, then lines 5–6 are wrong. Show that $x.p$ must be black at the start of case 1, so that the professors have nothing to worry about.

At the start of case 1 we check that $w$, the other child of $x.p$ is red. If it is, it means that $x.p$ has to be black (if it was red, it would have a red child, which violates property 4).