# Exercise 13.3.4

Professor Teach is concerned that RB-INSERT-FIXTUP might set $T.nil.color$ to RED, in which case the test in line 1 would not cause the loop to terminate when $z$ is the root. Show that the professor's concern is unfounded by arguing that RB-INSERT-FIXUP never sets $T.nil.color$ to RED.

The professor worries too much.

We only set the color to red of $z.p.p$ and the text goes at great lengths to establish that it always exists (because $z.p$ is RED, which means it can't be the root, which means $z.p.p$ is not NIL).