# data structures – If a key in a red-black tree has exactly one child (which isn’t null) then he is always red

I have the following claim:

If a key in a red-black tree has exactly one child (which isn’t null) then he is always red. prove or disprove it.

My attempt:

$$Disproof.$$

we shall represent a counter-example:

This tree satisfies the conditions of being a red-black tree,

since:

1. the root is black.
2. all leaves are black.
3. there isn’t a red key.
4. in each path there is the same amount of black keys, in particular, we have three black keys in such paths.

However, we have two keys in level-1, which have one child and he is black.

$$qquad qquad qquad qquad qquad qquad qquad qquad qquad qquad qquad qquad qquad qquad blacksquare$$

Is this disproof right? because perhaps I missed something, and this counter-example doesn’t represent a counter-example. Thanks!