I've been reading about fixing up after an insertion into a red black tree. (http://web.cse.ohio-state.edu/~lai/2331/0.Red-Black%20Trees.pdf)
The most surprising part is not that there are 6 things that we need to do after inserting into a red black tree. i.e. if both parent, uncle red, then parent, uncle black, grandparents red, replace inserted value with grandparent. The most surprising part is that wouldn't this blatantly mess up the BST ordering such that a node x is always greater than the left side and less than the right side?
In above link, page 10, the author just replaced grandparent with the newly inserted node x. Wouldn't this completely mess up the BST ordering? Can someone explain if BST ordering should be preserved in a red-black tree and why rotation/fix up after insertion will not have any affect on this ordering?