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Introduction to Algorithms (Cormen, Leiserson & Rivest) present a much more detailed analysis of Red-Black trees from this perspective.
It is sufficient to implement a Red-Black tree by treating it exactly the same as a 2-3-4 tree taking into account the colors of node in determining whether you are about to step into a 4-node (for insertion) or a 2-node (for deletion).
You also need to make sure that no red node has red children.