In this video, Kevin Kline discusses the transitive property of indexes. He starts out by discussing how the transitive property works in algebra. Then he shares how the transitive property in algebra can be applied to Microsoft SQL Server. He goes over a few examples of how you can incorporate the transitive property into JOIN and WHERE subclauses.
Both Kevin and Aaron stress the importance of explicitly declaring every statement rather than assuming that SQL Server knows what should be in the statement based on the property.