Let's introduce three routing table principles, as described by Alex Zinin in his book, Cisco IP Routing.
Principle 1: "Every router makes its decision alone, based on the information it has in its own routing table."
Principle 2: "The fact that one router has certain information in its routing table does not mean that other routers have the same information."
Principle 3: "Routing information about a path from one network to another does not provide routing information about the reverse, or return path."