Definition-Use coverage is used in data flow testing. I have generated test paths that covers all definition-use chain of a variable. But my question is, how to prove that? How can I prove that all DU is covered by the test paths?
One method is to use statement coverage. If your cases execute all statements, it is reasonable to assume that you have a high quality tests. Even though statement coverage is a not as robust a test as path coverage, it dose increase confidence that most of the paths are covered.
The answer to the second part is more difficult and is a function of time. From a perspective off is their an absolute proof, I don't know of any. By spending time to do more analysis you might reach a high confidence level but no positive proof.
My first suggestion is always to take the simpler methods into considerations. You might use the method "Basic Path Technique" using the DUs as nodes in a graph. Every single and independent path within the graph will validate whichever you current test scenarios are.