Is there any way to prove that an admissible heuristic may not be consistent? Most proof I came across are through examples .Is there a generalized proof?
If you want to prove a heuristic is not consistent a counterexample is all you need, you don't need a more "generalized" proof. A counterexample is proof enough.
This is because a heuristic is consistent if some property always holds. It is not consistent if the property doesn't hold once. An example is all you need to show something happens once, if you want to show something always holds then you need a general proof.