How do you prove a heuristic is admissible? How does one prove that a suggested heuristic is admissible? Is this even possible?  

For Example: Let's say I have the game Free Cell.
Rules: https://en.wikipedia.org/wiki/FreeCell  

How can I prove that the number of cards not in the foundation plus every out of order card is an admissible heuristic?
Proving a heuristic is admissible usually means proving two things:


it follows the triangular inequality principle
given the same preconditions, the heuristic never overestimates the actual solution