Proof of correctness of A star search algorithm I've been looking for the proof of correctness for the A star (A*) algorithm but none of the texts and websites offer it. Mostly they are talking about the proof of optimality of the A* algorithm. I'm looking for a proof that if the heuristic is admissible, A* will always give an optimal path.

Please help me understand.

To clarify, I want a proof that the path found by A* is correct (i.e., is the cheapest/shortest path to the destination), not a proof that the A* algorithm is optimal (i.e., that any other algorithm that uses the same heuristic will expand at least as many nodes as A*).  Also, I'm looking for a proof that only uses the assumption that the heuristic is admissible (without assuming that the heuristic is monotonic or consistent).  I've looked in CLRS and haven't found any such proof.
Check the original paper which talks about its correctness - 

Hart, Peter E., Nils J. Nilsson, and Bertram Raphael. "A formal basis for the heuristic determination of minimum cost paths." Systems Science and Cybernetics, IEEE Transactions on 4.2 (1968): 100-107.

See especially Section II and Theorem 1.