Proving optimality of A* employing graph-search I

Step 1 : If h(n) is consistent, then the values of f (n) along any path are nondecreasing h(n) ≤ c(n, a, n′) + h(n′) If h is consistent and n′ is a successor of n, we have f (n′) = g(n′) + h(n′) = g(n) + c(n, a, n′) + h(n′) ≥ g(n) + h(n) = f (n)