title: A* with reopening when heuristics is only admissible but not consistent
body: <p>The A* pseudocode I follow is given here:
  <a href="https://i.stack.imgur.com/EAddW.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/EAddW.png" alt="enter image description here"></a></p>
  
  <p>My question is: How are we sure that we can return when a goal state is found? As it is with all other CLOSED states, they could be reopened from new OPEN states. So, if I have a state that I got from OPEN and I see that I can take a better path to the CLOSED goal from that state, then I should update its value at least. Shouldn't we wait till all the states are closed?</p>