Determine a precise Loop Invariant for the Dijkstra's Algorithm, clearly stating your Initialization, Maintenance, and Termination statements. Prove that your loop invariant holds, clearly and carefully justifying each step in your proof.

Process or set of rules that allow for the solving of specific, well-defined computational problems through a specific series of commands. This topic is fundamental in computer science, especially with regard to artificial intelligence, databases, graphics, networking, operating systems, and security.