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Discrete math problem: The length of a path between vertices u and v is the sum...

Discrete math problem:

The length of a path between vertices u and v is the sum of the weights of its edges. A path between vertices u and v is called a shortest path if and only if it has the minimum length among all paths from u to v. Is a shortest path between two vertices in a weighted graph unique if the weights of edges are distinct? Give a proof.

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