Proof: Using induction, we define an infinite sequence of nodes x0, x1, . . ., forming an infinite path in T . At stage 0 of the induction, let x0 be the root of T , which has infinitely many successors by the hypothesis that T is infinite. At stage n ≥ 1, assume we have already selected nodes x0, x1, . . . , xn−1 so far, forming a path of length n−1, such that xn−1 has infinitely many successo...

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