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•Kőnig's infinity lemma states that an infinite rooted tree that has finite branching at every node has an infinite path.•We present a variation of the lemma about any binary relation over the nodes of two trees, source and target.•Under certain conditions every path in the target tree has a corresponding path in the source tree.•The proof utilizes Kőnig's lemma, and Kőnig's lemma follows from this...
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