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  "body": "\n## Statement\n\nLet $T$ be a finite [[tree|0MJ0JS72DZ]] with at least two vertices.\nThen $T$ has a vertex of [[degree|0T0F6CCS9W]] $1$.\n\n## Remarks\n\nIn fact $T$ has at least two leaves: the two ends of a longest path are leaves.\nProof idea: take a longest path $v_0, \\dots, v_k$. A neighbour of $v_k$ other than $v_{k-1}$ would extend the path or close a cycle, so $\\deg(v_k) = 1$.\nThe lemma is the base of induction proofs on trees, as in the proof that [[a tree on n vertices has n − 1 edges|0VSNHTHK8T]].\n\n## Explanations\n\n### L1 human\n\nA finite tree with at least one edge always has an end point.\nWalk along the tree as far as you can without going back. You stop at a vertex with only one edge.\n",
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