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  "body": "\n## Statement\n\nLet $G$ be a [[graph|0JD5C82QMB]] and let $u, v$ be vertices of $G$.\nSuppose that there is a [[walk|0VJZM0F9YM]] $W$ from $u$ to $v$.\nThen there is a [[path|0JDE56HWQ8]] from $u$ to $v$ whose vertices and edges are vertices and edges of $W$.\n\n## Remarks\n\nProof idea: if a walk visits a vertex $x$ twice, delete the closed part between the two visits. Each deletion makes the walk shorter, so the process stops with a path.\nA consequence: a shortest walk from $u$ to $v$ is a path. Thus the [[distance|0WPZ5YPAGR]] can be defined with paths.\n\n## Explanations\n\n### L1 human\n\nIf you can walk from $u$ to $v$, you can also do it without visiting any place twice.\nWhenever you come back to a place, cut out the loop that you just made.\n",
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