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  "body": "\n## Statement\n\nLet $D \\subseteq \\mathbb{R}$ and let $f \\colon D \\to \\mathbb{R}$ be [[Lipschitz|0QNVQ4VD9T]].\nThen $f$ is [[uniformly continuous|0Q4DR37DVE]].\n\n## Remarks\n\nLet $K \u003e 0$ be a Lipschitz constant. Given $\\varepsilon \u003e 0$, take $\\delta = \\varepsilon / K$.\nThe converse fails. The function $\\sqrt{x}$ is uniformly continuous on $[0, 1]$ but not Lipschitz.\nMathlib states it as `LipschitzWith.uniformContinuous`.\n\n## Explanations\n\n### L1 human\n\nA Lipschitz bound controls the change of $f$ in the same way at every point.\nSo one input tolerance works for the whole domain.\n",
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