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  "body": "\n## Statement\n\nLet $a \\le b$ and let $f \\colon [a, b] \\to \\mathbb{R}$ be continuous.\nThen $f([a, b]) = [m, M]$, where $m$ and $M$ are the minimum and the maximum of $f$ on $[a, b]$.\n\n## Remarks\n\nThe [[extreme value theorem|0WS1A8E2P9]] gives $m$ and $M$ as values of $f$. The [[intermediate value theorem|00KAFBR32E]] gives all values in between.\nThe image can be a single point, when $f$ is constant.\nMathlib states it as `ContinuousOn.image_Icc`.\n\n## Explanations\n\n### L1 human\n\nA continuous function maps a closed bounded interval onto a closed bounded interval.\nThe graph reaches a lowest and a highest point, and it takes every height in between.\n",
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