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  "body": "\n## Statement\n\nThe exponential function is strictly increasing on $\\mathbb{R}$.\nThat is, $x \u003c y$ implies $\\exp(x) \u003c \\exp(y)$.\n\n## Remarks\n\nThe derivative is [[$\\exp$ itself|0EX9GFJ0B3]], and it is [[positive|0P9BNBW2W3]]. Then [[positive derivative|07J5X2T1ZX]] gives the claim.\nAlso $\\exp(x) \\to \\infty$ as $x \\to \\infty$ and $\\exp(x) \\to 0$ as $x \\to -\\infty$. So $\\exp$ is a bijection from $\\mathbb{R}$ onto $(0, \\infty)$.\nMathlib states it as `Real.exp_strictMono`.\n\n## Explanations\n\n### L1 human\n\nThe exponential function always grows as $x$ grows.\nSo it takes each positive value exactly once.\n",
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