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  "body": "\n## Statement\n\nFor every real $x$,\n$$1 + x \\le e^x,$$\nwith equality if and only if $x = 0$.\n\n## Remarks\n\nThe line $y = 1 + x$ is the tangent to the graph of $e^x$ at $0$. The graph of a [[convex function|0D7GRZ2ADX]] lies above its tangent lines, by [[the derivative criterion|005JT76HCK]].\nFor $x \\ge 0$ the claim also follows from the series, since the other terms are nonnegative.\nTaking logarithms gives [[$\\ln y \\le y - 1$|04CBRA4JRK]] for $y \u003e 0$. Mathlib states the inequality as `Real.add_one_le_exp`.\n\n## Explanations\n\n### L1 human\n\nThe graph of $e^x$ lies above its tangent line at $0$.\nThat tangent line is $y = 1 + x$.\n",
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