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  "body": "\n## Statement\n\nLet $P(z)$ be a property of [[integers|0C4JS9RF5M]] $z$.\nSuppose that $P(0)$ holds.\nSuppose that for each natural number $n$, $P(n)$ implies $P(n + 1)$.\nSuppose that for each natural number $n$, $P(-n)$ implies $P(-n - 1)$.\nThen $P(z)$ holds for every integer $z$.\n\n## Remarks\n\nThe proof applies ordinary [[induction|0ASJVEFA9J]] two times: one time to $P(n)$ and one time to $P(-n)$, for natural numbers $n$.\nEach integer is $n$ or $-n$ for some natural number $n$, thus the two inductions cover all of $\\mathbb{Z}$.\n\n## Explanations\n\n### L1 human\n\nYou start at $0$ and you walk in both directions on the number line.\nOne induction goes up through $1, 2, 3, \\dots$, and the other goes down through $-1, -2, -3, \\dots$.\n",
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