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  "body": "\n## Summary\n\nA direct proof of an [[implication|0ZNX6DQ3EJ]] $p \\to q$ assumes $p$ and then gets $q$ by a chain of valid steps.\nThe steps use axioms, definitions and theorems that are already proved.\n\n## Remarks\n\nExample: if $n$ is odd, then $n^2$ is odd. Write $n = 2k + 1$. Then $n^2 = 2(2k^2 + 2k) + 1$, which is odd.\nWhen a direct proof is hard, a [[proof by contrapositive|0BB5TPGQ1N]] or a [[proof by contradiction|0J0XBKG64S]] can help.\n\n## Explanations\n\n### L1 human\n\nIn a direct proof you go straight from the hypothesis to the conclusion.\nYou write down what the hypothesis means, then you compute or reason until you reach the conclusion.\n",
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