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  "body": "\n## Summary\n\nA substitution replaces each variable of a [[term|6D3WA7N2W4]] by another term, all at the same time.\nIt is the syntactic counterpart of plugging values into a formula.\nSubstitution is one of the rules of equational logic, and it is the basic operation of unification and term rewriting.\n\n## Explanations\n\n### L1 human\n\nTake the term $x + y$ and replace $x$ by $z \\cdot z$ and $y$ by $1$.\nThe result is the term $z \\cdot z + 1$.\nAll variables are replaced at once, so substituting $x \\mapsto y$ and $y \\mapsto x$ in $x + y$ gives $y + x$, not $x + x$.\nA law such as $x + y \\approx y + x$ stays true after any substitution, which is why laws can be applied to arbitrary expressions.\n",
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