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  "body": "\n## Statement\n\nLet $L$ be a lattice with join $\\vee$ and meet $\\wedge$.\nThen $a \\vee (a \\wedge b) = a$ and $a \\wedge (a \\vee b) = a$ for all $a, b \\in L$.\n\n## Remarks\n\nIn a lattice defined as a partially ordered set, the proof is short. Since $a \\wedge b \\le a$, the join of $a$ and $a \\wedge b$ is $a$. The second law is dual.\nIn the algebraic definition of a lattice, the two absorption laws are axioms, together with associativity and commutativity.\nThe absorption laws imply idempotence: $a \\vee a = a \\vee (a \\wedge (a \\vee a)) = a$.\n\n## Explanations\n\n### L1 human\n\nAbsorption says that combining $a$ with something made from $a$ gives back $a$.\nFor sets: $A \\cup (A \\cap B) = A$, because $A \\cap B$ is already inside $A$.\n",
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