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  "body": "\n## Summary\n\nA sublattice of a [[lattice|WH4SFAACAS]] $L$ is a nonempty subset of $L$ that is closed under the [[join and meet|J2T75ATRV5]] of $L$.\nIt is a lattice in its own right, with the operations of $L$.\nSublattices play the role that subgroups play for groups, and forbidden sublattices characterise classes of lattices, such as the distributive ones.\n\n## Explanations\n\n### L1 human\n\nTake a lattice and keep only some of its elements.\nThe kept part is a sublattice when the join and the meet of any two kept elements, computed in the big lattice, are again kept.\nFor example, in the subsets of $\\set{1, 2, 3}$, the four sets $\\emptyset$, $\\set{1}$, $\\set{2}$, $\\set{1, 2}$ form a sublattice.\nA subset can be a lattice in its own order without being a sublattice, because its joins may differ from those of the big lattice.\n",
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