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  "body": "\n## Summary\n\nA sequent calculus is a proof system whose lines are sequents $\\Gamma \\vdash \\Delta$.\nSuch a sequent is read as \"if all formulas of $\\Gamma$ hold, then some formula of $\\Delta$ holds\".\nGentzen introduced the systems LK for classical logic and LJ for intuitionistic logic in 1934.\nEach connective has rules that introduce it on the left and on the right.\nThis symmetry makes the calculus the main tool of structural [[proof theory|N4EDJNMTEF]].\n\n## Explanations\n\n### L1 human\n\nA sequent is a pair of lists of formulas, written $\\Gamma \\vdash \\Delta$.\nIt says that the assumptions on the left together force at least one of the claims on the right.\nProofs are trees of sequents that grow downward, from axioms $A \\vdash A$ to the sequent one wants.\nFor example, from $A \\vdash A$ the rule for \"and\" on the left gives $A \\wedge B \\vdash A$.\nEvery rule only adds structure, except one rule, the cut, which removes a formula.\n",
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