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  "body": "\n## Statement\n\nLet $\\psi_1 (x_1 , x_2)$ and $\\psi_2 (x_1 , x_2)$ be formulae with free variables $x_1$ and $x_2$.\n\nThen there are sentence $\\varphi_1$ and $\\varphi_2$ such that $T \\vdash \\varphi_1 \\leftrightarrow \\psi_1(\\ulcorner \\varphi_1 \\urcorner, \\ulcorner \\varphi_2 \\urcorner)$ and $T \\vdash \\varphi_2 \\leftrightarrow \\psi_2(\\ulcorner \\varphi_1 \\urcorner, \\ulcorner \\varphi_2 \\urcorner)$.\n\nThe case with $n$ many formulae is similar.\n",
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        "locator": "Diagonal lemma, section Some generalizations \u003e Simultaneous diagonal lemma",
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  "name": "Simultaneous diagonal lemma",
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  "role": "lemma",
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    "next": [
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        "what": "edge uses out",
        "note": "each definition that the statement needs",
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