{
  "authority": "local_conservative_templates_not_Alpha_admissions",
  "edges": [],
  "historical_sha256": "32da2185fd21fb1d0b400404f9b832425a4c35e75be392a3f5b5f73f8464aebf",
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    {
      "ast": [
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          ],
          [
            "add",
            [
              "add",
              [
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                ]
              ],
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                ],
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                ]
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            ],
            [
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              ],
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                  ]
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            ]
          ],
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          ]
        ]
      ],
      "dependencies": [],
      "id": "ND0388",
      "name": "IQuadProductReal",
      "parameters": [
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        "an",
        "bp",
        "bn",
        "cp",
        "cn",
        "dp",
        "dn",
        "rp",
        "rn"
      ],
      "source": "rp + (ap · cn + an · cp + 2 · (bp · dn + bn · dp)) = ap · cp + an · cn + 2 · (bp · dp + bn · dn) + rn"
    },
    {
      "ast": [
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      "dependencies": [],
      "id": "ND0389",
      "name": "IQuadProductRadical",
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        "an",
        "bp",
        "bn",
        "cp",
        "cn",
        "dp",
        "dn",
        "sp",
        "sn"
      ],
      "source": "sp + (ap · dn + an · dp + (bp · cn + bn · cp)) = ap · dp + an · dn + (bp · cp + bn · cn) + sn"
    }
  ],
  "theorem_uses": [
    {
      "definition": "ND0157",
      "kind": "theorem_uses_definition",
      "theorem": "SN002"
    },
    {
      "definition": "ND0157",
      "kind": "theorem_uses_definition",
      "theorem": "SN003"
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    {
      "definition": "ND0388",
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      "definition": "ND0389",
      "kind": "theorem_uses_definition",
      "theorem": "SN003"
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    {
      "definition": "ND0157",
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      "theorem": "RN001"
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    {
      "definition": "ND0157",
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      "theorem": "RN002"
    },
    {
      "definition": "ND0388",
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      "theorem": "RN002"
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      "definition": "ND0389",
      "kind": "theorem_uses_definition",
      "theorem": "RN002"
    },
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      "definition": "ND0388",
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      "theorem": "QN001"
    },
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      "definition": "ND0389",
      "kind": "theorem_uses_definition",
      "theorem": "QN001"
    }
  ]
}