{
  "aliases": null,
  "backlinks": null,
  "body": "\n## Summary\n\nIn mathematical logic, a **redundant proof** is a [[proof|0B94TKFQJX]] that has a subset that is a shorter proof of the same result. In other words, a proof is redundant if it has more proof steps than are actually necessary to prove the result. Formally, a proof $\\psi$ of $\\kappa$ is considered redundant if there exists another proof $\\psi^{\\prime}$ of $\\kappa^{\\prime}$ such that $\\kappa^{\\prime}\\subseteq\\kappa$ (i.e. $\\kappa^{\\prime} \\;\\text{subsumes}\\; \\kappa$) and $|\\psi^{\\prime}|\u003c|\\psi|$ where $|\\varphi|$ is the number of nodes in $\\varphi$.\n",
  "commit": "4a3290d299c8b2cd6493fce2296920ba7f82d942",
  "front": {
    "inventory": [
      "MG1QZ4NM1A"
    ],
    "kind": "concept",
    "name": "Redundant proof",
    "same_as": {
      "wikidata": "Q15964428",
      "wikipedia": "Redundant proof"
    },
    "sources": [
      {
        "locator": "Redundant proof",
        "mention": "wikipedia://en/42158532",
        "note": "adopted",
        "sections": [
          "Summary"
        ],
        "wikipedia": "en:42158532@r1191444096"
      }
    ],
    "tag": "FFH6M3M077"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/FFH6M3M077/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/FFH6M3M077.md",
  "msc": null,
  "name": "Redundant proof",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/FFH/FFH6M3M077.md",
  "status": null,
  "tag": "FFH6M3M077",
  "uri": "m2://FFH6M3M077",
  "url": "https://math2.tamnd.com/wiki/redundant-proof/",
  "writing": {
    "tag": "FFH6M3M077",
    "kind": "concept",
    "level": "W1",
    "next": [
      {
        "what": "edge defines in",
        "note": "at least one definition",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge instance_of in",
        "note": "at least two examples",
        "have": 0,
        "want": 2
      },
      {
        "what": "edge not_instance_of in",
        "note": "at least one non-example",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge specializes both",
        "note": "the more general notions and the special cases",
        "have": 0,
        "want": 1
      }
    ]
  }
}