{
  "aliases": [
    "axiom-k",
    "streichers-axiom-k"
  ],
  "backlinks": null,
  "body": "\n## Statement\n\nIn type theory, **uniqueness of identity proofs** (UIP) is a possible axiom for dependent type theory which asserts that any two proofs of the same equality are themselves equal. An equivalent and closely related axiom is **Streicher's axiom K**, which asserts that any proof of an equality $x = x$ is equal to the trivial reflexivity proof.\n",
  "commit": "4a3290d299c8b2cd6493fce2296920ba7f82d942",
  "front": {
    "aliases": [
      "axiom-k",
      "streichers-axiom-k"
    ],
    "inventory": [
      "PW69FH3KNF"
    ],
    "kind": "statement",
    "name": "Uniqueness of identity proofs",
    "role": "proposition",
    "same_as": {
      "wikidata": "Q132573452",
      "wikipedia": "Uniqueness of identity proofs"
    },
    "sources": [
      {
        "locator": "Uniqueness of identity proofs",
        "mention": "wikipedia://en/79140369",
        "note": "adopted",
        "sections": [
          "Statement"
        ],
        "wikipedia": "en:79140369@r1277745965"
      }
    ],
    "tag": "5H3JRM0WSS"
  },
  "kind": "statement",
  "link": "https://math2.tamnd.com/node/5H3JRM0WSS/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/5H3JRM0WSS.md",
  "msc": null,
  "name": "Uniqueness of identity proofs",
  "prov": null,
  "role": "proposition",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/5H3/5H3JRM0WSS.md",
  "status": null,
  "tag": "5H3JRM0WSS",
  "uri": "m2://5H3JRM0WSS",
  "url": "https://math2.tamnd.com/wiki/uniqueness-of-identity-proofs/",
  "writing": {
    "tag": "5H3JRM0WSS",
    "kind": "statement",
    "level": "W0",
    "next": [
      {
        "what": "edge uses out",
        "note": "each definition that the statement needs",
        "have": 0,
        "want": 1
      }
    ]
  }
}