{
  "prefix": {
    "pe": "https://proofengine.info/proofs/the-binary-operator-eml-is-defined-by-the-expression-text-eml-a-b-exp-a-ln-b/",
    "prov": "http://www.w3.org/ns/prov#",
    "xsd": "http://www.w3.org/2001/XMLSchema#",
    "schema": "http://schema.org/"
  },
  "entity": {
    "pe:claim": {
      "prov:type": "pe:Claim",
      "prov:label": "The binary operator eml is defined by the expression \\(\\text{eml}(a, b) = \\exp(a) - \\ln(b)\\) (where exp is the exponential function and ln is the principal branch of the natural logarithm). The expression \\(\\text{eml}(1, 1)\\) equals the base of the natural logarithm \\(e\\).",
      "prov:value": "The binary operator eml is defined by the expression \\(\\text{eml}(a, b) = \\exp(a) - \\ln(b)\\) (where exp is the exponential function and ln is the principal branch of the natural logarithm). The expression \\(\\text{eml}(1, 1)\\) equals the base of the natural logarithm \\(e\\)."
    },
    "pe:evidence-A1": {
      "prov:type": "pe:ComputedEvidence",
      "prov:label": "exp(1) = e (symbolic verification)",
      "pe:factId": "A1",
      "pe:evidenceType": "computed",
      "pe:method": "SymPy symbolic evaluation: simplify(exp(1) - E); verify equals 0",
      "pe:result": "Confirmed: exp(1) = e"
    },
    "pe:evidence-A2": {
      "prov:type": "pe:ComputedEvidence",
      "prov:label": "ln(1) = 0 (symbolic verification)",
      "pe:factId": "A2",
      "pe:evidenceType": "computed",
      "pe:method": "SymPy symbolic evaluation of ln(1); verify equals 0",
      "pe:result": "Confirmed: ln(1) = 0"
    },
    "pe:evidence-A3": {
      "prov:type": "pe:ComputedEvidence",
      "prov:label": "eml(1, 1) - e = 0 (symbolic simplification)",
      "pe:factId": "A3",
      "pe:evidenceType": "computed",
      "pe:method": "SymPy symbolic simplification of exp(1) - ln(1) - E; verify result is 0",
      "pe:result": "Confirmed: residual = 0"
    },
    "pe:verdict": {
      "prov:type": "pe:Verdict",
      "prov:label": "Verdict: PROVED",
      "prov:value": "PROVED",
      "pe:doi": "10.5281/zenodo.19635611"
    }
  },
  "activity": {
    "pe:determine-verdict": {
      "prov:type": "pe:VerdictDetermination",
      "prov:label": "Determine verdict from evidence",
      "prov:endTime": "2026-04-16"
    }
  },
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    "pe:proof-engine": {
      "prov:type": "prov:SoftwareAgent",
      "prov:label": "Proof Engine",
      "schema:version": "1.18.0",
      "schema:url": "https://github.com/yaniv-golan/proof-engine"
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  "wasGeneratedBy": {
    "pe:gen-verdict": {
      "prov:entity": "pe:verdict",
      "prov:activity": "pe:determine-verdict"
    }
  },
  "wasDerivedFrom": {
    "pe:deriv-A3-from-A1": {
      "prov:generatedEntity": "pe:evidence-A3",
      "prov:usedEntity": "pe:evidence-A1"
    },
    "pe:deriv-A3-from-A2": {
      "prov:generatedEntity": "pe:evidence-A3",
      "prov:usedEntity": "pe:evidence-A2"
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  "wasAttributedTo": {
    "pe:attr-verdict": {
      "prov:entity": "pe:verdict",
      "prov:agent": "pe:proof-engine"
    }
  },
  "used": {
    "pe:used-A1": {
      "prov:activity": "pe:determine-verdict",
      "prov:entity": "pe:evidence-A1"
    },
    "pe:used-A2": {
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      "prov:entity": "pe:evidence-A2"
    },
    "pe:used-A3": {
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