183.lean`

Explanation legend Lean4 Domain Explanation Language (L4DEL)

L4DEL explanations are a separate layer. They do not change the Lean source. Intuition is explanatory prose; numbered items are a reading path; sources link the wording back to evidence.

L4DEL: Lean4 Domain Explanation Language

Annotation provenance. This overlay contains 10 curated AI-written annotations and 7190 mechanical source-derived annotations. They have not been human-reviewed as explanations; treat them as unverified and not mathematical authority. Retained generation history: The 71 original curated annotations were produced in a Claude Sonnet 5.5 session at medium effort; Claude Opus 5.5 is recorded in that session as the advisor model, not the direct author. The bulk source-derived expansion was generated mechanically from pinned source comments by tooling developed in a GPT-5.6 Sol session at ultra reasoning; GPT-5.6 Sol did not originate the quoted source prose. On 2026-10-17 the mechanically generated source-comment annotations of the Formal Conjectures, Carleson, FLT, PFR, CompFiles, Mathematics in Lean and Theorem Proving in Lean overlays were regenerated by the same generator after three corrections made in a Claude Sonnet 5.5 session: titles no longer cut a sentence inside mathematics or end on a dangling word, workflow markers are removed from the quoted prose, and declaration names follow the scanner's namespace resolution. The boilerplate step line was dropped, and comments that were only a row of dashes no longer yield annotations. No new prose was written and no human review is claimed.

Credit: The upstream authors and contributors retain credit for the project and mathematics. lean4-explainer only renders their pinned source and adds the separately disclosed explanation layer.

Project sources: Pinned project documentation, Formal Conjectures paper, arXiv v1

4 declarations, 2 contain sorry, 0 declared as axioms

Erdős Problem 183

References:

erdosproblems.com/183
[Er61] Erdős, P., Graph theory and probability. II. Canad. J. Math. (1961), 346-352.
[OpenAI26] OpenAI, Ten advances in mathematics and theoretical computer science. (2026).

Imports (1)

FormalConjecturesUtil

def Erdos183.ForcesMonochromaticTriangle n forces a monochromatic triangle on k colours when every k-colouring of the edges of K_n has a colour class containing a triangle line 39 source
Source documentation
n forces a monochromatic triangle on k colours when every k-colouring of the edges of K_n has a colour class containing a triangle.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: SimpleGraph.TopEdgeLabeling, Fin, Not, SimpleGraph.TopEdgeLabeling.CliqueFree, OfNat.ofNat
1 instances, coercions and auxiliary constants left out.
```
def ForcesMonochromaticTriangle (n k : ℕ) : Prop :=
…
```
def Erdos183.multicolourTriangleRamsey $R(3;k)$, the minimal n such that every k-colouring of the edges of K_n contains a monochromatic triangle line 44 source
Source documentation
$R(3;k)$, the minimal n such that every k-colouring of the edges of K_n contains a monochromatic triangle.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: InfSet.sInf, Set.ofPred, Erdos183.ForcesMonochromaticTriangle
1 instances, coercions and auxiliary constants left out.
```
noncomputable def multicolourTriangleRamsey (k : ℕ) : ℕ :=
…
```
theorem Erdos183.erdos_183 sorry line 58 source
depends on sorry what this means
Statement uses: Filter.Tendsto, Nat, Real, HPow.hPow, Erdos183.multicolourTriangleRamsey, HDiv.hDiv, OfNat.ofNat, Filter.atTop
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
23 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem Erdos183.erdos_183.variants.explicit_lower_bound sorry line 69 source
depends on sorry what this means
Statement uses: Nat, LE.le, OfNat.ofNat, Real, HPow.hPow, HDiv.hDiv, HMul.hMul, Real.exp, Real.log, Erdos183.multicolourTriangleRamsey
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
40 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.