128.lean`

Explanation legend Lean4 Domain Explanation Language (L4DEL)

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L4DEL: Lean4 Domain Explanation Language

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

1 declarations, 1 contain sorry, 0 declared as axioms

Erdős Problem 128

Reference: erdosproblems.com/128

Imports (1)

FormalConjecturesUtil

theorem Erdos128.erdos_128 Let G be a graph with n vertices such that every induced subgraph on ≥ $n/2$ vertices has more than $n^2/50$ edges sorry line 37 source
Source documentation
Let G be a graph with n vertices such that every induced subgraph on ≥ $n/2$ vertices has more than $n^2/50$ edges. Must G contain a triangle?

depends on sorry what this means
Statement uses: Iff, True, Fintype, SimpleGraph, Set, GE.ge, Nat, HAdd.hAdd, HMul.hMul, OfNat.ofNat, Set.ncard, Fintype.card, GT.gt, Sym2, SimpleGraph.edgeSet, SimpleGraph.induce, HPow.hPow, Not, SimpleGraph.CliqueFree
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
24 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_128 :
    answer(sorry) ↔ ∀ (V : Type) [Fintype V] (G : SimpleGraph V),
      (∀ V' : Set V, 2 * V'.ncard + 1 ≥ Fintype.card V →
        50 * (G.induce V').edgeSet.ncard > Fintype.card V ^ 2) → ¬ G.CliqueFree 3 := by
…
```