847.lean`

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L4DEL: Lean4 Domain Explanation Language

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

2 declarations, 1 contain sorry, 0 declared as axioms

Erdős Problem 847

References:

erdosproblems.com/847
[RRS24] Reiher, Christian and R"odl, Vojt\v ech and Sales, Marcelo, Colouring versus density in integers and {H}ales-{J}ewett cubes. J. Lond. Math. Soc. (2) (2024) arXiv:2311.08556

Imports (1)

FormalConjecturesUtil

def Erdos847.HasFew3APs Documented declaration: HasFew3APs line 38 source
Source documentation
HasFew3APs A means that $A \subset \mathbb{N}$ is a set for which there exists some $\epsilon > 0$ such that in any subset of $A$ of size $n$ there is a subset of size at least $\epsilon n$ which contains no three-term arithmetic progression.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Set, Nat
Proof uses: Exists, Real, And, GT.gt, OfNat.ofNat, LE.le, Finite, GE.ge, Set.ncard, HMul.hMul, ThreeAPFree
11 instances, coercions and auxiliary constants left out.
```
def HasFew3APs (A : Set ℕ) := ∃ (ε : ℝ), ε > 0 ∧ ∀ (B : Set ℕ), B ⊆ A → Finite B →
…
```
theorem Erdos847.erdos_847 sorry line 56 source
depends on sorry what this means
Statement uses: Iff, False, Set, Nat, Infinite, Erdos847.HasFew3APs, Exists, Fin, And, ThreeAPFree, Eq, Set.iUnion
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous, OfNat.ofNat
5 instances, coercions and auxiliary constants left out.

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