185.lean`

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

3 declarations, 2 contain sorry, 0 declared as axioms

Erdős Problem 185

References:

erdosproblems.com/185
[Er73] Erdős, P., Problems and results on combinatorial number theory. A survey of combinatorial theory (Proc. Internat. Sympos., Colorado State Univ., Fort Collins, Colo., 1971) (1973), 117-138.
[FuKa91] Furstenberg, H. and Katznelson, Y., A density version of the Hales-Jewett Theorem. Journal d'Analyse Mathématique (1991), 64-119.

Imports (1)

FormalConjecturesUtil

def Erdos185.f3 $f_3(n)$ is the maximal size of a subset of $\{0,1,2\}^n$ which contains no three points on a line (in $\mathbb{R}^n$) line 40 source
Source documentation
$f_3(n)$ is the maximal size of a subset of $\{0,1,2\}^n$ which contains no three points on a line (in $\mathbb{R}^n$).

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: SupSet.sSup, Set.ofPred, Exists, Finset, Fin, OfNat.ofNat, And, Membership.mem, Ne, Not, Collinear, Real, Insert.insert, Set, Singleton.singleton, Eq, Finset.card
20 instances, coercions and auxiliary constants left out.
```
noncomputable def f3 (n : ℕ) : ℕ :=
…
```
theorem Erdos185.erdos_185 sorry line 59 source
depends on sorry what this means
Statement uses: Iff, True, Asymptotics.IsLittleO, Nat, Real, Filter.atTop, Erdos185.f3, HPow.hPow, OfNat.ofNat
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 Erdos185.erdos_185.variants.moser Moser showed that $f_3(n) \gg \frac{3^n}{\sqrt{n}}$ sorry line 64 source
Source documentation
Moser showed that $f_3(n) \gg \frac{3^n}{\sqrt{n}}$.

depends on sorry what this means
Statement uses: Asymptotics.IsBigO, Nat, Real, Filter.atTop, HDiv.hDiv, HPow.hPow, OfNat.ofNat, Real.sqrt, Erdos185.f3
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
30 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_185.variants.moser :
    (fun n : ℕ => (3 : ℝ) ^ n / √n) =O[atTop] fun n : ℕ => (f3 n : ℝ) := by
…
```
Mentions: Erdos185.f3