155.lean`

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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 155

Reference: erdosproblems.com/155

Imports (1)

FormalConjecturesUtil

abbrev Erdos155.F Let $F(N)$ be the size of the largest Sidon subset of $\{1, \dots, N\}$ line 35 source
Source documentation
Let $F(N)$ be the size of the largest Sidon subset of $\{1, \dots, N\}$.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: Finset.maxSidonSubsetCard, Finset.Icc, OfNat.ofNat
5 instances, coercions and auxiliary constants left out.
```
noncomputable abbrev F (N : ℕ) : ℕ := Finset.maxSidonSubsetCard (Finset.Icc 1 N)
…
```
Mentions: Finset.maxSidonSubsetCard
theorem Erdos155.erdos_155 Is it true that for every $k \geq 1$ we have $$ F(N + k) \leq F(N) + 1 $$ for all sufficiently large $N$? sorry line 45 source
Source documentation
Is it true that for every $k \geq 1$ we have $$ F(N + k) \leq F(N) + 1 $$ for all sufficiently large $N$?

depends on sorry what this means
Statement uses: Iff, True, Nat, GE.ge, OfNat.ofNat, Filter.Eventually, LE.le, Erdos155.F, HAdd.hAdd, Filter.atTop
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
10 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_155 : answer(sorry) ↔ ∀ k ≥ 1, ∀ᶠ N in atTop, F (N + k) ≤ F N + 1 := by
…
```
Mentions: Erdos155.F