197.lean`

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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 197

Reference: erdosproblems.com/197

Imports (1)

FormalConjecturesUtil

theorem Erdos197.erdos_197 Can $\mathbb{N}$ be partitioned into two sets, each of which can be permuted to avoid monotone 3-term arithmetic progressions? sorry line 37 source
Source documentation
Can $\mathbb{N}$ be partitioned into two sets, each of which can be permuted to avoid monotone 3-term arithmetic progressions?

depends on sorry what this means
Statement uses: Iff, True, Exists, Set, Nat, And, IsCompl, Equiv, Not, HasMonotoneAP, Function.comp, Subtype, Membership.mem, OfNat.ofNat
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_197 :
    answer(sorry) ↔ ∃ A B : Set ℕ, IsCompl A B ∧
      (∃ f : ℕ ≃ A, ¬HasMonotoneAP (Subtype.val ∘ f) 3) ∧
      (∃ g : ℕ ≃ B, ¬HasMonotoneAP (Subtype.val ∘ g) 3) := by
…
```
Mentions: HasMonotoneAP