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Source labels openChecked July 26, 2026

Erdős ProblemsCombinatorics

Erdős Problem 197

Can N\mathbb{N} be partitioned into two sets, each of which can be permuted to avoid monotone 3-term arithmetic progressions?

Mathematical statement

Can N\mathbb{N} be partitioned into two sets, each of which can be permuted to avoid monotone 3-term arithmetic progressions?

Statement source: Erdős Problems statement material

Statement terms: Source-specific

Source-specific terms. Therefore does not assert reuse rights beyond attributed display.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

erdos_197

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem erdos_197 :    answer(sorry)   A B : Set , IsCompl A B       ( f :  ≃ A, ¬HasMonotoneAP (Subtype.val ∘ f) 3)       ( g :  ≃ B, ¬HasMonotoneAP (Subtype.val ∘ g) 3) := by  sorry
Statement source
Formal Conjectures
Lean version
v4.27.0
Placeholder
Present; no proof artifact
Source evidence
Pinned source index
Fidelity review
Community formulation

References