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Source labels openChecked July 26, 2026

Erdős ProblemsCombinatorics

Erdős Problem 1167

Finite-target case.* When all κα\kappa_\alpha are finite, κα+1\kappa_\alpha + 1 is the ordinary natural-number successor. Special case of erdos_1167.

Mathematical statement

Finite-target case.* When all κα\kappa_\alpha are finite, κα+1\kappa_\alpha + 1 is the ordinary natural-number successor. Special case of erdos_1167.

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

finite_targets

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem finite_targets (r : ) (hr : 2  r) (lam : Cardinal.{u}) (hlam : ℵ₀  lam)    (γ : Ordinal.{u}) (hγ : 2  γ) (n : γ.ToType  ) :    cardinalPartitionRel ((2 : Cardinal.{u}) ^ lam) (r + 1) γ        (fun α => (n α : Cardinal.{u}) + 1)     cardinalPartitionRel lam r γ (fun α => (n α : Cardinal.{u})) := 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