Source labels openChecked July 26, 2026

VCₙ dimension of convex sets in ℝⁿ, ℝⁿ⁺¹, ℝⁿ⁺²

If $n \ge 2$ , every convex set in $\mathbb R^{n + 1}$ has $\mathrm{VC}_n$ dimension at most 1.

Combinatorics AMS 5 AMS 52

Mathematical statement

If $n \ge 2$ , every convex set in $\mathbb R^{n + 1}$ has $\mathrm{VC}_n$ dimension at most 1.

Statement source: Other 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

hasAddVCNDimAtMost_n_one_of_convex_rn_add_one

Canonical source

Complete statement target, proof intentionally absentLean 4

lemma hasAddVCNDimAtMost_n_one_of_convex_rn_add_one {n : ℕ} (hn : 2 ≤ n) {C : Set (Fin (n + 1) → ℝ)}    (hC : Convex ℝ C) : HasAddVCNDimAtMost C n 1 := 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

Pinned Formal Conjectures sourceformalization