Source labels openChecked July 26, 2026

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

For every $n$ there exists some $d$ such that every convex set in $\mathbb R^{n + 1}$ has $\mathrm{VC}_n$ dimension at most $d$ .

Combinatorics AMS 5 AMS 52

Mathematical statement

For every $n$ there exists some $d$ such that every convex set in $\mathbb R^{n + 1}$ has $\mathrm{VC}_n$ dimension at most $d$ .

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

exists_hasAddVCNDimAtMost_n_of_convex_rn_add_one

Canonical source

Complete statement target, proof intentionally absentLean 4

lemma exists_hasAddVCNDimAtMost_n_of_convex_rn_add_one (n : ℕ) :    ∃ d : ℕ, ∀ C : Set (Fin (n + 1) → ℝ), Convex ℝ C → HasAddVCNDimAtMost C n d := 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