Documentation

FormalSLT.VC.VCDimension

Compatibility import: VC dimension #

The implementation lives in FormalSLT.VC.Dimension. This alias preserves the earlier verbose namespace and import path.

Alias of FormalSLT.VC.Dimension.sauerShelahFiniteSetFamily.


Sauer-Shelah lemma for finite set families, binomial-sum form.

This claim-facing wrapper is the finite combinatorial core behind the vc-dimension page's growth-function statement. A hypothesis class restricted to a fixed finite sample is represented as a finite family of subsets of the sample. Mathlib's Finset.card_le_card_shatterer gives Pajor's trace bound, and Finset.card_shatterer_le_sum_vcDim gives the Sauer-Shelah binomial bound in terms of the VC dimension of that finite family.