Theorems · Definition · combinatorics
Finset.Shatters
{α : Type u_1} → [DecidableEq α] → Finset (Finset α) → Finset α → PropA set family 𝒜 shatters a set s if all subsets of s can be obtained as the intersection
of s and some element of the set family, and we denote this 𝒜.Shatters s. We also say that s
is traced by 𝒜.
- Defined in
- Mathlib.Combinatorics.SetFamily.Shatter
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
Cited by20
Results whose statement or proof uses this declaration.
- Finset.shattererproof · cited by 11
- Finset.mem_shattererstatement and proof · cited by 5
- Finset.Shatters.exists_supersetstatement and proof · cited by 2
- Finset.shatterer_compress_subset_shattererproof · cited by 1
- Finset.shatters_iffstatement and proof · cited by 1
- Finset.shatters_of_forall_subsetstatement · cited by 1
- Finset.shatters_shattererstatement · cited by 1
- Finset.Shatters.card_le_vcDimstatement and proof · cited by 1
- Finset.Shatters.exists_inter_eq_singletonstatement and proof · cited by 1
- Finset.Shatters.mono_leftstatement and proof · cited by 1
- Finset.Shatters.mono_rightstatement and proof · cited by 1
- Finset.Shatters.nonemptystatement and proof · cited by 1