Theorems · Definition · combinatorics
Matroid.closure
{α : Type u_2} → Matroid α → Set α → Set αThe closure of X ⊆ M.E is the intersection of all the flats of M containing X.
A set X that doesn't satisfy X ⊆ M.E has the junk value M.closure X := M.closure (X ∩ M.E).
- Defined in
- Mathlib.Combinatorics.Matroid.Closure
- Cited by
- 272 results in Mathlib
- Foundations
- Depth 6 from the axioms, rests on 24 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.ofPredproof · cited by 6,101
- Matroidstatement and proof · cited by 1,258
- Matroid.Eproof · cited by 550
- Set.sInterproof · cited by 225
- Matroid.IsFlatproof · cited by 27
Cited by276
Results whose statement or proof uses this declaration.
- Matroid.loopsproof · cited by 52
- Matroid.closure_subset_closurestatement · cited by 24
- Matroid.subset_closurestatement · cited by 23
- Matroid.closure_subset_groundstatement · cited by 23
- Matroid.closure_inter_groundstatement · cited by 22
- Matroid.fundCircuitproof · cited by 19
- Matroid.IsBasis.subset_closurestatement and proof · cited by 15
- Matroid.closure_closurestatement and proof · cited by 14
- Matroid.IsBasis.closure_eq_closurestatement and proof · cited by 13
- Matroid.IsBasis'.closure_eq_closurestatement and proof · cited by 12
- Matroid.IsBase.closure_eqstatement · cited by 9
- Matroid.restrict_closure_eq'statement and proof · cited by 9
Showing the 200 most cited of 276.