Theorems · Definition · combinatorics
Matroid.dual
{α : Type u_1} → Matroid α → Matroid αThe dual of a matroid; the bases are the complements (w.r.t. M.E) of the bases of M.
- Defined in
- Mathlib.Combinatorics.Matroid.Dual
- Cited by
- 79 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Matroidstatement and proof · cited by 1,258
- IndepMatroid.matroidproof · cited by 4
- Matroid.dualIndepMatroidproof · cited by 2
Cited by86
Results whose statement or proof uses this declaration.
- Matroid.contractproof · cited by 103
- Matroid.IsColoopproof · cited by 38
- Matroid.coloopsproof · cited by 34
- Matroid.IsCocircuitproof · cited by 32
- Matroid.freeOnproof · cited by 25
- Matroid.Coindepproof · cited by 24
- Matroid.dual_dualstatement · cited by 22
- Matroid.dual_contractstatement and proof · cited by 9
- Matroid.dual_delete_dualstatement · cited by 9
- Matroid.dual_groundstatement · cited by 9
- Matroid.dual_isBase_iffstatement and proof · cited by 9
- Matroid.fundCocircuitproof · cited by 9