Theorems · Theorem · combinatorics
Matroid.dual_isBase_iff
∀ {α : Type u_1} {M : Matroid α} {B : Set α},
autoParam (B ⊆ M.E) Matroid.dual_isBase_iff._auto_1 → (M✶.IsBase B ↔ M.IsBase (M.E \ B))- Defined in
- Mathlib.Combinatorics.Matroid.Dual
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Disjointproof · cited by 2,201
- Matroidstatement and proof · cited by 1,258
- Matroid.Estatement and proof · cited by 550
- Matroid.Indepproof · cited by 367
- Matroid.IsBasestatement and proof · cited by 239
- Maximalproof · cited by 211
- Matroid.dualstatement and proof · cited by 79
- Matroid.isBase_iff_maximal_indepproof · cited by 5
- maximal_subset_iffproof · cited by 5
- Matroid.isBase_compl_iff_maximal_disjoint_isBaseproof · cited by 1
Cited by9
Results whose statement or proof uses this declaration.
- Matroid.dual_dualproof · cited by 22
- Matroid.IsBase.compl_isBase_dualproof · cited by 6
- Matroid.dual_rankPos_iff_exists_isCircuitproof · cited by 3
- Matroid.dual_isBase_iff'proof · cited by 2
- Matroid.ground_not_isBaseproof · cited by 1
- Matroid.map_dualproof · cited by 1
- Matroid.uniqueBaseOn_dual_eqproof · cited by 1
- Matroid.comapOn_dual_eq_of_bijOnproof · cited by 1
- Matroid.base_iff_dual_isBase_complproof · cited by 0