Theorems · Theorem · combinatorics
Matroid.IsBase.compl_isBase_dual
∀ {α : Type u_1} {M : Matroid α} {B : Set α}, M.IsBase B → M✶.IsBase (M.E \ B)- Defined in
- Mathlib.Combinatorics.Matroid.Dual
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Matroidstatement and proof · cited by 1,258
- Matroid.Estatement · cited by 550
- Matroid.IsBasestatement and proof · cited by 239
- Matroid.dualstatement · cited by 79
- Matroid.IsBase.subset_groundproof · cited by 30
- Set.sdiff_sdiff_cancel_leftproof · cited by 21
- Matroid.dual_isBase_iffproof · cited by 9
Cited by6
Results whose statement or proof uses this declaration.
- Matroid.isColoop_tfaeproof · cited by 4
- Matroid.fundCocircuit_isCocircuitproof · cited by 2
- Matroid.IsBase.inter_isBasis_iff_compl_inter_isBasis_dualproof · cited by 1
- Matroid.IsBase.encard_compl_eqproof · cited by 0
- Matroid.eRank_add_eRank_dualproof · cited by 0
- Matroid.IsBase.mem_fundCocircuit_iff_mem_fundCircuitproof · cited by 0