Theorems · Theorem · combinatorics
Matroid.dual_rankPos_iff_exists_isCircuit
∀ {α : Type u_1} {M : Matroid α}, M✶.RankPos ↔ ∃ C, M.IsCircuit C- Defined in
- Mathlib.Combinatorics.Matroid.Circuit
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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.Eproof · cited by 550
- Matroid.IsBaseproof · cited by 239
- Matroid.IsCircuitstatement and proof · cited by 108
- Matroid.dualstatement and proof · cited by 79
- not_iff_commproof · cited by 32
- Set.sdiff_emptyproof · cited by 25
- Matroid.RankPosstatement · cited by 22
- Matroid.IsCircuit.subset_groundproof · cited by 15
- Matroid.dual_isBase_iffproof · cited by 9
- Matroid.rankPos_iffproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- Matroid.exists_isCircuitproof · cited by 1
- Matroid.IsCircuit.dual_rankPosproof · cited by 0
- Matroid.rankPos_iff_exists_isCocircuitproof · cited by 0