Theorems · Theorem · combinatorics
Matroid.eRank_eq_zero_iff
∀ {α : Type u_1} {M : Matroid α}, M.eRank = 0 ↔ M = Matroid.loopyOn M.E- Defined in
- Mathlib.Combinatorics.Matroid.Rank.ENat
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 111 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.
- Setproof · cited by 53,352
- ENatstatement and proof · cited by 4,985
- Matroidstatement and proof · cited by 1,258
- Matroid.Estatement and proof · cited by 550
- Matroid.closureproof · cited by 272
- Matroid.IsBaseproof · cited by 239
- Matroid.eRankstatement and proof · cited by 36
- Matroid.loopyOnstatement and proof · cited by 32
- Matroid.exists_isBaseproof · cited by 15
- Set.encard_eq_zeroproof · cited by 12
- Matroid.IsBase.encard_eq_eRankproof · cited by 10
- Matroid.IsBase.closure_eqproof · cited by 9
Cited by2
Results whose statement or proof uses this declaration.
- Matroid.eq_loopyOn_iff_eRankproof · cited by 0
- Matroid.eRank_emptyOnproof · cited by 0