Theorems · Theorem · combinatorics
Matroid.exists_isBase
∀ {α : Type u_1} (self : Matroid α), ∃ B, self.IsBase BThere is at least one Base.
- Defined in
- Mathlib.Combinatorics.Matroid.Basic
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
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.
- Setstatement · cited by 53,352
- Matroidstatement and proof · cited by 1,258
- Matroid.IsBasestatement · cited by 239
Cited by15
Results whose statement or proof uses this declaration.
- Matroid.empty_indepproof · cited by 8
- Matroid.isLoop_tfaeproof · cited by 3
- Matroid.rankFinite_iff_cRank_lt_aleph0proof · cited by 3
- Matroid.rankFinite_or_rankInfiniteproof · cited by 2
- Matroid.eRank_eq_zero_iffproof · cited by 2
- Matroid.eRank_ne_top_iffproof · cited by 1
- Matroid.toENat_cRank_eqproof · cited by 1
- Matroid.IsColoop.isNonloopproof · cited by 1
- Matroid.not_rankFiniteproof · cited by 1
- Matroid.not_rankInfiniteproof · cited by 1
- Matroid.exists_isNonloopproof · cited by 0
- Matroid.one_le_eRankproof · cited by 0