Theorems · Theorem · combinatorics
Matroid.eRk_le_one_iff
∀ {α : Type u_1} {M : Matroid α} {X : Set α} [M.Nonempty],
autoParam (X ⊆ M.E) Matroid.eRk_le_one_iff._auto_1 → (M.eRk X ≤ 1 ↔ ∃ e ∈ M.E, X ⊆ M.closure {e})- Defined in
- Mathlib.Combinatorics.Matroid.Rank.ENat
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Matroid.Nonempty
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Cites22
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
- ENatstatement and proof · cited by 4,985
- LE.le.transproof · cited by 3,151
- Matroidstatement and proof · cited by 1,258
- Matroid.Estatement and proof · cited by 550
- Matroid.closurestatement and proof · cited by 272
- Matroid.IsBasisproof · cited by 219
- Matroid.eRkstatement and proof · cited by 101
- Set.empty_subsetproof · cited by 70
- Matroid.Indep.subset_groundproof · cited by 61
- Matroid.IsBasis.indepproof · cited by 51
- Set.encard_singletonproof · cited by 26
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