Theorems · Theorem · combinatorics
Matroid.spanning_iff_eRk_le
∀ {α : Type u_1} {M : Matroid α} {X : Set α} [M.RankFinite],
autoParam (X ⊆ M.E) Matroid.spanning_iff_eRk_le._auto_1 → (M.Spanning X ↔ M.eRank ≤ M.eRk X)- Defined in
- Mathlib.Combinatorics.Matroid.Rank.ENat
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Matroid.RankFinite
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Cites9
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 · cited by 4,985
- Matroidstatement and proof · cited by 1,258
- Matroid.Estatement and proof · cited by 550
- Matroid.eRkstatement and proof · cited by 101
- Matroid.Spanningstatement · cited by 63
- Matroid.eRankstatement and proof · cited by 36
- Matroid.RankFinitestatement and proof · cited by 33
- Matroid.spanning_iff_eRk_le'proof · cited by 1
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