Theorems · Theorem · combinatorics
Matroid.Spanning.isBase_of_le_cRank
∀ {α : Type u} {M : Matroid α} {X : Set α} [M.RankFinite], M.Spanning X → Cardinal.mk ↑X ≤ M.cRank → M.IsBase X- Cited by
- 1 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Matroid.RankFinite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- Set.Elemstatement and proof · cited by 7,166
- LE.le.transproof · cited by 3,151
- Cardinalstatement · cited by 2,598
- Matroidstatement and proof · cited by 1,258
- Cardinal.mkstatement and proof · cited by 942
- Eq.geproof · cited by 375
- Matroid.IsBasestatement and proof · cited by 239
- Cardinal.toENatproof · cited by 92
- Matroid.Spanningstatement and proof · cited by 63
- Matroid.RankFinitestatement and proof · cited by 33
- Matroid.cRankstatement and proof · cited by 17
Cited by1
Results whose statement or proof uses this declaration.
- Matroid.Spanning.isBase_of_le_cRank_of_finiteproof · cited by 1