Theorems · Definition · combinatorics
Matroid.cRank
{α : Type u} → Matroid α → Cardinal.{u}The rank (supremum of the cardinalities of bases) of a matroid M as a Cardinal.
See Matroid.eRank for a better-behaved ℕ∞-valued version.
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Set.Elemproof · cited by 7,166
- Cardinalstatement · cited by 2,598
- iSupproof · cited by 2,415
- Matroidstatement and proof · cited by 1,258
- Cardinal.mkproof · cited by 942
- Matroid.IsBaseproof · cited by 239
Cited by18
Results whose statement or proof uses this declaration.
- Matroid.cRkproof · cited by 29
- Matroid.IsBase.cardinalMk_eq_cRankstatement · cited by 6
- AlgebraicIndependent.matroid_cRank_eqstatement · cited by 4
- Matroid.rankFinite_iff_cRank_lt_aleph0statement and proof · cited by 3
- Matroid.IsBase.cardinalMk_le_cRankstatement · cited by 3
- Matroid.IsBasis'.cardinalMk_eq_cRkproof · cited by 3
- Matroid.Indep.isBase_of_cRank_lestatement and proof · cited by 2
- Matroid.toENat_cRank_eqstatement and proof · cited by 1
- Matroid.rankInfinite_iff_aleph0_le_cRankstatement · cited by 1
- Matroid.Spanning.cRank_le_cardinalMkstatement and proof · cited by 1
- Matroid.cRank_restrictstatement · cited by 1
- Matroid.Spanning.isBase_of_le_cRankstatement and proof · cited by 1