Theorems · Definition · combinatorics
Matroid.eRank
{α : Type u_1} → Matroid α → ℕ∞The rank Matroid.eRank M of M is the ℕ∞-valued cardinality of each base of M.
(See Matroid.cRank for a worse-behaved cardinal-valued version)
- Defined in
- Mathlib.Combinatorics.Matroid.Rank.ENat
- Cited by
- 36 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- ENatstatement · cited by 4,985
- iSupproof · cited by 2,415
- Matroidstatement and proof · cited by 1,258
- Set.encardproof · cited by 327
- Matroid.IsBaseproof · cited by 239
Cited by37
Results whose statement or proof uses this declaration.
- Matroid.eRkproof · cited by 101
- Matroid.eRank_defstatement and proof · cited by 12
- Matroid.IsBase.encard_eq_eRankstatement · cited by 10
- Matroid.eRank_eq_zero_iffstatement and proof · cited by 2
- Matroid.eRank_loopyOnstatement · cited by 2
- Matroid.Spanning.eRk_eqstatement and proof · cited by 2
- Matroid.eRk_le_eRankstatement · cited by 1
- Matroid.toENat_cRank_eqstatement and proof · cited by 1
- Matroid.eRk_union_groundstatement and proof · cited by 1
- Matroid.eRank_eq_topstatement · cited by 1
- Matroid.eRank_eq_top_iffstatement and proof · cited by 1
- Matroid.eRank_ne_top_iffstatement · cited by 1