Theorems · Theorem · combinatorics
Matroid.eRk_eq_top_iff
∀ {α : Type u_1} {M : Matroid α} {X : Set α}, M.eRk X = ⊤ ↔ ¬M.IsRkFinite X- Defined in
- Mathlib.Combinatorics.Matroid.Rank.ENat
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Top.topstatement and proof · cited by 9,680
- ENatstatement and proof · cited by 4,985
- Set.Finiteproof · cited by 1,814
- Matroidstatement and proof · cited by 1,258
- Set.Infiniteproof · cited by 263
- Matroid.eRkstatement · cited by 101
- Matroid.IsBasis'proof · cited by 101
- Matroid.IsRkFinitestatement and proof · cited by 53
- Matroid.exists_isBasis'proof · cited by 30
- Matroid.IsBasis'.eRk_eq_encardproof · cited by 9
- Set.encard_eq_top_iffproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Matroid.eRk_eq_of_eRk_insert_le_forallproof · cited by 0