Theorems · Theorem · combinatorics
Matroid.le_eRk_iff
∀ {α : Type u_1} {M : Matroid α} {X : Set α} {n : ℕ∞}, n ≤ M.eRk X ↔ ∃ I ⊆ X, M.Indep I ∧ I.encard = n- Defined in
- Mathlib.Combinatorics.Matroid.Rank.ENat
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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 and proof · cited by 4,985
- LE.le.transproof · cited by 3,151
- Matroidstatement and proof · cited by 1,258
- Matroid.Indepstatement and proof · cited by 367
- Set.encardstatement and proof · cited by 327
- Matroid.eRkstatement and proof · cited by 101
- Matroid.IsBasis'proof · cited by 101
- Matroid.Indep.subsetproof · cited by 42
- Matroid.exists_isBasis'proof · cited by 30
- Matroid.IsBasis'.indepproof · cited by 27
- Matroid.IsBasis'.subsetproof · cited by 25
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.