Theorems · Theorem · combinatorics
Matroid.eRk_le_encard
∀ {α : Type u_1} (M : Matroid α) (X : Set α), M.eRk X ≤ X.encard- Defined in
- Mathlib.Combinatorics.Matroid.Rank.ENat
- Cited by
- 10 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.
Cites10
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
- Matroidstatement and proof · cited by 1,258
- Set.encardstatement and proof · cited by 327
- Matroid.eRkstatement · cited by 101
- Matroid.IsBasis'proof · cited by 101
- Matroid.exists_isBasis'proof · cited by 30
- Matroid.IsBasis'.subsetproof · cited by 25
- Matroid.IsBasis'.eRk_eq_encardproof · cited by 9
- Set.encard_monoproof · cited by 8
Cited by10
Results whose statement or proof uses this declaration.
- Matroid.Dep.eRk_lt_encardproof · cited by 1
- Matroid.eRk_lt_encard_of_dep_of_finiteproof · cited by 1
- Matroid.eRk_union_le_encard_add_eRkproof · cited by 1
- Matroid.eRk_inter_add_eRk_union_leproof · cited by 1
- Matroid.eRank_le_encard_groundproof · cited by 0
- Matroid.eRk_le_one_iffproof · cited by 0
- Matroid.IsRkFinite.indep_of_encard_le_eRkproof · cited by 0
- Matroid.eRk_singleton_leproof · cited by 0
- Matroid.eRk_union_le_eRk_add_encardproof · cited by 0
- Matroid.eRk_insert_le_add_oneproof · cited by 0