Theorems · Theorem · combinatorics
Matroid.Dep.eRk_lt_encard
∀ {α : Type u_1} {M : Matroid α} {X : Set α} [M.RankFinite], M.Dep X → M.eRk X < X.encard- Defined in
- Mathlib.Combinatorics.Matroid.Rank.ENat
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Matroid.RankFinite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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 · cited by 4,985
- Matroidstatement and proof · cited by 1,258
- Set.encardstatement and proof · cited by 327
- LE.le.lt_of_neproof · cited by 116
- Matroid.eRkstatement and proof · cited by 101
- Matroid.Depstatement and proof · cited by 76
- Matroid.RankFinitestatement and proof · cited by 33
- Matroid.Dep.not_indepproof · cited by 14
- Matroid.eRk_le_encardproof · cited by 10
- Matroid.indep_iff_eRk_eq_encardproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Matroid.eRk_lt_encard_iff_depproof · cited by 0