Theorems · Theorem · combinatorics
Matroid.Indep.eRk_eq_encard
∀ {α : Type u_1} {M : Matroid α} {I : Set α}, M.Indep I → M.eRk I = I.encard- Defined in
- Mathlib.Combinatorics.Matroid.Rank.ENat
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Matroid.Indepstatement and proof · cited by 367
- Set.encardstatement · cited by 327
- Matroid.eRkstatement · cited by 101
- Matroid.Indep.subset_groundproof · cited by 61
- Matroid.Indep.isBasis_selfproof · cited by 12
- Matroid.eq_eRk_iffproof · cited by 1
Cited by15
Results whose statement or proof uses this declaration.
- Matroid.IsBasis'.eRk_eq_encardproof · cited by 9
- Matroid.IsBasis.eRk_eq_encardproof · cited by 7
- Matroid.indep_iff_eRk_eq_encard_of_finiteproof · cited by 5
- Matroid.IsBasis.eRk_eq_eRkproof · cited by 3
- Matroid.IsBasis'.eRk_eq_eRkproof · cited by 2
- Matroid.indep_iff_eRk_eq_encardproof · cited by 1
- Matroid.Indep.isBasis'_of_eRk_geproof · cited by 1
- Matroid.eRk_insert_eq_add_oneproof · cited by 1
- Matroid.eRk_le_iffproof · cited by 0
- Matroid.le_eRk_iffproof · cited by 0
- Matroid.eRk_lt_encard_iff_depproof · cited by 0
- Matroid.IsBase.eRk_eq_eRankproof · cited by 0