Theorems · Theorem · combinatorics
Matroid.IsBase.encard_eq_eRank
∀ {α : Type u_1} {M : Matroid α} {B : Set α}, M.IsBase B → B.encard = M.eRank- Defined in
- Mathlib.Combinatorics.Matroid.Rank.ENat
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 102 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
- iSupproof · cited by 2,415
- Matroidstatement and proof · cited by 1,258
- Set.encardstatement and proof · cited by 327
- Matroid.IsBasestatement and proof · cited by 239
- ciSup_constproof · cited by 43
- Matroid.eRankstatement · cited by 36
- Matroid.IsBase.encard_eq_encard_of_isBaseproof · cited by 4
Cited by10
Results whose statement or proof uses this declaration.
- Matroid.IsBasis'.encard_eq_eRkproof · cited by 8
- Matroid.Spanning.eRk_eqproof · cited by 2
- Matroid.eRank_eq_zero_iffproof · cited by 2
- Matroid.eRank_ne_top_iffproof · cited by 1
- Matroid.toENat_cRank_eqproof · cited by 1
- Matroid.eRk_dual_add_eRankproof · cited by 1
- Matroid.one_le_eRankproof · cited by 0
- Matroid.IsBase.encard_compl_eqproof · cited by 0
- Matroid.eRank_add_eRank_dualproof · cited by 0
- Matroid.eRank_mapproof · cited by 0