Theorems · Theorem · combinatorics
Matroid.eRk_inter_ground
∀ {α : Type u_1} (M : Matroid α) (X : Set α), M.eRk (X ∩ M.E) = M.eRk X- Defined in
- Mathlib.Combinatorics.Matroid.Rank.ENat
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 108 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
- Matroid.Estatement and proof · cited by 550
- Matroid.eRkstatement and proof · cited by 101
- Matroid.IsBasis'proof · cited by 101
- Matroid.exists_isBasis'proof · cited by 30
- Matroid.IsBasis'.isBasis_inter_groundproof · cited by 14
- Matroid.IsBasis.eRk_eq_eRkproof · cited by 3
- Matroid.IsBasis'.eRk_eq_eRkproof · cited by 2
Cited by12
Results whose statement or proof uses this declaration.
- Matroid.eRk_le_eRankproof · cited by 1
- Matroid.eRk_union_groundproof · cited by 1
- Matroid.restrict_eRk_eq'proof · cited by 1
- Matroid.eRk_eq_zero_iff'proof · cited by 1
- Matroid.exists_eRk_insert_eq_add_one_of_ltproof · cited by 1
- Matroid.eRk_univ_eqproof · cited by 0
- Matroid.eRk_compl_union_of_disjointproof · cited by 0
- Matroid.eRk_dual_add_eRank'proof · cited by 0
- Matroid.eRk_eq_eRankproof · cited by 0
- Matroid.eRk_ground_interproof · cited by 0
- Matroid.eRank_le_encard_add_eRk_complproof · cited by 0
- Matroid.eRk_insert_of_notMem_groundproof · cited by 0