Theorems · Theorem · combinatorics
Matroid.IsBasis.eRk_eq_eRk
∀ {α : Type u_1} {M : Matroid α} {I X : Set α}, M.IsBasis I X → M.eRk I = M.eRk X- Defined in
- Mathlib.Combinatorics.Matroid.Rank.ENat
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 107 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 and proof · cited by 4,985
- Matroidstatement and proof · cited by 1,258
- Set.encardproof · cited by 327
- Matroid.IsBasisstatement and proof · cited by 219
- Matroid.eRkstatement and proof · cited by 101
- Matroid.IsBasis.indepproof · cited by 51
- Matroid.Indep.eRk_eq_encardproof · cited by 15
- Matroid.IsBasis.encard_eq_eRkproof · cited by 9
Cited by3
Results whose statement or proof uses this declaration.
- Matroid.eRk_inter_groundproof · cited by 12
- Matroid.IsBasis.eRk_eq_encardproof · cited by 7
- Matroid.spanning_iff_eRk_le'proof · cited by 1