Theorems · Theorem · combinatorics
Matroid.Indep.isBase_of_eRk_ge
∀ {α : Type u_1} {M : Matroid α} {I : Set α}, M.Indep I → I.Finite → M.eRank ≤ M.eRk I → M.IsBase I- Defined in
- Mathlib.Combinatorics.Matroid.Rank.ENat
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Set.Finitestatement and proof · cited by 1,814
- Matroidstatement and proof · cited by 1,258
- Matroid.Eproof · cited by 550
- Matroid.Indepstatement and proof · cited by 367
- Matroid.IsBasestatement · cited by 239
- Eq.trans_leproof · cited by 155
- Matroid.eRkstatement and proof · cited by 101
- Matroid.Indep.subset_groundproof · cited by 61
- Matroid.eRankstatement and proof · cited by 36
- Matroid.Indep.isBasis_of_eRk_geproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Matroid.spanning_iff_eRk_le'proof · cited by 1