Theorems · Theorem · combinatorics
Matroid.Indep.rankPos_of_nonempty
∀ {α : Type u_1} {M : Matroid α} {I : Set α}, M.Indep I → I.Nonempty → M.RankPos- Defined in
- Mathlib.Combinatorics.Matroid.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 63 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
- Set.Nonemptystatement and proof · cited by 2,627
- Matroidstatement and proof · cited by 1,258
- Matroid.Indepstatement and proof · cited by 367
- Matroid.IsBaseproof · cited by 239
- Set.Nonempty.monoproof · cited by 88
- Matroid.RankPosstatement · cited by 22
- Matroid.Indep.exists_isBase_supersetproof · cited by 18
- Matroid.IsBase.rankPos_of_nonemptyproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Matroid.IsNonloop.rankPosproof · cited by 0