Theorems · Theorem · combinatorics
Matroid.RankPos.empty_not_isBase
∀ {α : Type u_1} {M : Matroid α} [self : M.RankPos], ¬M.IsBase ∅The empty set isn't a base
- Defined in
- Mathlib.Combinatorics.Matroid.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
- Assumes
- Matroid.RankPos
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Matroidstatement and proof · cited by 1,258
- Matroid.IsBasestatement · cited by 239
- Matroid.RankPosstatement and proof · cited by 22
Cited by1
Results whose statement or proof uses this declaration.
- Matroid.empty_not_isBaseproof · cited by 2