Theorems · Theorem · combinatorics
Matroid.IsBase.infinite
∀ {α : Type u_1} {M : Matroid α} {B : Set α} [M.RankInfinite], M.IsBase B → B.Infinite- Defined in
- Mathlib.Combinatorics.Matroid.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Matroid.RankInfinite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Matroidstatement and proof · cited by 1,258
- Set.Infinitestatement and proof · cited by 263
- Matroid.IsBasestatement and proof · cited by 239
- Matroid.RankInfinitestatement and proof · cited by 13
- Matroid.RankInfinite.exists_infinite_isBaseproof · cited by 1
- Matroid.IsBase.infinite_of_infiniteproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Matroid.not_rankFiniteproof · cited by 1
- Matroid.not_rankInfiniteproof · cited by 1