Theorems · Theorem · combinatorics
Matroid.IsBase.finite
∀ {α : Type u_1} {M : Matroid α} {B : Set α} [M.RankFinite], M.IsBase B → B.Finite- Defined in
- Mathlib.Combinatorics.Matroid.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Matroid.RankFinite
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
- Set.Finitestatement and proof · cited by 1,814
- Matroidstatement and proof · cited by 1,258
- Matroid.IsBasestatement and proof · cited by 239
- Matroid.RankFinitestatement and proof · cited by 33
- Matroid.IsBase.finite_of_finiteproof · cited by 2
- Matroid.RankFinite.exists_finite_isBaseproof · cited by 2
Cited by7
Results whose statement or proof uses this declaration.
- Matroid.Indep.finiteproof · cited by 4
- Matroid.IsBasis'.finite_iff_isRkFiniteproof · cited by 3
- Matroid.IsRkFinite.finite_of_isBasis'proof · cited by 2
- Matroid.eRank_ne_top_iffproof · cited by 1
- Matroid.not_rankFiniteproof · cited by 1
- Matroid.not_rankInfiniteproof · cited by 1
- Matroid.Spanning.isBase_of_le_cRankproof · cited by 1