Mathlib Map

Theorems · Theorem · combinatorics

Matroid.RankFinite.exists_finite_isBase

∀ {α : Type u_1} {M : Matroid α} [self : M.RankFinite], ∃ B, M.IsBase B ∧ B.Finite

There is a finite base

Defined in
Mathlib.Combinatorics.Matroid.Basic
Cited by
2 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
Assumes
Matroid.RankFinite
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Matroid.IsBase.finite · cited by 7IsBase.finiteMatroid.IsRkFinite.exists_finite_isBasis' · cited by 3IsRkFinite.exists_finite_…Set · cited by 53352SetSet.Finite · cited by 1814Set.FiniteMatroid · cited by 1258MatroidMatroid.IsBase · cited by 239Matroid.IsBaseMatroid.RankFinite · cited by 33Matroid.RankFiniteRankFinite.exists_finite_isBa…CITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.