Theorems · Theorem · combinatorics
Matroid.Indep.finite
∀ {α : Type u_1} {M : Matroid α} {I : Set α} [M.RankFinite], M.Indep I → I.Finite- Defined in
- Mathlib.Combinatorics.Matroid.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 104 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.
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.Finitestatement and proof · cited by 1,814
- Matroidstatement and proof · cited by 1,258
- Matroid.Indepstatement and proof · cited by 367
- Set.Finite.subsetproof · cited by 285
- Matroid.IsBaseproof · cited by 239
- Matroid.RankFinitestatement and proof · cited by 33
- Matroid.Indep.exists_isBase_supersetproof · cited by 18
- Matroid.IsBase.finiteproof · cited by 7
Cited by4
Results whose statement or proof uses this declaration.
- Matroid.Indep.isBase_of_cRank_leproof · cited by 2
- Matroid.spanning_iff_eRk_le'proof · cited by 1
- Matroid.isRkFinite_setproof · cited by 1
- Matroid.IsBasis.Finiteproof · cited by 0