Theorems · Theorem · combinatorics
Matroid.rankFinite_iff_cRank_lt_aleph0
∀ {α : Type u} {M : Matroid α}, M.RankFinite ↔ M.cRank < Cardinal.aleph0- Cited by
- 3 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Cardinalstatement · cited by 2,598
- Set.Finiteproof · cited by 1,814
- Matroidstatement and proof · cited by 1,258
- LE.le.trans_ltproof · cited by 795
- Cardinal.aleph0statement and proof · cited by 521
- Matroid.IsBaseproof · cited by 239
- Matroid.RankFinitestatement and proof · cited by 33
- Matroid.cRankstatement and proof · cited by 17
- Matroid.exists_isBaseproof · cited by 15
- Cardinal.lt_aleph0_iff_finiteproof · cited by 8
- Matroid.IsBase.cardinalMk_eq_cRankproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- Matroid.rankInfinite_iff_aleph0_le_cRankproof · cited by 1
- Matroid.isRkFinite_iff_cRk_lt_aleph0proof · cited by 0
- Matroid.Indep.isBase_of_cRank_le_of_finiteproof · cited by 0