Theorems · Theorem · combinatorics
Matroid.IsBase.cardinalMk_le_cRank
∀ {α : Type u} {M : Matroid α} {B : Set α}, M.IsBase B → Cardinal.mk ↑B ≤ M.cRank- Cited by
- 3 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
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.Elemstatement · cited by 7,166
- Cardinalstatement · cited by 2,598
- Matroidstatement and proof · cited by 1,258
- Cardinal.mkstatement · cited by 942
- Matroid.IsBasestatement and proof · cited by 239
- le_ciSupproof · cited by 57
- Cardinal.bddAbove_of_smallproof · cited by 37
- Matroid.cRankstatement · cited by 17
Cited by3
Results whose statement or proof uses this declaration.
- Matroid.IsBasis'.cardinalMk_le_cRkproof · cited by 5
- Matroid.rankFinite_iff_cRank_lt_aleph0proof · cited by 3
- Matroid.cRank_le_iffproof · cited by 0