Theorems · Theorem · combinatorics
Matroid.IsBase.cardinalMk_eq_cRank
∀ {α : Type u} {M : Matroid α} {B : Set α} [M.InvariantCardinalRank], M.IsBase B → Cardinal.mk ↑B = M.cRank- Cited by
- 6 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.
Cites11
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 and proof · cited by 7,166
- Cardinalstatement · cited by 2,598
- iSupproof · cited by 2,415
- Matroidstatement and proof · cited by 1,258
- Cardinal.mkstatement and proof · cited by 942
- Matroid.IsBasestatement and proof · cited by 239
- ciSup_constproof · cited by 43
- Matroid.InvariantCardinalRankstatement and proof · cited by 25
- Matroid.cRankstatement · cited by 17
- Matroid.IsBase.cardinalMk_eqproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- IsTranscendenceBasis.lift_cardinalMk_eq_trdegproof · cited by 7
- Matroid.rankFinite_iff_cRank_lt_aleph0proof · cited by 3
- Matroid.IsBasis'.cardinalMk_eq_cRkproof · cited by 3
- Matroid.toENat_cRank_eqproof · cited by 1
- Matroid.Spanning.isBase_of_le_cRankproof · cited by 1
- Matroid.Spanning.cRank_le_cardinalMkproof · cited by 1