Theorems · Theorem · combinatorics
Matroid.Indep.cardinalMk_le_cRank
∀ {α : Type u} {M : Matroid α} {I : Set α}, M.Indep I → Cardinal.mk ↑I ≤ M.cRank- Cited by
- 1 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.
Cites12
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
- Matroidstatement and proof · cited by 1,258
- Cardinal.mkstatement and proof · cited by 942
- Matroid.Indepstatement and proof · cited by 367
- Matroid.IsBaseproof · cited by 239
- Cardinal.bddAbove_of_smallproof · cited by 37
- Cardinal.mk_le_mk_of_subsetproof · cited by 37
- le_ciSup_of_leproof · cited by 22
- Matroid.Indep.exists_isBase_supersetproof · cited by 18
- Matroid.cRankstatement and proof · cited by 17
Cited by1
Results whose statement or proof uses this declaration.
- Matroid.Indep.isBase_of_cRank_leproof · cited by 2