Theorems · Theorem · combinatorics
Matroid.cRk_closure
∀ {α : Type u} (M : Matroid α) [M.InvariantCardinalRank] (X : Set α), M.cRk (M.closure X) = M.cRk X- Cited by
- 1 results in Mathlib
- Foundations
- Depth 88 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.
- Setstatement and proof · cited by 53,352
- Set.Elemproof · cited by 7,166
- Cardinalstatement and proof · cited by 2,598
- Matroidstatement and proof · cited by 1,258
- Cardinal.mkproof · cited by 942
- Matroid.closurestatement · cited by 272
- Matroid.IsBasis'proof · cited by 101
- Matroid.exists_isBasis'proof · cited by 30
- Matroid.cRkstatement and proof · cited by 29
- Matroid.InvariantCardinalRankstatement and proof · cited by 25
- Matroid.IsBasis'.isBasis_closure_rightproof · cited by 4
- Matroid.IsBasis'.cardinalMk_eq_cRkproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Matroid.cRk_closure_congrproof · cited by 2