Theorems · Theorem · combinatorics
Matroid.uniqueBaseOn_closure_eq
∀ {α : Type u_2} (I E X : Set α), (Matroid.uniqueBaseOn I E).closure X = X ∩ I ∩ E ∪ E \ I- Defined in
- Mathlib.Combinatorics.Matroid.Closure
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 89 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
- Matroidproof · cited by 1,258
- Matroid.Eproof · cited by 550
- Matroid.closurestatement and proof · cited by 272
- Set.inter_assocproof · cited by 67
- Set.inter_selfproof · cited by 63
- Matroid.freeOnproof · cited by 25
- Matroid.uniqueBaseOnstatement · cited by 17
- Set.inter_right_commproof · cited by 9
- Matroid.restrict_closure_eq'proof · cited by 9
- Matroid.freeOn_groundproof · cited by 3
- Matroid.freeOn_closure_eqproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Matroid.uniqueBaseOn_isLoop_iffproof · cited by 0