Theorems · Theorem · combinatorics
Matroid.isBasis_union_iff_indep_closure
∀ {α : Type u_2} {M : Matroid α} {X I : Set α}, M.IsBasis I (I ∪ X) ↔ M.Indep I ∧ X ⊆ M.closure I- Defined in
- Mathlib.Combinatorics.Matroid.Closure
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- LE.le.transproof · cited by 3,151
- Matroidstatement and proof · cited by 1,258
- Matroid.Indepstatement and proof · cited by 367
- Matroid.closurestatement and proof · cited by 272
- Matroid.IsBasisstatement and proof · cited by 219
- Set.subset_union_leftproof · cited by 142
- Set.subset_union_rightproof · cited by 123
- Set.union_subsetproof · cited by 71
- Matroid.Indep.subset_groundproof · cited by 61
- Matroid.IsBasis.indepproof · cited by 51
- Matroid.subset_closureproof · cited by 23
Cited by1
Results whose statement or proof uses this declaration.
- Matroid.isBasis_iff_indep_closureproof · cited by 2