Theorems · Theorem · combinatorics
Matroid.isBasis_iff_indep_subset_closure
∀ {α : Type u_2} {M : Matroid α} {X I : Set α}, M.IsBasis I X ↔ M.Indep I ∧ I ⊆ X ∧ 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.
Cites9
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
- 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
- Matroid.IsBasis.indepproof · cited by 51
- Matroid.IsBasis.subsetproof · cited by 45
- Matroid.IsBasis.subset_closureproof · cited by 15
- Matroid.Indep.isBasis_of_subset_of_subset_closureproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- Matroid.isBase_iff_indep_closure_eqproof · cited by 0