Theorems · Theorem · combinatorics
Matroid.Indep.isBase_of_ground_subset_closure
∀ {α : Type u_2} {M : Matroid α} {I : Set α}, M.Indep I → M.E ⊆ M.closure I → M.IsBase 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.Estatement and proof · cited by 550
- Matroid.Indepstatement and proof · cited by 367
- Matroid.closurestatement and proof · cited by 272
- Matroid.IsBasestatement · cited by 239
- Matroid.Indep.subset_groundproof · cited by 61
- Matroid.isBasis_ground_iffproof · cited by 10
- Matroid.Indep.isBasis_of_subset_of_subset_closureproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- Matroid.Indep.isBase_iff_ground_subset_closureproof · cited by 0