Theorems · Theorem · combinatorics
Matroid.Indep.isBase_of_spanning
∀ {α : Type u_2} {M : Matroid α} {I : Set α}, M.Indep I → M.Spanning I → M.IsBase I- Defined in
- Mathlib.Combinatorics.Matroid.Closure
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.IsBasestatement and proof · cited by 239
- Matroid.Spanningstatement and proof · cited by 63
- Matroid.IsBase.eq_of_subset_indepproof · cited by 8
- Matroid.Spanning.exists_isBase_subsetproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- Matroid.IsBasis.isBase_of_spanningproof · cited by 2
- Matroid.Spanning.isBase_restrict_iffproof · cited by 2
- Matroid.Spanning.isBase_of_indepproof · cited by 0
- Matroid.Indep.eq_of_spanning_subsetproof · cited by 0