Theorems · Theorem · combinatorics
Matroid.Spanning.exists_isBase_subset
∀ {α : Type u_2} {M : Matroid α} {S : Set α}, M.Spanning S → ∃ B, M.IsBase B ∧ B ⊆ S- Defined in
- Mathlib.Combinatorics.Matroid.Closure
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.IsBasestatement · cited by 239
- Matroid.Spanningstatement and proof · cited by 63
- Matroid.Spanning.subset_groundproof · cited by 13
- Matroid.spanning_iff_exists_isBase_subsetproof · cited by 4
Cited by6
Results whose statement or proof uses this declaration.
- Matroid.Indep.isBase_of_spanningproof · cited by 4
- Matroid.isBase_iff_minimal_spanningproof · cited by 2
- Matroid.IsBase.eq_of_superset_spanningproof · cited by 1
- Matroid.Spanning.isBase_of_le_cRankproof · cited by 1
- Matroid.Spanning.isBase_of_le_cRank_of_finiteproof · cited by 1
- Matroid.Spanning.cRank_le_cardinalMkproof · cited by 1