Theorems · Theorem · combinatorics
Matroid.isBase_iff_minimal_spanning
∀ {α : Type u_2} {M : Matroid α} {B : Set α}, M.IsBase B ↔ Minimal M.Spanning B- Defined in
- Mathlib.Combinatorics.Matroid.Closure
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 93 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.IsBasestatement and proof · cited by 239
- Minimalstatement · cited by 150
- Matroid.Spanningstatement and proof · cited by 63
- Matroid.Spanning.exists_isBase_subsetproof · cited by 6
- Matroid.IsBase.spanningproof · cited by 4
- minimal_subset_iffproof · cited by 3
- Matroid.IsBase.eq_of_superset_spanningproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Matroid.IsBase.compl_closure_sdiff_singleton_isCocircuitproof · cited by 1
- Matroid.Spanning.isBase_of_minimalproof · cited by 0