Theorems · Theorem · combinatorics
Matroid.IsBase.spanning
∀ {α : Type u_2} {M : Matroid α} {B : Set α}, M.IsBase B → M.Spanning B- Defined in
- Mathlib.Combinatorics.Matroid.Closure
- Cited by
- 4 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.
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 and proof · cited by 239
- Matroid.Spanningstatement · cited by 63
- Matroid.IsBase.subset_groundproof · cited by 30
- Matroid.IsBase.closure_eqproof · cited by 9
Cited by4
Results whose statement or proof uses this declaration.
- Matroid.isBase_iff_minimal_spanningproof · cited by 2
- Matroid.IsBase.compl_closure_sdiff_singleton_isCocircuitproof · cited by 1
- Matroid.IsBase.spanning_of_supersetproof · cited by 1
- Matroid.spanning_iff_exists_isBase_subset'proof · cited by 1