Theorems · Theorem · combinatorics
Matroid.spanning_iff
∀ {α : Type u_2} (M : Matroid α) (S : Set α), M.Spanning S ↔ M.closure S = M.E ∧ S ⊆ M.E- Defined in
- Mathlib.Combinatorics.Matroid.Closure
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
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.Estatement and proof · cited by 550
- Matroid.closurestatement and proof · cited by 272
- Matroid.Spanningstatement and proof · cited by 63
- Matroid.Spanning.casesOnproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- Matroid.spanning_iff_closure_eqproof · cited by 7
- Matroid.contract_spanning_iffproof · cited by 1
- Matroid.restrict_spanning_iffproof · cited by 0
- Matroid.restrict_spanning_iff'proof · cited by 0
- Matroid.loopyOn_spanning_iffproof · cited by 0