Theorems · Theorem · combinatorics
Matroid.Spanning.subset_ground
∀ {α : Type u_2} {M : Matroid α} {S : Set α}, M.Spanning S → S ⊆ M.E- Defined in
- Mathlib.Combinatorics.Matroid.Closure
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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 · cited by 550
- Matroid.Spanningstatement and proof · cited by 63
Cited by13
Results whose statement or proof uses this declaration.
- Matroid.Spanning.exists_isBase_subsetproof · cited by 6
- Matroid.Spanning.eRk_eqproof · cited by 2
- Matroid.Spanning.isBase_restrict_iffproof · cited by 2
- Matroid.spanning_iff_eRk_le'proof · cited by 1
- Matroid.spanning_iff_exists_isBase_subset'proof · cited by 1
- Matroid.Indep.exists_isBase_subset_spanningproof · cited by 1
- Matroid.contract_spanning_iff'proof · cited by 1
- Matroid.Spanning.union_leftproof · cited by 0
- Matroid.Spanning.union_rightproof · cited by 0
- Matroid.Spanning.closure_eq_of_supersetproof · cited by 0
- Matroid.Spanning.compl_coindepproof · cited by 0
- Matroid.ext_spanningproof · cited by 0