Theorems · Theorem · combinatorics
Matroid.spanning_iff_closure_eq
∀ {α : Type u_2} {M : Matroid α} {S : Set α},
autoParam (S ⊆ M.E) Matroid.spanning_iff_closure_eq._auto_1 → (M.Spanning S ↔ M.closure S = M.E)- Defined in
- Mathlib.Combinatorics.Matroid.Closure
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext
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 · cited by 63
- Matroid.spanning_iffproof · cited by 5
Cited by7
Results whose statement or proof uses this declaration.
- Matroid.isColoop_iff_sdiff_closureproof · cited by 2
- Matroid.IsBasis.spanning_iff_spanningproof · cited by 2
- Matroid.coindep_iff_closure_compl_eq_groundproof · cited by 1
- Matroid.spanning_iff_ground_subset_closureproof · cited by 1
- Matroid.closure_spanning_iffproof · cited by 1
- Matroid.Spanning.closure_eq_of_supersetproof · cited by 0
- Matroid.not_spanning_iff_closure_ssubsetproof · cited by 0