Theorems · Theorem · combinatorics
Matroid.coindep_iff_compl_spanning
∀ {α : Type u_2} {M : Matroid α} {I : Set α},
autoParam (I ⊆ M.E) Matroid.coindep_iff_compl_spanning._auto_1 → (M.Coindep I ↔ M.Spanning (M.E \ I))- Defined in
- Mathlib.Combinatorics.Matroid.Closure
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.IsBaseproof · cited by 239
- Matroid.Spanningstatement and proof · cited by 63
- Matroid.Coindepstatement · cited by 24
- Matroid.spanning_iff_exists_isBase_subsetproof · cited by 4
- Matroid.coindep_iff_existsproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- Matroid.spanning_iff_compl_coindepproof · cited by 2
- Matroid.coindep_iff_closure_compl_eq_groundproof · cited by 1
- Matroid.Indep.contract_isBase_iffproof · cited by 1
- Matroid.ext_spanningproof · cited by 0
- Matroid.Coindep.compl_spanningproof · cited by 0