Theorems · Theorem · combinatorics
Matroid.coindep_iff_closure_compl_eq_ground
∀ {α : Type u_2} {M : Matroid α} {X : Set α},
autoParam (X ⊆ M.E) Matroid.coindep_iff_closure_compl_eq_ground._auto_1 → (M.Coindep X ↔ M.closure (M.E \ X) = M.E)- Defined in
- Mathlib.Combinatorics.Matroid.Closure
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.Coindepstatement · cited by 24
- Matroid.spanning_iff_closure_eqproof · cited by 7
- Matroid.coindep_iff_compl_spanningproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- Matroid.Coindep.closure_complproof · cited by 1