Theorems · Theorem · combinatorics
Matroid.Indep.mem_closure_iff_of_notMem
∀ {α : Type u_2} {M : Matroid α} {e : α} {I : Set α}, M.Indep I → e ∉ I → (e ∈ M.closure I ↔ M.Dep (insert e I))- Defined in
- Mathlib.Combinatorics.Matroid.Closure
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 87 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.Indepstatement and proof · cited by 367
- Matroid.closurestatement and proof · cited by 272
- Matroid.Depstatement · cited by 76
- Set.mem_sdiffproof · cited by 31
- Matroid.Indep.insert_dep_iffproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Matroid.isLoop_tfaeproof · cited by 3
- Matroid.Indep.insert_indep_iff_of_notMemproof · cited by 3