Theorems · Theorem · combinatorics
Matroid.Indep.insert_indep_iff_of_notMem
∀ {α : Type u_2} {M : Matroid α} {e : α} {I : Set α}, M.Indep I → e ∉ I → (M.Indep (insert e I) ↔ e ∈ M.E \ M.closure I)- Defined in
- Mathlib.Combinatorics.Matroid.Closure
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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.Indepstatement and proof · cited by 367
- Matroid.closurestatement · cited by 272
- Set.mem_insertproof · cited by 109
- not_imp_notproof · cited by 63
- Matroid.Indep.subset_groundproof · cited by 61
- Set.insert_subset_iffproof · cited by 35
- Set.mem_sdiffproof · cited by 31
- Matroid.dep_iffproof · cited by 9
- Matroid.Indep.mem_closure_iff_of_notMemproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Matroid.Indep.insert_indep_iffproof · cited by 4
- Matroid.Indep.insert_isCircuit_of_forallproof · cited by 2
- Matroid.IsNonloop.closure_eq_closure_iff_isCircuit_of_neproof · cited by 1