Theorems · Theorem · combinatorics
Matroid.Indep.insert_dep_iff
∀ {α : Type u_2} {M : Matroid α} {e : α} {I : Set α}, M.Indep I → (M.Dep (insert e I) ↔ e ∈ M.closure I \ I)- Defined in
- Mathlib.Combinatorics.Matroid.Closure
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 · cited by 272
- Set.insert_eq_of_memproof · cited by 118
- Matroid.Depstatement and proof · cited by 76
- Set.mem_sdiffproof · cited by 31
- Matroid.Indep.not_depproof · cited by 7
- Matroid.Indep.mem_closure_iffproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- Matroid.IsBasis.contract_eq_contract_deleteproof · cited by 3
- Matroid.Indep.mem_closure_iff_of_notMemproof · cited by 2
- Matroid.Indep.insert_isCircuit_of_forallproof · cited by 2
- Matroid.contract_isLoop_iff_mem_closureproof · cited by 0