Theorems · Theorem · combinatorics
Matroid.dep_iff
∀ {α : Type u_1} {M : Matroid α} {D : Set α}, M.Dep D ↔ ¬M.Indep D ∧ D ⊆ M.E- Defined in
- Mathlib.Combinatorics.Matroid.Basic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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 · cited by 550
- Matroid.Indepstatement · cited by 367
- Matroid.Depstatement · cited by 76
Cited by9
Results whose statement or proof uses this declaration.
- Matroid.indep_singletonproof · cited by 12
- Matroid.Indep.mem_closure_iff'proof · cited by 5
- Matroid.Indep.contract_dep_iffproof · cited by 4
- Matroid.Indep.notMem_closure_iffproof · cited by 3
- Matroid.Indep.insert_indep_iff_of_notMemproof · cited by 3
- Matroid.delete_dep_iffproof · cited by 2
- Matroid.IsNonloop.closure_eq_closure_iff_isCircuit_of_neproof · cited by 1
- Matroid.indep_iff_not_depproof · cited by 1
- Matroid.mem_closure_insertproof · cited by 1