Theorems · Definition · combinatorics
Matroid.Dep
{α : Type u_1} → Matroid α → Set α → PropA subset of M.E is Dependent if it is not Independent .
- Defined in
- Mathlib.Combinatorics.Matroid.Basic
- Cited by
- 76 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.Eproof · cited by 550
- Matroid.Indepproof · cited by 367
Cited by77
Results whose statement or proof uses this declaration.
- Matroid.IsCircuitproof · cited by 108
- Matroid.IsCircuit.depstatement · cited by 15
- Matroid.Dep.not_indepstatement and proof · cited by 14
- Matroid.not_indep_iffstatement · cited by 11
- Matroid.dep_iffstatement · cited by 9
- Matroid.singleton_depstatement and proof · cited by 8
- Matroid.Indep.not_depstatement and proof · cited by 7
- Matroid.Dep.subset_groundstatement and proof · cited by 7
- Matroid.Dep.supersetstatement and proof · cited by 6
- Matroid.Indep.mem_closure_iffstatement and proof · cited by 6
- Matroid.Dep.exists_isCircuit_subsetstatement and proof · cited by 5
- Matroid.Indep.isBasis_of_forall_insertstatement and proof · cited by 5