Theorems · Theorem · combinatorics
Matroid.not_indep_iff
∀ {α : Type u_1} {M : Matroid α} {X : Set α}, autoParam (X ⊆ M.E) Matroid.not_indep_iff._auto_1 → (¬M.Indep X ↔ M.Dep X)- Defined in
- Mathlib.Combinatorics.Matroid.Basic
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses propext
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 and proof · cited by 550
- Matroid.Indepstatement and proof · cited by 367
- Matroid.Depstatement · cited by 76
Cited by11
Results whose statement or proof uses this declaration.
- Matroid.IsBasis.mapproof · cited by 6
- Matroid.isColoop_tfaeproof · cited by 4
- Matroid.isCircuit_iff_dep_forall_sdiff_singleton_indepproof · cited by 3
- Matroid.comap_isBasis_iffproof · cited by 2
- Matroid.isCircuit_iff_minimal_not_indepproof · cited by 1
- Matroid.IsBasis.dep_of_ssubsetproof · cited by 1
- Matroid.IsBase.insert_depproof · cited by 0
- Matroid.eRk_lt_encard_iff_depproof · cited by 0
- Matroid.eRk_lt_encard_iff_dep_of_finiteproof · cited by 0
- Matroid.ext_isCircuit_not_indepproof · cited by 0
- Matroid.singleton_not_indepproof · cited by 0