Theorems · Theorem · combinatorics
Matroid.indep_singleton
∀ {α : Type u_1} {M : Matroid α} {e : α}, M.Indep {e} ↔ M.IsNonloop e- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Matroidstatement and proof · cited by 1,258
- Matroid.Eproof · cited by 550
- Matroid.Indepstatement and proof · cited by 367
- Set.singleton_subset_iffproof · cited by 206
- Matroid.IsNonloopstatement · cited by 65
- not_imp_notproof · cited by 63
- Matroid.Indep.subset_groundproof · cited by 61
- Matroid.dep_iffproof · cited by 9
- Matroid.singleton_depproof · cited by 8
- Matroid.isNonloop_iffproof · cited by 6
Cited by12
Results whose statement or proof uses this declaration.
- Matroid.restrict_isNonloop_iffproof · cited by 3
- Matroid.IsNonloop.indepproof · cited by 3
- Matroid.delete_isNonloop_iffproof · cited by 2
- Matroid.IsNonloop.exists_mem_isBaseproof · cited by 1
- Matroid.IsNonloop.of_contractproof · cited by 1
- Matroid.comap_isNonloop_iffproof · cited by 0
- Matroid.freeOn_isNonloop_iffproof · cited by 0
- Matroid.IsNonloop.closure_eq_closure_iff_eq_or_depproof · cited by 0
- Matroid.eRk_eq_one_iffproof · cited by 0
- Matroid.eRk_singleton_eq_one_iffproof · cited by 0
- Matroid.uniqueBaseOn_isNonloop_iffproof · cited by 0
- Matroid.Indep.isNonloopproof · cited by 0