Theorems · Theorem · combinatorics
Matroid.IsNonloop.indep
∀ {α : Type u_1} {M : Matroid α} {e : α}, M.IsNonloop e → M.Indep {e}Alias of the reverse direction of Matroid.indep_singleton.
- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
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 · cited by 53,352
- Matroidstatement and proof · cited by 1,258
- Matroid.Indepstatement · cited by 367
- Matroid.IsNonloopstatement · cited by 65
- Matroid.indep_singletonproof · cited by 12
Cited by3
Results whose statement or proof uses this declaration.
- Matroid.IsNonloop.eRk_eqproof · cited by 3
- Matroid.IsNonloop.rankPosproof · cited by 0
- Matroid.IsNonloop.contractElem_indep_iffproof · cited by 0