Theorems · Theorem · combinatorics
Matroid.isNonloop_iff
∀ {α : Type u_1} (M : Matroid α) (e : α), M.IsNonloop e ↔ ¬M.IsLoop e ∧ e ∈ M.E- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.Estatement and proof · cited by 550
- Matroid.IsNonloopstatement and proof · cited by 65
- Matroid.IsLoopstatement and proof · cited by 55
- Matroid.IsNonloop.casesOnproof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- Matroid.indep_singletonproof · cited by 12
- Matroid.isNonloop_iff_mem_compl_loopsproof · cited by 2
- Matroid.isNonloop_iff_notMem_loopsproof · cited by 1
- Matroid.IsNonloop.isNonloop_of_mem_closureproof · cited by 1
- Matroid.isLoop_or_isNonloopproof · cited by 0
- Matroid.isLoop_of_not_isNonloopproof · cited by 0