Theorems · Theorem · combinatorics
Matroid.isNonloop_of_loopless
∀ {α : Type u_1} {M : Matroid α} {e : α} [M.Loopless],
autoParam (e ∈ M.E) Matroid.isNonloop_of_loopless._auto_1 → M.IsNonloop e- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext
- Assumes
- Matroid.Loopless
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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.IsNonloopstatement · cited by 65
- Set.notMem_emptyproof · cited by 35
- Matroid.Looplessstatement and proof · cited by 16
- Matroid.isLoop_iffproof · cited by 6
- Matroid.not_isLoop_iffproof · cited by 5
- Matroid.loops_eq_emptyproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- Matroid.IsRestriction.isRestriction_removeLoopsproof · cited by 1
- Matroid.Loopless.ground_eqproof · cited by 1
- Matroid.not_isLoopproof · cited by 1
- Matroid.loopless_iff_forall_isNonloopproof · cited by 1
- Matroid.eRk_singleton_eqproof · cited by 0
- Matroid.subsingleton_indepproof · cited by 0