Theorems · Theorem · combinatorics
Matroid.IsNonloop.mem_ground
∀ {α : Type u_1} {M : Matroid α} {e : α}, M.IsNonloop e → e ∈ M.E- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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 · cited by 550
- Matroid.IsNonloopstatement and proof · cited by 65
Cited by6
Results whose statement or proof uses this declaration.
- Matroid.IsNonloop.mem_closure_singletonproof · cited by 2
- Matroid.Loopless.ground_eqproof · cited by 1
- Matroid.removeLoops_isRestrictionproof · cited by 1
- Matroid.IsNonloop.closure_eq_closure_iff_isCircuit_of_neproof · cited by 1
- Matroid.IsNonloop.closure_eq_closure_iff_eq_or_depproof · cited by 0
- Matroid.not_isNonloop_iff_closureproof · cited by 0