Theorems · Theorem · combinatorics
Matroid.IsNonloop.mem_closure_singleton
∀ {α : Type u_1} {M : Matroid α} {e f : α}, M.IsNonloop e → e ∈ M.closure {f} → f ∈ M.closure {e}- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
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.closurestatement and proof · cited by 272
- Set.union_emptyproof · cited by 78
- Matroid.IsNonloopstatement and proof · cited by 65
- Set.singleton_unionproof · cited by 22
- Matroid.IsNonloop.mem_groundproof · cited by 6
- Matroid.closure_exchangeproof · cited by 3
- Matroid.isNonloop_iff_notMem_loopsproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Matroid.IsNonloop.mem_closure_commproof · cited by 0
- Matroid.IsNonloop.closure_eq_of_mem_closureproof · cited by 0