Theorems · Theorem · combinatorics
Matroid.IsLoop.closure
∀ {α : Type u_1} {M : Matroid α} {e : α}, M.IsLoop e → M.closure {e} = M.loops- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.closurestatement · cited by 272
- Set.singleton_subset_iffproof · cited by 206
- Matroid.IsLoopstatement and proof · cited by 55
- Matroid.loopsstatement · cited by 52
- Matroid.closure_eq_loops_of_subsetproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Matroid.isLoop_iff_closure_eq_loops_and_mem_groundproof · cited by 1
- Matroid.IsLoop.eRk_eqproof · cited by 0