Theorems · Theorem · combinatorics
Matroid.closure_empty
∀ {α : Type u_1} (M : Matroid α), M.closure ∅ = M.loops- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 8 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.closurestatement · cited by 272
- Matroid.loopsstatement · cited by 52
Cited by5
Results whose statement or proof uses this declaration.
- Matroid.closure_union_loops_eqproof · cited by 2
- Matroid.closure_sdiff_loops_eqproof · cited by 2
- Matroid.restrict_loops_eq'proof · cited by 2
- Matroid.isLoop_iff_closure_eq_loops_and_mem_groundproof · cited by 1
- Matroid.closure_eq_of_subset_coloopsproof · cited by 0