Theorems · Theorem · combinatorics
Matroid.IsNonloop.mem_closure_comm
∀ {α : Type u_1} {M : Matroid α} {e f : α}, M.IsNonloop e → M.IsNonloop f → (f ∈ M.closure {e} ↔ e ∈ M.closure {f})- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites5
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.IsNonloopstatement and proof · cited by 65
- Matroid.IsNonloop.mem_closure_singletonproof · cited by 2
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