Theorems · Theorem · combinatorics
Matroid.closure_eq_of_subset_coloops
∀ {α : Type u_1} {M : Matroid α} {K : Set α}, K ⊆ M.coloops → M.closure K = K ∪ M.loops- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
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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_commproof · cited by 99
- Matroid.loopsstatement and proof · cited by 52
- Set.empty_unionproof · cited by 52
- Matroid.coloopsstatement and proof · cited by 34
- Matroid.closure_emptyproof · cited by 5
- Matroid.closure_union_eq_of_subset_coloopsproof · cited by 4
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