Theorems · Theorem · combinatorics
Matroid.closure_inter_eq_of_subset_coloops
∀ {α : Type u_1} {M : Matroid α} {K : Set α} (X : Set α), K ⊆ M.coloops → M.closure X ∩ K = X ∩ K- Defined in
- Mathlib.Combinatorics.Matroid.Loop
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 98 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 and proof · cited by 53,352
- Matroidstatement and proof · cited by 1,258
- Matroid.closurestatement and proof · cited by 272
- Set.inter_assocproof · cited by 67
- Set.inter_eq_self_of_subset_rightproof · cited by 39
- Matroid.coloopsstatement and proof · cited by 34
- Matroid.closure_inter_coloops_eqproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Matroid.closure_disjoint_of_disjoint_of_subset_coloopsproof · cited by 1