Theorems · Theorem · combinatorics
Matroid.IsBasis.closure_eq_closure
∀ {α : Type u_2} {M : Matroid α} {X I : Set α}, M.IsBasis I X → M.closure I = M.closure X- Defined in
- Mathlib.Combinatorics.Matroid.Closure
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Matroid.IsBasisstatement and proof · cited by 219
- subset_antisymmproof · cited by 150
- Set.subset_insertproof · cited by 96
- Matroid.IsBasis.indepproof · cited by 51
- Matroid.IsBasis.subsetproof · cited by 45
- Set.insert_subsetproof · cited by 35
- Matroid.closure_subset_closureproof · cited by 24
- Matroid.closure_closureproof · cited by 14
- Matroid.IsBasis.isBasis_subsetproof · cited by 12
Cited by13
Results whose statement or proof uses this declaration.
- Matroid.IsBasis.subset_closureproof · cited by 15
- Matroid.IsBasis'.closure_eq_closureproof · cited by 12
- Matroid.IsBase.closure_eqproof · cited by 9
- Matroid.IsCircuit.closure_sdiff_singleton_eqproof · cited by 5
- AlgebraicIndependent.matroid_closure_eqproof · cited by 3
- Matroid.IsBasis.contract_eq_contract_deleteproof · cited by 3
- Matroid.map_closure_eqproof · cited by 2
- Matroid.IsBasis.spanning_iff_spanningproof · cited by 2
- Matroid.IsBasis.contract_isBasis_of_isBasis'proof · cited by 2
- Matroid.IsBasis.closure_eq_rightproof · cited by 1
- Matroid.IsRkFinite.closure_eq_closure_of_subset_of_eRk_ge_eRkproof · cited by 1
- Matroid.mem_closure_insertproof · cited by 1