Theorems · Theorem · combinatorics
Matroid.subset_closure
∀ {α : Type u_2} (M : Matroid α) (X : Set α), autoParam (X ⊆ M.E) Matroid.subset_closure._auto_1 → X ⊆ M.closure X- Defined in
- Mathlib.Combinatorics.Matroid.Closure
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.Estatement and proof · cited by 550
- Matroid.closurestatement · cited by 272
- Matroid.IsFlatproof · cited by 27
- Matroid.closure_def'proof · cited by 3
Cited by23
Results whose statement or proof uses this declaration.
- Matroid.closure_closureproof · cited by 14
- Matroid.mem_closure_of_memproof · cited by 4
- Matroid.closure_union_eq_of_subset_coloopsproof · cited by 4
- Matroid.Indep.closure_inter_eq_self_of_subsetproof · cited by 4
- Matroid.closure_groundproof · cited by 3
- Matroid.closure_subset_closure_iff_subset_closureproof · cited by 3
- Matroid.IsFlat.closureproof · cited by 3
- Matroid.IsBasis.contract_eq_contract_deleteproof · cited by 3
- Matroid.IsCircuit.subset_closure_sdiff_singletonproof · cited by 2
- Matroid.Indep.closure_insert_sdiff_eq_of_mem_closureproof · cited by 2
- Matroid.isBasis_union_iff_indep_closureproof · cited by 1
- Matroid.IsBase.compl_closure_sdiff_singleton_isCocircuitproof · cited by 1