Theorems · Theorem · combinatorics
Matroid.Indep.closure_inter_eq_self_of_subset
∀ {α : Type u_2} {M : Matroid α} {I J : Set α}, M.Indep I → J ⊆ I → M.closure J ∩ I = J- Defined in
- Mathlib.Combinatorics.Matroid.Closure
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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.Indepstatement and proof · cited by 367
- Matroid.closurestatement and proof · cited by 272
- Set.subset_interproof · cited by 74
- Matroid.Indep.subset_groundproof · cited by 61
- Matroid.Indep.subsetproof · cited by 42
- Set.insert_subsetproof · cited by 35
- Matroid.subset_closureproof · cited by 23
- subset_antisymm_iffproof · cited by 17
- Matroid.IsBasis.mem_of_insert_indepproof · cited by 9
- Matroid.Indep.isBasis_closureproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- Matroid.Indep.closure_sInter_eq_biInter_closure_of_forall_subsetproof · cited by 3
- Matroid.indep_iff_forall_notMem_closure_sdiffproof · cited by 3
- Matroid.Indep.closure_ssubset_closureproof · cited by 3
- Matroid.IsBasis.eq_of_closure_subsetproof · cited by 0